lagrangian dispersion of 222rn, h2o and co2 within amazonian rain forest
TRANSCRIPT
Lagrangian dispersion of 222Rn, H2O and CO2 within
Amazonian rain forest
Eric Simon a,*, B.E. Lehmann b,�, C. Ammann c, L. Ganzeveld d,U. Rummel e, F.X. Meixner a, A.D. Nobre f, A. Araujo g, J. Kesselmeier a
a Biogeochemistry Department, Max Planck Institute for Chemistry, P.O. Box 3060, D-55020 Mainz, Germanyb Physics Institute, University of Bern, Switzerland
c Swiss Federal Research Station for Agroecology and Agriculture, Zurich, Switzerlandd Atmospheric Chemistry Department, Max Planck Institute for Chemistry, Mainz, Germany
e Meteorologisches Observation Lindenberg, Deutscher Wetterdienst, Germanyf Divisao de Sensoriamento Remoto, Instituto Nacional de Pesquisas Espaciais, Sao Jose dos Campos, Brazil
g Faculty of Earth Sciences, University Amsterdam, Netherlands
Received 1 September 2004; received in revised form 8 August 2005; accepted 12 August 2005
Abstract
The present study focuses on the description of the vertical dispersion of trace gases within the Amazon rain forest. A Lagrangian
approach is parameterised using in-canopy turbulence measurements made at a site in Rondonia (Reserva Jaru). In contrast to
common scaling schemes that solely depend on friction parameters measured above the canopy, a combined scaling that also
includes night-time free convective mixing in the lower part of dense vegetation canopies is proposed here. 222Rn concentration
profiles and soil flux measurements made at a second site near Manaus (Reserva Cuieiras) are used to evaluate the derived
parameterisation and the uncertainties of the forward (prediction of concentration profiles) and inverse (prediction of vertical
source/sink distributions) solution of the transfer equations. Averaged day- and night-time predictions of the forward solution agree
with the observations within their uncertainty range. During night-time, a weak, but effective free convective mixing process in the
lower canopy ensures a relatively high flushing rate with residence times of <1 h at half canopy height in contradiction to earlier
estimates for Amazon rain forest.
The inverse solution for 222Rn source/sink distributions shows a high sensitivity to small measurement errors, especially for day-
time conditions, when there is efficient turbulent mixing in the upper canopy and profile gradients are small. The inverse approach is
also applied to CO2 and H2O profiles. The predicted net fluxes show a reasonable agreement with Eddy Covariance (EC)
measurements made above the forest canopy, although the scatter is large and the day-time solutions for CO2 are very sensitive to
measurement errors. However, this is not the case for typical night-time conditions, where the CO2 profile gradients in the upper
canopy are large. The inverse approach predicts a mean CO2 emission flux of 7.5 mmol m�2 s�1 for the investigation period. This
value is somewhat larger compared to estimates based on EC measurements, which are quite uncertain at night-time and thus
reduces the upper bound of the estimated carbon sink strength for Amazonian rain forest.
# 2005 Elsevier B.V. All rights reserved.
Keywords: Canopy layer turbulence; First-order closure; Lagrangian simulation model; Nocturnal processes; Rain forest; Radon
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Agricultural and Forest Meteorology 132 (2005) 286–304
* Corresponding author. Tel.: +49 6131 305 308;
fax: +49 6131 305 542.
E-mail address: [email protected] (E. Simon).� Passed away on 16 July 2005.
0168-1923/$ – see front matter # 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.agrformet.2005.08.004
1. Introduction
Until the end of the 1980s, in-canopy turbulence was
treated in most transport schemes analogously to
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 287
Nomenclature
asc function for convective based scaling of
sw(z) with coefficients ac{1,2} (m s�1)
asf function for friction based scaling of
sw(z) with coefficients af{0,1,2}
AG-A–D radon devices A–D (alphaguard)
C(zj), Cref ensemble averaged scalar concentra-
tion at zj and zref, respectively
C222(zj)222Rn activity concentration at zj (Bq m�3)
d(i, j) coefficient of the dispersion matrix with
superscripts far and near denoting the far
and near field, respectively (s m�1)
EC Eddy Covariance
F trace gas net flux at zref
Fc CO2 net flux at zref (mmol m�2 s�1)
hc mean canopy height (m)
Ix(a, b) the incomplete beta function (with free
parameters a and b)
J{220,222} soil flux of 220Rn and 222Rn (Bq m�2 s�1)
kfar far-field diffusivity (m2 s�1)
knear near-field kernel (m2 s�1)
Ls, Lw canopy and Eulerian length scales,
respectively (m)
LAI leaf area index
LE latent heat flux at zref (W m�2)
LNF Localised Near-Field theory
m, n number of source layers and concentra-
tion profile heights, respectively (m)
Px(a) incomplete gamma function (with free
parameter a)
Rnet net radiation observed at zref (W m�2)
RBJ-A Rondonia tower
RH relative humidity above the canopy (%)
Si source/sink of layer i
Ta ambient temperature observed at zref (K)
TE, TL(z) the Eulerian and Lagrangian timescales,
respectively (s)
u* friction velocity at zref (m s�1)
uref mean horizontal wind speed at zref (m s�1)
z, zref height above ground and reference height
>hc, respectively (m)
zs{c,f} scaling heights for asc and asf (m)
ZF2-K34 Cuieiras tower (Manaus)
x the dimensionless height (z � zi)/
[sw(zi)TL(zi)]
nref(zi) effective velocity for transfer from zi to zref
(m s�1)
sw(z) standard deviation of vertical wind speed
(m s�1)tref(zi) timescale for transfer from zi to zref (s)
molecular diffusion by applying a flux–gradient
relationship, known as ‘‘K-theory’’. It is now widely
accepted, that K-theory fails within the vegetation as a
consequence of the inhomogeneous, intermittent nature
of in-canopy turbulence (Finnigan and Raupach, 1987;
Raupach, 1988; Kaimal and Finnigan, 1994). Based on
a Lagrangian analysis of canopy transfer processes,
Raupach (1989b) presented the Localised Near-Field
(LNF) theory, which led to the development of several
new approaches, e.g. one-dimensional Lagrangian
models (Raupach, 1989b; Warland and Thurtell,
2000), higher order closure models (Katul and
Albertson, 1999), hybrid Eulerian–Lagrangian models
(Siqueira et al., 2000) and two-dimensional stochastic
Lagrangian models (Reynolds, 1998; Hsieh et al.,
2003). Most applications of the LNF theory are related
to the so-called inverse approach, which is used to infer
vertical source/sink distributions of a trace gas
compound from observed concentration profiles (Rau-
pach et al., 1992; Kruijt et al., 1996; Katul et al., 1997;
Nemitz et al., 2000; Denmead et al., 2000; Leuning,
2000). However, due to numerical reasons, the inverse
application is much more sensitive to the input data, i.e.
the concentration profile measurements and their
inevitable errors compared to the forward approach,
which is applied to calculate the concentration profile
for a given source/sink distribution. Furthermore, the
evaluation of the inverse approach is difficult because
model predictions, i.e. the source/sink distributions (Si)
are unknown in most cases. Pioneering work in this
respect was done by Coppin et al. (1986), who measured
heat dispersion from an artificial source in a wind
tunnel. This rare data set with a known source strength
was used to develop and evaluate the initial version of
the LNF technique (Raupach, 1989a), as well as the
analytical solution of Warland and Thurtell (2000) and
the hybrid approach of Siqueira et al. (2000). For real
canopies, the inverse solution can be evaluated in part
by comparing the canopy net flux, as the height
integrated sum of Si, with common micrometeorologi-
cal measurements applied above the canopy (in
particular Eddy Covariance) or as shown in a few
studies, in-canopy or soil flux measurements (Denmead
and Raupach, 1993; Kruijt et al., 1996; Katul et al.,
1997).
