Ecological Modelling 176 (2004) 291–312
A simple tropical ecosystem model of carbon,
water and energy fluxes
Silvia N. Monteiro Santos, Marcos Heil Costa∗
Department of Agricultural Engineering, Federal University of Viçosa, Av. P. H. Rolfs, s/n, Viçosa MG 36571-000, Brazil
Received 13 August 2002; received in revised form 14 October 2003; accepted 29 October 2003
Abstract
A simple tropical ecosystem model (SITE) was developed to study the response of tropical ecosystems to environmental
conditions. SITE fills the niche of an ecosystem model of intermediate complexity, sophisticated enough to be used to study
the fast dynamics of tropical ecosystems, while simple enough to be used to introduce the ecosystem modelling concepts to
students and inexperienced modellers. SITE is a dynamic model that incorporates several processes: canopy infrared radiation
balance, solar radiation balance, aerodynamic processes, canopy physiology and transpiration, balance of water intercepted by
the canopy, transport of mass and energy in the atmosphere, soil heat flux, soil water flux and carbon balance. It is structured
with one canopy layer and two soil layers, and is forced by hourly data of temperature, radiation balance, precipitation, humidity
and wind, and simulates the fluxes of CO2 , water and energy, as well as the dynamics of carbon in the ecosystem. For calibration
and validation, we used fluxes of CO2 , water vapour and sensible heat, measured at a primary evergreen forest site in Eastern
Amazonia, Brazil. Even though SITE is considerably less complex than other models of similar goals, it reproduces well the
hourly variability of the fluxes of CO2 and water vapour, and simulates the seasonal scale balance of those elements properly.
SITE is available as a 1200-line FORTRAN code, and as a computer spreadsheet. We believe the model will be useful to help
train the next generation of tropical ecologists in the use of ecosystem models.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Tropical forest; Ecosystem model; Carbon flux; Water vapour flux; Biosphere–atmosphere interaction
1. Introduction
The interannual and interdecadal variability in climate, and other changes in the environment, like rising atmospheric CO2 concentration and large-scale
changes in land cover, have motivated several studies
about the behaviour of ecosystems in a changing environment. Such studies lead to the development of
∗ Corresponding author. Tel.: +55-31-3899-1899;
fax: +55-31-3899-2735.
E-mail addresses: [email protected], [email protected]
(M.H. Costa).
several numerical models to understand the effects of
these changes on the carbon, water and energy fluxes
between the ecosystems and the atmosphere. These
fluxes are strongly coupled, so the integrated representation of the carbon, water and energy balance components is fundamental to the understanding of the
functioning of an ecosystem.
Hurtt et al. (1998) grouped terrestrial ecosystem
models developed to study global changes according
to their objectives: biogeochemical models (type I) like
CENTURY (Parton et al., 1988), BGC (Running and
Gower, 1991), and TEM (Raich et al., 1991; Melillo
et al., 1993); biophysical models (type II) like BATS
0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2003.10.032
292
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
(Dickinson et al., 1984), SiB (Sellers et al., 1986) and
LSX (Pollard and Thompson, 1995); and biogeographical models (type III) like DOLY (Woodward, 1987),
BIOME (Prentice et al., 1992; Haxeltine and Prentice,
1996), and MAPSS (Neilson, 1995). However, there
are integrated models that fit in more than one category, like IBIS (Foley et al., 1996), that would be classified as type I + II + III, or LSM (Bonan, 1996), type
I + II. Models whose objectives spread through more
than one category allow a deeper study of the interactions between biosphere and atmosphere, in particular
the several feedback mechanisms involved. The development of these models let several authors to discuss
the potential effects of the changes of the vegetation
cover on the regional and global climate, concentrating
on the dynamical evolution of the ecological, biophysical, biogeochemical and biogeographical processes
that happen in different time scales (Hurtt et al., 1998).
