AGMET-3919; No of Pages 21

Measurement of horizontal and vertical advection of CO2

within a forest canopy

Ray Leuning a,*, Steven J. Zegelin a, Kevin Jones b, Heather Keith c, Dale Hughes a

aCSIRO Marine and Atmospheric Research, PO Box 3023, Canberra, ACT 2601, Australiab Institute of Atmospheric and Environmental Science, School of GeoSciences, The University of Edinburgh, Edinburgh EH9 3JK,

United KingdomcThe Fenner School of Environment and Society, Australian National University, Canberra, ACT 0200, Australia

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x

a r t i c l e i n f o

Article history:

Received 20 July 2007

Received in revised form

19 June 2008

Accepted 20 June 2008

Keywords:

Advection

Forest respiration

Micrometeorological mass balance

Eddy covariance fluxes

a b s t r a c t

Eddy covariance measurements often underestimate the net exchange of CO2 between

forest canopies and the atmosphere under stable atmospheric conditions, when horizontal

and vertical advection are significant. A novel experimental design was used to measure all

terms in the mass balance of CO2 in a 50 m � 50 m wide, 6 m tall control volume (CV) located

on the floor of a 40 m tall Eucalyptus forest to examine the contributions of the eddy flux, the

change in storage and the horizontal and vertical advection terms. Horizontal flux diver-

gences between the four vertical walls of the CV were determined using perforated tubing

arranged parallel to the ground to measure CO2 mixing ratios. The change in storage was

calculated using CO2 concentration profiles measured in the centre of the CV. Vertical

advection was calculated using these profiles, combined with vertical velocities, wc, calcu-

lated using the mass continuity equation and horizontal velocities measured at the mid-

point of each wall of the CV. Vertical and horizontal advection and the eddy flux terms all

contributed significantly to the mass balance of the CV at night, while the eddy flux term was

dominant and negative for a short period around noon when photosynthesis exceeded

respiration. Large vertical gradients of CO2 at night cause estimates of vertical advection to

be extremely sensitive to small errors in wc with standard errors of the mean flux exceeding

3 mmol CO2 m�2 s�1. Vertical velocities need be measured to an accuracy better than

1 mm s�1 to minimize errors in vertical advection when vertical gradients of CO2 ratios

are very large at night. Calculated horizontal advection is sensitive to errors in the wind

vectors through the faces of the CV when horizontal concentrations gradients are large.

Errors in eddy fluxes and change in storage are smaller than for the advection terms and

errors for all components are smaller during the day than at night.

Crown Copyright# 2008 Published by Elsevier B.V. All rights reserved.

avai lab le at www.sc iencedi rec t .com

journal homepage: www.e lsev ier .com/ locate /agr formet

1. Introduction

Micrometeorological measurements of night-time fluxes of

CO2 above vegetation are often lower than expected from

concurrent biological measurements of respiration (Wofsy

et al., 1993; Goulden. et al., 1996; Aubinet et al., 2002; Miller

* Corresponding author.E-mail address: Ray.Leuning@csiro.au (R. Leuning).

Please cite this article in press as: Leuning, R., et al., Measurement o

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

0168-1923/$ – see front matter. Crown Copyright # 2008 Published bdoi:10.1016/j.agrformet.2008.06.006

et al., 2004; van Gorsel et al., 2007). Errors are particularly

severe under stable atmospheric conditions when cold-air

drainage flows in sloping terrain results in significant vertical

and horizontal advection of CO2 (Aubinet et al., 2003). While

vertical advection can be estimated from knowledge of vertical

concentration gradients and velocities measured on a single

f horizontal and vertical advection of CO2 within a forest canopy.

y Elsevier B.V. All rights reserved.

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x2

AGMET-3919; No of Pages 21

tower (Lee, 1998), this is not possible for horizontal advection,

since this requires knowledge of horizontal concentration

gradients. To avoid problems associated with advection, the

current practice in the micrometeorological community is to

use the so-called ‘u� � filter’ (Goulden. et al., 1996; Falge et al.,

2001; Gu et al., 2005) to select flux data when turbulence levels

are high and the advection terms in the mass balance equation

are assumed to be small. The selected flux measurements are

then used to develop functional relationships between ecosys-

tem respiration, Reco, and air or soil temperatures to estimate

respiration rates for the periods of missing data. van Gorsel et al.

(2007) have found that atsome sites, theu� � filter does not yield

an objective threshold for u� above which the respiration fluxes

remain constant (for any given temperature), thereby con-

tributing to uncertainties in the derived relationships between

Reco and temperature. As an alternative to the u� � filter, van

Gorseletal. (2007)proposed estimatingReco using the maximum

in the eddy flux plus the change in storage term in the period

following the onset of stable stratification to develop relation-

ships between Reco and temperature.

These approaches rely on interpretations of flux and

concentration measurements made on single towers, com-

plemented in some cases by concurrent chamber measure-

ments of soil and plant respiration (Goulden. et al., 1996; van

Gorsel et al., 2007). We may ask whether estimates of

nocturnal respiration can be improved by measuring all

components of the mass balance of a control volume

encompassing the canopy? The measurement problem is

intrinsically three-dimensional and this significantly

increases the complexity of the experimental design and

the number of instruments required to obtain the required flux

terms. Studies that have attempted to measure all the terms

(e.g. Aubinet et al., 2000, 2003, 2005; Feigenwinter et al., 2004,

2008; Staebler and Fitzjarrald, 2004; Marcolla et al., 2005; Sun

et al., 2006; Sun et al., 2007) are difficult to perform because

drainage flows, which result in advection, are dependent on

atmospheric stability, canopy structure and on local topo-

graphy (Horst and Doran, 1986; Mahrt et al., 2001; Turnipseed

et al., 2003; Froelich et al., 2005; Staebler and Fitzjarrald, 2005;

Yi et al., 2005; Heinesch et al., 2007).

Oneofthemostadvancedadvectionmeasurementstudiesto

date was reported by Feigenwinter et al. (2008). They used four

vertical arrays of sonic anemometers and air inlets mounted on

towers at the corners of a trapezoid surrounding a fifth, central

instrumented tower to measure the 3D wind vectors and CO2

concentration fields in three European forests. They used

numerical, bi-linear interpolation of data to construct the wind

and concentration fields within each control volume (CV) and

used these to calculate the mass balance for the CV.

In contrast to the point-sampling and numerical inter-

polation approach adopted by these authors, the current paper

describes an experimental setup that examines the feasibility

of using physical sampling to estimate the integrals needed to

calculate the horizontal advection term in the mass balance

equation. As described below, this was achieved by measuring

horizontal windspeed-weighted CO2 concentrations along the

side walls of a 50 m � 50 m (wide) � 6 m (tall) CV located on the

floor of a Eucalyptus forest in south eastern Australia. Vertical

advection was estimated using measured CO2 concentration

profiles, combined with vertical velocities obtained from a

Please cite this article in press as: Leuning, R., et al., Measurement o

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

sonic anemometer and from solution of the continuity

equation for air flow through the upper surface of the CV.

Results from using an exact equation for vertical advection

developed in this study are compared to those obtained using

the approximate expression of Lee (1998). Finally, the

calculations were used to examine the relative contributions

of the vertical eddy fluxes, changes in storage, horizontal

advection and vertical advection to the mass balance of CO2.

Sources of error and uncertainties in the estimated fluxes and

the measurement precision and instrumentation needed to

reduce them are discussed, followed by recommendations for

improvements in future experimental designs.

2. Theory

Following Leuning (2004), the conservation equation for a scalar

quantity c in a CV of height h and length of side L is given by

Fc ¼ Fcð0Þ þ1

L2

ZL0

ZL0

Zh0

Scdz dx dy

¼ 1

L2

ZL0

ZL0

Zh0

cd@xc

@tdz dx dy

þ 1

L2

ZL0

ZL0

Zh0

ucd@xc

@xþvcd

@xc

@yþwcd

@xc

@z

� �dz dx dy

þ 1

L2

ZL0

ZL0

Zh0

@cdu0x0c@x

þ @cdv0x0c@y

þ @cdw0x0c@z

� �dz dx dy

; (1)

where u;v;w (m s�1) are the wind vector components in the

x; y; z directions orthogonal to the walls of the CV defined in

Fig.1a, t is time, cd is theconcentrationofdryair (mol m�3)andxc

is the mole fraction of the trace gas relative to dry air

(mol mol�1). Note that the coordinate system is defined by the

directions normal to the walls of the CV. Standard Reynold’s

notationisusedtoexpressthe instantaneousvalueofaquantity

asthesumofthemeanandfluctuationsaboutthemean,andthe

overbar represents the time averaging operator. The term Fc

(mol m�2 s�1) represents the time- and space-average flux den-

sity of the trace gas at the lower boundary of the CV, Fcð0Þ, plus

the fluxes originating at the vegetation elements within the CV,

Sc (mol m�3 s�1). The first term in the second equality of Eq. (1) is

the rate of change of constituent c in the CV, the second term is

the sum of mean horizontal and vertical flux divergences and

the third term is the sum of eddy flux divergences.