Currently, the importance of stability effects for the
transport schemes described above is discussed (Leun-
ing, 2000; Leuning et al., 2000; Siqueira et al., 2000;
Siqueira and Katul, 2002; Hsieh et al., 2003). Leuning
(2000) for a rice paddy and Siqueira and Katul (2002)
for a pine forest plantation apply surface stability
parameters to distinguish stable, neutral and unstable
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304288
stratification classes. However, for the Amazon rain
forest, it has been shown, that the lower canopy can be
strongly decoupled, showing a contrasting thermal
stratification to the surface- and boundary layer above
(Kruijt et al., 2000; Rummel, 2005). During day-time,
the upper canopy is heated by global radiation resulting
in a maximum temperature at this height and a stable
stratification within the lower canopy. This effect is
favoured by the shape of vertical biomass distribution
showing a leaf area density maximum in the upper
canopy (Kruijt et al., 2000). During night-time, the in-
canopy gradient can become negative due to radiative
cooling of the crown region generating a weakly
unstable free convective layer. This general observation
for dense vegetation (Jacobs et al., 1994; Bosveld et al.,
1999a,b; Simon, 1999) is hypothesised to have a
significant impact on nocturnal exchange, especially
during calm nights, when radiative cooling is strongest
and forced mixing is weak.
The noble gas radon is produced by rock material
in all natural soils in the a-decay chains of uranium
(222Rn with a half-life of 3.85 days) and thoronium
(220Rn with a half-life of 56 s). The short-lived 220Rn
has been applied in several studies of near-surface
turbulent transport (Lehmann et al., 1999; Gut et al.,
2002a), whereas the longer lived species 222Rn is
applied in studies of soil diffusivity (Lehmann et al.,
2000; Gut et al., 2002b) and of whole canopy
exchange (Ussler et al., 1994; Butterweck et al., 1994;
Lehmann et al., 2000; Martens et al., 2002, 2004). As
an inert trace gas it is an ideal candidate for dispersion
studies, since the vertical exchange is not affected by
biological removal or production nor by chemical
reactions. Based on in-canopy profiles of 222Rn and
CO2 measured at a rain forest site near Manaus,
Trumbore et al. (1990) calculated a mean canopy
residence time of �1 and 3.4–5.5 h for day- and
night-time conditions, respectively. In complementary
studies, this estimate was applied to interpret
observed profiles of ozone and nitrogen oxides within
the Amazon (Fan et al., 1990; Bakwin et al., 1990).
The residence time determines the efficiency of
removal and production by biological and chemical
processes within the canopy, e.g. the canopy reduction
effect on soil-biogenic NOx emissions (Jacob and
Wofsy, 1990; Jacob and Bakwin, 1991; Yienger and
Levy, 1995; Ganzeveld et al., 2002b). Despite its
relevance for global scale applications (Yienger and
Levy, 1995; Ganzeveld et al., 2002a) only few studies
focus explicitly on characteristic timescales and
mixing rates within the forest canopy (e.g. in Kruijt
et al., 2000; Rummel, 2005).
In the present study, we assess the dispersion of
vertical trace gases within an Amazonian rain forest
canopy using the Localised Near-Field approach in its
original form (Raupach, 1989a,b,c). A model para-
meterisation is derived from direct turbulence mea-
surements at a site in Rondonia (Brazil). The
significance of night-time free convective mixing
inside the canopy is assessed by applying a combined
(=friction + convective based) scaling of vertical
turbulence properties. The model is then applied to222Rn, CO2 and H2O profile measurements made at a
second site near Manaus (Brazil). By using 222Rn as an
inert tracer, the forward and inverse LNF solution can
be evaluated separately which helps to discriminate
uncertainties related to the turbulence parameterisation
and the inversion of the transfer equations. The
observed and predicted effective transfer velocities
and timescales of 222Rn transport are compared to the
estimates of Trumbore et al. (1990).
As mentioned above, Eddy Covariance (EC) flux
measurements made above the canopy are often used to
evaluate the inverse LNF approach. In the present study,
we used the EC technique as an additional and
independent evaluation method. For this purpose, the
model scheme is inversely applied to CO2 and H2O
concentration profiles measured at the Manaus site. The
height integrated source/sink distributions inferred by
the Lagrangian model are compared to simultaneously
made EC measurements of H2O and CO2 net fluxes
above the canopy. For CO2 the inverse analysis is
extended against the background of carbon sequestra-
tion. Estimates of the carbon budget derived from EC
measurements suggest a strong carbon sink for the
Amazon basin (Grace et al., 1995; Malhi et al., 1998;
Carswell et al., 2002; Araujo et al., 2002). However, the
EC technique is very uncertain for typical night-time
conditions (Goulden et al., 1996; Mahrt, 1999; Araujo
et al., 2002). Therefore, the averaged day- and night-
time carbon fluxes predicted by the Lagrangian model
are discussed as an independent estimate of the carbon
budget of the rain forest site under investigation.
2. Material and method
2.1. Background
Vertical dispersion within the canopy links leaf and
soil surface sources and sinks to the profile of mean
trace gas concentration. For a horizontally homogenous
vegetation layer and steady-state environmental condi-
tions, this relationship can be described universally by
the equation system
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 289
Cðz jÞ � Cref ¼Xm
i
dði; jÞSi Dzi (1)
where C(zj) and Cref represent the concentration at
height zj and well above the canopy (at reference height
zref) and d(i, j) is the dispersion matrix element con-
necting the source Si in layer i = 1, . . ., m to the
concentration at height zj, j = 1, . . ., n. Eq. (1) refers
to the forward problem of canopy dispersion. The
spatial and temporal integration of the surface exchange
(i.e. the measurement of Si) is usually not easily possible
(Ehleringer and Field, 1993), whereas C(zj) can gen-
erally be measured on a routine basis. When the number
of profile measurement levels is higher than the number
of source layers (n > m), Eq. (1) can be inverted to infer
Si by applying a least-squares optimisation method,
which is referred to as the inverse approach (Raupach,
1989a).
