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

www.elsevier.com/locate/agrformet

Agricultural and Forest Meteorology 132 (2005) 286–304

* Corresponding author. Tel.: +49 6131 305 308;

fax: +49 6131 305 542.

E-mail address: simon@mpch-mainz.mpg.de (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 study

the 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 the

profile 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 gas

exchange 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 not

be 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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