The following sections describe the theory and measure-

ments used to estimate the terms in Eq. (1): change in storage,

horizontal advection, vertical advection, and the vertical eddy

flux at h.

2.1. The rate of change in storage

In finite-difference form, the change in storage term in Eq. (1)

is given by

Fc;s ¼cd

Dt

Zh0

hxcidz

������t¼Dt

�Zh0

hxcidz

������t¼0

24

35; (2)

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 1 – (a) Schematic drawing of a Cartesian control volume (CV) placed over a vegetated surface in the lowest 6 m of the

forest. (b) A 1 km T 1 km topographic map of the Tumbarumba field site showing the location of the main mast and the

experimental CV (square). The contour interval is 5 m.

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x 3

AGMET-3919; No of Pages 21

where the angle brackets represent horizontal spatial

averages in the x- and y-directions. Here the result of applying

the time-averaging operator is written explicitly as the differ-

ence between the vertically integrated molar concentration,

cdhxci, within the CV at time t + Dt and at time t, where Dt is the

averaging period (Finnigan, 2006).

Please cite this article in press as: Leuning, R., et al., Measurement o

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

2.2. Horizontal advection

The experimental design used in this study to estimate the

horizontal advection terms in Eq. (1) builds on previous work

by Denmead et al. (1998) and Leuning et al. (1999). They

measured methane emissions from cattle and sheep placed

f horizontal and vertical advection of CO2 within a forest canopy.

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x4

AGMET-3919; No of Pages 21

within a CV using the following equation for horizontal flux

divergence:

Fc;h ¼1

L2

ZL0

Zh0

ucd xcjx¼L � xcjx¼0

� �dz dy

þ 1

L2

ZL0

Zh0

vcdðxcjy¼L � xcjy¼0Þdz dx; (3)

where Fc is the average flux density of methane from the

animals in the CV determined from xc(z) measured at four

heights at x = L, x = 0, y = L and y = 0. In their experiments there

were negligible changes in storage of CH4 within the CV and

the walls were sufficiently high to ensure no fluxes of CH4

through its upper surface, so it was not necessary to measure

all terms in Eq. (1) to determine the emissions.

Denmead et al. (1998) and Leuning et al. (1999) estimated the

terms in Eq. (3) by measuring concentrations in each of four

perforated air lines arranged horizontally on the four walls of

the CV, multiplying the changes in mole fraction between

down-wind and up-wind walls by the corresponding u- and

v-windspeeds at each level, and then calculating the vertical

integrals numerically. The benefit of using the horizontal

sampling lines is that it provides horizontal, cross-wind

integration through physical sampling. The integrals in Eq. (3)

require continuous measurementsateach level to construct the

correct time-average, but a period of 45 min was needed to cycle

through the 16 air lines used by Leuning et al. (1999). Hence each

air line was sampled for only a small fraction of the total cycle.

Although they used 46 litre buffer volumes in the air lines to

provide some temporal filtering, their design provided unsa-

tisfactory results when the wind direction varied during the

averaging period required to construct the mass balance. We

anticipate that problems in estimating the horizontal advection

associated with unsteady conditions will be even more severe

under the intermittent turbulence typically found within the

forest under stable stratification (Mahrt et al., 2001).

One solution to these limitations is to use a gas-sampling

and measurement system that eliminates buffer volumes and

cycles through all the air lines very rapidly. This option was

not available to us, so we designed a sampling scheme to

estimate horizontal advection by recognizing that terms such

as ucdxc in Eq. (3) can be thought of windspeed-weighted mole

fractions. This is because the horizontal molar fluxes of dry air

ucd and vcd in Eq. (3) are closely approximated by the product of

the mean velocity and the mean molar concentration of dry

air: ucd and vcd (Leuning, 2004).

We next define the normalized windspeed profiles:

SðzÞ ¼ uðzÞuh¼ vðzÞ

vh; (4)

where uh and vh are the u and v windspeed components mea-

sured at height h. Vertical profiles of uðzÞ and vðzÞ were mea-

sured only in the centre of the CV and hence it was necessary to

assume that S(z) was independent of horizontal position within

the CVwithin a given averaging period. Wealso assume thatS(z)

is determined by the drag on the wind by foliage, branches and

the ground and hence is independent of wind direction.

With these simplifications, and neglect of the horizontal

eddy flux divergence terms, the horizontal advection terms in

Please cite this article in press as: Leuning, R., et al., Measurement o

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

Eq. (1) may be written as

Fc;h ¼ cduh

L

Zh0

SðzÞ xch idz

������x¼L

�Zh0

SðzÞ xch idz

������x¼0

24

35

þ cdvh

L

Zh0

SðzÞ xch idz

������y¼L

�Zh0

SðzÞ xch idz

������y¼0

264

375: (5)

Here xch i represents the average of the mixing ratio in both

time and in the cross-wind direction. The mean molar con-

centration of dry air, cd, has been taken outside the integrals in

Eq. (5) because the variation in cd will be<1% for the maximum

temperature gradient of 3 8C observed over 6 m during the field

campaign. Horizontal variation in cd will be << 1% for

expected horizontal temperature gradients. Eq. (5) can be

further simplified for practical evaluation of Fc;h by writing

it in finite-difference form:

Fc;h ¼ cduh

L

X6

j¼1

W j xc; j

D E������x¼L

�X6

j¼1

W j xc; j

D E������x¼0

24

35

þ cdvh

L

X6

j¼1

W j xc; j

D E������y¼L

�X6

j¼1

W j xc; j

D E������y¼0

264

375; (6)

where the summation is over the six air lines on each wall of

the CV used in our experimental design (see below). The

weighting factors Wj are given by

W j ¼ Sðz jÞDz j: (7)

They account for both the normalized horizontal wind-

speed at each height and the variable vertical spacing between

the perforated tubing used to sample the air. As described

below, the Wj were pre-set using a mean S(z) profile that was

determined using horizontal windspeeds measured prior to

the main field campaign (see Fig. 4).

2.3. Vertical advection and vertical velocity

The vertical advection term in Eq. (1) is given by the equivalent

expressions:

hFc;vi¼ cd

Zh0

hwi @hxci@z

� �dz ¼ cdhwðhÞihxcðhÞi �cd

Zh0

hxci@hwi@z

� �dz;

(8)

Because of the difficulty in accurately measuring the

vertical velocity directly using sonic anemometers, we

followed Vickers and Mahrt (2006) and Heinesch et al. (2007)

in using the continuity equation for mass to evaluate wðzÞ. For

the CV shown in Fig. 1a we may write

�cdL2hwcðzÞi ¼ cdLZL0

@

@x

Zz0

huðzÞidz

24

35dx

þ cdLZL0

@

@y

Zz0

hvðzÞidz

24

35dy: (9)

This expression states that the vertical flux of dry air through a

horizontal surface at height z and area L2 is equal and opposite

f horizontal and vertical advection of CO2 within a forest canopy.

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x 5

AGMET-3919; No of Pages 21

to the sum of the horizontal flux divergences in the x and y

directions, integrated across width L and height z. Writing hwciemphasizes that this value of w is obtained from solution of

the continuity equation and hence it is a temporal and spatial

average horizontally. It is assumed that cd is constant through

the volume and that the vertical velocity at the ground,

hwð0Þi ¼ 0.

