wwwelseviercomlocateepsl

=Earth and Planetary Science L

Release of gas bubbles from lake sediment traced by

noble gas isotopes in the sediment pore water

Matthias S BrennwaldaT Rolf Kipferac Dieter M Imbodenb

aDepartment of Water Resources and Drinking Water Swiss Federal Institute for Environmental Science and Technology

Dubendorf SwitzerlandbDepartment of Environmental Sciences Swiss Federal Institute of Technology Zurich Switzerland

cDepartment of Isotope Geochemistry and Mineral Resources Swiss Federal Institute of Technology Zurich Switzerland

Received 29 September 2004 received in revised form 11 February 2005 accepted 4 March 2005

Available online 23 May 2005

Editor K Parley

Abstract

The release of gas bubbles from lacustrine or oceanic sediments into the overlying water (ebullition) is a major mechanism

for the discharge of biogenic or geogenic gases into the water body Ebullition of methane or carbon dioxide for instance

contributes considerably to the release of these potent greenhouse gases through the sedimentwater interface Depending on the

rate of ebullition the pore water will show a depletion in dissolved atmospheric noble gases because the poorly soluble noble

gases escape from the pore water into the gas bubbles

In this study the depletion of dissolved noble gases in sediment pore water was analyzed for the first time to study bubble

formation and ebullition in sediments The noble gases in the pore water of the sediments of Soppensee (Switzerland) show a

distinct depletion due to ebullition of biologically produced methane This depletion is lowest in the deep sediment and increases

towards the sediment surface The noble gas isotope ratios in the pore water indicate that vertical diffusion barely affects the

observed noble gas profiles The isotope ratios further show that the methane bubbles remain long enough in the sediment to

attain noble gas solubility equilibrium before escaping into the overlying water The volume of gas released from the sediment by

ebullition can therefore be reconstructed from the extent of the noble gas depletion in the pore water using a simple gas-

equilibration model The noble gas profiles in the sediment indicate that ebullition increased in Soppensee during the Holocene

and that ebullition contributed strongly to the release of methane from the sediment Our case study thus illustrates that noble

gases are sensitive proxies for the release of gas from lacustrine and marine sediments or similar aquatic environments

D 2005 Elsevier BV All rights reserved

Keywords lake sediment pore water Soppensee methane carbon dioxide ebullition

0012-821X$ - see front matter D 2005 Elsevier BV All rights reserved

doi101016jepsl200503004

T Corresponding author

E-mail address matthiasbrennwaldeawagch

(MS Brennwald)

1 Introduction

The concentrations of dissolved atmospheric noble

gases in lake sediment pore water have been shown to

etters 235 (2005) 31ndash44

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4432

reflect the (past) noble gas concentrations in the

overlying water [12] This noble gas archive allowed

the paleosalinity and lake level to be reconstructed in

Lake Issyk-Kul (Kyrgyzstan) [2] Further recent work

has shown that if gas bubbles are present in the

sediment eg due to supersaturation with biogenic

CH4 noble gases tend to escape from the sediment

pore water into these bubbles resulting in a character-

istic noble gas depletion of the pore water [1] Noble

gases are therefore expected to be useful tracers to

study the release of gas bubbles from lacustrine or

marine sediments (ebullition)

Ebullition has been identified as a major process

for the transport of CH4 and CO2 through the

sedimentwater interface and may therefore play an

important role in the release of these potent green-

house gases into the atmosphere [3ndash6] Apart from

biological gas production depletion of dissolved

noble gases due to removal by gas bubbles can be

used to study gaswater partitioning in hydrothermal

systems in the ocean eg at mid-ocean ridges or in the

Red Sea where noble gas depletion indicates that

fluids cycling through the subsurface are partially

degassed due to boiling in a hydrothermal system

before they are fed back into the deep water [7]

Further the gas release from submarine gas vents that

are often associated with mud volcanoes or the

occurrence of gas hydrates in the sediment can be

studied based on noble gas depletion in the water

above the vents (eg in the Black Sea [89]) The

noble gas signature of the pore water of the sediment

in the vicinity of gas vents is expected to reflect the

Zurich

Bern

Soppensee

Basel

50 km

Fig 1 Left map of Switzerland showing the geographical location of

(after [12])

amount and geochemical origin of the gases released

Finally noble gases can be removed from ground-

water by incorporation into gas bubbles escaping from

the groundwater into the unsaturated zone Analo-

gously to surface waters the resulting noble gas

depletion of the groundwater can therefore be used to

study degassing in aquifers [1011]

Until now however noble gas depletion in

sediment pore water due to gas loss into bubbles

has only been considered as an artifact interfering

with the reconstruction of past noble gas concen-

trations and the corresponding environmental con-

ditions in the overlying water [1] but not as a proxy

for ebullition and the formation of gas bubbles in the

sediment

In this study we analyzed noble gas concentrations

in the sediment pore water of Soppensee a eutrophic

lake in Switzerland These data are used to study the

gas partitioning between pore water and gas bubbles

and the vertical transport of noble gases in the

sediment Our study therefore illustrates the useful-

ness of the pore water as a noble gas archive for the

reconstruction of ebullition in the past

2 Methods

21 Study site

Soppensee (central Switzerland Fig 1) is a small

freshwater lake with a surface area of 023 km2 and a

maximum water depth of 27 m situated at an

Sampling site8ordm488E 47ordm542N

100 m

12 m

24 m

20 m

16 m

8 m

Soppensee (596 masl) Right bathymetric map of Soppensee

06 08 1

0

1

2

3

4

5

6

7

φ [vv]

C

V

H

Sed

imen

t dep

th [m

]

YD

0

02

10

39

68

98

132

145

Sed

imen

t age

[kyr

]

Fig 2 Sediment lithology and porosity (unpublished data M

Sturm EAWAG) determined from a long core taken at the centre

of the lake (SO89-23 [19]) The lithological units (simplified after

[19]) are homogeneous sediment (H) (partly) varved sediment

(V) homogeneous clay (C) YD marks the Younger Dryas cold

period [18]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 33

elevation of 596 masl The Soppensee sediments

have been thoroughly studied with a view to

ascertaining the paleoclimatic conditions prevailing

in and around the lake since 14 kyr BP [12ndash19]

At the centre of the lake the sediment is 7 m thick

Between 6 and 7 m the sediment consists of

homogeneous clay (Fig 2) whereas above 6 m it is

rich in organic material Between 27 and 6 m

sediment depth the sediment is varved whereas

above 27 m it is homogeneous [19] The distribution

pattern of chironomids in the sediment indicates

qualitatively that Soppensee was oligotrophic during

Ne Ar

25 50 75 100 25 50 75 100

Ci

0

1

2

3

4

5

6

7

Sed

imen

t dep

th [m

]

Fig 3 Leftmost panel arrangement of the overlapping sediment cores and

gas concentrations Ci (normalized to the atmospheric equilibrium concentra

age The circles correspond to the pore water the squares to the overlying w

than the circles representing the data and are therefore not shown

the Younger Dryas and increasingly eutrophic during

the Holocene [18] Because of intense agriculture in

its catchment area Soppensee has become hyper-

trophic in recent decades [19] Correspondingly the

sediment shows a high rate of CH4 production as a

result of the biological degradation of organic matter

[20] The deep water (with an annual mean temper-

ature of 55 8C) is anoxic during the warm season

when the hypolimnion is well separated from the

epilimnion by chemical and temperature gradients

During the cold season the lake is well mixed and the

deep water becomes oxic [20] The existence of

varves in the sediment deposited during the earlier

Holocene indicates that such seasonal cycling in the

oxic conditions of the deep water has been occurring

since the beginning of the Holocene [20]

22 Noble gas sampling and analysis

Sediment samples for noble gas analysis [1] were

collected in the centre of the lake using an UWITEC

piston corer operated from a floating platform [21]

Three 3-m long vertically overlapping sediment

segments were taken Together these segments cover

the whole sediment series (Fig 3) To minimize the

lateral offset between the three segments the platform

was fixed by an anchor and by ropes fixed at the

shore The resulting lateral offset of the segments is

expected to be ]1 m

In addition a gravity core covering the uppermost

70 cm of the sediment was taken The water just

above the sediment surface was sampled for noble gas

Kr Xe

25 50 75 100 25 50 75 100

Ci []

00

02

10

39

68

98

132

145

Sed

imen

t age

[kyr

]

the sampling ports (black dots) Remaining panels measured noble

tions in the overlying water Ci) plotted against sediment depth and

ater Note that the error bars of the measurements would be smaller

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4434

analysis [22] from the sediment liner of this gravity

core No gas bubbles were observed in the gravity

core during the first few minutes after recovery when

the overlying water was sampled

Sediment samples for noble gas analysis were

prepared immediately after recovery of the sediment

cores to minimize exsolution of supersaturated CH4 in

the cores Bulk sediment was transferred from the

sediment cores into the sample containers (Cu tubes)

without exposure to the atmosphere or other gas

reservoirs [1] The noble gases were then extracted

from the pore water by degassing the sediment in an

evacuated extraction vessel [1] The noble gas

abundance was then analyzed by mass spectrometry

with an overall 1r uncertainty of ~ 2 in the

concentrations and ~ 01 in the isotope ratios

following the experimental procedures described in

[1] and [22]

Samples were collected at sediment depths of 050

m 111 m 396 m 496 m 656 m and 686 m (Fig

3) Inspection of the cores after sampling indicated

that the uncertainty in the sampling depth due to

squeezing is about 5 cm Excessive gas exsolution

prevented reliable sediment sampling between 15 and

35 m sediment depth Replicate samples were

Table 1

Noble gas concentrations and isotope ratios measured in the sediment por

above the sediment surface

z (m) Concentrations

(cmSTP3 g)

Ne108 Ar104 Kr108

Sediment pore water

05 0301 121 418

111 0474 197 646

396 123 290 782

396 0988 290 804

496 142 343 917

496 117 324 867

656 162 348 859

656 153 341 836

686 170 360 885

686 169 368 911

Overlying water

ndash 182 390 960

ndash 186 392 963

The analytical errors are b 2 for the concentrations and b 01 for the iso

depth where the errors in the 20Ne22Ne ratios are larger (04 and

spectrometric analysis were affected by the low Ne abundance in these sa

collected from each sampling depth except at 050

m and 111 m where only one sample could be taken

before the formation of gas bubbles prevented further

reliable sediment sampling

During noble gas analysis radiogenic He can be

released from the sediment grains as a result of the

heating of the sample during gas extraction [1] To

assess the amount of He released from the sediment

grains a stepwise heating experiment as described in

[1] was carried out for two sediment samples (one

from the clayey sediment and one from the facies rich

in organic matter) This showed that the He concen-

trations measured in Soppensee may exceed the actual

He concentrations in the pore water by up to 20

Because it is impossible to quantify reliably the

contribution of the He released from the sediment

grains to the total He measured the He data will not

be discussed further

3 Results and discussion

Fig 3 shows the noble gas concentration profiles

measured in the sediment pore water and in the

overlying lake water (see also Table 1) The noble gas

e water at sediment depth z and in the overlying water immediately

Isotope ratios

Xe108 20Ne22Ne 36Ar40Ar103

0878 989 3398

126 982 3387

131 982 3382

134 976 3378

145 978 3382

144 978 3382

131 981 3388

132 978 3382

137 976 3382

141 977 3382

146 979 3383

144 979 3374

tope ratios (relative 1r errors) except at 05 m and 111 m sediment

025 respectively) because the counting statistics of the mass-

mples

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 35

concentrations are undersaturated relative to the

atmospheric equilibrium concentrations computed

from the temperature of the overlying water In the

sediment this undersaturation is greatest just below

the sediment surface and decreases with increasing

sediment depth In the overlying water the noble gas

concentrations are also depleted (confirming previous

observations [23]) but to a much lesser extent than in

the sediment pore water This is due to noble gas

stripping by the gas bubbles rising through the water

body

The observed noble gas depletion decreases with

increasing atomic mass and hence with gas solubility

Such a depletion pattern is indicative of the loss of

dissolved noble gases to a gas or oil phase which was

initially free of noble gases [11124] Given the high

rate of CH4 production in the Soppensee sediment the

depletion pattern can be attributed to degassing into

gas bubbles which form in the sediment due to CH4

supersaturation

It may be expected that part of the observed noble

gas depletion arose during sediment sampling

because gas bubbles formed in the sediment after

recovery of the sediment cores The replicate samples

taken at 4 m and 5 m sediment depth show slightly

different Ne concentrations whereby the samples

which were taken first show a smaller depletion than

the subsequent samples This might be interpreted as

an indication that during sampling part of the

dissolved Ne was stripped into gas bubbles which

were not captured in the sediment sample However

the measured concentrations of the heavier noble

gases do not support this interpretation as the Ar Kr

and Xe concentrations of the replicate samples agree

within the analytical uncertainty The discrepancy of

the Ne replicates at 4 m and 5 m sediment depth

therefore seems to be due to an unknown artifact other

than degassing during sampling This is supported by

the fact that the noble gases are undersaturated even in

the overlying water [23] which shows a residence

time of about 1 yr as estimated from 3H3He data from

the deep water Also the 20Ne22Ne and 36Ar40Ar

isotope ratios in the pore water indicate that gas

exchange has attained steady state (see Section 31)