Process-based models, when used in conjunction
with data collected at micrometeorological sites, are
really useful tools to understand the functioning of an
ecosystem. However, most comprehensive ecosystem
models are extremely sophisticated, theoretically and
mathematically, and are usually seen as “black boxes”
by the users.
In this work we develop a model of intermediate
complexity to estimate carbon, water vapour and energy fluxes between a tropical forest ecosystem and
the atmosphere. In order to appropriately represent the
functioning of the ecosystem, the model considers the
main physical, chemical and biological processes involved in the mentioned fluxes. The model fills the
niche of an ecosystem model of intermediate complexity, sophisticated enough to be used to study the fast
dynamics of tropical ecosystems, while simple enough
to be used to introduce the ecosystem modelling concepts to students and inexperienced modellers.
2. Model description
The main purpose of Simple Tropical Ecosystem
Model (SITE) is to reliably simulate mass and energy
fluxes between the ecosystem and the atmosphere in a
simple way. According to the model classification of
Hurtt et al. (1998), SITE is classified as I + II type, the
same category of LSM (Bonan, 1996). Users of SITE
include researchers that want quick modelling analy-
ses but, due to its relative simplicity, it is a fine model
to be used in intermediary-level modelling courses of
the atmosphere-biosphere interaction.
The model reconciles simplicity with a rigorous
treatment of the several physical, chemical and biological processes involved: canopy solar and infrared
radiation balances, aerodynamic processes, canopy
physiology and transpiration, canopy water balance,
mass and energy transport in the atmosphere, soil
heat flux, soil water flux and carbon balance.
SITE is based on previously developed models,
mainly LSX (Pollard and Thompson, 1995), LSM
(Bonan, 1996), IBIS (Foley et al., 1996), and SiB2
(Sellers et al., 1996), being much simpler, though.
The strategy for simplification included the following
steps: (a) a careful study of these models and of the
most recent modelling literature; (b) among the several modelling alternatives considered, selection of
the simplest methodology used to simulate each process; (c) elimination of unnecessary model elements;
and finally (d) simplification of the mathematics and
numerical methods used. Steps (c) and (d) were repeated several times, advancing and retroceding in
the simplification process to evaluate the quality of
the simulation, compared against observed data, the
numerical stability of the solution, and the respect
to the physical principles. It was also assumed that
the model would be used in heavily instrumented
areas like micrometeorological sites, where there is a
good availability of data that could be used for model
calibration and validation.
Some intended characteristics and uses of the model
defined some important simplifications. For example,
the intended restricted use of the model for tropical regions allowed the elimination of snow and ice thermodynamics. The assumption that the model will be used
in instrumented areas, where the albedo is known, permitted important simplifications in the solar radiation
equations.
SITE is a dynamical point model that uses an integration time step (dt) of one hour, representing a point
of land totally covered by an evergreen broadleaf forest. Small modifications may be necessary for the representation of other tropical ecosystems.
The model is structured with one layer of canopy
and two layers of soil (Fig. 1). It is forced by eight
hourly data measured above the canopy: air temperature (T) and specific humidity (q), horizontal wind
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
56
that depends on the leaf and stem density. The components of the infrared radiation balance are shown in
Fig. 1. Iu , Is and Ig are the net infrared radiation flux
absorbed by leaves, stems and soil surface (W m−2 );
I↑ and I↓ are the upward and downward infrared radiation flux below tree level per overall area (W m−2 );
Ia is the downward infrared radiation flux from the
atmosphere (W m−2 ) and I is the net long wave radiation measured above the canopy. The solutions for the
calculation of infrared radiation balance for each component of the canopy are similar to those used in the
LSX model (Pollard and Thompson, 1995, Appendix
4, Eqs. (A18)–(A25)).
za
50
Ia
z1
height (m)
40
z12
30
layers u and s
z2
Iu
Is
I
I
20
10
0
293
Ig
zg
layer g
zd
layer d
2.2. Canopy solar radiation balance
Fig. 1. Schematic representation of the model and the infrared
radiation balance: u, s, g, and d, refer to leaves, stems, ground
soil layer and deep soil layer, respectively.
speed (u), incident short wave radiation (S), net long
wave radiation (I), albedo (α), precipitation (P) and
atmospheric pressure (Patm ). The model also uses parameters of the biophysical characteristics of the vegetation (Table 1). The main output variables of the
model are latent heat flux, sensible heat flux, water
vapour flux and net ecosystem production. The next
sections present a detailed description of each module
of the model.