Eq. (9) can be simplified by using S(z) to express hwcðzÞi in

terms of the differences in horizontal wind components at

height h on each of the four walls of the CV:

hwcðzÞi ¼�1L½huhijx¼L � huhijx¼0 þ hvhijy¼L � hvhijy¼0�

Zz0

SðzÞdz;

(10)

and hence

@hwcðzÞi@z

¼ �1Lhuhijx¼L � huhijx¼0 þ hvhijy¼L � hvhijy¼0

h iSðzÞ: (11)

Eliminating the term in square brackets in Eq. (11) and

using Eq. (10) gives

@hwcðzÞi@z

¼ hwcðhÞiSðzÞZh0

SðzÞdz

24

35�1

: (12)

Substitution of Eq. (12) into the RHS of Eq. (8) results in the

following exact expression for the vertical advection term:

hFc;vðhÞi ¼ cdhwðhÞihxcðhÞi � cd

Zh0

hxci@hwi@z

� �dz

¼ cd wcðhÞh i hxcðhÞi �R h

0 hxcðzÞiSðzÞdzR h0 SðzÞdz

" #(13)

In contrast, Lee (1998) proposed that the vertical advection

term be evaluated using

hFc;vðhÞi ¼ cd

Zh0

hwi @hxci@z

� �dz

� cdhwðhÞi hxcðhÞi �1h

Zh0

hxcðzÞidz

24

35: (14)

Use of this expression assumes that @w=@z � wðhÞ=h is

constant (Lee, 1998; Finnigan, 1999; Baldocchi et al., 2000), an

approximation that is not strictly valid because S(z) and hence

@w=@z must vary with height (Eq. (12); Figs. 4 and 5).

A one-dimensional version of Eq. (14) was used to calculate

the vertical advection of CO2 by Paw et al. (2000), Baldocchi

et al. (2000), Aubinet et al. (2003,2005), Feigenwinter et al. (2004,

2008), Staebler and Fitzjarrald (2004), Marcolla et al. (2005);

Vickers and Mahrt (2006), Heinesch et al. (2007) and Mammar-

ella et al. (2007). An analogous equation was used by Moderow

et al. (2007) to estimate the vertical advection of sensible heat

in a forest.

2.4. Mass balance equation used in computations

Spatial averages were available only for the horizontal

advection terms in this study, whereas the change in storage,

Please cite this article in press as: Leuning, R., et al., Measurement o

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

vertical advection and eddy flux terms were calculated using

measurements made on the mast in the centre of the CV on

the assumption that these were representative of the whole

CV. Thus the mass balance of the CV described in the following

section was calculated using

Fc ¼cd

Dt

X6

j¼1

xc; j Dz j

������t¼Dt

�X6

j¼1

xc; j Dz j

������t¼0

24

35

þ cd uh

L

X6

j¼1

W jhxc; ji

������x¼L

�X6

j¼1

W jhxc; ji

������x¼0

24

35

þ cd vh

L

X6

j¼1

W jhxc; ji

������y¼L

�X6

j¼1

W jhxc; ji

������y¼0

264

375

þcd w0x0��hþcd wcðhÞh i xcðhÞh i �

R h0 hxcðzÞiSðzÞdzR h

0 SðzÞdz

" #

(15)

3. Methods

3.1. Site description

The Tumbarumba flux station site is located in south eastern

New South Wales (35839020.60 0S, 148809007.50 0E, elevation

1200 m; Leuning et al., 2005). It is moderately open,

consisting of 40 m tall trees with a leaf area index,

Lai = 1.38 m2 m�2. Dominant species in the wet sclerophyll

forest are Eucalyptus delegatensis (R.T. Baker) and E. dalrym-

pleana (Maiden), while the understorey consists of a layer of

grasses and herbs and a patchy distribution of shrubs from

0.5 to 3 m in height, with an Lai of 1.49 m2 m�2 (Keith, 2008;

pers. comm.). The foliage area volume density (FAVD) profile

shown in Fig. 2 is the mean of measurements made at eight

sites within the flux footprint surrounding the main mast

using EchidnaTM, a ground based laser that scans a full

hemisphere from a point 2 m above the canopy floor (Jupp,

2008; pers. comm.). The FAVD profile is bimodal, with a peak

of 0.07 m�1 between 7 and 8 m due to saplings and another

peak of 0.1 m�1 around 35 m due to the trees. While grasses

and shrubs were present below 2 m, these were not

measured using the EchidnaTM.

Significant horizontal and vertical advection occurs at this

site (van Gorsel et al., 2007) due to cold-air drainage down the

long axis of the main north–south gully shown in the contour

map of Fig. 1b. To test a new experimental design and the

suitability of using Eq. (15) to compute the advection terms,

we constructed a 50 m � 50 m � 6 m CV, 240 m to the south-

west of the main mast (Fig. 1b). In an effort to ensure wind

flow through the CV was mainly unidirectional for each

averaging period, the CV was located on a relatively flat,

uniform slope on the side of the main gully, whose long axis

has a downward slope of 3.58 from south to north and a 3.08

downward slope from east to west (Fig. 1a). Vegetation within

the CV is similar to that surrounding the main flux station

mast. Measurements were restricted to the forest floor

because of the technical difficulties and cost of constructing

a CV for the full 40 m forest. All measurements reported here

were made during an intensive field campaign from 6 to 21

March 2005.

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 2 – Foliage area volume density (FAVD) profile for the

forest within the footprint surrounding the main mast as

measured using EchidnaTM, a ground-based lidar (Jupp,

2008; pers. comm.).

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x6

AGMET-3919; No of Pages 21

3.2. Instrumentation

3.2.1. Gas sampling and measurement for horizontaladvectionCommercial drip-irrigation tubing (50 m long, 6 mm i.d., 8 mm

o.d., hole spacing 0.30 m) was used to sample the air at six

heights (0.2, 0.4, 0.8, 1.6, 3.2 and 6.0 m) on each face of the CV

(Fig. 3a). Sampling at multiple air-intake points using

perforated tubing arranged parallel to the slope in each face

minimizing cross-contamination of horizontal and vertical

CO2 gradients (Aubinet et al., 2005; Heinesch et al., 2007). Errors

in horizontal gradients arise from small uncertainties in

sampling height due to variations in local micro-topography

and can be particularly severe in the presence of large vertical

gradients at night.

Air was pumped from three take-off points, located at 9, 25

and 41 m along the length of each sampling air line (Fig. 3b),

and thus the maximum distance the air had to travel from a

hole in the tubing to a take-off point was 9 m at each end and

8 m in the middle section of the sampling tube. This

arrangement minimizes the longitudinal variation of pressure

and flow rate through the holes, and minimizes the time taken

for air to travel from a given hole to each take-off point. Tubes

from the three take-off points in each horizontal air sampling

line were joined to form a single air line for each height and a

needle valve in the line was used to adjust the volumetric flow

rate, fj, for each height according to

f j ¼W jP6j¼1W j

f total (16)

where Wj is the weighting factor required for each level and

ftotal is the total flow that can be delivered by the pump

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connected to each face of the CV. The weighted air flows from

the six levels on a given face were then combined in a manifold

and the single air line from the each of the four faces was

flushed continuously using a pump for each line. A gas-

switching system connected to a separate pump was used

to pass blended air from each of the four faces in turn through

a CO2 and water vapour analyser (Type LI-7000, Licor, Lincoln,

Nebraska, USA). The first 45 s were used to flush the analysis

cell and measurements were recorded for the remaining 15 s

of each minute. A complete measurement cycle of weighted

concentrations for the four faces of the CV was obtained every

4 min.

From Eq. (16) we see that the weighted sums required for

Eq. (6) are given by

X6

j¼1

W jhxc; ji ¼1

f total

X6

i¼1

Wi

X6

j¼1

½ f jhxc; ji� (17)

This sampling scheme uses different flow rates for each

height and thus air from each line has been sampled at

different times when it reaches the mixing manifold for each

wall. Sampling along the tube is also skewed in time because,

with every additional hole towards the take-off point, the

length of tubing decreases and the cumulative air flow within

the tube increases. Air travelling from holes more distant from

the take-off point is thus sampled earlier than air coming from

nearby holes and both these factors may cause errors in the

estimate of horizontal advection under non-stationary con-

ditions. Results of laboratory tests presented in Appendix A

show there was <13% variation in flow between holes along a

10 m length of drip-irrigation tubing at all flow rates relevant

to this study. Appendix A also shows that at flow rates

>1.0 l min�1, air reaching the take-off point will have been

sampled along>90% of its length within the past 2 min, which

is half the cycle time used to calculate the horizontal

advection terms. This time is also short relative to the 1-h

averaging period used to construct the mass balance of the CV,

so our experimental arrangement provided an acceptably

small skew in the sampling times at the flow rates used in this

study (0.12, 0.36, 1.0, 2.9, 3.8 and 6 l min�1 for the six air intake

heights).