which is expected to occur within several hours

[2526] whereas the noble gas samples were collected

from the sediment core within a few minutes after

recovery It is therefore concluded that the noble gases

were not stripped from the water during sampling but

rather by gas bubbles which formed in the sediment

prior to sampling

31 Transfer of noble gases from the pore water into

CH4 bubbles

The transfer of dissolved noble gases into gas

bubbles forming in the sediment occurs by diffusion

through the gaswater interface between the gas

bubble and the pore water until the gas bubble

escapes from the sediment or until solubility equili-

brium is attained

If the gas bubbles escape from the sediment

before solubility equilibrium is approached the

noble gas abundance in the pore water will show

an isotopic fractionation corresponding to the extent

of degassing [1127] the lighter isotopes are more

mobile and are therefore removed from the pore

water more easily which results in a relative

enrichment of the heavier isotopes in the pore water

During the initial phase of the noble gas partitioning

between the bubbles and the pore water ie as long

as the gas exchange process is far from steady state

the noble gas concentrations in the bubble are much

smaller than the equilibrium concentrations Then

the loss of a species i from the pore water into the

gas bubble is controlled by its diffusion through the

gaswater interface The concentration decrease dCi

during a time interval dt is approximately propor-

tional to DiCidt [2829] where Di is the diffusivity

and Ci is the concentration of species i in the pore

water (see Table 2 for the notation used here) The

ratio of the concentration changes of two species i

and j is therefore given by

dCi

dCj

frac14 DiCi

DjCj

The solution of this differential equation is given

by the Rayleigh equation [28]

Ci

Cj

frac14 Ci0

Cj0

Cj

Cj0

DiDj1

where the subscript 0 denotes the initial state before

degassing With RijuCiCj the ratio of the concen-

trations of two species i and j in the pore water

fjuCjCj0 the fraction of species j remaining in the

Table 2

List of symbols

Symbol Description Dimension

t Time [T]

z Sediment depth positive down-

wards z =0 at the sediment surface

[L]

BBt Time derivative for z = const

(Eulerian derivative) Note that this

is generally not equal to the time

derivative in a fixed sediment layer

eg in the layer deposited in the

year 1950 (Lagrangian derivative)

Ci Concentration of species i in the

pore water (STP-volume of dis-

solved gas per unit mass of pore

water)

[L3M]

Rij Concentration ratio of two species i

and j in the pore water

[ndash]

Di0 Molecular diffusivity of solute i in

bulk water

[L2T]

Di Effective diffusivity of solute i in

the pore water

[L2T]

a ij Fractionation parameter [ndash]

Porosity (fraction of pore volume

per unit volume of bulk sediment)

[ndash]

a Tortuosity parameter of the sedi-

ment pore space

[ndash]

ri Production rate of species i per unit

volume of pore water

[NTL3]

U Burial velocity of pore water rela-

tive to the sediment surface

[LT]

x Burial velocity of solid sediment

relative to the sediment surface

[LT]

B STP bubble volume per unit mass

of pore water (dry gas)

[L3M]

Hi Henry coefficient of species i [(MLT2)(L3M)]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4436

pore water and aijuDiDj1 the bfractionationparameterQ the Rayleigh equation reads

Rij frac14 Rij0 faijj eth1THORN

To compare the concentration ratio of species i and

j (Rij) with that of two other species k and l (Rkl) one

can write

fj

flfrac14 Cj=Cj0

Cl=Cl0frac14 Rjl

Rjl0frac14zeth1THORN

fajll

Thus fj = fajl +1l Combining this with Eq (1) allows

Rij and Rkl to be expressed simultaneously as

functions of fl

Rij frac14 Rij0 fajlaijthornaijl and Rkl frac14 Rkl0 f

akll eth2THORN

Fig 4 compares the measured 20Ne22Ne and36Ar40Ar ratios with the Rayleigh fractionation

expected from Eq (2) where i =20Ne j =22Ne

k =36Ar l =40Ar and f40Ar ranges from 30 (max

observed 40Ar depletion) to 100 (no depletion)

The fractionation parameters were calculated by

assuming that the ratios of the noble gas isotope

diffusivities in the sediment are the same as the

respective ratios of the molecular diffusivities in bulk

water (Table 3)

The predicted Rayleigh fractionation corresponds

to changes in the isotope ratios of up to 9

(20Ne22Ne) and 7 (36Ar40Ar) In contrast the

measured isotope ratios correspond to the atmospheric

equilibrium ratios within the analytical uncertainties

of 02 (20Ne22Ne) and 01 (36Ar40Ar)

The noble gas partitioning between the pore water

and the gas bubbles is therefore not controlled by

diffusion On the contrary the noble gas depletion

rather reflects a solubility equilibrium between pore

water and gas bubbles This is in line with the

expectation that equilibrium between pore water and

gas bubble is attained within a few hours [2526]

whereas bubble growth in the sediment occurs on a

time scale of several days or weeks [3031]

32 Vertical noble gas transport in the sediment

pore space

The vertical transport of noble gases within the

pore space may be controlled either by vertical

diffusion (such as in Lake Zug [32]) or by pore-water

advection relative to the sediment surface (such as in

Lake Issyk-Kul [2]) This leads to the two following

hypotheses to explain the noble gas concentration

profiles observed in Soppensee

Hypothesis A (Diffusion hypothesis) The vertical

transport of noble gases is controlled by vertical

diffusion The existence of vertical concentration

gradients therefore implies that noble gas profiles

reflect a dynamic state This leads to the following

interpretation (see also Fig 5) ebullition was (vir-

tually) absent before it abruptly set in during recent

decades or centuries Before the onset of ebullition

the noble gas concentrations in the pore water were

the same as those in the overlying water The noble

gas depletion observed in the sediment which was

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4432

reflect the (past) noble gas concentrations in the

overlying water [12] This noble gas archive allowed

the paleosalinity and lake level to be reconstructed in

Lake Issyk-Kul (Kyrgyzstan) [2] Further recent work

has shown that if gas bubbles are present in the

sediment eg due to supersaturation with biogenic

CH4 noble gases tend to escape from the sediment

pore water into these bubbles resulting in a character-

istic noble gas depletion of the pore water [1] Noble

gases are therefore expected to be useful tracers to

study the release of gas bubbles from lacustrine or

marine sediments (ebullition)

Ebullition has been identified as a major process

for the transport of CH4 and CO2 through the

sedimentwater interface and may therefore play an

important role in the release of these potent green-

house gases into the atmosphere [3ndash6] Apart from

biological gas production depletion of dissolved

noble gases due to removal by gas bubbles can be

used to study gaswater partitioning in hydrothermal

systems in the ocean eg at mid-ocean ridges or in the

Red Sea where noble gas depletion indicates that

fluids cycling through the subsurface are partially

degassed due to boiling in a hydrothermal system

before they are fed back into the deep water [7]

Further the gas release from submarine gas vents that

are often associated with mud volcanoes or the

occurrence of gas hydrates in the sediment can be

studied based on noble gas depletion in the water

above the vents (eg in the Black Sea [89]) The

noble gas signature of the pore water of the sediment

in the vicinity of gas vents is expected to reflect the

Zurich

Bern

Soppensee

Basel

50 km

Fig 1 Left map of Switzerland showing the geographical location of

(after [12])

amount and geochemical origin of the gases released

Finally noble gases can be removed from ground-

water by incorporation into gas bubbles escaping from

the groundwater into the unsaturated zone Analo-

gously to surface waters the resulting noble gas

depletion of the groundwater can therefore be used to

study degassing in aquifers [1011]

Until now however noble gas depletion in

sediment pore water due to gas loss into bubbles

has only been considered as an artifact interfering

with the reconstruction of past noble gas concen-

trations and the corresponding environmental con-

ditions in the overlying water [1] but not as a proxy

for ebullition and the formation of gas bubbles in the

sediment

In this study we analyzed noble gas concentrations

in the sediment pore water of Soppensee a eutrophic

lake in Switzerland These data are used to study the

gas partitioning between pore water and gas bubbles

and the vertical transport of noble gases in the

sediment Our study therefore illustrates the useful-

ness of the pore water as a noble gas archive for the

reconstruction of ebullition in the past

2 Methods

21 Study site

Soppensee (central Switzerland Fig 1) is a small

freshwater lake with a surface area of 023 km2 and a

maximum water depth of 27 m situated at an

Sampling site8ordm488E 47ordm542N

100 m

12 m

24 m

20 m

16 m

8 m

Soppensee (596 masl) Right bathymetric map of Soppensee

06 08 1

0

1

2

3

4

5

6

7

φ [vv]

C

V

H

Sed

imen

t dep

th [m

]

YD

0

02

10

39

68

98

132

145

Sed

imen

t age

[kyr

]

Fig 2 Sediment lithology and porosity (unpublished data M

Sturm EAWAG) determined from a long core taken at the centre

of the lake (SO89-23 [19]) The lithological units (simplified after

[19]) are homogeneous sediment (H) (partly) varved sediment

(V) homogeneous clay (C) YD marks the Younger Dryas cold

period [18]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 33

elevation of 596 masl The Soppensee sediments

have been thoroughly studied with a view to

ascertaining the paleoclimatic conditions prevailing

in and around the lake since 14 kyr BP [12ndash19]

At the centre of the lake the sediment is 7 m thick

Between 6 and 7 m the sediment consists of

homogeneous clay (Fig 2) whereas above 6 m it is

rich in organic material Between 27 and 6 m

sediment depth the sediment is varved whereas

above 27 m it is homogeneous [19] The distribution

pattern of chironomids in the sediment indicates

qualitatively that Soppensee was oligotrophic during

Ne Ar

25 50 75 100 25 50 75 100

Ci

0

1

2

3

4

5

6

7

Sed

imen

t dep

th [m

]

Fig 3 Leftmost panel arrangement of the overlapping sediment cores and

gas concentrations Ci (normalized to the atmospheric equilibrium concentra

age The circles correspond to the pore water the squares to the overlying w

than the circles representing the data and are therefore not shown

the Younger Dryas and increasingly eutrophic during

the Holocene [18] Because of intense agriculture in

its catchment area Soppensee has become hyper-

trophic in recent decades [19] Correspondingly the

sediment shows a high rate of CH4 production as a

result of the biological degradation of organic matter

[20] The deep water (with an annual mean temper-

ature of 55 8C) is anoxic during the warm season

when the hypolimnion is well separated from the

epilimnion by chemical and temperature gradients

During the cold season the lake is well mixed and the

deep water becomes oxic [20] The existence of

varves in the sediment deposited during the earlier

Holocene indicates that such seasonal cycling in the

oxic conditions of the deep water has been occurring

since the beginning of the Holocene [20]

22 Noble gas sampling and analysis

Sediment samples for noble gas analysis [1] were

collected in the centre of the lake using an UWITEC

piston corer operated from a floating platform [21]

Three 3-m long vertically overlapping sediment

segments were taken Together these segments cover

the whole sediment series (Fig 3) To minimize the

lateral offset between the three segments the platform

was fixed by an anchor and by ropes fixed at the

shore The resulting lateral offset of the segments is

expected to be ]1 m

In addition a gravity core covering the uppermost

70 cm of the sediment was taken The water just

above the sediment surface was sampled for noble gas

Kr Xe

25 50 75 100 25 50 75 100

Ci []