2.2. Site descriptions and measurement overview
The two rain forest locations under investigation
(Table 1) are main research sites of the Large-Scale
Biosphere–Atmosphere Experiment in Amazonia
(LBA) that coordinates many international climate
research studies within the Amazon basin (Andreae
et al., 2002). The Rondonia site is part of the Reserva
Biologica Jaru and belongs to the Instituto Brasileiro do
Meio Ambiente e dos Recursos Naturais Renovaveis
(IBAMA). Field data used here have been collected
from September to November 1999 during the second
intensive field campaign of LBA-EUSTACH (the
European contribution to LBA), coinciding with the
dry-to-wet season transition period. The Manaus site is
part of the Reserva Biologica do Cuieiras and located
�60 km NNW of the city of Manaus in central
Amazonia. It belongs to the Instituto Nacional de
Pesquisas da Amazonia (INPA) and is accessible by a
small road (ZF2), with the tower at about 34 km down
this road (ZF2-K34). Employed measurements from
this site took place during the Cooperative LBA
Airborne Regional Experiment in July 2001 (LBA/
CLAIRE-2001).
Table 1
Sites and measurement overview (LAI represents the leaf area index)
Jaru (Rondonia)
Measurements LAI; in-canopy turbulence
Period September–November 1999
Tower (height) RBJ-A (53 m)
Location 108405500S–6185504800WObject Turbulence parameterisation
The Jaru forest is classified as a Floresta Ombrofila
Aberta (palm-rich open tropical rain forest) in contrast
to the Cuieiras forest (Floresta Ombrofila Densa, dense
tropical rain forest see Kruijt et al., 2000). However,
both can be characterised as a lowland (terra firma)
tropical rain forest growing on deeply weathered clayey
soils. A mean canopy height of hc = 40 m is assumed,
which represents the upper limit of the range of
estimates given by several authors (Kruijt et al., 2000;
Rummel, 2005). Leaf area index (LAI) was measured
with two optical sensors of a commercial device (LAI-
2000, LI-COR, Lincoln, USA). At the Cuieiras site, LAI
was measured at eight differential levels (40.0, 33.0,
29.5, 25.5, 21.5, 17.5, 13.5, 9.5 and 5.5 m). At each
height level, 12 equally distributed individual measure-
ments were performed in a concentric circle just around
the tower. On the 5 and 16 July, a total number of three
ascending and descending profiles could be measured
under prevailing cloudy conditions. In a similar way,
five LAI profiles have been sampled at the Jaru tower on
15 September and 2 (3x) and 3 November 1999 at 21
heights ranging from 0 to 36 m (G. Kirkman, personal
communication, 2004).
The turbulence data used for model parameterisation
has been measured at the Jaru site. The measurement
protocol is described in detail by Rummel et al. (2002)
and Rummel (2005). High resolution horizontal and
vertical wind components were measured with three-
dimensional sonic anemometers (Gill Instruments,
Lymington, Hampshire, UK). Most of the time, three
instruments were operated simultaneously at 53, 11 and
1 m height above the ground. During short periods, the
11 and 1 m devices were mounted alternatively at 42.2,
31.3 and 20.5 m. Half hourly mean values for each
height level are divided into day-time (8:30–16:30 h)
and night-time (22:00–4:30 h) cases. In addition, a
classification into low (u � 2 m s�1) and high wind
speed (u > 2 m s�1) conditions is used to assess the
model sensitivity to the uncertainty and variability of
the turbulence profiles. For night-time conditions, the
separation for wind speed is only performed for the
levels at 1, 42.2 and 53 m height as too few data points
Cuieiras (Manaus)
LAI; radon, CO2, H2O (flux and profiles)
July 2001
ZF2-K34 (53 m)
283503300S–6081202700WLagrangian model application
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304290
are available for high wind speed conditions. Periods
with rain were not considered.
2.3. Flux and profile measurements made at the
Cuieiras site
Measurements of the CO2 and H2O concentration
profiles (at 51.1, 42.5, 35.5, 28.0, 15.6 and 5.2 m height)
and Eddy Covariance fluxes (at 53 m height) at the
Cuieiras site used for the inverse LNF application are
part of a long-term monitoring project described in
detail by Araujo et al. (2002). The original data with a
time resolution of 30 min were smoothed by calculating
a moving average for 2 h (including the turbulence
forcing variable of the LNF model, i.e. the standard
deviation of vertical wind speed above the forest, swref).
Radon activity measurements used for the forward
and inverse LNF application were performed with four
a-decay detector units (AG-A–D; ALPHAGUARD
2000 PRO, Genitron Instruments, Frankfurt, Germany)
calibrated for 222Rn by the manufacturer. The precision
and detection limits are �10% and 3 Bq m�3 for a
10 min sampling interval. Air was pumped through
Teflon tubes (1/4 in. diameter) from six sample heights
(Fig. 1a). The flow rate was 300 cm3 min�1 and
controlled by pressure sensors (AG-C and AG-D) or
regulated by mass flow controllers (AG-A and AG-B).
Data acquisition operated on the shortest possible time
interval of 1 min. Units AG-C and AG-D were installed
at 24 and 42 m height, respectively. Unit AG-D
measured continuously at the 43 m level above the
canopy, whereas a valve system in unit AG-C switched
every 30 min between the 27 and 15 m height level.222Rn activity at the three remaining height levels (0.1, 2
and 5 m) was measured by unit AG-B over time
Fig. 1. Heights j = 1, . . ., n of concentration profiles (zj) and source layers
application to 222Rn (a) and the inverse application to H2O and CO2 (b). The fo
C(zj) for a given source/sink distribution S(zi), whereas the inverse approac
intervals of 40 min. On the way to the detectors of the
profile system the air passed through a mixing device
(2 l plastic bottle), where the short-lived 220Rn
practically totally removed by decay. Each first
10 min of sampling time for the lower five levels
switching between different heights were generally
discarded (flushing time). The integration period for the
upper (AG-D and AG-C) and lower units (AG-B) are 30
and 40 min, respectively (inclusive of flushing time).
The observed activity of 222Rn at 43 m was usually
very small and close to the detection limit of the radon
devices. Thus, the temporal evolution of the radon
profile is strongly masked by the random-like variability
resulting in larger relative measurement uncertainties.
The accuracy of individual profile measurements is also
limited due to the fact that a complete profile sampling
cycle took about 2 h for all six measurement levels.
Therefore, the 30 and 40 min interval measurements are
smoothed by applying a symmetric triangular weighted
moving average covering an interval of 2 h before and
after mean sampling time. The smoothed profile data
are divided into day- and night-time and high and low
wind speed condition classes in the same way as
described for the turbulence measurements at the Jaru
site (see above). The air stream for the lower three levels
was sporadically switched to a closed circuit to derive
the radon soil fluxes from a static chamber system
containing the units AG-B and AG-A. Before reaching
the mixing device of AG-B, the air passed the fourth
unit AG-A, where the summed activity of 220Rn and222Rn was measured. The static chamber system and the
flux calculations are described in detail in Lehmann
et al. (2004). Note that the activity of radon (in units of
decays per second ! Bq) is directly proportional to the
scalar concentration, depending only on the decay
i = 1, . . ., m of the LNF scheme (Eq. (1)) for the forward and inverse
rward problem incorporates the simulation of the concentration profile
h infers S(zi) from C(zj).