No leaks were detected in the gas sampling system when

nitrogen was supplied to each of the air lines in turn at the

completion of the field campaign.

3.3. Instrumentation within the control volume and mainmast

A 3D sonic anemometer (Type HS, Gill Instruments Ltd.,

Lymington, UK) and an open-path infrared analyser (Type LI-

7500, Licor Inc., Lincoln, Nebraska, USA) were mounted at

6.0 m on a mast at the centre of the CV (Fig. 3) to measure

turbulent fluxes of momentum, heat, water vapour and CO2

through the upper surface of the CV (Leuning and Judd, 1996).

The theory of Webb et al. (1980) and Leuning (2004) was used to

correct latent heat and CO2 fluxes for the effects of density

fluctuations arising from sensible and latent heat fluxes.

Sensible heat fluxes were calculated using the sonic virtual

temperature (Schotanus et al., 1983; Hignett, 1992). Signals

from the sensors were sampled at 20 Hz and fluxes were

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 3 – (a) Schematic drawing of the gas sampling system used to measured weighted CO2 concentrations on the four faces

of the CV. The control valves in each line were adjusted to set the flow rates according to Eq. (16), the air from each line was

mixed and then connected to a manifold and pump. Air from each wall was sampled in turn through a gas switch before

being analysed for CO2 using an infrared gas analyser. Also shown are the central mast and the 3D sonic anemometers

located a height of 1.65 m at the centres of each face of the CV. The inset (b) shows the three air take-off points at 9, 25 and

41 m along each of the 50-m perforated sampling tubes. This limits the distance travelled by an air parcel entering the tube

to the take-off point.

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calculated using 1-h block-averages, with double coordinate

rotations calculated separately for each hour.

The w� axis of the central sonic anemometer was

carefully aligned to the vertical. In terms of wind compo-

nents ðum; vm;wmÞmeasured by the anemometer at height h,

the windspeed normal to the upper surface of the CV is

given by

wnðhÞ ¼ �um sin a cos bþ vm sin bþwm cos a cos b (18)

where a = �3.58 and b = �3.08 are the slope angles in the south–

north and east–west directions as defined in Fig. 1a. With these

values wn ¼ �0:061um � 0:052vm þ 0:997wm.

Windspeed, temperature, water vapour and CO2 concen-

trations were measured on the central mast at heights of 0.2,

0.4, 0.8, 1.6, 3.2 and 6.0 m. The u- and v� components of the

horizontal wind vector were measured using 2D sonic

anemometers (Windsonic, Gill Instruments Ltd., Lymington,

UK), while 100 mm copper–constantin thermocouples

mounted beneath radiation shields and referenced to an

isothermal terminal block in the data logger were used to

measure temperature. All temperature sensors were brought

to the same height during a calibration period to remove any

electrical offsets between the individual thermocouples.

Water vapour and CO2 concentrations were measured at each

height using an infrared gas analyser (LI-6262, Licor Inc.,

Lincoln, Nebraska., USA), via a gas switching system similar to

that used for the air lines on the walls of the CV to provided a

15 s measurement at each height every 6 min.

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Unventilated copper–constantan thermocouples were also

used to measure air temperature at heights 0.4, 4.3, 10.3, 26.3,

34.4, 42.5 and 70.3 m on the main flux station mast. CO2 mixing

ratios were measured using a LI-6262 instrument at heights of

1.0, 5.0, 10.0, 18.0, 26.0, 34.0, 42.0, 56.0 and 70.0 m using a gas

switching system.

A 3D sonic anemometer (R-3, Gill Instruments Ltd.,

Lymington, UK) was placed at 1.65 m above the ground at

the centre of each of the four faces of the CV (Fig. 3). The

relationship between horizontal velocities measured using

the sonic anemometer and the true components parallel to

the ground are given by ut ¼ um cos a�wm sin a and

vt ¼ vm cos b�wm sin b. Calculation of wcðhÞ via Eq. (10)

requires the u- and v� velocities at z ¼ h, and these were

obtained from the measurements at zm = 1.65 m using

uðhÞutð1:65Þ ¼

vðhÞvtð1:65Þ ¼

1Sð1:65Þ : (19)

3.4. Soil and plant respiration

Soil respiration was measured using the absorption of CO2

by soda lime in static chambers as described by Keith and

Wong (2006). Measurements were made continuously for 10

days using 12 cylindrical chambers (volume 6.9 L, basal area

0.08 m2) located randomly within the 50 m � 50 m area of

the CV. Alternate chambers were used for daytime and

f horizontal and vertical advection of CO2 within a forest canopy.

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night-time hours. Soil respiration for the plot was estimated

from the mean of the chamber measurements.

Dark respirations of leaves of the grass and shrub under-

storey were measured at night using a temperature-controlled

leaf cuvette connected to an infra-red gas analyser (LI6400, Li-

Cor Inc., Lincoln, Nebraska, USA). Leaf respiration rates varied

from 0.5 to 2.8 mmol m�2 leaf s�1 at temperatures ranging from

�5 to 30 8C (Keith, 2008; pers. comm.). Temperature response

functions derived for each leaf type were used to calculate leaf

respiration on an hourly basis from air temperature data and

the resultant rates summed for the night-time hours. Leaf area

indices for each vegetation type was used to convert

respiration rate from a leaf-area to a land-area basis.

Respiration by woody components was measured using

chambers attached to trunks, branches and coarse roots of

nine trees and to shrub stems (Keith, 2008; pers. comm.).

Measurements were made four or five times over the course of

a day to obtain efflux data over a wide range of temperatures.

Temperature response functions derived for each component

were used to calculate wood respiration from temperature

data on an hourly basis and summed for daytime and night-

time hours. Wood respiration was measured on a sapwood

volume basis and scaled up to the plot using inventory

measurements of total sapwood volume for each component

(m3 m�2). Total plant respiration was calculated for vegetation

below the 6 m height of the CV.

4. Results and discussion

The following sections provide the information needed to

construct the full mass balance for a CV using the above theory

and experimental design. We first present the normalized

windspeed profile, S(z), measured prior to the main field

campaign that was needed to calculate the weights Wj.

Vertical gradients of xc measured in the centre of the CV

are compared to measurements of xc from the main flux

station mast. Wind flow patterns below the canopy at night are

discussed because the theory requires wind direction to be

constant within the CV during each averaging period. Time

series for pre-weighted CO2 concentrations on the walls of the

CV and forxc measured on the mast in the centre of the CV are

then presented. Accurate knowledge of vertical velocity is

crucial to calculating correctly the vertical advection term and

results obtained using w obtained from the continuity

equation and from the sonic anemometer at 6 m are

contrasted. The data are used to calculate the mass balance

of the CV and results for the net night-time CO2 flux are then

compared to biological measurements.

4.1. Normalized windspeed shape function

Our experimental design requires knowledge of S(z) to

compute the weighting factors Wj used to calculate the

horizontal advection term via Eqs. (5) and (17). To obtain

these factors we measured horizontal windspeeds,

U ¼ ðu2 þ v2Þ1=2, in the month before the main field campaign

to construct an ensemble-mean shape function S(z) = U(z)/

U(h). Fig. 4a–c shows 15-min averages values of U measured at

three heights plotted against the reference windspeed at

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6.4 m. There is relatively little scatter of data around the

regression lines except at the lowest height, even though

windspeeds for all stability classes were included. The mean

shape function S(z) in Fig. 4d is given by the slopes of the linear

regression lines plotted as a function of height, with the

inclusion of the points S(0) = 0, S(h) = 1. The exponential

function:

SðzÞ ¼ a½1� expð�bzÞ�; (20)

with a = 1.017 and b = 1.292 as parameters, provides an excel-

lent fit to S(z) over the height range 0–6.4 m, and this was

assumed to characterize the variation of both the u- and v�components of the horizontal wind vector with height.

The exponential shape function defined by Eq. (20)

was justified by the ensemble-mean windspeed data

collected prior to the field campaign (Fig. 4), and the need

to pre-set the flow rates for use in Eqs. (16) and (17). During

daytime, unstable atmospheric conditions, the exponential

function increases monotonically from 0 at z = 0 to 1 at

z = h = 6.4 m, and it satisfactorily describes horizontal

windspeed profiles measured during the main campaign

(Fig. 5a). However, Eq. (20) is unable to account for the

maximum ‘jet’ in the windspeed at heights of 2–3 m that

was often observed under stable conditions during the field

campaign (Fig. 5b). For these profiles, the log-normal

function:

S1ðzÞ ¼ ac exp � 12

lnðz=zcÞbc

� �2" #

; (21)

provides an excellent fit to the normalized hourly mean

wind profiles observed under both stable and unstable con-

ditions (Fig. 5), provided the parameters ac, bc and zc are

determined for each 1-h average profile. This was especially

necessary at night because the shape of each hourly profile

varied significantly under strong stable stratification.