2.1. Canopy infrared radiation balance
The infrared radiation is treated as if each vegetation
level is a semi-transparent plane with an emissivity
The solutions for the calculation of the canopy solar
radiation balance used in most models (e.g., Dickinson
et al., 1984; Sellers et al., 1986, 1996; Pollard and
Thompson, 1995; Bonan, 1996) are based on the individual representation of direct and diffuse fluxes, usually dividing calculations between visible and near infrared bands. These solutions are mathematically very
complex, and are beyond the intended uses of this
model. Considering that one of the objectives of this
work is the development of a simple model, that the
model is designed to be used in experimental areas
where the albedo is assumed to be known, and that
there is a significant uncertainty on the canopy transmissivity values, we propose a simple mathematical
solution of the problem. Assuming that all reflection
occurs on the top of the canopy, which requires a dense
evergreen forest, the equations for the canopy solar
radiation balance are independent of the calculations
of direct and diffuse solar radiation for the visible and
near infrared bands. Despite this simplification, the
Table 1
Vegetation biophysical parameters
Variable
Symbol
Used value
Source
Specific leaf area (m2 leaf kg−1 C)
Stem area index (m2 m−2 )
Top height of upper canopy (m)
Bottom height of upper canopy (m)
Atmospheric roughness length for the canopy (m)
Atmospheric roughness length for the soil surface (m)
Zero-plane displacement (m)
Intermediate height of upper canopy (m)
Sl
SAI
z1
z2
zoa
zog
d
z12
13
1
40
30
2.35
0.005
30.0
32.35
Medina and Cuevas (1996); Roberts et al. (1996)
Estimated
Measured on site
Measured on site
Shuttleworth (1988)
Shuttleworth et al. (1984)
Carswell et al. (2002)
d + zoa
294
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
S
Sr
z
u
za
logarithmic profile of
the wind – high z0
Su
Ss
u1
z1
z12
d
z2
u12
u2
u2g
Sg
Fig. 2. Schematic representation of the solar radiation balance.
proposed treatment conserves energy throughout the
canopy. The components of the canopy solar radiation balance are shown in Fig. 2, where Su , Ss and Sg
are the solar radiation flux absorbed by leaves, stems
and the soil surface (W m−2 ), respectively, and are
computed using Eqs. (1)–(3):
Su = (1 − α − τu )S
(1)
Ss = τu S(1 − τs )
(2)
Sg = τu τs S
(3)
where Sr is the solar radiation reflected by the canopy
(Sr = αS), τ u and τ s are the leaf and stem transmissivities.
This assumption implies that the radiation reflected
by the ground is negligible, which usually requires
that Sg S (τ u τ s ∼ 0). The more open the canopy
is, and the higher the ground albedo is, the less valid
Eqs. (1)–(3) are. However, this assumption may also
be valid in ecosystems other than a dense tropical
forest. For example, if the ground albedo is very
low (<0.1, like in a wetland) and the canopy is relatively open (τ u τ s ∼ 0.1), the error in the radiation
absorbed by the soil surface is still on the order of
1% of S.
2.3. Aerodynamic processes
Following several authors (Pollard and Thompson,
1995; Sellers et al., 1996; Campbell and Norman,
1998), we assumed the vertical wind profile shown
in Fig. 3. Between the levels za and z1 , airflow is as-
z0a1
exponential
profile of the
wind
logarithmic profile of
the wind – low z0
z02g
0
u
Fig. 3. Schematic representation of the wind profile.
sumed to be predominantly turbulent with a high value
of aerodynamic roughness, with the horizontal wind
speed decreasing logarithmically from za to z1 . The
wind profile decreases exponentially from z1 downwards to z2 , and a logarithmic wind profile is assumed
between the levels z2 and the surface, with a zero-plane
displacement equal to zero and a low value of aerodynamic roughness, characteristic of the soil surface
(Table 1). These conditions imply a wind speed nearly
constant between z2 and z = 0 levels.