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 291
constant (l222 = 2.1 � 10�6 s�1). To avoid the ambig-
uous term ‘‘activity profile’’, the expression ‘‘activity
concentration profile’’ (denoted by C222(z) is used
hereafter; Butterweck et al., 1994).
2.4. Implementation of the Localised Near-Field
theory
For modelling 222Rn dispersion with the LNF
approach, the canopy is divided into two layers: a
bottom layer from 0 to 0.1 m representing the soil
surface, and an overlaying canopy layer from 0.1 to
canopy height (Fig. 1a). A sensitivity analysis indicated
that the forward predictions are not very sensitive to the
choice of the soil layer height (results not shown here).
For the inverse application to H2O and CO2, a scheme
with three source layers is chosen consisting of a bottom
(soil and ground vegetation), middle (palms and
emerging trees) and upper layer (crown region) from 0
to 5, 5 to 20 and 20 to 40 m height, respectively (Fig. 1b).
The predicted source/sink distributions inferred from the
input concentration profiles are evaluated by comparing
the resulting canopy net fluxes with the EC measure-
ments above the canopy. It has been shown by Katul et al.
(1997) that, in contrast to the forward approach, the
inverse solution is sensitive to the choice of Dz, i.e. the
discretisation of S. However, the number of source layers
(m) andDz are restricted by the number of profile heights
(n) to satisfy the condition m < n (see Section 1).
In the LNF theory, Eq. (1) is decomposed into a
diffusive-like far-field and a persistent near-field
(di; j ¼ dfari; j þ dnear
i; j ). The solution for both fields results
from the integrated reciprocal far-field diffusivity kfar and
the approximated near-field kernel knear. Both quantities
depend on the standard deviation of vertical wind speed
sw(z) and the Lagrangian timescale TL(z) according to
Table 2
Different parameterisations of the standard deviation of vertical wind spee
Reference LAI hc [m]
Raupach (1989a)a >3
Raupach (1989a)b 0.23 0.06
Raupach et al. (1992) 3.5 0.75
Kruijt et al. (1996) �5.5 �32
Katul et al. (1997) �5 13
Nemitz et al. (2000) 5.3 1.4
Leuning et al. (2000) 3.1 0.73
Denmead et al. (2000)c 5 2.75
Parameterisations based on u* are derived for near neutral stability conditia Family portrait.b Elevated heat source.c Based on leaf area index (LAI).
kfarðzÞ ¼ s2wðzÞTLðzÞ (2)
knearðxÞ � �0:39894 ln½1 � expð�xÞ�
� 0:15623 expð�jxjÞ; (3)
where x represents the dimensionless height (z � zi)/
[sw(zi)TL(zi)]. More details of the LNF theory are given
in Raupach (1989a,b,c). For an individual canopy, the
vertical profiles sw(z) and TL(z) have to be specified a
priori. Since the turbulent flow within the canopy is
dominated by shear, friction velocity (u*) or swref
represent appropriate scaling parameters (Raupach,
1989a). This approach is supported by turbulence obser-
vations within very different canopy types (Raupach,
1988). For a wide range of canopy heights (0.06–
16.2 m) and LAI values (0.23–4), sw(z)/u* decreases
from a typical value of 1.25 above canopy height (hc) to
a small value of 0–0.5 close to the ground as expressed
by the friction based scaling principle
swðz=hcÞswref
� swðz=hcÞ1:25u�
¼ asf (4)
where asf is a monotonic increasing function of height
with asf(0) � 0.5 and asf(z/hc 1) = 1. Table 2 com-
piles several implementations of Eq. (4). If no turbu-
lence measurements are available to derive asf, the
analytical model of (Massman and Weil, 1999) can
be used.
In the present study, night-time free convection is
included as an additional source of vertical mixing in
the lower canopy by applying a combined scaling
approach. Thereby, sw(z) is decomposed into a friction
part that scales with swref (Eq. (4)) and a solely height
d (sw) given in the literature
sw (hc) sw (0 m) Shape
1.25u* 0.25u* Linear
1.25u* 0.5u* Linear
1.3u* 0.2u* Power
swref 0.15swref Power
swref 0.9sw (9 m) Linear
�1.25u* �0.1u* Power
1.25u* 0.2u* Exp
swref 0.15swref Linear
ons (hc represents the canopy height).
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304292
dependent free convective part asc that is independent of
swref
swðzÞ ¼ asfswref þ asc (5)
asf and asc were implemented as the well known
incomplete beta function Ix and the gamma density
function Px, respectively (see Press, 1997). The friction
scaling function is given by
asfðzÞ ¼ max½af0; IxðzÞðaf1; af2Þ� (6)
where x(z) = z/zsf with asf(z zsf) = 1. The coefficients
af1 and af2 are dimensionless determining the shape of
the distribution and af0 is a minimum value of asf close
to the ground. The convective scaling function is given
by
asc ¼PxðzÞðac1Þ
ac2
(7)
where x(z) = zscz/(ac2hc). The parameters ac1, ac2 and
zsc determine the profile shape, and the size and location
of the convection maximum. All coefficient values are
derived by least-square optimisation from the Jaru
turbulence measurements. These ‘‘useful’’ functions
(Press, 1997) are very flexible and expected to be also
feasible for other canopy types by appropriate modifi-
cation of the free parameters. This would also simplify a
comparison of different parameterisation schemes as
listed in Table 2.
The parameterisation for TL(z) is more speculative
since it is an intrinsic Lagrangian quantity that cannot
be measured by stationary sensors. However, the
following two empirical relationships to Eulerian
quantities can be applied:
Fig. 2. Comparison of accumulated (shaded boxes) and differential (white bo
above 5 m. (a) Additionally, the height levels of the turbulence measureme
TLðzÞ �LwðzÞswðzÞ
� 0:71Ls
swref
: (8)
Lw is the Eulerian length scale of the vertical wind and
can be estimated from the Eulerian timescale (TE) and
horizontal wind speed (u) as
LwðzÞ ¼ uðzÞTEðzÞ (9)
using Taylor’s frozen turbulence hypothesis (Raupach,
1989a). The right-hand side of Eq. (8) represents the
simpler approach using the canopy length scale
Ls � 0.5hc (Raupach et al., 1996). It gives the constant
value TLswref/hc � 0.4, respectively, TLu*/hc � 0.3
which is compared in the present study to the height
dependent parameterisation
TLðzÞswref ¼uðzÞTEðzÞswðzÞ
: (10)
3. Results and discussion
3.1. Comparison of canopy structure
The single LAI profiles sampled at each site have
been averaged. The mean profile for Jaru is linearly
interpolated for comparison to the sampling height
levels of the Cuieiras tower (Fig. 2). The measurements
represent the conditions close to the tower. Note that a
storm in October 1999 produced a gap at one side of the
Cuieiras tower. Therefore, the observed value of the
total leaf area index (LAI) of 4.6 may be under-
estimated. However, this value fits in the range of 4–6
estimated by other authors for terra firma forest (e.g. in
McWilliam et al., 1993; Kruijt et al., 2000; Andreae
xes) leaf area index (LAI) observed at the Jaru (a) and Cuieiras sites (b)
nts.