The peak in horizontal windspeed at 2–3 m indicates sub-

sidence associated with an accelerating air flow within the

canopy.

As a consequence of the shape function varying from one

run to next, it was necessary to adjust results obtained using

the pre-weighted horizontal advection terms in Eqs. (5) and (6)

by the factor:

ss ¼

R h0:001 xcðzÞS1ðzÞdz

h iR h

0:001xcðzÞSðzÞdzh i (22)

where S and S1 are the shape functions defined by Eqs. (20) and

(21), respectively. The lower limit of integration has been set to

an arbitrarily small value of z = 0.001 m because S1(z) is unde-

fined at z = 0. Individual, hourly average profiles of windspeed

and CO2 mole fraction measured on the central mast of the CV

were used to evaluate the integrals in Eq. (22) using numerical

integration. The average value of ss was 1.07 (n = 342) with a

range from 0.83 to 1.64.

4.2. Vertical profiles of CO2 and potential temperature

Evaluation of Eq. (22) requires expressions for the vertical

profiles of xc and Fig. 6a shows that under night-time, stable

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 4 – (a–c) Total horizontal windspeed measured at heights 0.5, 1.6 and 3.3 m plotted against windspeed measured at the

reference height of 6.4 m in the month prior to the main field campaign. (d) The variation of the slopes of the regressions in

a–c as a function of height. S(z) is well represented by the exponential function SðzÞ ¼ a½1� expð�bzÞ�.

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atmospheric conditions, the profiles of hourly mean values of

xcðzÞ are well approximated by the exponential function:

xcðzÞ ¼ xc0;n þ xc;n expð�bc;nzÞ; (23)

when the empirical coefficients are evaluated for each 1-h

averaging period. An exponential function with coefficients

varying for each hour also provided an excellent fit to hourly

means of night-time potential temperature (upot, Fig. 6c), indi-

cating similarity in the profile shapes.

Values of xc at 3.2 m appear to be anomalously high during

daytime unstable conditions (Fig. 6b) and hence no simple

function was able to fit all the profiles. The vertical variation in

xc was small compared to night-time and the profiles were

approximated using a linear function:

xcðzÞ ¼ xc0;d þmcz; (24)

where again the coefficients were evaluated for each 1-h

averaging period. Exponential functions provided a satisfac-

tory fit to the daytime profiles of upot in the lowest 6 m, but as

for xc, the values at 3.2 m were a little higher than expected

from the fitted profile (Fig. 6d). These results suggest that

sources/sinks associated with the shrub layer caused differing

air flow regimes and concentration gradients above and below

this height.

Profiles of xc and upot measured at night on the main 70 m

flux station mast confirm the very strong gradients seen in the

previous figure. Fig. 7a and c shows that gradients in the lowest

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10 m are typically �15 ppm m�1 for xc, and 1.2 8C m�1 for upot

but that gradients in xc are significantly smaller above 10 m,

even though the air within the canopy was still stably

stratified. Fig. 7b and d shows that gradients in both xc and

upot are quite small between 10 and 70 m during the day when

the air is either neutrally or unstably stratified but that strong

gradients can occur in the lowest 10 m.

4.3. Wind direction below and above the canopy at night

Inspection of Eqs. (5) and (13) shows that horizontal and

vertical advection will be significant whenever there are large

gradients in xc, as occurs under stable stratification at night.

Implicit in the use of these equations is that the direction of

the horizontal wind vector is the same laterally and vertically

throughout the CV during each averaging period. These

conditions were closely met at night, as shown by wind

directions measured by the anemometers at the midpoint of

the four walls and by the 3D anemometer at 6 m on the central

mast, for four successive nights with strongly stable stratifica-

tion (Fig. 8a). Average wind directions during the four nights

for the east, west, south, north and central anemometers were

1848, 1928, 1758, 1798 and 1878, respectively, with a combined

average of 184 � 118 (S.D., n = 236). Wind direction was also

constant with height during each 1-h averaging period, with

wind directions obtained from the 2D anemometers on the

central mast (Fig. 8b) of 1768, 1798, 1828, 1828 and 1888 at heights

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 5 – Examples of normalized windspeed profiles

observed during the field campaign for (a) daytime, and (b)

night-time. Both S(z) (Eq. (20), dashed line) and S1(z)

(Eq. (21), solid line) provide a satisfactory fit to

monotonically increasing windspeeds observed during

the day. Under stable, night-time conditions S(z) does not

capture the peak in normalized windspeed between 2 and

3 m, whereas S1(z) provides a satisfactory fit to the data.

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0.4, 0.8, 1.6, 3.2 and 6.0 m, respectively (combined average of

181 � 128 (S.D., n = 240). Similar results were obtained for other

nights with stable stratification (data not shown). The

constancy of wind direction within the canopy at night is

associated with cold-air drainage down the long south-north

gully shown in Fig. 1b. The direction of air flow within the CV

was quite different to that measured above the canopy at 71 m

(Fig. 8c). There the wind direction was from the east, north and

north-west for the nights shown, rather than from the south

within the forest. This further illustrates the decoupling of the

flow within the forest from that above.

4.4. Time series of CO2 mole fractions

Windspeed-weighted CO2 mole fractions for the north and

south walls of the CV are shown in Fig. 9a and for the east and

west walls in Fig. 9b for 13–18 March. Although the absolute

values varied between day and night, there was little

difference between the weighted mole fractions for the north

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and south walls either during the day or night, indicating that

horizontal advection was small in the N-S direction. Small

differences in hxci were also observed in the E-W direction

except on the nights of 13 and 14 March, when weighted mole

fractions on the western wall were up to 50 ppm higher than

on the eastern wall, possibly because this wall was located on

the eastern edge of the main gully where CO2 may have

accumulated. Despite these large gradients, we show below

that advection in the y-direction direction was generally small

at night because the wind direction was predominately in the

x-direction and hence the v� component of the velocity vector

was small. Weighted mole fractions were identical for all walls

during the day, indicating that horizontal advection was then

negligible.

Time series of CO2 mole fractions measured on the central

mast in the CV are shown in Fig. 10a for the period 13–18

March, illustrating two nights that were calm, one associated

with a cold front that brought 18 mm of rain during 15–16

March, and one windy night on 17 March. Mole fractions on

the calm nights were typically 600 ppm at 0.2 and 420–440 ppm

at 6 m and were associated with strong temperature inver-

sions (T0.2 � T6.0 < �2 8C), whereas they ranged from 390 to

370 ppm on the windy night of 17 March when temperature

inversions were weak (T0.2 � T6.0 > �0.5 8C). Night-time mole

fraction gradients were also relatively small due to higher

windspeeds prior to the frontal passage. Daytime CO2 mole

fractions, in contrast, varied by <3 ppm between 0.2 and 6 m

as a consequence of unstable thermal stratification and higher

windspeeds than at night.

4.5. Vertical velocity and vertical advection

The u- and v� components from the four 3D sonic anem-

ometers located at the centres of the faces of the CV were used

to calculate wcðhÞ via Eq. (10) with the revised normalized

windspeed profile S1(z) given by Eq. (21). There was a poor

correlation (R2 = 0.017, data not shown) between wcðhÞ and

wnðhÞ, the velocity normal to the upper surface of the CV,

computed using Eq. (18) with um, vm and wm measured by the

central sonic anemometer. Simply using the measured

vertical velocity, wmðhÞ, at 6 m without allowing for the slope

of the ground provides a much better correlation with wcðhÞ, as

shown in Fig. 11. Night-time values of wmðhÞ are generally

positive whereas wcðhÞ is more evenly distributed around zero,

while there is a good correlation between the two estimates of

vertical velocity during the daytime. The slope of the

regression (0.796) for the combined night- and daytime data

is close to unity and the intercept (0.012 m s�1) is close to zero,

however there is a large scatter in the data (R2 = 0.444).