Using diabatic correction factors to account for
thermally induced turbulence (Campbell and Norman,
1998, pp. 96–97), the wind speed at different levels
can be calculated using Eqs. (4)–(8). In the regions
where the wind profile is logarithmic, if the wind
speed in the upper part of the profile, and the values
of d and zo are known, the friction velocity of the
profile (a1 or 2g) is determined by Eq. (4) or (8).
Subsequently, wind speed at any height in the region
(e.g., z1 ) can be calculated by Eq. (5). In the region
where the wind profile is exponential, if the wind
speed at the top of the region and the attenuation
coefficient are known, the speed at any level can be
calculated by Eqs. (6) and (7).
Friction velocity in the profile a1 :
0.41u
u∗a1 =
[ln((za − d)/zoa ) + ψma1 ]
(4)
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
Wind speed at level z1 :
u∗
u1 = a1 [ln((z1 − d)/zoa ) + ψma1 ]
0.41
295
q12
(5)
ru=1/su
Wind speed at level z12 :
z12
−1
u12 = u1 exp a
z1
Wind speed at level z2 :
z2
u2 = u1 exp a
−1
z1
Friction velocity in the profile 2g :
0.41u2
u∗2g =
[ln(z2 /zog )ψm2g ]
(6)
rs
(7)
qu
(8)
Fig. 4. Schematic representation of the leaf transpiration.
2.4. Canopy physiology and transpiration
This module of SITE is based on the equations
proposed by Farquhar et al. (1980), Farquhar and
Sharkey (1982), Collatz et al. (1991, 1992), Sellers
et al. (1996), Foley et al. (1996) and Campbell and
Norman (1998).
The transpiration per unit area of leaf is calculated
dividing the difference of the air specific humidity by
the resistance to the water vapour flux (Fig. 4).
(qu − q12 )LAI
(1/su ) + (1/gs )
qu – q12
rs + ru
rs=1/gs
where a is the wind coefficient for a forest and ψmi
is diabatic correction factors for momentum, where i
denote the a1 and 2g profiles.
The turbulent transfer coefficient atmosphere–
atmosphere (σ a , m s−1 ) is calculated integrating the
flux between the levels z12 and za (Fig. 6) (Campbell
and Norman, 1998, pp. 98). The soil–atmosphere turbulent transfer coefficient (σ g ) is calculated similarly.
The diffusive transfer coefficients between leaves and
the atmosphere (su , m s−1 ) and between stems and the
atmosphere (ss , m s−1 ) are calculated using empirical
approximations based on wind tunnels experiments
(Campbell and Norman, 1998, pp. 101).
Etu =
Etu =
(9)
where Etu is the transpiration (kg H2 O m−2 s−1 ) and
gs is the canopy conductance.
In Fig. 4, the canopy resistance (rs = 1/gs ) is controlled by the degree of opening of the stomata, which
is associated to several factors like CO2 concentration, temperature, humidity, and the whole physiological process in the plant. The canopy boundary layer
resistance (ru = 1/su ) depends directly on the wind
and on leaf characteristics, such as structure, size and
shape, as described in Section 2.3. Etu assumes only
positive values, i.e., Etu = 0 if q12 > qu .
The stomata are parameterised by a connected
photosynthesis–conductance scheme, which considers the diffusion of CO2 between leaf and air. The
photosynthesis rate is simulated according to the Farquhar equations (Farquhar et al., 1980; Farquhar and
Sharkey, 1982). CO2 diffusion from atmosphere to
chloroplasts does not occur as a gas, but in liquid
phase, as CO2 molecules are dissolved in water in the
cell vicinity (Fig. 5). The CO2 diffusion through the
stomata is described by the equations of Collatz et al.