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 293
et al., 2002). The differential profiles have a maximum
leaf area density at 0.65hc (Cuieiras) and 0.45hc (Jaru).
Obviously, the canopy structure at both sites is
relatively similar and the differences related to the
vegetation type (Section 2.2) can also be found locally
at the ecosystem scale. The Manaus area exhibits a
small-scale relief of plateaus and lowlands that has
favoured a pattern of dense vegetation with higher
trees on the plateaus and a palm-rich open forest in
the lowlands (Ribeiro et al., 1999). As demonstrated
by Araujo et al. (2002), the footprint of the Cuieiras
Fig. 3. (a) Mean and standard deviation of sw(z) measurements for day- and n
time conditions, no separation for wind speed is performed at the 11, 20.5 an
sw(z) = asfswref + asc for two different sampling heights and day- and night-t
respectively).
tower (ZF2-K34) shows a relatively low fraction of
plateaus (40% within 1 km radius) compared to a
tower 11 km nearby (ZF2-C14, 53% within 1 km
radius).
3.2. Parameterisation of in-canopy turbulence
profiles
The mean observed profiles sw(z) at the Jaru site are
shown in Fig. 3a. During day-time, sw(z) increases
linearly from close to zero at 1 m height up 0.25–
ight-time and different horizontal wind speed (u) conditions. For night-
d 31.3 m height levels because of lacking data. (b–e) Linear regression
ime conditions (symbols and lines represent observations and linear fit,
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304294
Table 3
Coefficient values for the friction and convective based scaling functions (as{f,c}) of the standard deviation of vertical wind speed (sw(z), Eqs. (6) and
(7))
Function a0 [m s�1] a1 a2 zs
asf for day-time 0.054 � 0.01 1.05 � 0.05 0.58 � 0.02 hc � 15%
asf for night-time 0.0 � 0.054 3.0 � 0.2 0.8 � 0.1 hc � 15%
asc for night-time – 1.6 � 0.1 8.0 � 2.0 26.7 m
0.5 m s�1 at the third level (20.5 m). At canopy height
(hc = 40 m), the profile reflecting high wind speed
conditions exhibits a global maximum. Averaged night-
time values are generally smaller in absolute numbers
but also in variability and vertical gradients.
For the parameterisation of the sw profile, the linear
Eq. (5) is fitted in a first step to measured data of each
single height, divided into day- and night-time cases
(Section 2.2). For a purely friction based relationship, a
zero intercept can be expected. In contrast, a significant
positive intercept indicates an additional source of
vertical mixing that is independent of swref (i.e. free
convective mixing). Exemplified, this is shown for the
day- and night-time measurements at the 42.2 m
(1.05hc) and 11 m (0.28hc) level (Fig. 3b–e). An
Fig. 4. Comparison of derived profile functions and representative measure
wind speed sw(z), decomposed into a forced fraction (swf) that scales with to
(swc; c). Symbols in (a–c) represent observed slope and intercept values of t
represent results for all data, and high and low wind speed cases, respectively
represent derived uncertainties for high (HU) and low (LU) wind speed condi
sw(z). Open and filled circles represent day- and night-time values, respec
intercept close to zero, which indicates purely friction
based scaling, is obtained for all levels for day-time
conditions and above hc for night-time conditions
(Fig. 3b–d). A significant positive intercept is obtained
in contrast to all levels below 32 m for night-time
conditions, with a maximum value of 0.065 m s�1 at
0.28hc (Fig. 3d). This indicates an additional source of
vertical mixing within the canopy, i.e. free convection.
In a second step, the derived intercept (asc(zi)) and
slope (asf(zi)) parameters are fitted to Eqs. (6) and (7),
respectively. For the friction based function, a minimum
value af0 = 0.054 and zero are obtained for day- and night-
time conditions, respectively. The optimal scaling height
varies between 32.4 m (night-time, u > 2 m s�1), 36.5 m
(day-time, u > 2 m s�1) and 46.1 m (day-time, u � 2
ments (after regression analysis) for the standard deviation of vertical
p-level values (swref; a and b) and a night-time free convective fraction
he linear fit to Eq. (4). Open circles, plus symbols and minus symbols
. The solid lines represent the fitted functions, whereas the dotted lines
tions as listed in Table 3. (d) Scatter plot for all measured and modelled
tively.
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 295
Fig. 5. Vertical profile of the Lagrangian timescale TL. The simple
constant normalised value (dashed line) and the height dependent rela-
tionship (symbols and solid line) are applied (see Section 2.4). Open and
filled symbols represent day- and night-time conditions, circles and
triangles represent low (u < 2 m s�1) and high (u 2 m s�1) wind
speed conditions, respectively. The solid line represents mean values
for all conditions, with standard deviations as error bars.
m s�1) resulting in zsf = hc � 20%. All derived para-
meter values for the two height functions are listed in
Table 3.
Uncertainties are estimated from the variability of
optimal parameters for different wind speed conditions.
The optimised profile functions with the derived slope
and intercept parameters for single height levels are
shown in Fig. 4a–c. A comparison of all measurements
with the predictions of the derived parameterisation
shows excellent agreement (R2 = 0.98, standard
error � 0.02 m s�1, see Fig. 4d).
Fig. 6. Overview of the meteorological conditions observed at the Cuieiras
mean horizontal wind speed uref, daily rainfall as column bars, ambient tem
data except rainfall (daily sum) represent half hourly mean values.
The Lagrangian timescale parameter TL has a much
higher uncertainty than sw. Fig. 5 shows a comparison
between the simple and the height dependent relation-
ship introduced in Section 2.4. Error bars represent the
variance for the different conditions and reflect the
uncertainties of the parameterisation. In the crown layer
(0.5–0.9hc), where only a few data points are available,
the height dependent parameterisation shows a bow-
shape inflection of TL(z) that resembles the observed
profiles of Legg et al. (1986) who derived TL by
inverting the far-field diffusivity relationship (Eq. (2)).
Consistent with these observations, Lai et al. (2002)
inferred a normalised in-canopy night-time profile
TL(z)u*/hc for a loblolly pine stand which decreases
linearly between 0.4hc and 1hc from 0.3 to 0.05,
respectively. Thus, a height dependence of TL might be
discussed and should be investigated experimentally in
more detail. However, the height levels with enough
data points available (height levels at 1, 42.2 and 53 m)
match the constant approach TLswref/hc = 0.4 (see
Section 2.4) reasonably well. The latter is therefore
also applied in the present study.