From these results we may expect relatively poor agree-

ment between night-time vertical advection fluxes of CO2

calculated using the two estimates of vertical velocity at

height h. This is confirmed in Fig. 12a, which shows means and

standard errors of vertical advection fluxes calculated using

Eq. (13) for each night of the field campaign with either wcðhÞand wmðhÞ, and with S1(z) for each averaging period replacing

the ensemble-mean S(z). Average fluxes calculated using

hourly values of wmðhÞ were always negative, ranging from

�17.3 to �0.5 mmol CO2 m�2 s�1, whereas fluxes computed

using wcðhÞwere smaller in magnitude (range�7.7 to 4.7 mmol

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 6 – Examples of vertical variation in hourly average CO2 mole fractions for: (a) night-time, stable conditions as indicated

by the positive potential temperature gradients in (c), and b) for daytime unstable conditions when the potential

temperature gradients are negative as shown in (d). Exponential curves (Eq. (23)) were fitted to the night-time CO2 data and

straight lines to the daytime CO2 data (Eq. (24)).

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CO2 m�2 s�1), except for the nights 14, 15 and 16 of March when

the fluxes were strongly positive.

It is clearly imperative that wðhÞ be known to a high degree

of accuracy to obtain reliable estimates of Fc;v whenever CO2

gradients are large. Even though wcðhÞwas quite small for the

nights of 14, 15 and 16 March (wcðhÞ ¼ �0:008 to �0.014 m s�1,

Fig. 12b), the calculated vertical advection fluxes are large (11.6

to 14.7 mmol CO2 m�2 s�1) because of the strong vertical

gradients in CO2 mole fraction at those times (Fig. 10a).

Heinesch et al. (2007) also found that uncertainties in w

provided the greatest source of error in computing the

advection term. The reason for the disparity in vertical fluxes

calculated using the two estimates of vertical velocity is clear;

despite careful alignment of the central sonic anemometer,

wmðhÞ was always positive at night, with an average of

0.015 m s�1 (Fig. 12b), whereas wcðhÞ had a variable sign and an

average of 0.000 m s�1. There is better agreement between

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daytime values of Fc;v obtained by using wcðhÞ and wmðhÞ(Fig. 12c). Vertical gradients in CO2 mole fraction are small

during the day and hence the calculated fluxes are generally

smaller in magnitude than the night-time fluxes, despite wcðhÞand wmðhÞ being three to four times greater in the day than the

night (Fig. 12b and d). Both wcðhÞ and wmðhÞ are generally

negative during daytime, a result likely caused by measurement

uncertainties. Eq. (10) shows that errors in Du and Dv are

reduced by the factor ð1=LÞR h

0 S1ðzÞdz � 6=50 ¼ 0:12 when

calculating wcðhÞ for our CV. Differences in horizontal velocities

across the CV thus need to be accurate to 10 mm s�1 to

determine wcðhÞ to 1 mm s�1. Uncertainties in aligning thesonic

anemometer will contribute to errors in wmðhÞ. Lee (1998), Paw

et al. (2000), Wilczak et al. (2001) and others have proposed

various methods for removing the effects of anemometer tilt or

sloping topography on the measured vertical velocity by

assuming that the true, long-term wðhÞ ¼ 0. While these

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 7 – Profiles of CO2 mixing ratios and potential temperatures measured on the main mast at the Tumbarumba flux

station. Night-time profiles (a and c); daytime profiles (b and d).

Table 1 – Average vertical advection flux density W -standard error of mean (mmol CO2 mS2 sS1) calculatedusing Eq. (13) with the revised normalized windspeedprofile function S1ðzÞ and fitted functions for wðzÞ andxcðzÞApproach Night Day

Fitted functions 1.63 � 0.69 (199) 1.63 � 0.32 (143)

Lee (1998) 1.94 � 0.90 (199) 1.78 � 0.32 (143)

Also shown are fluxes calculated using the assumption of constant

@w=@z (Lee, 1998. Eq. (14)). The number of hourly mean values are

shown in parentheses.

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methods do eliminate bias in wmðhÞ, they can also remove any

systematic component of vertical velocity that may result from

vertical entrainment of air into drainage flows under stable

conditions (Aubinet et al., 2003; Froelich et al., 2005; Vickers and

Mahrt, 2006; Heinesch et al., 2007), thereby leading to incorrect

estimates of vertical advection. When the vertical velocity

depends on both topography and stability it is difficult to

measure mean vertical velocity to the required accuracy of

better than 1 mm s�1 using a sonic anemometer. As a result of

this large uncertainty in the directly measured wmðhÞ, all

subsequent calculations of Fc;v use wcðhÞ because this had zero

bias and because it is calculated using differences in horizontal

velocities that are relatively large and readily measured.

Means and standard errors of Fc;v are shown in Table 1. The

fluxes were calculated using Eq. (13) with S1(z) for each

averaging period replacing the ensemble-mean S(z), and with

Eq. (14), where it is assumed that @w=@z is constant (Lee, 1998).

The mean for the night-time vertical advection flux calculated

using fitted profiles for wðzÞ and xcðzÞ was 1.63 � 0.69 mmol

CO2 m�2 s�1, whereas it is 19% higher at 1.94 � 0.90 mmol

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CO2 m�2 s�1 when calculated using the assumption of Lee

(1998). There was little difference between estimates of the

daytime vertical advection fluxes. The two estimates are

expected to differ because S1(z) is not constant over the height

of the CV (Fig. 5) and hence this term cannot be taken outside

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 8 – (a) Wind direction at night as measured at the

central mast within the CV and by each of the four, 3D

sonic anemometers located at 1.65 m above the ground

near the centre of the faces of the CV, (b) wind directions

measured at five heights on the central mast using the 2D

sonic anemometers, and (c) measured using a 3D sonic

mounted at 71 m on the main mast. Note that the date

labels are centred on midday.

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the integral on the right hand side of Eq. (13). However, the two

estimates are similar for night-time because, close to the

ground, S1(z) < 1 where xcðzÞ> hxci, the mean mole fraction in

the CV, and hence the product S1(z)xc(z) remains roughly

constant with height. There is relatively little variation of xc(z)

during the day and hence results from Lee’s approach are in

good agreement with the correct calculations. Despite this

apparent agreement, we recommend that the mathematically

correct Eq. (13) be used to calculate the vertical advection term.

4.6. Mass balance components

For most nights of the field campaign, the eddy flux term was

smaller than the vertical and horizontal advection terms

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(Fig. 13), a result similar to that found by Marcolla et al. (2005).

The calculated advection terms generally have the same sign,

in contrast to theoretical predictions by Finnigan (1999) and

Katul et al. (2006) that the two advection terms should have

opposite sign and be approximately equal in magnitude in the

absence of sources or sinks within the CV. The advection

fluxes on 14, 15 and 16 March appear to be unreasonably large

when compared to independent chamber estimates of

respiration (Fig. 15). The change in storage term was very

small when averaged over the 12 h for each night. During

daytime the vertical and horizontal advection of CO2 was also

mostly positive but was smaller in magnitude (<6 mmol

CO2 m�2 s�1) than at night (<15 mmol CO2 m�2 s�1). The

change in storage term was negligible while the eddy flux

had variable sign and magnitude from day to day.

Fig. 14a shows means and standard errors of a composite

of the vertical and horizontal advection fluxes averaged for

each hour of the day of the 15 days of the campaign, while

Fig. 14b shows the means and standard errors for the change

in storage and eddy flux terms. Standard errors include both

natural day-to-day variability and measurement uncertain-

ties. The statistics were computed from 9 to 15 hourly data,

depending on the availability of all components of the mass

balance. The vertical and horizontal advection terms are

significant for most of hours of the night but are smaller in

magnitude during the day as a result of the small vertical and

horizontal gradients. The eddy flux term for the understorey

is positive at night and negative for only a short period

around noon. The change in storage term was strongly

negative from 06:00 to 08:00 h, indicating a flushing of high

CO2 concentrations from the CV in the morning. The opposite

occurs in the early evening (17:00–19:00 h) when the change

in storage term is positive due to a build up of CO2

concentrations within the CV (Fig. 10). The changes in

storage and eddy flux are larger than the advection terms in

the hour around sunset. This observation supports the

proposal of van Gorsel et al. (2007) that the sum of

these two terms provides a good estimate of night-time

respiration at that time. They propose using relationships

between air temperature and the maximum in the sum of the

storage and eddy flux terms following sunset to estimate

respiration for the remainder of the night when the

advection terms are significant and impossible to measure

on a single flux tower.

Uncertainties in each of the vertical and horizontal

advection terms are large, especially at night when standard

errors of the mean exceed 3 mmol CO2 m�2 s�1 (Fig. 14a).