(1991).
The net photosynthesis rate (An ) or dry matter
production is the balance between the processes of
absorption (Ag ) and release of CO2 (Ru ). The model
considers that the gross photosynthesis (Ag ) is the
minimum between two potential capacities (Je and Jc ):
Ag = min(Je , Jc )
(10)
The gross photosynthesis rate limited by light (mol
CO2 m−2 s−1 ) is expressed as:
CO2i − Γ∗
Je = α3 APAR
(11)
CO2i + 2Γ∗
296
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
active radiation (mol photons m−2 s−1 ). The gross
photosynthesis rate limited by the activity of the
Rubisco enzyme (mol m−2 s−1 ) is given by:
CO2a
rb=1/gb
Vm (CO2i − Γ∗ )
CO2i + Kc (1 + ([O2 ]/Ko ))
Jc =
An
CO2s
rs=1/gs
1.6 rs
CO2i
Fig. 5. Representation of the net CO2 flux through the plant
stomata.
where Γ∗ = [O2 ]/2τ is the compensation point for
gross photosynthesis (mol mol−1 ); [O2 ] is the oxygen
concentration, equal to 0.210 mol mol−1 ; CO2i is the
CO2 concentration in the intercellular spaces of the
leaves (mol mol−1 ); α3 is the intrinsic quantum efficiency for C3 plants (mol CO2 mol−1 photons); τ is
the CO2 /O2 ratio of kinetic parameters; and APAR
is the density flux of the absorbed photosynthetically
(12)
where Kc and Ko are Michaelis constants, the first
constant is used to fix CO2 and the second to inhibit
oxygenation (mol mol−1 ), respectively.
The leaf respiration (mol CO2 m−2 s−1 ) is calculated as:
Ru = γVm Tm
(13)
where γ is the leaf respiration coefficient of the Rubisco enzyme (Collatz et al., 1991). The maximum Rubisco enzyme capacity (Vm , mol CO2 m−2 s−1 ) for the
carboxylase function is calculated through the Vmax
parameter and attenuated by soil moisture stress (St)
and temperature stress (Tvm ).
Vm = Vmax Tvm St
St =
1 − exp(Stfac awc)
1 − exp(Stfac )
(14)
(15)
where Stfac is the coefficient for soil moisture stress
and awc is the available water content in the soil. The
physiological parameters used by the model are shown
in Table 2.
Table 2
Physiologic parameters used in the SITE model, where the values of τ m , Kc , Ko , and Tvm are obtained from the respective equation, and
the other values (Vmax , b, m, α3 , γ) are obtained from the literature and optimised during the calibration process
Variable
Symbol
CO2 /O2 ratio of kinetic parameters
τ
Michaelis constants (fix CO2 ) (mol mol−1 )
Kc
Michaelis constants (inhibit O2 ) (mol mol−1 )
Ko
Factor of temperature stress (K)
Tvm
Maximum Rubisco enzyme capacity (mol CO2 m−2 s−1 )
Coefficient for minimum stomatal conductance when net
photosynthesis is zero broadleaf trees (mol CO2 m−2 s−1 )
Coefficient for stomatal angular conductance for broadleaf trees
Intrinsic quantum efficiency for C3 plant (mol CO2 mol−1 photons)
Leaf respiration coefficient of the broadleaf trees
Vmax
b
75 × 10−6
0.010
m
α3
γ
10
0.060
0.0150
Tf = Tu − 273.16. Source: Collatz et al. (1991, 1992); Leuning (1995).