00

02

10

39

68

98

132

145

Sed

imen

t age

[kyr

]

the sampling ports (black dots) Remaining panels measured noble

tions in the overlying water Ci) plotted against sediment depth and

ater Note that the error bars of the measurements would be smaller

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4434

analysis [22] from the sediment liner of this gravity

core No gas bubbles were observed in the gravity

core during the first few minutes after recovery when

the overlying water was sampled

Sediment samples for noble gas analysis were

prepared immediately after recovery of the sediment

cores to minimize exsolution of supersaturated CH4 in

the cores Bulk sediment was transferred from the

sediment cores into the sample containers (Cu tubes)

without exposure to the atmosphere or other gas

reservoirs [1] The noble gases were then extracted

from the pore water by degassing the sediment in an

evacuated extraction vessel [1] The noble gas

abundance was then analyzed by mass spectrometry

with an overall 1r uncertainty of ~ 2 in the

concentrations and ~ 01 in the isotope ratios

following the experimental procedures described in

[1] and [22]

Samples were collected at sediment depths of 050

m 111 m 396 m 496 m 656 m and 686 m (Fig

3) Inspection of the cores after sampling indicated

that the uncertainty in the sampling depth due to

squeezing is about 5 cm Excessive gas exsolution

prevented reliable sediment sampling between 15 and

35 m sediment depth Replicate samples were

Table 1

Noble gas concentrations and isotope ratios measured in the sediment por

above the sediment surface

z (m) Concentrations

(cmSTP3 g)

Ne108 Ar104 Kr108

Sediment pore water

05 0301 121 418

111 0474 197 646

396 123 290 782

396 0988 290 804

496 142 343 917

496 117 324 867

656 162 348 859

656 153 341 836

686 170 360 885

686 169 368 911

Overlying water

ndash 182 390 960

ndash 186 392 963

The analytical errors are b 2 for the concentrations and b 01 for the iso

depth where the errors in the 20Ne22Ne ratios are larger (04 and

spectrometric analysis were affected by the low Ne abundance in these sa

collected from each sampling depth except at 050

m and 111 m where only one sample could be taken

before the formation of gas bubbles prevented further

reliable sediment sampling

During noble gas analysis radiogenic He can be

released from the sediment grains as a result of the

heating of the sample during gas extraction [1] To

assess the amount of He released from the sediment

grains a stepwise heating experiment as described in

[1] was carried out for two sediment samples (one

from the clayey sediment and one from the facies rich

in organic matter) This showed that the He concen-

trations measured in Soppensee may exceed the actual

He concentrations in the pore water by up to 20

Because it is impossible to quantify reliably the

contribution of the He released from the sediment

grains to the total He measured the He data will not

be discussed further

3 Results and discussion

Fig 3 shows the noble gas concentration profiles

measured in the sediment pore water and in the

overlying lake water (see also Table 1) The noble gas

e water at sediment depth z and in the overlying water immediately

Isotope ratios

Xe108 20Ne22Ne 36Ar40Ar103

0878 989 3398

126 982 3387

131 982 3382

134 976 3378

145 978 3382

144 978 3382

131 981 3388

132 978 3382

137 976 3382

141 977 3382

146 979 3383

144 979 3374

tope ratios (relative 1r errors) except at 05 m and 111 m sediment

025 respectively) because the counting statistics of the mass-

mples

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 35

concentrations are undersaturated relative to the

atmospheric equilibrium concentrations computed

from the temperature of the overlying water In the

sediment this undersaturation is greatest just below

the sediment surface and decreases with increasing

sediment depth In the overlying water the noble gas

concentrations are also depleted (confirming previous

observations [23]) but to a much lesser extent than in

the sediment pore water This is due to noble gas

stripping by the gas bubbles rising through the water

body

The observed noble gas depletion decreases with

increasing atomic mass and hence with gas solubility

Such a depletion pattern is indicative of the loss of

dissolved noble gases to a gas or oil phase which was

initially free of noble gases [11124] Given the high

rate of CH4 production in the Soppensee sediment the

depletion pattern can be attributed to degassing into

gas bubbles which form in the sediment due to CH4

supersaturation

It may be expected that part of the observed noble

gas depletion arose during sediment sampling

because gas bubbles formed in the sediment after

recovery of the sediment cores The replicate samples

taken at 4 m and 5 m sediment depth show slightly

different Ne concentrations whereby the samples

which were taken first show a smaller depletion than

the subsequent samples This might be interpreted as

an indication that during sampling part of the

dissolved Ne was stripped into gas bubbles which

were not captured in the sediment sample However

the measured concentrations of the heavier noble

gases do not support this interpretation as the Ar Kr

and Xe concentrations of the replicate samples agree

within the analytical uncertainty The discrepancy of

the Ne replicates at 4 m and 5 m sediment depth

therefore seems to be due to an unknown artifact other

than degassing during sampling This is supported by

the fact that the noble gases are undersaturated even in

the overlying water [23] which shows a residence

time of about 1 yr as estimated from 3H3He data from

the deep water Also the 20Ne22Ne and 36Ar40Ar

isotope ratios in the pore water indicate that gas

exchange has attained steady state (see Section 31)

which is expected to occur within several hours

[2526] whereas the noble gas samples were collected

from the sediment core within a few minutes after

recovery It is therefore concluded that the noble gases

were not stripped from the water during sampling but

rather by gas bubbles which formed in the sediment

prior to sampling

31 Transfer of noble gases from the pore water into

CH4 bubbles

The transfer of dissolved noble gases into gas

bubbles forming in the sediment occurs by diffusion

through the gaswater interface between the gas

bubble and the pore water until the gas bubble

escapes from the sediment or until solubility equili-

brium is attained

If the gas bubbles escape from the sediment

before solubility equilibrium is approached the

noble gas abundance in the pore water will show

an isotopic fractionation corresponding to the extent

of degassing [1127] the lighter isotopes are more

mobile and are therefore removed from the pore

water more easily which results in a relative

enrichment of the heavier isotopes in the pore water

During the initial phase of the noble gas partitioning

between the bubbles and the pore water ie as long

as the gas exchange process is far from steady state

the noble gas concentrations in the bubble are much

smaller than the equilibrium concentrations Then

the loss of a species i from the pore water into the

gas bubble is controlled by its diffusion through the

gaswater interface The concentration decrease dCi

during a time interval dt is approximately propor-

tional to DiCidt [2829] where Di is the diffusivity

and Ci is the concentration of species i in the pore

water (see Table 2 for the notation used here) The

ratio of the concentration changes of two species i

and j is therefore given by

dCi

dCj

frac14 DiCi

DjCj

The solution of this differential equation is given

by the Rayleigh equation [28]

Ci

Cj

frac14 Ci0

Cj0

Cj

Cj0

DiDj1

where the subscript 0 denotes the initial state before

degassing With RijuCiCj the ratio of the concen-

trations of two species i and j in the pore water

fjuCjCj0 the fraction of species j remaining in the

Table 2

List of symbols

Symbol Description Dimension

t Time [T]

z Sediment depth positive down-

wards z =0 at the sediment surface

[L]

BBt Time derivative for z = const

(Eulerian derivative) Note that this

is generally not equal to the time

derivative in a fixed sediment layer

eg in the layer deposited in the

year 1950 (Lagrangian derivative)

Ci Concentration of species i in the

pore water (STP-volume of dis-

solved gas per unit mass of pore

water)

[L3M]

Rij Concentration ratio of two species i

and j in the pore water

[ndash]

Di0 Molecular diffusivity of solute i in

bulk water

[L2T]

Di Effective diffusivity of solute i in

the pore water

[L2T]

a ij Fractionation parameter [ndash]

Porosity (fraction of pore volume

per unit volume of bulk sediment)

[ndash]

a Tortuosity parameter of the sedi-

ment pore space

[ndash]

ri Production rate of species i per unit

volume of pore water

[NTL3]

U Burial velocity of pore water rela-

tive to the sediment surface

[LT]

x Burial velocity of solid sediment

relative to the sediment surface

[LT]

B STP bubble volume per unit mass

of pore water (dry gas)

[L3M]

Hi Henry coefficient of species i [(MLT2)(L3M)]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4436

pore water and aijuDiDj1 the bfractionationparameterQ the Rayleigh equation reads

Rij frac14 Rij0 faijj eth1THORN

To compare the concentration ratio of species i and

j (Rij) with that of two other species k and l (Rkl) one

can write

fj

flfrac14 Cj=Cj0

Cl=Cl0frac14 Rjl

Rjl0frac14zeth1THORN

fajll

Thus fj = fajl +1l Combining this with Eq (1) allows

Rij and Rkl to be expressed simultaneously as

functions of fl

Rij frac14 Rij0 fajlaijthornaijl and Rkl frac14 Rkl0 f

akll eth2THORN

Fig 4 compares the measured 20Ne22Ne and36Ar40Ar ratios with the Rayleigh fractionation

expected from Eq (2) where i =20Ne j =22Ne

k =36Ar l =40Ar and f40Ar ranges from 30 (max

observed 40Ar depletion) to 100 (no depletion)

The fractionation parameters were calculated by

assuming that the ratios of the noble gas isotope

diffusivities in the sediment are the same as the

respective ratios of the molecular diffusivities in bulk

water (Table 3)

The predicted Rayleigh fractionation corresponds

to changes in the isotope ratios of up to 9

(20Ne22Ne) and 7 (36Ar40Ar) In contrast the

measured isotope ratios correspond to the atmospheric

equilibrium ratios within the analytical uncertainties

of 02 (20Ne22Ne) and 01 (36Ar40Ar)

The noble gas partitioning between the pore water

and the gas bubbles is therefore not controlled by

diffusion On the contrary the noble gas depletion

rather reflects a solubility equilibrium between pore

water and gas bubbles This is in line with the

expectation that equilibrium between pore water and

gas bubble is attained within a few hours [2526]

whereas bubble growth in the sediment occurs on a

time scale of several days or weeks [3031]

32 Vertical noble gas transport in the sediment

pore space

The vertical transport of noble gases within the

pore space may be controlled either by vertical

diffusion (such as in Lake Zug [32]) or by pore-water

advection relative to the sediment surface (such as in

Lake Issyk-Kul [2]) This leads to the two following

hypotheses to explain the noble gas concentration

profiles observed in Soppensee

Hypothesis A (Diffusion hypothesis) The vertical

transport of noble gases is controlled by vertical

diffusion The existence of vertical concentration

gradients therefore implies that noble gas profiles

reflect a dynamic state This leads to the following

interpretation (see also Fig 5) ebullition was (vir-

tually) absent before it abruptly set in during recent

decades or centuries Before the onset of ebullition

the noble gas concentrations in the pore water were

the same as those in the overlying water The noble

gas depletion observed in the sediment which was

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

06 08 1

0

1

2

3

4

5

6

7

φ [vv]

C

V

H

Sed

imen

t dep

th [m

]

YD

0

02

10

39

68

98

132

145

Sed

imen

t age

[kyr

]

Fig 2 Sediment lithology and porosity (unpublished data M

Sturm EAWAG) determined from a long core taken at the centre

of the lake (SO89-23 [19]) The lithological units (simplified after

[19]) are homogeneous sediment (H) (partly) varved sediment

(V) homogeneous clay (C) YD marks the Younger Dryas cold

period [18]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 33

elevation of 596 masl The Soppensee sediments

have been thoroughly studied with a view to

ascertaining the paleoclimatic conditions prevailing

in and around the lake since 14 kyr BP [12ndash19]

At the centre of the lake the sediment is 7 m thick

Between 6 and 7 m the sediment consists of

homogeneous clay (Fig 2) whereas above 6 m it is

rich in organic material Between 27 and 6 m

sediment depth the sediment is varved whereas

above 27 m it is homogeneous [19] The distribution

pattern of chironomids in the sediment indicates

qualitatively that Soppensee was oligotrophic during

Ne Ar

25 50 75 100 25 50 75 100

Ci

0

1

2

3

4

5

6

7

Sed

imen

t dep

th [m

]

Fig 3 Leftmost panel arrangement of the overlapping sediment cores and

gas concentrations Ci (normalized to the atmospheric equilibrium concentra

age The circles correspond to the pore water the squares to the overlying w

than the circles representing the data and are therefore not shown

the Younger Dryas and increasingly eutrophic during

the Holocene [18] Because of intense agriculture in

its catchment area Soppensee has become hyper-

trophic in recent decades [19] Correspondingly the

sediment shows a high rate of CH4 production as a

result of the biological degradation of organic matter

[20] The deep water (with an annual mean temper-

ature of 55 8C) is anoxic during the warm season

when the hypolimnion is well separated from the

epilimnion by chemical and temperature gradients

During the cold season the lake is well mixed and the

deep water becomes oxic [20] The existence of

varves in the sediment deposited during the earlier

Holocene indicates that such seasonal cycling in the

oxic conditions of the deep water has been occurring

since the beginning of the Holocene [20]