Large variability in calculated vertical advection was also

reported by Aubinet et al. (2003), Feigenwinter et al. (2004,

2008) and by Heinsch et al. (2007). Calculated horizontal

advection is sensitive to errors in the windspeed and

direction through the faces of the CV. Small variations in

wind direction either side of the predominantly southerly

flow at night resulted in changes in sign of the horizontal

advection flux because of large east–west CO2 concentration

gradients at night (Fig. 9). Uncertainties in the vertical

windspeed also lead to large errors in the vertical advection

due to the strong vertical CO2 concentration gradients

(Fig. 10). Standard errors of the eddy fluxes and change in

storage terms are generally smaller than for the other two

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 9 – Time series for the weighted mole fractions of CO2 for: (a) the north and south and (b) the east and west faces of the

CV. Note that the date labels are centred on midday.

Fig. 10 – Time series of: (a) CO2 mole fractions, and (b) potential temperatures for the period 13–18 March 2005.

Measurements were made at six heights on the 6 m mast at the centre of the CV. Note that the date labels are centred on

midday. Missing data are the result of a passing storm.

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Please cite this article in press as: Leuning, R., et al., Measurement of horizontal and vertical advection of CO2 within a forest canopy.

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

Fig. 11 – Scatter plot of hourly-mean vertical velocities

measured with a 3D sonic anemometer at 6 m on the

central mast, wsðhÞ, and those determined using the

continuity equation, wðhÞ.

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components and errors for all components are smaller

during the day than at night.

Averages for the components of the mass balance of CO2 for

the control volume during the 15-day campaign are presented

in Table 2. The night-time vertical advection and eddy flux

terms are similar in magnitude and �5 times greater than the

horizontal advection term. There is little day–night variability

in the vertical advection term, while the horizontal advection

term doubled from night to day and the eddy flux decreased

from 1.59 to 0.92 mmol CO2 m�2 s�1. The change in storage

term is smallest and has a similar magnitude but opposite sign

Fig. 12 – Vertical advection flux densities of CO2 calculated using

as measured by the 3D sonic anemometer located at 6 m in the c

and (d) show the corresponding vertical velocities for night and

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Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

between day and night, resulting in zero net flux over 24 h.

According to the mass balance approach, there was an average

net efflux of 3.41 mmol CO2 m�2 s�1 from the CV when

averaged over 24 h. The net efflux was greater at night than

during the day, suggesting photosynthetic uptake of CO2 by

the grass and shrubs of the understorey during the day.

Night-time respiration by vegetation and soil within the CV

was also measured using chambers during the field campaign.

Fig. 15 shows that about 60% of the total respiration was from

the soil, 30% from leaves, and 10% from the wood. The sum of

the three components ranged from a low of 4.2 mmol

CO2 m�2 s�1 on the night of 8 March to a high of 6.0 mmol

CO2 m�2 s�1 on 15 March, with an overall mean of 5.2 � 0.2

(S.E., N = 10) mmol CO2 m�2 s�1. This is similar to the night-

time average of 3.68 � 0.96 (S.E., N = 204) mmol CO2 m�2 s�1

obtained from the mass balance approach.

Agreement between the two estimates of the mean night-

time respiration fluxes is fortuitous, given the large uncer-

tainties in the vertical and horizontal advection terms that

contribute significantly to the night-time mass balance of the

CV. For vertical advection, this is the result of multiplying

relatively small vertical velocities (Fig. 11) by large vertical

mole fraction gradients (Fig. 10), while for the horizontal term

it results from multiplying relatively larger horizontal velo-

cities by smaller horizontal gradients (Fig. 9). Small errors in

vertical velocities and horizontal concentration gradients can

produce large errors in the mass balance for the CV. In contrast

estimates of respiration obtained using the chambers are

considered highly reliable because they are consistent with

independent estimates of annual changes in carbon stored in

the trees and understorey (Keith, 2008; pers. comm.) and with

a model of the forest carbon balance (Kirschbaum et al., 2007).

the vertical velocity derived from the continuity Eq. (10) or

entre of the CV for: (a) night-time and (c) daytime. Panels (b)

day.

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 13 – Components of the mass balance for CO2 in the CV

for: (a) night-time and (b) daytime. The vertical advection

component is calculated using the vertical velocity from

the continuity equation.

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AGMET-3919; No of Pages 21

The above results show that all components of the mass

balance equation must be considered to estimate night-time

respiration. Because the advection terms are significant, it is

clear that accurate construction of mass balances requires

very precise estimates of the vertical velocity through the

upper surface of the CV, the variation of @w=@z with height and

accurate measurements of horizontal concentration gradi-

ents. Spatial and temporal variability in vertical velocities and

in horizontal concentration gradients make direct measure-

ments of the advection terms extremely difficult, suggesting

that it may not be possible to deduce precisely the source term

Fc from the CO2 budget in Eq. (15) (Aubinet et al., 2003;

Heinesch et al., 2007). This contrasts with findings of

Mammarella et al. (2007) who obtained good agreement

between chamber measurements of CO2 exchange, an

ecosystem model, and the sum of eddy fluxes, the change

in storage and vertical advection at Hyytiala, a site with

moderately complex topography. They were unable to

Table 2 – Average components of the mass balance of CO2 (mmcampaign

Averaging period Vertical advection Horizontal adv

Night (18:00–07:00 h) 1.63 0.33

Day (08:00–17:00 h) 1.63 0.64

24 h 1.63 0.46

Averaging periods are for night, day and 24 h.

Please cite this article in press as: Leuning, R., et al., Measurement o

Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

measure horizontal advection but concluded this term was

small.

Our experimental design involved the use of perforated

tubes arranged parallel to the slope to calculate the horizontal

advection terms using CO2 concentrations, pre-weighted by a

mean, normalized windspeed profile. This has the advantage

of providing horizontal averaging in the cross-wind directions

and allowing rapid scanning of the four resultant CO2

concentrations. However, the pre-weighting did not account

for windspeeds in the lowest 6 m being greatest at�3 m during

very stable conditions, and it was thus necessary to adjust the

pre-weighted concentrations using the factor given in Eq. (22).

The experimental design used in this study could be simplified

by not inserting the needle valves in each air line to pre-weight

the mole fractions from each level. This would apply equal

weighting to air from each line on the wall of the CV before

blending them for gas analysis. In this case the scaling factor

defined in Eq. (22) becomes

ss ¼

R h0:001 xcS1ðzÞdz

h i6R h

0:001 xcdzh i (25)

The average value of ss was 0.95 (n = 342) with a range from

0.73 to 1.44, similar to the revised scaling factors reported

earlier. In either case, it is necessary to measure the wind-

speed and mole fraction profiles in the centre of the CV to

calculate the scaling factors. A more satisfactory solution

would be to measure the concentrations at each level by

rapidly measuring the CO2 concentration in each air line in

turn to minimize errors associated with non-stationary

conditions.

An alternative solution was adopted by Feigenwinter et al.

(2008). They used vertical arrays of sonic anemometers and air

inlets mounted on towers at the corners of a trapezoid to

construct the 3D wind vector and CO2 concentration fields

numerically using bi-linear interpolation of the data. These

fields were then used to calculate the mass balance for the CV

by numerical integration of Eq. (1). Success of calculating the

fluxes normal to the surfaces of the CV in their approach rests

on the validity of the bi-linear interpolation to describe the

wind and concentration fields. Success in the approach

adopted in this paper depends on very accurate knowledge

of the spatially averaged vertical velocity at the upper surface

of the CV and the horizontal gradients of CO2 obtained through

physical sampling along the walls of the CV. Both approaches

are technically demanding and require a large number of

instruments in the field, resources not generally available to

the micrometeorological community.

ol mS2 sS1) for the control volume during the 15-day field

ection Change in storage Eddy flux Flux sum

0.14 1.59 3.68

-0.19 0.92 2.99

0.00 1.32 3.41

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 14 – A composite of the daily variation of the four flux components calculated using averages for each hour of the day of

the campaign. (a) Means and standard errors of the vertical and horizontal advection terms, and (b) means and standard

errors of the change in storage and eddy flux terms.