Used value
1
1
4500exp −5000
−
288.16
Tf
1
1
1.5 × 10−4 exp 6000
−
288.16
Tf
1
1
0.25 exp 1400
−
288.16
Tf
exp[3500((1/288.16) − (1/Tf ))]
[1 + exp(2 − 0.40Tf )][1 + exp(0.40Tf − 20)]
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
297
2.5. Balance of water intercepted by the canopy
T
q
The balance of water stored in the leaves (Wu )
and stems (Ws ) (kg H2 O m−2 ) surfaces is described
through linear differential equations (Pollard and
Thompson, 1995):
dWu
Wu
= Pu − Eiu −
dt
τdrip
(16)
dWs
Ws
= Ps − Es −
dt
τdrip
(17)
E
H
Eu Hu
Tu Wu
Ts Ws
T12
q12
ss
Eg
Hg
where τ drip is a time constant for leaf and stem liquid
drip (12 h); Wu /τ drip (or dripu ) represents the dripping
of water stored on the leaves; and Ws /τ drip (or drips )
represents the dripping of water stored on the stems.
The precipitation rate intercepted by leaves (Pu ) and
stems (Ps ) is given by:
Pu = P(1 − e−0.5LAI )
(18)
Ps = P(1 − e−0.5SAI )
(19)
where P is the pluviometric precipitation rate measured above the canopy (kg H2 O m−2 s−1 ).The evaporation of the water intercepted by the leaves, Eiu , and
stems, Es (kg H2 O m−2 s−1 ) are given by:
Eiu = fwetu su (qu − q12 )LAI
(20)
Es = fwets ss (qs − q12 )SAI
(21)
where fwetu = Wu /Wumax is the wet fraction of upper canopy leaf area and fwets = Ws /Wsmax is the wet
fraction of upper canopy stem area. When qu < q12 ,
dew is allowed to condense. In this case, the water flux
is not proportional to the wet fraction of leaves/stems,
and the condensation is not allowed to exceed the storage capacity of leaves and stems. In Eqs. (20) and
(21), it is assumed that only the upper part of leaves
and stems are wet.
The leaf evapotranspiration flux (Eu ) is equal to the
sum of evaporation of the water stored on the leaf
surface and transpiration.
Eu = Etu + Eiu
su
Es Hs
σa
(22)
Maximum interception of water by the canopy leaf
area, Wumax , and by the stems, Wsmax (kg H2 O m−2 ),
are calculated assuming that the maximum height of
water stored in the leaves or stems is 0.1 mm, or 0.1 kg
per m2 of leaf.
Gg
σg
Tg
qg
Fig. 6. Schematic representation of the mass and energy transport
in the atmosphere.
2.6. Water and energy transport in the atmosphere
The parameterisations of mass and energy transport
in the biosphere–atmosphere are based on the mass
and energy conservation principles. Prognostic temperature of leaves (Tu ), stems (Ts ), soil surface (Tg ),
and air in the middle of the leaves (T12 ) are calculated
through the balance of energy, according to Fig. 6 and
Eqs. (23)–(25).
(Ci + cw Wi )
dTi
= Si + I i − H i − L v Ei
dt
dTg
= Sg + Ig − Hg − Lv Eg − Gg
dt
dT12
C12
= Hg + H u + H s − H a
dt
Cg
(23)
(24)
(25)
where the subscript i denote leaves (i = u) or stems
(i = s); cw is the specific heat of water; Lv is the
latent heat of vaporisation of water; Lv Ei is the latent
heat flux (W m−2 ); Ci is the heat capacity of leaves
or stems (J m−2 K−1 ); Cg is the heat capacity of the
top soil layer (J m−2 K−1 ) and Gg is the heat flux into
the soil, calculated in Section 2.8.
298
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
The calculation of sensible heat flux requires the
computation of the components of the canopy Hu and
Hs , of the soil, Hg and of the atmosphere, H
Hu = ρcp su (Tu − T12 )2LAI
(26)
Hs = ρcp ss (Ts − T12 )2SAI
(27)
H = ρcp σa (T12 − T)
(28)
Hg = ρcp σg (Tg − T12 )
(29)
Pg
SR
zg
+ss (Ts − T12 )2SAI = 0
(30)
Air specific humidity inside of the canopy, q12
(kg kg−1 ), is calculated using the principle of water
mass conservation:
dq12
(31)
= Eg + Eu + Es − E
dt
where Eg = σg ρ(qg − q12 ) is the evaporative flux of
water from the soil, and E = σg ρ(q12 − q) is the total evaporation flux from canopy into the atmosphere.