22 Noble gas sampling and analysis

Sediment samples for noble gas analysis [1] were

collected in the centre of the lake using an UWITEC

piston corer operated from a floating platform [21]

Three 3-m long vertically overlapping sediment

segments were taken Together these segments cover

the whole sediment series (Fig 3) To minimize the

lateral offset between the three segments the platform

was fixed by an anchor and by ropes fixed at the

shore The resulting lateral offset of the segments is

expected to be ]1 m

In addition a gravity core covering the uppermost

70 cm of the sediment was taken The water just

above the sediment surface was sampled for noble gas

Kr Xe

25 50 75 100 25 50 75 100

Ci []

00

02

10

39

68

98

132

145

Sed

imen

t age

[kyr

]

the sampling ports (black dots) Remaining panels measured noble

tions in the overlying water Ci) plotted against sediment depth and

ater Note that the error bars of the measurements would be smaller

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4434

analysis [22] from the sediment liner of this gravity

core No gas bubbles were observed in the gravity

core during the first few minutes after recovery when

the overlying water was sampled

Sediment samples for noble gas analysis were

prepared immediately after recovery of the sediment

cores to minimize exsolution of supersaturated CH4 in

the cores Bulk sediment was transferred from the

sediment cores into the sample containers (Cu tubes)

without exposure to the atmosphere or other gas

reservoirs [1] The noble gases were then extracted

from the pore water by degassing the sediment in an

evacuated extraction vessel [1] The noble gas

abundance was then analyzed by mass spectrometry

with an overall 1r uncertainty of ~ 2 in the

concentrations and ~ 01 in the isotope ratios

following the experimental procedures described in

[1] and [22]

Samples were collected at sediment depths of 050

m 111 m 396 m 496 m 656 m and 686 m (Fig

3) Inspection of the cores after sampling indicated

that the uncertainty in the sampling depth due to

squeezing is about 5 cm Excessive gas exsolution

prevented reliable sediment sampling between 15 and

35 m sediment depth Replicate samples were

Table 1

Noble gas concentrations and isotope ratios measured in the sediment por

above the sediment surface

z (m) Concentrations

(cmSTP3 g)

Ne108 Ar104 Kr108

Sediment pore water

05 0301 121 418

111 0474 197 646

396 123 290 782

396 0988 290 804

496 142 343 917

496 117 324 867

656 162 348 859

656 153 341 836

686 170 360 885

686 169 368 911

Overlying water

ndash 182 390 960

ndash 186 392 963

The analytical errors are b 2 for the concentrations and b 01 for the iso

depth where the errors in the 20Ne22Ne ratios are larger (04 and

spectrometric analysis were affected by the low Ne abundance in these sa

collected from each sampling depth except at 050

m and 111 m where only one sample could be taken

before the formation of gas bubbles prevented further

reliable sediment sampling

During noble gas analysis radiogenic He can be

released from the sediment grains as a result of the

heating of the sample during gas extraction [1] To

assess the amount of He released from the sediment

grains a stepwise heating experiment as described in

[1] was carried out for two sediment samples (one

from the clayey sediment and one from the facies rich

in organic matter) This showed that the He concen-

trations measured in Soppensee may exceed the actual

He concentrations in the pore water by up to 20

Because it is impossible to quantify reliably the

contribution of the He released from the sediment

grains to the total He measured the He data will not

be discussed further

3 Results and discussion

Fig 3 shows the noble gas concentration profiles

measured in the sediment pore water and in the

overlying lake water (see also Table 1) The noble gas

e water at sediment depth z and in the overlying water immediately

Isotope ratios

Xe108 20Ne22Ne 36Ar40Ar103

0878 989 3398

126 982 3387

131 982 3382

134 976 3378

145 978 3382

144 978 3382

131 981 3388

132 978 3382

137 976 3382

141 977 3382

146 979 3383

144 979 3374

tope ratios (relative 1r errors) except at 05 m and 111 m sediment

025 respectively) because the counting statistics of the mass-

mples

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 35

concentrations are undersaturated relative to the

atmospheric equilibrium concentrations computed

from the temperature of the overlying water In the

sediment this undersaturation is greatest just below

the sediment surface and decreases with increasing

sediment depth In the overlying water the noble gas

concentrations are also depleted (confirming previous

observations [23]) but to a much lesser extent than in

the sediment pore water This is due to noble gas

stripping by the gas bubbles rising through the water

body

The observed noble gas depletion decreases with

increasing atomic mass and hence with gas solubility

Such a depletion pattern is indicative of the loss of

dissolved noble gases to a gas or oil phase which was

initially free of noble gases [11124] Given the high

rate of CH4 production in the Soppensee sediment the

depletion pattern can be attributed to degassing into

gas bubbles which form in the sediment due to CH4

supersaturation

It may be expected that part of the observed noble

gas depletion arose during sediment sampling

because gas bubbles formed in the sediment after

recovery of the sediment cores The replicate samples

taken at 4 m and 5 m sediment depth show slightly

different Ne concentrations whereby the samples

which were taken first show a smaller depletion than

the subsequent samples This might be interpreted as

an indication that during sampling part of the

dissolved Ne was stripped into gas bubbles which

were not captured in the sediment sample However

the measured concentrations of the heavier noble

gases do not support this interpretation as the Ar Kr

and Xe concentrations of the replicate samples agree

within the analytical uncertainty The discrepancy of

the Ne replicates at 4 m and 5 m sediment depth

therefore seems to be due to an unknown artifact other

than degassing during sampling This is supported by

the fact that the noble gases are undersaturated even in

the overlying water [23] which shows a residence

time of about 1 yr as estimated from 3H3He data from

the deep water Also the 20Ne22Ne and 36Ar40Ar

isotope ratios in the pore water indicate that gas

exchange has attained steady state (see Section 31)

which is expected to occur within several hours

[2526] whereas the noble gas samples were collected

from the sediment core within a few minutes after

recovery It is therefore concluded that the noble gases

were not stripped from the water during sampling but

rather by gas bubbles which formed in the sediment

prior to sampling

31 Transfer of noble gases from the pore water into

CH4 bubbles

The transfer of dissolved noble gases into gas

bubbles forming in the sediment occurs by diffusion

through the gaswater interface between the gas

bubble and the pore water until the gas bubble

escapes from the sediment or until solubility equili-

brium is attained

If the gas bubbles escape from the sediment

before solubility equilibrium is approached the

noble gas abundance in the pore water will show

an isotopic fractionation corresponding to the extent

of degassing [1127] the lighter isotopes are more

mobile and are therefore removed from the pore

water more easily which results in a relative

enrichment of the heavier isotopes in the pore water

During the initial phase of the noble gas partitioning

between the bubbles and the pore water ie as long

as the gas exchange process is far from steady state

the noble gas concentrations in the bubble are much

smaller than the equilibrium concentrations Then

the loss of a species i from the pore water into the

gas bubble is controlled by its diffusion through the

gaswater interface The concentration decrease dCi

during a time interval dt is approximately propor-

tional to DiCidt [2829] where Di is the diffusivity

and Ci is the concentration of species i in the pore

water (see Table 2 for the notation used here) The

ratio of the concentration changes of two species i

and j is therefore given by

dCi

dCj

frac14 DiCi

DjCj

The solution of this differential equation is given

by the Rayleigh equation [28]

Ci

Cj

frac14 Ci0

Cj0

Cj

Cj0

DiDj1

where the subscript 0 denotes the initial state before

degassing With RijuCiCj the ratio of the concen-

trations of two species i and j in the pore water

fjuCjCj0 the fraction of species j remaining in the

Table 2

List of symbols

Symbol Description Dimension

t Time [T]

z Sediment depth positive down-

wards z =0 at the sediment surface

[L]

BBt Time derivative for z = const

(Eulerian derivative) Note that this

is generally not equal to the time

derivative in a fixed sediment layer

eg in the layer deposited in the

year 1950 (Lagrangian derivative)

Ci Concentration of species i in the

pore water (STP-volume of dis-

solved gas per unit mass of pore

water)

[L3M]

Rij Concentration ratio of two species i

and j in the pore water

[ndash]

Di0 Molecular diffusivity of solute i in

bulk water

[L2T]

Di Effective diffusivity of solute i in

the pore water

[L2T]

a ij Fractionation parameter [ndash]

Porosity (fraction of pore volume

per unit volume of bulk sediment)

[ndash]

a Tortuosity parameter of the sedi-

ment pore space

[ndash]

ri Production rate of species i per unit

volume of pore water

[NTL3]

U Burial velocity of pore water rela-

tive to the sediment surface

[LT]

x Burial velocity of solid sediment

relative to the sediment surface

[LT]

B STP bubble volume per unit mass

of pore water (dry gas)

[L3M]

Hi Henry coefficient of species i [(MLT2)(L3M)]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4436

pore water and aijuDiDj1 the bfractionationparameterQ the Rayleigh equation reads

Rij frac14 Rij0 faijj eth1THORN

To compare the concentration ratio of species i and

j (Rij) with that of two other species k and l (Rkl) one

can write

fj

flfrac14 Cj=Cj0

Cl=Cl0frac14 Rjl

Rjl0frac14zeth1THORN

fajll

Thus fj = fajl +1l Combining this with Eq (1) allows

Rij and Rkl to be expressed simultaneously as

functions of fl

Rij frac14 Rij0 fajlaijthornaijl and Rkl frac14 Rkl0 f

akll eth2THORN

Fig 4 compares the measured 20Ne22Ne and36Ar40Ar ratios with the Rayleigh fractionation

expected from Eq (2) where i =20Ne j =22Ne

k =36Ar l =40Ar and f40Ar ranges from 30 (max

observed 40Ar depletion) to 100 (no depletion)

The fractionation parameters were calculated by

assuming that the ratios of the noble gas isotope

diffusivities in the sediment are the same as the

respective ratios of the molecular diffusivities in bulk

water (Table 3)

The predicted Rayleigh fractionation corresponds

to changes in the isotope ratios of up to 9

(20Ne22Ne) and 7 (36Ar40Ar) In contrast the

measured isotope ratios correspond to the atmospheric

equilibrium ratios within the analytical uncertainties

of 02 (20Ne22Ne) and 01 (36Ar40Ar)

The noble gas partitioning between the pore water

and the gas bubbles is therefore not controlled by

diffusion On the contrary the noble gas depletion

rather reflects a solubility equilibrium between pore

water and gas bubbles This is in line with the

expectation that equilibrium between pore water and

gas bubble is attained within a few hours [2526]

whereas bubble growth in the sediment occurs on a

time scale of several days or weeks [3031]

32 Vertical noble gas transport in the sediment

pore space

The vertical transport of noble gases within the

pore space may be controlled either by vertical

diffusion (such as in Lake Zug [32]) or by pore-water

advection relative to the sediment surface (such as in

Lake Issyk-Kul [2]) This leads to the two following

hypotheses to explain the noble gas concentration

profiles observed in Soppensee

Hypothesis A (Diffusion hypothesis) The vertical

transport of noble gases is controlled by vertical

diffusion The existence of vertical concentration

gradients therefore implies that noble gas profiles

reflect a dynamic state This leads to the following

interpretation (see also Fig 5) ebullition was (vir-

tually) absent before it abruptly set in during recent

decades or centuries Before the onset of ebullition

the noble gas concentrations in the pore water were

the same as those in the overlying water The noble

gas depletion observed in the sediment which was

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4434

analysis [22] from the sediment liner of this gravity

core No gas bubbles were observed in the gravity

core during the first few minutes after recovery when

the overlying water was sampled

Sediment samples for noble gas analysis were

prepared immediately after recovery of the sediment

cores to minimize exsolution of supersaturated CH4 in

the cores Bulk sediment was transferred from the

sediment cores into the sample containers (Cu tubes)

without exposure to the atmosphere or other gas

reservoirs [1] The noble gases were then extracted

from the pore water by degassing the sediment in an

evacuated extraction vessel [1] The noble gas

abundance was then analyzed by mass spectrometry

with an overall 1r uncertainty of ~ 2 in the

concentrations and ~ 01 in the isotope ratios

following the experimental procedures described in

[1] and [22]