3.3. Observed meteorological conditions and radon
fluxes at the Cuieiras site
Fig. 6 gives an overview of the meteorological
conditions observed during the intensive investigation
period at the Cuieiras site. At the beginning of the two-
week period, cloudy conditions and frequent rain events
site (tower ZF2-K34) between 15 and 27 July 2001 (net radiation Rnet,
perature Ta as open circles and relative humidity RH as solid line). All
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304296
Fig. 7. Frequency distribution of derived 220Rn (a) and 222Rn (b) flux (J220 and J222, respectively) and flux correlation (c). The dotted line represents
predictions of a simple soil diffusion model using the ratio of mean values for J220 and J222 and a varying water filled soil space of 0.2–0.5 as input
(see text). The solid line is obtained after linear regression.
were observed. At the end of the first week, global
radiation, horizontal wind speed and diurnal amplitudes
of ambient temperature and relative humidity increased.
The general clear weather conditions that lasted until
the end of July were interrupted by a second period with
clouds and rain between July 22 and 24. Longer periods
with heavy rainfall were not observed. Consequently,
the radon soil fluxes were not expected to have been
suppressed by soil water logging.
A total number of 15 simultaneous soil flux
measurements for 220Rn (J220) and 222Rn (J222) have
been derived. Observed values for the short-lived 220Rn
ranged from 10 to 25 Bq m�2 s�1 with a mean value of
17.7 � 4.2 Bq m�2 s�1, whereas the fluxes of the longer
lived 222Rn are one order of magnitude lower (0.019–
0.052 Bq m�2 s�1) with a mean value of
36.6 � 10.1 mBq m�2 s�1. The frequency distributions
for J220 and J222 are shown in Fig. 7a and b. Table 4
compiles the actual data and those found in the literature
for the Amazon basin. Compared to the wet season
measurements made by Trumbore et al. (1990), our
fluxes are higher by a factor of 4.5 and they are two
times higher than the global average estimate of
Wilkening et al. (1972). However, there is good
agreement with the observations of Gut et al. (2002b,
using the same detectors) for the Jaru site and with
observations of Martens et al. (2004) during the dry
Table 4
Comparison of mean observed radon soil flux (J222) with corresponding m
mBq m�2 s�1)
Reference Range (mean)
Trumbore et al. (1990) 5.3–13.7 (8.0)
Gut et al. (2002b) 15.0–40.0 (28.3)
Martens et al. (2004) 24.9 � 3.33
Martens et al. (2004) 36.5 � 2.85
This study 19.0–52.1 (36.6)
a See Araujo et al. (2002).
season for a site near Santarem. In general, the observed
values are relatively high, especially for 220Rn, but not
unusually high (see Nazaroff, 1992).
The observed flux variability and the correlation
between the two radon species were evaluated by
applying a simple soil diffusion model (Nazaroff,
1992). With common parameter values given in
Lehmann et al. (2000) this model verifies whether
the species dependent life-time and assumed variability
of soil diffusivity can explain the range of observed
fluxes and correlation between J220 and J222. The ratio
of mean observed fluxes is J222 � 0:002J220. Changing
the model soil water content (volume ratio) over a range
from 10 to 100% results in a predicted variation and
correlation, which agrees with the observations within
their uncertainty (Fig. 7c).
3.4. Forward modelling of 222Rn activity
concentrations
The inferred turbulence parameterisation (Section
3.2) using the derived profile functions for sw(z) and
TL(z) is evaluated by comparing the forward predicted
and mean observed profiles of 222Rn activity concen-
tration. The mean observed radon soil flux
(J222 ¼ 36:6 mBq m�2 s�1) is used as a constant input
source of the soil layer (Fig. 1a). Sources or sinks within
easurements in other regions of the Amazon basin (values in units of
Season Soil
Wet (April–May 1987) Yellow oxisol
Late dry (October 1999) Orthic acrisol
Wet (June–July 2001) Clayey oxisol
Dry (October–December 2001) Clayey oxisol
Early dry (July 2001) Clayey oxisola
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 297
Fig. 8. Comparison of mean observed (squares) and forward predicted (lines) activity concentration profiles for night-time (a and c) and day-time (b
and d) conditions (where C222(zj) � C222ref is the activity concentration difference between height zj and zref at 43 m) using a mean soil flux
J222 ¼ 0:036 Bq m�2 s�1 (Section 3.3). Error bars represent standard deviations of the measurements. The dotted lines represent uncertainties
predicted for a 50% flux variation (s(J222); a and b) and the modified turbulence parameterisation for high (u 2 m s�1) and low (u < 2 m s�1) wind
speed conditions (s(HLU); c and d; see Section 3.2).
Fig. 9. Comparison of observed (filled squares) and predicted (lines)
night-time 222Rn activity concentrations (where C222(zj) � C222ref
represents the activity concentration difference between height zj
and zref at 43 m, see Fig. 8c) on a logarithmic scale applying
additionally a turbulence parameterisation for high wind speed where
night-time free convection is neglected (line with star symbols).
the canopy are neglected since they contribute less then
5% to the total exchange (Trumbore et al., 1990). To
assess the uncertainty of the forward predicted radon
profiles, a 50% uncertainty of the soil flux was assumed
and the turbulence parameterisations for high and low
wind speed conditions were applied (see Section 3.2).
A comparison of predicted and measured C222(z) is
shown in Fig. 8 (note the logarithmic y-axis scale). In
general, the model simulations match the observations
within their uncertainty range. Day- and night-time
profiles have a slightly different shape. The largest
gradients are generally observed and predicted in the
lowest 5 m. Day-time concentrations in the upper and
middle canopy decrease more rapidly with height
although the vertical gradients are small. The most
significant difference is found for the height level at
0.35hc. The range of predicted activities as a function of
different turbulence parameterisations (high and low
wind speed) is smaller for night-time (Fig. 8c)
compared to day-time conditions (Fig. 8d). Obviously,
the effect of depressed forced mixing for low wind
speed conditions (see Fig. 3a) is counterbalanced by
higher free convective mixing (Fig. 4c). Considering the
high uncertainty of the measured soil fluxes, the
predicted profiles agree reasonably well with the
observations.
For a reasonable prediction of the night-time
profiles, the combined scaling of sw(z) (Section 2.4)
is essential. Neglecting free convection provides
profiles with predicted radon concentrations two orders
of magnitude higher compared to observations in the
lower canopy (Fig. 9). The higher values of sw(z)
obtained from friction based scaling for high wind
speed (Fig. 4b) have only marginal effects, whereas the
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304298
free convective scaling with asc � 0.05 m s�1 (Fig. 4c)
has a large impact on the whole profile. Obviously,
night-time free convection couples the lower and upper
canopy very efficiently and is highly significant for the
vertical scalar distribution within the canopy.