Fig. 15 – Night-time respiration from the soil, the leaves of shrubs and grasses and by the wood of trees and shrubs within

the CV estimated using scaled-up respiration chamber measurements.

a g r i c u l t u r a l a n d f o r e s t m e t e o r o l o g y x x x ( 2 0 0 8 ) x x x – x x x 17

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5. Conclusions

Calculation of the night-time mass balance for CO2 in a CV

located on the floor of a 40 m tall Eucalyptus forest was very

sensitive to small errors in vertical velocities at the upper

surface of the CV. Vertical velocities need to be known with a

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Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

precision of <1 mm s�1 when vertical mixing ratio gradients

are large. This is not possible using sonic anemometers due to

difficulties in resolving such small velocities and to uncer-

tainties in aligning the anemometer with the coordinates of

the CV. Use of the continuity equation and measurements of

divergences in horizontal velocities offers better prospects for

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 16 – Network for resistance to air flow through

perforations (Rj, j = 1, n) and resistance to flow between

holes (R) in drip-irrigation tubing. Pa is atmospheric

pressure at the inlet of each perforation and Pj, j = 1, n is

the pressure at each node.

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calculating the vertical velocity. Calculated horizontal advec-

tion is sensitive to errors in the wind direction and speed

through the faces of the CV. Small variations in wind direction

either side of the predominantly southerly flow at night

resulted in changes in sign of the horizontal advection flux

because of large east–west CO2 concentration gradients at

night. During the day, errors in eddy fluxes and change in

storage are smaller than for the advection terms as a result of

enhanced mixing and small vertical and horizontal concen-

tration gradients. Daytime errors for all components are

smaller than at night. Our experience with measurements

within the lowest 6 m of a forest floor and during a relatively

short field campaign suggests that errors associated with

measurement uncertainties outweigh the advantages of the

micrometeorological mass balance approach. These errors are

largely systematic rather than random, so it unlikely that

longer measurement and averaging periods will lead to a

substantial reduction in the errors.

Acknowledgements

The authors thank Mark Kitchen for his invaluable assistance

in constructing the air sampling array and the field

campaign. Dr. David Jupp kindly provided the foliage area

density data shown in Fig. 2. We thank Kris Jacobsen for his

assistance with the chamber respiration measurements. RL

thanks Prof. Larry Mahrt (Oregon State University) for

suggesting the use of the continuity equation to calculate

the mean vertical velocity. Thanks also to Drs. Helen Cleugh,

Eva van Gorsel and Robert Clement for helpful comments on

the draft manuscript. This research was funded in part by the

Australian Climate Change Science Program supported by

the Australian Greenhouse Office and by a U.K. NERC grant

NER/S/J/2004/13118.

Appendix A. Air flow through drip-irrigationtubing

As shown in Fig. 3, air was sampled at six heights along

each of the walls of the control volume using 50 m lengths of

drip-irrigation tubing (8 mm o.d., 6 mm i.d., hole spacing

0.30 m). Uniformity of air sampling along the tube occurs

when the drop in pressure across each hole (Pa � Pj) is large

compared to the pressure drop between the holes (Pj � Pj�1),

where Pa is atmospheric pressure outside the tube and Pj is the

pressure at the jth hole, numbered from end of the tubing

opposite that connected to the suction pump (Fig. 16). To

confirm this, we varied the total flow rate from 0 to 15.8 l min�1

through a 5 m length of tubing containing 16 holes, and a 10 m

length with 34 holes, and measured the pressure and flow rate

just before the suction pump. The resistance network shown

in Fig. 16 was used to analyze the data.

It was assumed that the pressure drop across a small orifice

is a quadratic function of flow rate (Perry and Chilton, 1973, p.

5.11; Leuning et al., 1985), while the pressure drop between

holes is a linear function of flow rate. For the jth orifice we can

write

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Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

Pa � P j ¼a f j

Cd

!2

; (A.1)

where fi is the air flow rate through the orifice, a is a coefficient

accounting for orifice geometry and air density, while Cd is a

discharge coefficient whose value depends on fj (Perry and

Chilton, 1973). The pressure drop between holes along the tube

is the product of the resistance, R, and the total air flow rate, f,

between adjacent holes, and since f increases with each addi-

tional hole (Pa � Pj) is also given by

Pa � P j ¼ Pa � Pj�1 þ RXj�1

k¼1

f k: (A.2)

The system of Eqs. (A.1) and (A.2) is solved iteratively by

assuming initial values for the coefficients a, Cd and the

resistance R, and by assigning an initial value for f1, the flow

rate through the first hole. This allows calculation of

Pa � P2 = (Pa � P2) + Rf1 from (A.2) and thence f2 from (A.1):

f2 ¼Cd

a

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðPa � P2Þ

p: (A.3)

We can then calculate Pa � P3 = (Pa � P1) + R( f1 + f1), fol-

lowed by f3, and so on for all nholes. The values of f1, a,Cd andR

are adjusted using an optimizing algorithm to minimize the

square of the difference between the predicted and observed

air pressure at the pump, Pa � Pn.

Fig. 17a shows the results of the analysis for a series of

measurements of Pa � Pj versus f for two length of tubing

with 16 and 34 holes, respectively. Agreement between

the measurements and the model was almost perfect,

with a linear regression for flow rate yielding

y = 0.9949x + 0.0620 (l min�1), R2 = 0.9997, and for pressure,

y = 0.9994 + 0.0216 (Pa), R2 = 1.0000, where y is the model

value and x is the measurement. Measurements from both

the 5 and 10 m lengths of tubing were combined in these

regressions.

The variation in discharge coefficient with flow rate

through each hole that is needed to obtain this high level of

agreement is shown in Fig. 17b. These curves have a similar

shape to those shown in Fig. 5.18 of Perry and Chilton (1973) for

the discharge through square-edged orifices. Values for Cd are

equal at fj > 0.25 l min�1, but at lower flow rates, Cd is greater

for the tube with 34 holes than the tube with 16 holes. This

may arise because the coefficient a in Eq. (A.1) depends on the

f horizontal and vertical advection of CO2 within a forest canopy.

Fig. 17 – (a) Variation in measured and modelled pressure drop at the suction pump end of the tubing, Pa–Pn, as a function of

total flow rate, f, for a 5 m long tube with 16 holes and a 10 m tube with 34 holes. (b) Variation in the discharge coefficient,

Cd, as a function of flow rate per hole, fj, for tubing with 16 and 34 holes. (c) Percentage flow in hole j relative to flow through

hole 34 for a 10 m length of tube for total flow rates varying from 0.38 to 5.22 l minS1. (d) Variation in time delay between

when a parcel of air enters hole j and when it leaves the tubing at 10 m. The horizontal line is for a delay of 1 min.

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AGMET-3919; No of Pages 21

geometry of the holes relative to that of the tubing (Perry and

Chilton, 1973).

The calibrated model was used to calculate 100fj/fn, the

percentage flow through the jth hole along a 10 m tube relative

to that through the last hole before the suction pump (n = 34),

for total flow rates varying from 0.38 to 5.22 l min�1 (Fig. 17c).

Note that the percentage reduction is greatest for intermediate

flow rates (2.5 l min�1) becauseCd does not vary monotonically

with flow rate (Fig. 17b). Flow is least through the hole furthest

from the pump (j = 1), but in all cases this exceeded 87% of that

through the final hole, indicating that horizontal spatial

sampling of air is relatively uniform and adequate for the

purposes of our measurements. In contrast, sampling across

the length of the tubing in is not uniform in time because, with

every additional hole from j = 1 to n, the cumulative air flow

within the tube increases and the length of tubing to the take-

off point decreases. The time delay (minutes) for air to travel

from the jth hole to the take-off point is given by

t j ¼pr2ðL� 0:3ð j� 1ÞÞ

10P j

1

P jk f k

; (A.4)

where r is the radius of the tubing (cm), L is its length (m) and fkis flow rate through the kth hole. The factor 10 is required to

convert length to cm and l min�1 to cm3 min�1 and 0.3 (m) is

the spacing between the holes.

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Agric. Forest Meteorol. (2008), doi:10.1016/j.agrformet.2008.06.006

Time delay as a function of hole number and flow rate for a

10 m length of tubing is shown in Fig. 17d. Delays exceed

20 min for the first hole at f = 0.38 l min�1, but at this flow rate,

delays for j > 10 are less than 2 min, half the 4 min cycle time

used to calculate the horizontal advection terms. The delay is

<2 min for j > 2 at higher flow rates, indicating that air

reaching the take-off point from each line will have been

sampled along >90% of its length within the past 2 min. We

thus consider the use of drip-irrigation tubing to provide

acceptable air sampling for use in the advection study.

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