Samples were collected at sediment depths of 050

m 111 m 396 m 496 m 656 m and 686 m (Fig

3) Inspection of the cores after sampling indicated

that the uncertainty in the sampling depth due to

squeezing is about 5 cm Excessive gas exsolution

prevented reliable sediment sampling between 15 and

35 m sediment depth Replicate samples were

Table 1

Noble gas concentrations and isotope ratios measured in the sediment por

above the sediment surface

z (m) Concentrations

(cmSTP3 g)

Ne108 Ar104 Kr108

Sediment pore water

05 0301 121 418

111 0474 197 646

396 123 290 782

396 0988 290 804

496 142 343 917

496 117 324 867

656 162 348 859

656 153 341 836

686 170 360 885

686 169 368 911

Overlying water

ndash 182 390 960

ndash 186 392 963

The analytical errors are b 2 for the concentrations and b 01 for the iso

depth where the errors in the 20Ne22Ne ratios are larger (04 and

spectrometric analysis were affected by the low Ne abundance in these sa

collected from each sampling depth except at 050

m and 111 m where only one sample could be taken

before the formation of gas bubbles prevented further

reliable sediment sampling

During noble gas analysis radiogenic He can be

released from the sediment grains as a result of the

heating of the sample during gas extraction [1] To

assess the amount of He released from the sediment

grains a stepwise heating experiment as described in

[1] was carried out for two sediment samples (one

from the clayey sediment and one from the facies rich

in organic matter) This showed that the He concen-

trations measured in Soppensee may exceed the actual

He concentrations in the pore water by up to 20

Because it is impossible to quantify reliably the

contribution of the He released from the sediment

grains to the total He measured the He data will not

be discussed further

3 Results and discussion

Fig 3 shows the noble gas concentration profiles

measured in the sediment pore water and in the

overlying lake water (see also Table 1) The noble gas

e water at sediment depth z and in the overlying water immediately

Isotope ratios

Xe108 20Ne22Ne 36Ar40Ar103

0878 989 3398

126 982 3387

131 982 3382

134 976 3378

145 978 3382

144 978 3382

131 981 3388

132 978 3382

137 976 3382

141 977 3382

146 979 3383

144 979 3374

tope ratios (relative 1r errors) except at 05 m and 111 m sediment

025 respectively) because the counting statistics of the mass-

mples

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 35

concentrations are undersaturated relative to the

atmospheric equilibrium concentrations computed

from the temperature of the overlying water In the

sediment this undersaturation is greatest just below

the sediment surface and decreases with increasing

sediment depth In the overlying water the noble gas

concentrations are also depleted (confirming previous

observations [23]) but to a much lesser extent than in

the sediment pore water This is due to noble gas

stripping by the gas bubbles rising through the water

body

The observed noble gas depletion decreases with

increasing atomic mass and hence with gas solubility

Such a depletion pattern is indicative of the loss of

dissolved noble gases to a gas or oil phase which was

initially free of noble gases [11124] Given the high

rate of CH4 production in the Soppensee sediment the

depletion pattern can be attributed to degassing into

gas bubbles which form in the sediment due to CH4

supersaturation

It may be expected that part of the observed noble

gas depletion arose during sediment sampling

because gas bubbles formed in the sediment after

recovery of the sediment cores The replicate samples

taken at 4 m and 5 m sediment depth show slightly

different Ne concentrations whereby the samples

which were taken first show a smaller depletion than

the subsequent samples This might be interpreted as

an indication that during sampling part of the

dissolved Ne was stripped into gas bubbles which

were not captured in the sediment sample However

the measured concentrations of the heavier noble

gases do not support this interpretation as the Ar Kr

and Xe concentrations of the replicate samples agree

within the analytical uncertainty The discrepancy of

the Ne replicates at 4 m and 5 m sediment depth

therefore seems to be due to an unknown artifact other

than degassing during sampling This is supported by

the fact that the noble gases are undersaturated even in

the overlying water [23] which shows a residence

time of about 1 yr as estimated from 3H3He data from

the deep water Also the 20Ne22Ne and 36Ar40Ar

isotope ratios in the pore water indicate that gas

exchange has attained steady state (see Section 31)

which is expected to occur within several hours

[2526] whereas the noble gas samples were collected

from the sediment core within a few minutes after

recovery It is therefore concluded that the noble gases

were not stripped from the water during sampling but

rather by gas bubbles which formed in the sediment

prior to sampling

31 Transfer of noble gases from the pore water into

CH4 bubbles

The transfer of dissolved noble gases into gas

bubbles forming in the sediment occurs by diffusion

through the gaswater interface between the gas

bubble and the pore water until the gas bubble

escapes from the sediment or until solubility equili-

brium is attained

If the gas bubbles escape from the sediment

before solubility equilibrium is approached the

noble gas abundance in the pore water will show

an isotopic fractionation corresponding to the extent

of degassing [1127] the lighter isotopes are more

mobile and are therefore removed from the pore

water more easily which results in a relative

enrichment of the heavier isotopes in the pore water

During the initial phase of the noble gas partitioning

between the bubbles and the pore water ie as long

as the gas exchange process is far from steady state

the noble gas concentrations in the bubble are much

smaller than the equilibrium concentrations Then

the loss of a species i from the pore water into the

gas bubble is controlled by its diffusion through the

gaswater interface The concentration decrease dCi

during a time interval dt is approximately propor-

tional to DiCidt [2829] where Di is the diffusivity

and Ci is the concentration of species i in the pore

water (see Table 2 for the notation used here) The

ratio of the concentration changes of two species i

and j is therefore given by

dCi

dCj

frac14 DiCi

DjCj

The solution of this differential equation is given

by the Rayleigh equation [28]

Ci

Cj

frac14 Ci0

Cj0

Cj

Cj0

DiDj1

where the subscript 0 denotes the initial state before

degassing With RijuCiCj the ratio of the concen-

trations of two species i and j in the pore water

fjuCjCj0 the fraction of species j remaining in the

Table 2

List of symbols

Symbol Description Dimension

t Time [T]

z Sediment depth positive down-

wards z =0 at the sediment surface

[L]

BBt Time derivative for z = const

(Eulerian derivative) Note that this

is generally not equal to the time

derivative in a fixed sediment layer

eg in the layer deposited in the

year 1950 (Lagrangian derivative)

Ci Concentration of species i in the

pore water (STP-volume of dis-

solved gas per unit mass of pore

water)

[L3M]

Rij Concentration ratio of two species i

and j in the pore water

[ndash]

Di0 Molecular diffusivity of solute i in

bulk water

[L2T]

Di Effective diffusivity of solute i in

the pore water

[L2T]

a ij Fractionation parameter [ndash]

Porosity (fraction of pore volume

per unit volume of bulk sediment)

[ndash]

a Tortuosity parameter of the sedi-

ment pore space

[ndash]

ri Production rate of species i per unit

volume of pore water

[NTL3]

U Burial velocity of pore water rela-

tive to the sediment surface

[LT]

x Burial velocity of solid sediment

relative to the sediment surface

[LT]

B STP bubble volume per unit mass

of pore water (dry gas)

[L3M]

Hi Henry coefficient of species i [(MLT2)(L3M)]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4436

pore water and aijuDiDj1 the bfractionationparameterQ the Rayleigh equation reads

Rij frac14 Rij0 faijj eth1THORN

To compare the concentration ratio of species i and

j (Rij) with that of two other species k and l (Rkl) one

can write

fj

flfrac14 Cj=Cj0

Cl=Cl0frac14 Rjl

Rjl0frac14zeth1THORN

fajll

Thus fj = fajl +1l Combining this with Eq (1) allows

Rij and Rkl to be expressed simultaneously as

functions of fl

Rij frac14 Rij0 fajlaijthornaijl and Rkl frac14 Rkl0 f

akll eth2THORN

Fig 4 compares the measured 20Ne22Ne and36Ar40Ar ratios with the Rayleigh fractionation

expected from Eq (2) where i =20Ne j =22Ne

k =36Ar l =40Ar and f40Ar ranges from 30 (max

observed 40Ar depletion) to 100 (no depletion)

The fractionation parameters were calculated by

assuming that the ratios of the noble gas isotope

diffusivities in the sediment are the same as the

respective ratios of the molecular diffusivities in bulk

water (Table 3)

The predicted Rayleigh fractionation corresponds

to changes in the isotope ratios of up to 9

(20Ne22Ne) and 7 (36Ar40Ar) In contrast the

measured isotope ratios correspond to the atmospheric

equilibrium ratios within the analytical uncertainties

of 02 (20Ne22Ne) and 01 (36Ar40Ar)

The noble gas partitioning between the pore water

and the gas bubbles is therefore not controlled by

diffusion On the contrary the noble gas depletion

rather reflects a solubility equilibrium between pore

water and gas bubbles This is in line with the

expectation that equilibrium between pore water and

gas bubble is attained within a few hours [2526]

whereas bubble growth in the sediment occurs on a

time scale of several days or weeks [3031]

32 Vertical noble gas transport in the sediment

pore space

The vertical transport of noble gases within the

pore space may be controlled either by vertical

diffusion (such as in Lake Zug [32]) or by pore-water

advection relative to the sediment surface (such as in

Lake Issyk-Kul [2]) This leads to the two following

hypotheses to explain the noble gas concentration

profiles observed in Soppensee

Hypothesis A (Diffusion hypothesis) The vertical

transport of noble gases is controlled by vertical

diffusion The existence of vertical concentration

gradients therefore implies that noble gas profiles

reflect a dynamic state This leads to the following

interpretation (see also Fig 5) ebullition was (vir-

tually) absent before it abruptly set in during recent

decades or centuries Before the onset of ebullition

the noble gas concentrations in the pore water were

the same as those in the overlying water The noble

gas depletion observed in the sediment which was

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 35

concentrations are undersaturated relative to the

atmospheric equilibrium concentrations computed

from the temperature of the overlying water In the

sediment this undersaturation is greatest just below

the sediment surface and decreases with increasing

sediment depth In the overlying water the noble gas

concentrations are also depleted (confirming previous

observations [23]) but to a much lesser extent than in

the sediment pore water This is due to noble gas

stripping by the gas bubbles rising through the water

body

The observed noble gas depletion decreases with

increasing atomic mass and hence with gas solubility

Such a depletion pattern is indicative of the loss of

dissolved noble gases to a gas or oil phase which was

initially free of noble gases [11124] Given the high

rate of CH4 production in the Soppensee sediment the

depletion pattern can be attributed to degassing into

gas bubbles which form in the sediment due to CH4

supersaturation

It may be expected that part of the observed noble

gas depletion arose during sediment sampling

because gas bubbles formed in the sediment after

recovery of the sediment cores The replicate samples

taken at 4 m and 5 m sediment depth show slightly

different Ne concentrations whereby the samples

which were taken first show a smaller depletion than

the subsequent samples This might be interpreted as

an indication that during sampling part of the

dissolved Ne was stripped into gas bubbles which

were not captured in the sediment sample However

the measured concentrations of the heavier noble

gases do not support this interpretation as the Ar Kr

and Xe concentrations of the replicate samples agree

within the analytical uncertainty The discrepancy of

the Ne replicates at 4 m and 5 m sediment depth

therefore seems to be due to an unknown artifact other

than degassing during sampling This is supported by

the fact that the noble gases are undersaturated even in

the overlying water [23] which shows a residence

time of about 1 yr as estimated from 3H3He data from

the deep water Also the 20Ne22Ne and 36Ar40Ar

isotope ratios in the pore water indicate that gas

exchange has attained steady state (see Section 31)

which is expected to occur within several hours

[2526] whereas the noble gas samples were collected

from the sediment core within a few minutes after

recovery It is therefore concluded that the noble gases

were not stripped from the water during sampling but

rather by gas bubbles which formed in the sediment

prior to sampling

31 Transfer of noble gases from the pore water into

CH4 bubbles

The transfer of dissolved noble gases into gas

bubbles forming in the sediment occurs by diffusion

through the gaswater interface between the gas

bubble and the pore water until the gas bubble

escapes from the sediment or until solubility equili-

brium is attained

If the gas bubbles escape from the sediment

before solubility equilibrium is approached the

noble gas abundance in the pore water will show

an isotopic fractionation corresponding to the extent

of degassing [1127] the lighter isotopes are more

mobile and are therefore removed from the pore

water more easily which results in a relative

enrichment of the heavier isotopes in the pore water

During the initial phase of the noble gas partitioning

between the bubbles and the pore water ie as long

as the gas exchange process is far from steady state

the noble gas concentrations in the bubble are much

smaller than the equilibrium concentrations Then

the loss of a species i from the pore water into the

gas bubble is controlled by its diffusion through the

gaswater interface The concentration decrease dCi

during a time interval dt is approximately propor-

tional to DiCidt [2829] where Di is the diffusivity

and Ci is the concentration of species i in the pore

water (see Table 2 for the notation used here) The

ratio of the concentration changes of two species i

and j is therefore given by

dCi

dCj

frac14 DiCi

DjCj

The solution of this differential equation is given

by the Rayleigh equation [28]