3.5. Effective transfer velocities and timescales
Effective timescales and transfer velocities within
the canopy are of special interest for surface–atmo-
spheric exchange of reactive trace gases like nitric oxide
and ozone (Section 1). Since radon sources and sinks
within the canopy can be neglected, the effective
transfer velocities and timescales can be calculated
according to
nrefðziÞ ¼J222 þ dC222=dt
C222ðziÞ � C222ref
(11)
trefðziÞ ¼1
nrefðziÞðzref � ziÞ: (12)
tref(zi) represents the period needed by an air parcel with
a mean transfer velocity nref(zi) to emanate from height
zi within the canopy to zref (residence or flushing time),
which is 43 m in this case. Although the storage term
dC222/dt in Eq. (11) can become significant, it is small in
Fig. 10. (a–d) Comparison of effective timescales (tref as defined by Eq. (1
observed 222Rn profiles (symbols, Fig. 8) and predicted by the LNF mode
different wind conditions and turbulence parameterisations.
the current case with a constant source/sink distribution.
The resulting profiles tref(zi) and nref(zi) for the mean
measured and predicted C222(z) (Fig. 8) are shown in
Fig. 10. At 0.375hc (15 m), tref is �40 and �11 min for
night- and day-time conditions, respectively, suggesting
a much higher canopy ventilation rate than earlier
estimates for another site near Manaus: based on222Rn measurements, Trumbore et al. (1990) derived
a flushing time of tref = 3.4 h for the ventilation of the
entire canopy volume during night-time and a mean
transfer coefficient nref = 0.33 � 0.15 cm s�1. Com-
pared to the present study, the latter value only agrees
with the results found for the lowest 5 m. Our inferred
ventilation rates with tref < 10 min in the upper canopy
correspond also to recent results of Rummel (2005)
obtained by a surface renewal model for the Jaru site.
3.6. Inverse predictions of 222Rn fluxes
The forward LNF application to 222Rn addressed in
the previous section verifies the implemented turbu-
lence parameterisation for the rain forest site under
investigation. As mentioned in Section 1, the inverse
approach introduces another uncertainty to the model,
which will be addressed here. The same discretisation
of source layers and profile heights is used (Fig. 1a).
Uncertainties are inferred by calculating the sensitivity
(standard error) of the predicted source to systematic
2)) and transfer velocities (nref as defined by Eq. (11)) derived from
l (solid lines). Error bars are calculated from variances obtained for
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 299
changes of the input concentration profile (Simon et al.,
2002). It is assumed that 222Rn activity concentration
measurements have an accuracy of 3 Bq m�3 (Section
2.3). Ideally, the inferred soil source strength should
agree with the mean observed soil flux (36.6 mBq
m�2 s�1), whereas the predicted canopy source/sink
should be zero.
The obtained results are shown in Fig. 11. For day-
time conditions, the inferred soil flux agrees well with
the mean observation. Night-time predictions of the
soil flux are reduced to nearly 50% of the measured
values while a non-zero canopy source is calculated.
However, the predicted canopy layer source/sink term
is very uncertain due to the high sensitivity to the
input concentrations (Fig. 11b and c). A change of
1 Bq m�3 at one profile height level causes a
predicted source change of 20–40% in relation to
the observed soil flux. For day-time condition the
highest sensitivities are found for the 0.02 and 5 m
profile height level. Although the sensitivities for
night-times conditions are lower, the resulting canopy
source uncertainty for an assumed precision of
3 Bq m�3 is of the same order of magnitude compared
to the predicted night-time source (Fig. 11a, error
bars).
Fig. 11. (a) Mean observed and inversely predicted 222Rn source/sink distrib
and a soil and canopy layer from 0 to 0.01 and 0.01 to 40 m, respectively. The
whereas the canopy source/sink strength is assumed to be zero. Positive and
derived from the sensitivity. (b and c) Relative sensitivity of the predicted s
squares and open circles, respectively).
3.7. Net fluxes for CO2, latent and sensible heat
The inverse LNF approach is also applied to CO2 and
H2O exchange at the Cuieiras site (Fig. 1b). A four-day
period is selected for a detailed comparison of model
predicted net fluxes with EC measurements above the
canopy (Fig. 12a–d). The error calculations for model
predictions represent the standard errors resulting from
assumed measurement accuracies of 0.5 mmol mol�1
and 0.05 mmol mol�1 for CO2 and H2O concentrations,
respectively, and calculated as described for radon
(Section 3.6).
In general, the model predictions show a good
agreement with observations. The relative uncertainties
of simulated day-time CO2 fluxes (Fc) are one order of
magnitude higher compared to the latent heat flux (LE)
and may explain the disagreement between simulations
and observations at noon and especially on 19 July
(Fig. 12a). Given typical values swref = 0.3 m s�1,
Fc = 15 mmol m�2 s�1 and LE = 300 W m�2 the rela-
tive uncertainty for CO2 is DFc/Fc � 16% compared to
only 4% for H2O. These values increase to 42 and 9%,
respectively, for high turbulence intensities usually
observed at noon with swref � 0.8 m s�1. Although LE
has a much higher relative uncertainty for night-time
ution for the observed concentration profiles described in Section 2.3
observed soil source is equivalent to the mean measured soil flux (J222),
negative error bars for predictions represent estimated standard errors
ource Si to the input concentration Cj (soil and canopy layer as filled
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304300
Fig. 12. Comparison of observed (Eddy Covariance (EC) technique; (a and b) filled squares and (c and d) abscissa) and inversely predicted (LNF; (a
and b) open circles and (c and d) ordinates) net fluxes of CO2 (Fc; a and d) and latent heat (LE; b and c) for two hourly averaged input parameters.
Error bars for model predictions represent standard errors obtained with an uncertainty of 0.5 mmol mol�1 and 0.05 mmol mol�1 for CO2 and H2O
concentration, respectively.
conditions (50–100%), the resulting effect is small due
to very small fluxes (�10 W m�2). The night-time
fluxes for CO2 predicted by the LNF model are
significantly higher than the values observed by EC
method (Fig. 12d, see also Section 3.9). In general, the
scatter is very large reflecting the large uncertainties of
the inverse approach. Especially during day-time,
effective mixing in the upper canopy leads to small
gradients of the scalar profiles, which are for CO2 on a
similar order of magnitude to the measurement
accuracy.
3.8. Diurnal source/sink distributions for CO2 and
H2O
Mean diurnal courses of the predicted CO2 and H2O
source/sink distributions for the investigated period are
derived. Cases with very high turbulence intensities
(two hourly mean of swref > 0.6 m s�1) were discarded
due to the high uncertainty of model predictions
(Section 3.7). Day-time results for the lower (0–5 m),
middle (5–20 m) and upper (20–40 m) canopy are
shown in Fig. 13. The time indicated on the x-axis
represents the starting time for each interval (e.g. 9:00 h
from 9 to 10 h local time). Before noon, the total
budgets of CO2 and H2O are dominated by carbon
uptake and transpiration loss of the upper canopy. In the
afternoon, the exchange of the middle canopy becomes
more important, especially for carbon exchange.
Surprisingly, the LNF technique predicts a carbon
exchange close to zero for the upper canopy just after
15 h while the transpiration term is still significantly
positive. The exchange of the bottom canopy layer,
which mainly represents the soil activity, shows a less
pronounced diurnal course. It has a positive sign
(emission) for CO2 during the day suggesting only a
weak photosynthetic activity of the ground vegetation.
Predicted CO2 emissions are 3–10 mmol m�2 s�1, in
agreement with soil respiration measurements of Meir
et al. (1996) made at the Jaru site (5.5 �0.7 mmol m�2 s�1). Latent heat flux of the lower
canopy layer is less than 15% of the total evapotran-
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304 301
Fig. 13. Mean predicted diurnal source/sink distribution for: CO2 (a) and latent heat (b). Lower, middle and upper canopy layers are from 0 to 10, 10
to 20 and 20 to 40 m height, respectively (Fig. 1b).
spiration, which is a typical value for dense vegetation
(Jones, 1992).
It is not possible to evaluate these results quantita-
tively with independent measurements because appro-
priate methods for direct measurements of the canopy
source/sink distributions are not available. Alterna-
tively, the Lagrangian transport scheme can be coupled
in forward mode to an ecophysiological exchange
model that explicitly calculates the source/sink dis-
tributions of CO2 and water (Siqueira et al., 2002). In
this case, the forward predicted concentration profiles of
CO2 and H2O can be compared to measurements.
Recently this was also done for the present approach
with encouraging results (Simon et al., 2005).
Fig. 14. (a) Daily integrated carbon exchange (day-time averages from 6 to 1
and c) Frequency distribution and box chart of CO2 fluxes (Fc) at night-tim
3.9. Daily integrated net carbon exchange
The integrated carbon dioxide flux of the Amazon
rain forest is of special interest for regional as well as
global carbon and greenhouse gas budget studies.
Therefore, the mean diurnal courses of CO2 source/sink
distributions are integrated to a daily net ecosystem
production (NEP). Fig. 14 shows the accumulated day-
and night-time values and the total budget.
It predicts a net carbon sink of 0.032 mol
C m�2 day�1. On a simple yearly projection this results
in an annual sink of 1.4 t C ha�1 year�1, which is on the
lower range of the 1–8 t C ha�1 year�1 estimated by
Araujo et al. (2002) for a one year record of EC data for
8 h and night-time averages from 18 to 6 h local time, respectively). (b
e.
E. Simon et al. / Agricultural and Forest Meteorology 132 (2005) 286–304302
the same tower. Compared to this and earlier estimates
(Malhi et al., 1998; Carswell et al., 2002) the day-time
values derived for the short observational period agree
well with the EC measurements, although the uncer-
tainty range is high. Predicted night-time values are
significantly higher, especially for calm wind condi-
tions. This observation goes along with results from
recent studies stating that the net Amazonian carbon
sink is probably overestimated by EC method due to
underestimated night-time fluxes (Culf et al., 1999;
Martens et al., 2004). A reliable application of the EC
method requires fetch and turbulence conditions which
are probably not fulfilled within the stratified nocturnal
boundary layer when friction generated turbulence is
weak (Goulden et al., 1996; Mahrt, 1999). Thus, an
additional benefit of the presented LNF application is its
independent estimate of night-time CO2 exchange. A
more detailed analysis of the derived CO2 night-time
fluxes indicates a skewed frequency distribution as
shown in Fig. 14b and c. The arithmetic mean emission
value of �7.5 mmol m�2 s�1 is 1.5 mmol m�2 s�1
higher than the respective median value which in turn
agrees with the value of 5.8 mmol m�2 s�1 obtained
from integration of the mean diurnal course (Fig. 13a).
For conditions with high night-time friction velocities
(u* > 0.2), the estimate based on EC method is similar
to the LNF median value which results in the lower
range estimate of NEP (1 t C ha�1 year�1; Araujo et al.,
2002). However, for typical nocturnal mixing condi-
tions low friction velocities u* < 0.2 m s�1 prevail
(>89% of the data in a one year record in 1999/2000
sampled at the ZF2-K34 tower as given by Araujo et al.,
2002) with a corresponding night-time CO2 net
ecosystem exchange smaller than 5.4 mmol m�2 s�1.
4. Conclusions
The derived parameterisation of sw(z) for the Jaru site
shows a high accuracy compared to the direct
measurements. The application of statistical distribu-
tion functions allows suitable modifications for
different canopy types which simplifies their applica-
tion in future studies. There is a need for more reliable
parameterisations of the Lagrangian timescale (TL) as
shown by the evaluation of the actually available
empirical relationships.
I
t is demonstrated that 222Rn is a useful tracer to studythe vertical exchange of scalars within the canopy. As
one of the few studies, where the source/sink
distribution and concentration profile are known
simultaneously, the forward and inverse solution
could be evaluated separately.
T
he inverse approach shows a high sensitivity to theprofile measurements, especially for the upper canopy
and under high turbulence intensities. In future
applications, the resulting uncertainties should be
quantified as described here.
F
or reliable predictions of night-time trace gasexchange in closed canopies it is essential to include
free convective mixing in the lower canopy in the
turbulence parameterisation scheme. Although the
convective fraction of sw(z) is low in absolute values
(�0.065 m s�1), it is of the same order of magnitude as
friction induced values above the canopy, especially
during calm nights and sustains an effective coupling
between the lower and upper canopy.
E
arlier estimates of canopy residence time could notbe supported by the present findings. Much lower
values (�1 h for night-time and �10 min for day-time
conditions) are consistently observed and predicted
by independent methods which may affect, for
example, the predicted canopy reduction effect on
nitrogen oxide emitted from the soil, since chemical
and biological removal processes in the vegetation
layer would be less effective.
T
he application to CO2 exchange suggests 10–40%higher night-time emission fluxes compared to EC
method reducing the upper bound of the predicted net
carbon sink range for the Amazon rain forest.
Although the EC method has to be regarded as the
micrometeorological standard technique for the
determination of canopy net fluxes, the inverse
Lagrangian approach may help to reduce the high
uncertainties in night-time CO2 flux estimates.
Acknowledgements
The research is supported by the Max Planck Society
and the European Union (EUSTACH-LBA; ENV4-
CT97-0566). Additionally, the CLAIRE-2001 cam-
paign at the Cuieiras site was supported by the Instituto
Nacional do Pesquisas da Amazonia (INPA), Manaus.
We thank Dr. Grant Kirkman for providing the Jaru leaf
area index measurements and Drs. Bart Kruijt and Jan
Elbers from ALTERRA Institute in Wageningen for
supporting the CO2 and H2O measurements in Manaus.
We would also like to thank Lydia Lehmann and
Alessandro Sarmento Cavalcanti for their assistance
during the radon experiment.
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