Ci

Cj

frac14 Ci0

Cj0

Cj

Cj0

DiDj1

where the subscript 0 denotes the initial state before

degassing With RijuCiCj the ratio of the concen-

trations of two species i and j in the pore water

fjuCjCj0 the fraction of species j remaining in the

Table 2

List of symbols

Symbol Description Dimension

t Time [T]

z Sediment depth positive down-

wards z =0 at the sediment surface

[L]

BBt Time derivative for z = const

(Eulerian derivative) Note that this

is generally not equal to the time

derivative in a fixed sediment layer

eg in the layer deposited in the

year 1950 (Lagrangian derivative)

Ci Concentration of species i in the

pore water (STP-volume of dis-

solved gas per unit mass of pore

water)

[L3M]

Rij Concentration ratio of two species i

and j in the pore water

[ndash]

Di0 Molecular diffusivity of solute i in

bulk water

[L2T]

Di Effective diffusivity of solute i in

the pore water

[L2T]

a ij Fractionation parameter [ndash]

Porosity (fraction of pore volume

per unit volume of bulk sediment)

[ndash]

a Tortuosity parameter of the sedi-

ment pore space

[ndash]

ri Production rate of species i per unit

volume of pore water

[NTL3]

U Burial velocity of pore water rela-

tive to the sediment surface

[LT]

x Burial velocity of solid sediment

relative to the sediment surface

[LT]

B STP bubble volume per unit mass

of pore water (dry gas)

[L3M]

Hi Henry coefficient of species i [(MLT2)(L3M)]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4436

pore water and aijuDiDj1 the bfractionationparameterQ the Rayleigh equation reads

Rij frac14 Rij0 faijj eth1THORN

To compare the concentration ratio of species i and

j (Rij) with that of two other species k and l (Rkl) one

can write

fj

flfrac14 Cj=Cj0

Cl=Cl0frac14 Rjl

Rjl0frac14zeth1THORN

fajll

Thus fj = fajl +1l Combining this with Eq (1) allows

Rij and Rkl to be expressed simultaneously as

functions of fl

Rij frac14 Rij0 fajlaijthornaijl and Rkl frac14 Rkl0 f

akll eth2THORN

Fig 4 compares the measured 20Ne22Ne and36Ar40Ar ratios with the Rayleigh fractionation

expected from Eq (2) where i =20Ne j =22Ne

k =36Ar l =40Ar and f40Ar ranges from 30 (max

observed 40Ar depletion) to 100 (no depletion)

The fractionation parameters were calculated by

assuming that the ratios of the noble gas isotope

diffusivities in the sediment are the same as the

respective ratios of the molecular diffusivities in bulk

water (Table 3)

The predicted Rayleigh fractionation corresponds

to changes in the isotope ratios of up to 9

(20Ne22Ne) and 7 (36Ar40Ar) In contrast the

measured isotope ratios correspond to the atmospheric

equilibrium ratios within the analytical uncertainties

of 02 (20Ne22Ne) and 01 (36Ar40Ar)

The noble gas partitioning between the pore water

and the gas bubbles is therefore not controlled by

diffusion On the contrary the noble gas depletion

rather reflects a solubility equilibrium between pore

water and gas bubbles This is in line with the

expectation that equilibrium between pore water and

gas bubble is attained within a few hours [2526]

whereas bubble growth in the sediment occurs on a

time scale of several days or weeks [3031]

32 Vertical noble gas transport in the sediment

pore space

The vertical transport of noble gases within the

pore space may be controlled either by vertical

diffusion (such as in Lake Zug [32]) or by pore-water

advection relative to the sediment surface (such as in

Lake Issyk-Kul [2]) This leads to the two following

hypotheses to explain the noble gas concentration

profiles observed in Soppensee

Hypothesis A (Diffusion hypothesis) The vertical

transport of noble gases is controlled by vertical

diffusion The existence of vertical concentration

gradients therefore implies that noble gas profiles

reflect a dynamic state This leads to the following

interpretation (see also Fig 5) ebullition was (vir-

tually) absent before it abruptly set in during recent

decades or centuries Before the onset of ebullition

the noble gas concentrations in the pore water were

the same as those in the overlying water The noble

gas depletion observed in the sediment which was

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

Table 2

List of symbols

Symbol Description Dimension

t Time [T]

z Sediment depth positive down-

wards z =0 at the sediment surface

[L]

BBt Time derivative for z = const

(Eulerian derivative) Note that this

is generally not equal to the time

derivative in a fixed sediment layer

eg in the layer deposited in the

year 1950 (Lagrangian derivative)

Ci Concentration of species i in the

pore water (STP-volume of dis-

solved gas per unit mass of pore

water)

[L3M]

Rij Concentration ratio of two species i

and j in the pore water

[ndash]

Di0 Molecular diffusivity of solute i in

bulk water

[L2T]

Di Effective diffusivity of solute i in

the pore water

[L2T]

a ij Fractionation parameter [ndash]

Porosity (fraction of pore volume

per unit volume of bulk sediment)

[ndash]

a Tortuosity parameter of the sedi-

ment pore space

[ndash]

ri Production rate of species i per unit

volume of pore water

[NTL3]

U Burial velocity of pore water rela-

tive to the sediment surface

[LT]

x Burial velocity of solid sediment

relative to the sediment surface

[LT]

B STP bubble volume per unit mass

of pore water (dry gas)

[L3M]

Hi Henry coefficient of species i [(MLT2)(L3M)]

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4436

pore water and aijuDiDj1 the bfractionationparameterQ the Rayleigh equation reads

Rij frac14 Rij0 faijj eth1THORN

To compare the concentration ratio of species i and

j (Rij) with that of two other species k and l (Rkl) one

can write

fj

flfrac14 Cj=Cj0

Cl=Cl0frac14 Rjl

Rjl0frac14zeth1THORN

fajll

Thus fj = fajl +1l Combining this with Eq (1) allows

Rij and Rkl to be expressed simultaneously as

functions of fl

Rij frac14 Rij0 fajlaijthornaijl and Rkl frac14 Rkl0 f

akll eth2THORN

Fig 4 compares the measured 20Ne22Ne and36Ar40Ar ratios with the Rayleigh fractionation

expected from Eq (2) where i =20Ne j =22Ne

k =36Ar l =40Ar and f40Ar ranges from 30 (max

observed 40Ar depletion) to 100 (no depletion)

The fractionation parameters were calculated by

assuming that the ratios of the noble gas isotope

diffusivities in the sediment are the same as the

respective ratios of the molecular diffusivities in bulk

water (Table 3)

The predicted Rayleigh fractionation corresponds

to changes in the isotope ratios of up to 9

(20Ne22Ne) and 7 (36Ar40Ar) In contrast the

measured isotope ratios correspond to the atmospheric

equilibrium ratios within the analytical uncertainties

of 02 (20Ne22Ne) and 01 (36Ar40Ar)

The noble gas partitioning between the pore water

and the gas bubbles is therefore not controlled by

diffusion On the contrary the noble gas depletion

rather reflects a solubility equilibrium between pore

water and gas bubbles This is in line with the

expectation that equilibrium between pore water and

gas bubble is attained within a few hours [2526]

whereas bubble growth in the sediment occurs on a

time scale of several days or weeks [3031]

32 Vertical noble gas transport in the sediment

pore space

The vertical transport of noble gases within the

pore space may be controlled either by vertical

diffusion (such as in Lake Zug [32]) or by pore-water

advection relative to the sediment surface (such as in

Lake Issyk-Kul [2]) This leads to the two following

hypotheses to explain the noble gas concentration

profiles observed in Soppensee

Hypothesis A (Diffusion hypothesis) The vertical

transport of noble gases is controlled by vertical

diffusion The existence of vertical concentration

gradients therefore implies that noble gas profiles

reflect a dynamic state This leads to the following

interpretation (see also Fig 5) ebullition was (vir-

tually) absent before it abruptly set in during recent

decades or centuries Before the onset of ebullition

the noble gas concentrations in the pore water were

the same as those in the overlying water The noble

gas depletion observed in the sediment which was

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

31 32 33 34

88

9

92

94

96

98

10

36Ar 40Ar [10-3 ]

20N

e 22

Ne

337 338 339

975

98

985

36Ar 40Ar [10-3 ]

20N

e 22

Ne

Max observed 40Ar depletion

No depletion

Fig 4 20Ne22Ne vs 36Ar40Ar Left panel comparison of the Rayleigh fractionation line with the measured isotope ratios The solid line

reflects the isotopic signature expected from the Rayleigh Eq (2) The line spans the fractionation range expected from the observed 40Ar

depletion Right panel magnification of the measured data in the pore water (circles) and the overlying water (squares) The star represents the

isotope ratios of air-equilibrated water [22] The error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 37

deposited before the onset of ebullition is due to the

vertical rearrangement of the noble gas deficit by

vertical diffusion

Hypothesis B (Advection hypothesis) The vertical

noble gas transport is controlled by pore-water

advection due to sediment accumulation and compac-

tion In contrast to Hypothesis A this implies that

ebullition occurred throughout the entire Holocene

and increased gradually with time The noble gas

depletion resulting from degassing is archived in the

sediment by the continuous pore-water burial

These two complementary hypotheses are dis-

cussed using the advectionndashdiffusion model for the

vertical transport of solutes in sediment pore water

described in [32ndash34] For a steady-state porosity

Table 3

Molecular diffusivities of 20Ne 22Ne 36Ar and 40Ar in water at

55 8C (Di0 in 109 m2s) and the corresponding fractionation

factors a ij =Di0Dj

01 used in Eq (2)

i D0i ai 22Ne a i 40Ar

20Ne 2657 0049 ndash22Ne 2534 ndash 051936Ar 1758 ndash 005440Ar 1668 ndash ndash

The molecular diffusivities were calculated from empirical diffu-

sivity measurements [35] whereby the molecular diffusivities were

assumed to be inversely proportional to the square root of the

atomic mass

profile ie BBt=0 the vertical transport is charac-

terized by

zeth THORN BCi zteth THORNBt

frac14 B

Bz zeth THORNDi zeth THORN BCi zteth THORN

Bz

zeth THORNU zteth THORN BCi zteth THORNBz

thorn zeth THORNri zteth THORN eth3THORN

If it is assumed that a depth z exists below which

compaction is absent and if pore-water advection

relative to the sediment matrix is assumed to be zero

below zT then the burial velocities of the pore water

and the solid sediment are given by

U zteth THORN frac14ethzTHORN x teth THORN and x zteth THORN frac14

1 1 zeth THORN x teth THORN

eth4THORN

where T and xT are the porosity and the burial

velocity respectively of the sediment at depth zT

If vertical diffusion is the dominant transport

process (Hypothesis A) the loss of dissolved noble

gases from the bebullition zoneQ (the vertical range ofsediment from where gas bubbles are released) results

in a diffusive flux of noble gases both from the deeper

sediment and the overlying water into the ebullition

zone Fig 5 illustrates the relevant transport processes

and the temporal evolution of the resulting noble gas

profiles

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

Table 4

Henry coefficients Hi for Ne Ar Kr and Xe in freshwater at a

temperature of 55 8C in bar(cmSTP3 g) (STP=standard temperature

and pressure)

i Ne Ar Kr Xe

Hi 872 220 111 568

water

sediment ebullition zone

turbulent diffusion ebullition

molecular diffusion t3 gt t2 gt t1

Ci

Ci0

z

z=0z0

Fig 5 Illustration of the situation corresponding to Hypothesis A (bDiffusion hypothesisQ) Left diagram of the relevant transport processes

determining the vertical noble gas concentration profiles in the sediment pore water Right concentration profiles Ci(z) in the sediment

resulting from an abrupt onset of ebullition in the bebullition zoneQ between z =0 and z = z0 (at times t1 t2 and t3 after the onset of

ebullition)

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4438

For the upper boundary condition needed to solve

Eq (3) the concentrations in the overlying water were

assumed to correspond to the atmospheric equilibrium

concentrations in the overlying water which were

considered to be constant over time The small

degassing depletion of the overlying water was

neglected For the lower boundary condition the

underlying bedrock was assumed to present an

impermeable boundary at the bottom of the sediment

column For the initial condition (ie for the state

prevailing before the onset of ebullition) the noble

gas concentrations in the pore water were assumed to

correspond to the atmospheric equilibrium concen-

trations in the overlying water

After the onset of ebullition (at time t0) the rate of

bubble production per unit volume of pore water was

assumed to be time-independent and to be constant

throughout the entire ebullition zone ie in the

sediment between z =0 and z= z0 It was further

assumed that bubbles are formed only in the sediment

accumulating after the onset of ebullition Thus if x0

is the sediment accumulation rate z0(tz t0) =

x0 d (t t0) where x0=5 mmyr was estimated from

the chronology of the sediment deposited during the

last two centuries (Fig 2)

If the gas bubbles escape continuously from the

sediment (after noble gas equilibration with the pore

water) the loss of noble gas i from the pore water

per unit time and pore-water volume (ndashri in Eq

(3)) depends on the gas production rate per unit

volume of pore water (rb) and on the partial pressure

of noble gas i in the bubble Pi =HiCi where Hi is the

respective Henry coefficient at the temperature of the

pore water (55 8C Table 4) If Pb is the total gas

pressure in the bubbles and with kbu rbPb it follows

that

ri zteth THORNfrac14 Pi

Pbrbfrac14 HiCi

Pbrbfrac14kbHiCi for 0VzVz0 teth THORN

0 for zNz0 teth THORN

eth5THORNThe porosity profile shown in Fig 2 seems not to

reflect a steady state (ie BBt p 0) because the

porosity does not decrease steadily with depth and the

lithology of the sediment indicates several changes in

the sedimentary regime of the lake Under the

assumption that the vertical transport is controlled

by vertical diffusion (Hypothesis A) however the

non-stationarity in the pore-water advection relative to

the sediment matrix due to sediment compaction can

be neglected Constant values of U =x0 and =085

(typical for the uppermost 6 m of the sediment) were

therefore used to solve Eq (3) The effective noble

gas diffusivities in the pore space were calculated

from their molecular diffusivities in bulk water [35] at

the mean deep-water temperature (55 8C) and the

following tortuosity relation [36]

Di zeth THORN frac14 D0i

1thorn a 1 zeth THORNeth THORN

Practically the noble gas concentration profiles were

calculated by the numerical integration of Eq (3) [32]

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

-2 0 2 4

0

2

4

6

z [m

]

δNe

[]-2 0 2 4

δAr

[]

Fig 7 Comparison of the measured 20Ne22Ne and 36Ar40Ar

profiles with the modeled profiles corresponding to Hypothesis A

The d i are the relative deviations of the isotope ratios measured in

the pore water (Ri) from those of air-saturated water (Ri [22])

di =RiRi1

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 39

The unknown values of the parameters t0 kb and a

were determined by least-squares regression of the

modeled noble gas profiles on the measured noble gas

concentrations (t0c1800 AD kb=12 d 102 cmSTP

3

gbaryr ac103)

Fig 6 shows that the modeled concentration

profiles roughly agree with the measured profiles

although discrepancies are evident for the heavier

noble gases However using the same model to

calculate the concentration profiles of 20Ne 22Ne36Ar and 40Ar reveals that vertical noble gas diffusion

from the deep sediment into the ebullition zone would

strongly affect the 20Ne22Ne and 36Ar40Ar ratios

(Fig 7) because the lighter isotopes diffuse faster

than the heavier ones (see also Table 3) However the

measured profiles of the isotope ratios do not show

such an isotopic fractionation (Fig 7) This indicates

that the diffusive transport of dissolved noble gases

from the deep sediment into the ebullition zone is

insignificant Thus although the modeled profiles of

the element concentrations are (coincidentally) con-

sistent with the measured concentrations the diffusion

Hypothesis A must be rejected based on the isotope

ratio measurements It is therefore concluded that the

noble gas depletion at a given sediment depth reflects

the bubble production at the time when the pore water

at this depth was deposited (Hypothesis B)

0

2

4

6

z [m

]

0

2

4

6

z [m

]

Ne Ar

0 25 50 75 100

Kr

0 25 50 75 100

Xe

Ci Ci [] Ci Ci []

Fig 6 Comparison of the measured noble gas profiles with the

modeled profiles corresponding to Hypothesis A (bDiffusionhypothesisQ) The noble gas concentrations Ci are normalized to the

atmospheric equilibrium concentrations Ci in the overlying water

It should be noted however that compaction of the

bulk sediment causes a decrease in the pore-space

volume which results in an upward offset of the pore

water relative to the solid sediment [32ndash34] The pore

water at a given sediment depth can therefore be older

than the sediment matrix at the same depth In the

deep sediment ie below the compaction zone this

age difference can extend up to a few centuries [32]

To calculate the age difference reliably the sediment

porosity and the burial velocities of the pore water and

the solid sediment would have to be known as

functions of sediment depth and time throughout the

entire history of the lake However as this information

is not available for Soppensee we refrain from

attempting to calculate the exact pore-water offset

with respect to the solid sediment

33 Quantification of the gas loss from the sediment

by ebullition

As shown in Section 31 noble gas depletion in the

pore water can be modeled as the result of gas

equilibration between pore water and gas bubbles

The concentration Ci in the pore water after equili-

bration with a gas bubble is given by the initial

concentration in the water (ie the atmospheric

equilibrium concentration Ci) the STP volume of

dry gas per unit mass of pore water in the equilibrated

gas bubble (B) and the Henry coefficient Hi of noble

gas i (Table 4) As shown in [1] Ci can be computed

by the d1-step degassing modelT

Ci frac14Ci4

1thorn Bgii frac14 Ne Ar Kr Xe eth6THORN

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4440

where gi =HiP0 with the STP dry-gas pressure

P0=101325 bar1

In the case of repeated gas bubble formation and

noble gas equilibration the noble gas concentrations

in the pore water will follow a series of degassing

steps If B reflects the total amount of gas produced

after n such steps the mean STP volume of dry gas

per unit mass of pore water in each step is Bn If all

gas bubbles can be assumed to be of similar size Eq

(6) can be applied iteratively to yield the dcontinuousdegassing modelT for nYl

Ci frac14Ci4

1thorn Bngi

n YnYleBgiCi

4 ifrac14Ne AR Kr Xe

eth7THORN

where the limit nYl reflects a degassing series

consisting of an infinite number of consecutive

equilibration steps involving infinitesimally small

bubbles

The choice of which degassing model is to be

used for the interpretation of the noble gas depletion

depends on the mechanisms controlling bubble

growth in the sediment Bubbles were found to

grow on time scales of several weeks and bubble

sizes of up to a few centimeters in diameter have

been reported [3ndash5] The growth of isolated bubbles

in the sediment was modeled in [30] Due to the

inhomogeneous distribution of CH4 sources (organic

matter) in the sediment the bubbles were assumed to

be separated by distances much larger than their

diameter Also the bubbles were assumed to be

spherical which led to the interpretation that the

observed bubble growth times of several weeks are

due to the limitation of bubble growth by diffusive

transport of the dissolved CH4 from its source to the

bubble [30] However it was found later that

bubbles grow by fracturing the sediment which

results in flat disc-shaped bubbles [37] The surface-

area to volume ratio of such bubbles is much larger

than that of spherical bubbles The diffusion limit is

therefore much smaller for the growth of disc-shaped

bubbles than for the growth of spherical bubbles

1 Note that in [1] Eq (6) is written with the term ziCi in place of

g i (where zi is the volume fraction of gas i in dry air) This is

consistent with the notation chosen here because ziCi=HiP0=g i

according to Henryrsquos Law

[31] Thus bubble growth is not limited by CH4

diffusion but by the mechanical resistance of the

sediment [3137]

Consequently the available literature indicates that

noble gas equilibration occurs with relatively large

but few bubbles (and that bubbles grow slowly

enough for the noble gases to attain solubility

equilibrium) This tends to support the 1-step degass-

ing model rather than the continuous degassing

model However both models reflect extreme cases

of either a single degassing step or an infinite series of

degassing steps Note that in Section 32 the bubbles

were assumed to be continuously removed from the

sediment (continuous degassing model) which seems

inconsistent with the current discussion However the

choice of degassing model is irrelevant for the

conclusion reached in Section 32 because the argu-

ment needed to reject the diffusion hypothesis is that

the noble gas partitioning between the pore water and

the bubbles is controlled by Henryrsquos Law which

results in virtually no isotopic fractionation The

continuous degassing model was used in Section 32

because the current implementation of the computer

program used can only handle source terms ri of

zeroth or first order in Ci

Fig 8 compares the ratios of the measured noble

gas concentrations with those predicted by the two

degassing models In agreement with the above

discussion the 1-step degassing model fits the

measured data better than the continuous degassing

model In general the model curves of the 1-step

degassing model match the trends of the measured

data However a systematic offset between the model

curves and the measured data is apparent suggesting

that the noble gas concentrations are affected by an as

yet unknown process which is not accounted for by

either of the two degassing models However the

offset is smaller for the 1-step degassing model than

for the continuous degassing model

To quantify the amount of gaseous CH4 that was

released from the sediment the 1-step degassing

model was therefore used to estimate the degassing

parameter B by least-squares regression from the

measured Ne Ar Kr and Xe concentrations (Fig 9)

The atmospheric equilibration temperature was

assumed to be the same for all pore water samples

The value used for this was the present annual mean

temperature of the overlying water (55 8C) Because

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

5

1-stepdegassing

model

0degC5degC

10degC

continuousdegassing

model

6 7

1

15

2

25

3

KrXe

Ar

Xe

[104 ]

5 6 7

4

6

8

10

12

14

16

KrXe

Ne

Xe

15 2 25 3

4

6

8

10

12

14

16

ArXe [104]

Ne

Xe

25 3 35 405

1

15

2

ArKr [103]

Ne

Kr

Fig 8 Three-element plots of Ne Ar Kr and Xe The grey lines illustrate the various element ratios in air-saturated water at temperatures

ranging from 0 8C to 10 8C The black lines reflect the element ratios predicted by the 1-step degassing and continuous degassing models The

error bars illustrate the analytical 1r uncertainty

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 41

temperature mostly affects the concentrations of the

heavier noble gases which are least sensitive to

degassing the estimate of B is insensitive to the

temperature prevailing during gas equilibration with

0 20 40 60 80 100

0

2

4

6Sed

imen

t dep

th [m

]

B [10-3 cmSTPg]3

overlying water

Fig 9 Degassing parameter B estimated from measured Ne Ar Kr

and Xe concentrations using the 1-step degassing model The error

bars correspond to the differences between the measured noble gas

concentrations and the concentrations predicted by the 1-step

degassing model with the best-fit values of B

the atmosphere Sensitivity tests showed that the

estimates of B remain within the estimated uncertainty

(Fig 9) for temperatures between 4 8C and 7 8C atemperature range which is not expected to be

exceeded in the deep water of Soppensee

The number of bubbles produced per unit mass of

pore water is given by N =(P0B)(PbVb) where Vb is

the mean bubble volume and Pb is the pressure in the

gas bubbles which is assumed to correspond approx-

imately to the total ambient pressure in the sediment

Ptot (the pressure caused by the tension of the curved

bubble surface is neglected) Ptot is given by the sum

of the atmospheric pressure at the lake surface (~ 1

bar) and the hydrostatic pressure of the water column

(~ 27 bar at the sampling site) Hence Pbc37 bar

The volume of a typical bubble in the sediment

roughly corresponds to that of a spherical bubble with

a radius of 5 mm [31] thus Vbc05 cm3 With

BV (8F1)102 cmSTP3 g (Fig 9) these values yield

N N (44F5) bubbles per kilogram of water This

indicates that only few bubbles are involved in the

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4442

degassing process which conforms to the 1-step

degassing model

Gas bubbles can form in the sediment only if the

sum of the partial pressures Pi of all dissolved gases

exceeds the total ambient pressure in the sediment

ie ifP

i PiNPtot To estimate roughly the CH4

concentration which must be exceeded to trigger

bubble formation dissolved gases other than CH4

and O2 (which is consumed in the sediment) are

assumed to be conservative and to be mainly of

atmospheric origin Their partial pressures Pi there-

fore correspond to their partial pressures in the

atmosphere With PO2=0 the sum of the partial

pressures of the atmospheric gases ie the gases other

than CH4 isP

i pCH4Pic08 bar The partial pressure

of CH4 which must be exceeded to trigger bubble

formation is therefore PCH4frac14 Ptot

Pi p CH4

Pic29bar At 55 8C (the mean deep-water temperature) this

corresponds to a CH4 saturation concentration of 014

cmSTP3 g [38] which corresponds to about twice the

maximum value of B This means that the amount of

CH4 released from the sediment by ebullition is of a

similar magnitude to that which can be stored in the

sediment pore water

4 Conclusions

The noble gas concentrations in the pore water of

the Soppensee sediment show a pronounced depletion

pattern which reflects the gas loss by ebullition The20Ne22Ne and 36Ar40Ar ratios in the pore water

indicate that the noble gas depletion is not controlled

by the kinetics of diffusion through the gaswater

interface but rather reflects a solubility equilibrium

between pore water and gas bubbles The isotope

ratios further indicate that the vertical diffusion of

dissolved noble gases is insignificant The noble gas

profiles therefore correspond to the stratigraphy of the

sediment which allows a time scale to be associated

with the noble gas record While the mechanisms

responsible for the strong restriction of vertical

diffusion remain unknown this study supports the

speculation made in an earlier study [2] that vertical

diffusion in the pore water may be strongly restricted

in undisturbed and fine-grained sediments with low

permeability and anisotropic pore space such as the

Soppensee sediment

The uniform increase in the depletion of noble

gases from the deep sediment towards the sediment

surface indicates that ebullition in Soppensee

increased gradually throughout the entire Holocene

This is in line with the increase in the degree of

eutrophication of Soppensee that occurred during the

Holocene [1819] because the CH4 production rate in

the sediment increases with decreasing oxygen avail-

ability in the deep water and hence with increasing

eutrophication

In the recent sediment where noble gas depletion

is greatest the volume of CH4 released per unit

mass of pore water reaches values as high as

(8F1)102 cmSTP3 g which corresponds to about

60 of the maximum amount of CH4 that can be

dissolved in the pore water This indicates that the

amount of CH4 produced in the sediment signifi-

cantly exceeds the maximum amount of CH4 that

can be stored in the sediment and confirms that

ebullition does indeed play an important role in the

transport of CH4 from the sediment into the over-

lying water

Our study indicates that dissolved noble gases and

their isotopes can be employed as sensitive tracers to

study the formation of gas bubbles in sediments (and

possibly other aquatic environments) the dynamics of

gas partitioning between the bubbles and the sur-

rounding water and the gas fluxes associated with the

emission of these bubbles from the sediment The

analysis of noble gases dissolved in sediment pore

water thus has great potential as a method of

quantifying and reconstructing both the amount of

gas produced in lacustrine and marine sediments and

the associated gas fluxes that have pertained since the

sediment was deposited However because this

method is not yet fully established further studies

need to be conducted to assess its broader potential to

characterize the formation and release of gases not

only from lake sediments but also from other similar

environments such as oceanic sediments (eg at gas

vents) and aquifers

Acknowledgements

Thanks are due to M Hofer T Kulbe and F

Peeters for their assistance in the field and to K

Strassmann for valuable discussions on the ideas

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash44 43

presented in this work Further we thank D M

Livingstone and the two reviewers M C Castro and

G Winckler for their helpful comments and editing

assistance This research was made possible by

funding from the Swiss National Science Foundation

(SNF 2000-068191) EAWAG and ETH Zqrich

References

[1] MS Brennwald M Hofer F Peeters W Aeschbach-Hertig

K Strassmann R Kipfer DM Imboden Analysis of

dissolved noble gases in the pore water of lacustrine sedi-

ments Limnol Oceanogr Methods 1 (2003) 51ndash62

[2] MS Brennwald F Peeters DM Imboden S Giralt M

Hofer DM Livingstone S Klump K Strassmann R Kipfer

Atmospheric noble gases in lake sediment pore water as

proxies for environmental change Geophys Res Lett 31

(2004) L04202 doi1010292003GL019153

[3] RF Strayer JM Tiedje In situ methane production in a

small hypereutrophic hard-water lake loss of methane from

sediments by vertical diffusion and ebullition Limnol Ocean-

ogr 23 (1978) 1201ndash1206

[4] CS Martens JV Klump Biogeochemical cycling in an

organic-rich coastal marine basin 1 Methane sediment-water

exchange processes Geochim Cosmochim Acta 44 (1980)

471ndash490 doi1010160016-7037(80)90045-9

[5] JP Chanton CS Martens CA Kelley Gas-transport from

methane-saturated tidal fresh-water and wetland sediments

Limnol Oceanogr 34 (1989) 807ndash819

[6] I Ostrovsky Methane bubbles in Lake Kinneret quantifica-

tion and temporal and spatial heterogeneity Limnol Ocean-

ogr 48 (2003) 1030ndash1036

[7] G Winckler R Kipfer W Aeschbach-Hertig R Botz M

Schmidt S Schuler R Bayer Sub sea floor boiling of Red

Sea brines new indication from noble gas data Geochim

Cosmochim Acta 64 (2000) 1567ndash1575 doi101016S0016-

7037(99)00441-X

[8] CP Holzner S Klump H Amaral MS Brennwald R

Kipfer Using noble gases to study methane release from high-

intensity seeps in the Black Sea European Geosciences Union

1st General Assembly Geophysical Research Abstracts vol 6

Nice France 2004 p 01595

[9] CP Holzner H Amaral MS Brennwald S Klump R

Kipfer Assessment of methane emission from bubble plumes

in the Black Sea by noble gases Abstracts of the 14th Annual

VM Goldschmidt Conference 2004 Geochim Cosmochim

Acta vol 68 Elsevier Copenhagen Denmark 2004 p A323

[10] JM Thomas GB Hudson M Stute JF Clark Noble gas

loss may indicate groundwater flow across flow barriers in

southern Nevada Environ Geol 43 (2003) 568ndash579

doi101007s00254-002-0681-1

[11] CJ Ballentine R Burgess B Marty Tracing fluid origin

transport and interaction in the crust in D Porcelli CJ

Ballentine R Wieler (Eds) Noble Gases in Cosmochemistry

and Geochemistry Rev Mineral Geochem vol 47 Mi-

neralogical Society of America Geochemical Society 2002

pp 539ndash614

[12] AF Lotter Evidence of annual layering in Holocene sediments

of Soppensee Switzerland Aquat Sci 51 (1989) 19ndash30

[13] AF Lotter How long was the Younger Dryas Preliminary

evidence from annually laminated sediments of Soppensee

(Switzerland) Hydrobiologia 214 (1991) 53ndash57

[14] I Hajdas SD Ivy J Beer G Bonani D Imboden AF

Lotter M Sturm M Suter AMS radiocarbon dating and

varve chronology of Lake Soppensee 6000 to 12000 14C

years BP Clim Dyn 9 (1993) 107ndash116

[15] I Hajdas G Bonani B Zolitschka Radiocarbon dating of

varve chronologies Soppensee and Holzmaar Lakes after ten

years Radiocarbon 42 (2000) 349ndash353

[16] W Tinner AF Lotter Central European vegetation response

to abrupt climate change at 82 ka Geology 29 (2001) 551ndash554

doi1011300091-7613(2001)029b0551CEVRTAN20CO2

[17] DM Livingstone I Hajdas Climatically relevant periodicities

in the thicknesses of biogenic carbonate varves in Soppensee

Switzerland (9740ndash6870 calendar yr BP) J Paleolimnol 25

(2001) 17ndash24 doi101023A1008131815116

[18] W Hofmann Late-GlacialHolocene succession of the chiro-

nomid and cladoceran fauna of the Soppensee (Central Switzer-

land) J Paleolimnol 25 (2001) 411ndash420 doi101023

A1011103820283

[19] AF Lotter The palaeolimnology of Soppensee (Central

Switzerland) as evidenced by diatom pollen and fossil-

pigment analyses J Paleolimnol 25 (2001) 65 ndash 79

doi101023A1008140122230

[20] N Gruber B Wehrli A Wuest The role of biogeochemical

cycling for the formation and preservation of varved

sediments in Soppensee (Switzerland) J Paleolimnol 24

(2000) 277ndash291

[21] M Melles M Kulbe PP Overduin S Verkulich Reports on

polar research Technical Report 148 Alfred-Wegner-Institut

fqr Polar- und Meeresforschung Germany 1994

[22] U Beyerle W Aeschbach-Hertig DM Imboden H Baur T

Graf R Kipfer A mass spectrometric system for the analysis

of noble gases and tritium from water samples Environ Sci

Technol 34 (2000) 2042ndash2050 doi101021es990840h

[23] W Aeschbach-Hertig Helium und Tritium als Tracer fqrphysikalische Prozesse in Seen Diss ETH Nr 10714 ETH

Zqrich 1994 httpe-collectionethbibethzchshowtype=

dissampnr=10714

[24] A Bosch E Mazor Natural gas association with water and

oil as depicted by atmospheric noble gases case studies from

the Southeastern Mediterranean Coastal Plain Earth Planet

Sci Lett 87 (1988) 338ndash346 doi1010160012-821X(88)

90021-0

[25] J Holocher F Peeters W Aeschbach-Hertig M Hofer M

Brennwald W Kinzelbach R Kipfer Experimental inves-

tigations on the formation of excess air in quasi-saturated

porous media Geochim Cosmochim Acta 66 (2002)

4103ndash4117 doi101016S0016-7037(02)00992-4

[26] J Holocher F Peeters W Aeschbach-Hertig W Kinzelbach

R Kipfer Kinetic model of gas bubble dissolution in

MS Brennwald et al Earth and Planetary Science Letters 235 (2005) 31ndash4444

groundwater and its implications for the dissolved gas

composition Environ Sci Technol 37 (2003) 1337ndash1343

doi101021es025712z

[27] K Nagao N Takaoka O Matsabayashi Isotopic anomalies

of rare gases in the Nigorikawa geothermal area Hokkaido

Japan Earth Planet Sci Lett 44 (1979) 82ndash90 doi101016

0012-821X(79)90010-4

[28] JWS Rayleigh Theoretical considerations respecting the

separation of gases by diffusion and similar processes Philos

Mag 42 (1896) 493ndash498

[29] RP Schwarzenbach PM Gschwend DM Imboden Envi-

ronmental Organic Chemistry 2nd edition John Wiley and

Sons New York 2003

[30] BP Boudreau BS Gardiner BD Johnson Rate of growth

of isolated bubbles in sediments with a diagenetic source of

methane Limnol Oceanogr 46 (2001) 616ndash622

[31] BS Gardiner BP Boudreau BD Johnson Growth of disk-

shaped bubbles in sediments Geochim Cosmochim Acta 67

(2003) 1485ndash1494 doi101016S0016-7037(02)01072-4

[32] KM Strassmann MS Brennwald F Peeters R Kipfer

Dissolved noble gases in porewater of lacustrine sediments as

palaeolimnological proxies Geochim Cosmochim Acta 65

(7) (2005) 1665ndash1674 doi101016jgca200407037

[33] RA Berner Diagenetic models of dissolved species in the

interstitial waters of compacting sediments Am J Sci 275

(1975) 88ndash96

[34] DM Imboden Interstitial transport of solutes in non-steady

state accumulating and compacting sediments Earth Planet

Sci Lett 27 (1975) 221ndash228 doi1010160012-821X(75)

90033-3

[35] B J7hne G Heinz W Dietrich Measurement of the diffusion

coefficients of sparingly soluble gases in water J Geophys

Res 92 (1987) 10767ndash10776

[36] N Iversen BB Jbrgensen Diffusion coefficients of sulfate

and methane in marine sediments influence of porosity Geo-

chim Cosmochim Acta 57 (1993) 571ndash578 doi101016

0016-7037(93)90368-7

[37] BD Johnson BP Boudreau BS Gardiner R Maass

Mechanical response of sediments to bubble growth Mar Geol

187 (2002) 347ndash363 doi101016S0025-3227(02)00383-3

[38] DR Lide (Ed) CRC Handbook of Chemistry and Physics

75th edition CRC Press Boca Raton 1994