Neglecting the variation of specific humidity of the air
inside of the canopy as a function of time, the following solution is given:
eg
Fd
ed
zd
Neglecting the heat capacity of the air inside of the
canopy (C12 ), substituting Eqs. (26)–(29) in (25) and
dividing by ρcp , Eq. (25) can be rewritten as:
σa (T − T12 ) + σg (T12 − Tg ) + su (Tu − T12 )2LAI
Fg
D
Fig. 7. Schematic representation of the soil water flux.
to satisfy the conditions above. Sensitivity tests were
conducted to verify the numeric stability of the sensible heat flux of the soil (Hg ), and the thickness eg =
7.5 cm was chosen.
Obviously, the use of more soil layers would improve the representation of the physical processes in
the soil, but it leads to an undesirable additional complexity. Finally, we should point out that the 7.5 cm
layer g includes, in addition to the soil, a thin layer of
litter.
The balance of water stored in the layers g and
d of the soil is calculated applying the water mass
conservation in each layer
(32)
dWg
= Fg − Fd − Eg
dt
(33)
where qg is the specific humidity of air in the soil
pores (kg kg−1 ).
dWd
= Fd − D − Etu
dt
(34)
2.7. Soil water flux
where Fg is the infiltration into the layer g; Fd is the
infiltration into the layer d; and D = 1 × 10−8 mm s−1
is the deep drainage below the layer d (boundary condition).
The precipitation rate intercepted by the soil (Pg ,
kg H2 O m−2 s−1 ) reaches the soil through direct precipitation through canopy openings (P − Pu − Ps )
and through dripping from leaves and stems (Bonan,
1996).
σa (q − q12 ) + σg (qg − q12 ) + Eu + Es = 0
The treatment of soil physical processes in SITE
requests the division of the soil in two layers. Considering the soil water flux, the ground layer g provides
water to free evaporation, while the deep layer d determines the maximum depth where the root system
extracts water for transpiration (Fig. 7). Considering
the soil heat flux (described in Section 2.8), the temperature of the layer g depends mainly on its radiation
balance, while the layer d, deeper, works as a large
heat reservoir. These combined characteristics require
a layer g as thin as possible, respected the numerical stability of the model, and a layer d thick enough
Pg = P − Pu − Ps + dripu + drips
(35)
where dripu = Wu /τdrip represents the dripping of
water from leaves and drips = Ws /τdrip represents the
dripping of water from stems.
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
The fraction of soil moisture in the layers (θ i , m3
H2 O m−3 soil) is expressed as a function of the water
mass stored in the respective soil layers (Wi , kg H2 O
m−2 ):
θi =
Wi
ei ρw
(36)
where the subscript i represents the ground layer (i =
g) or the deep layer (i = d).
The capacity of the roots to remove water from the
soil depends on soil type and on a complex interaction
of forces, known as water matric potential in the soil
(ψ). The hydraulic properties (hydraulic conductivity
and matric potential) are calculated from the average
moisture content in each layer:
ψi = ψe xi−b
(37)
ki = ks xi2b+3
(38)
where ks is the saturation hydraulic conductivity
(mm s−1 ); ψe is the air entry water potential (mm);
xi = θi /θ s is the relative soil saturation in the layers g
and d; and θ s is the saturation water content.
Moisture content at field capacity (θ cc ) and wilting point of the soil (θ WILT ) are calculated inverting
Eq. (37) and setting ψ to 3.30 m (1/3 atm) and ψ to
150 m (15 atm), respectively.
The parameterisations of infiltration and runoff
follow Bonan (1996), where the maximum infiltration velocity of the soil (Imax ) is expressed from
Darcy’s law, at saturation conditions (Entenkhabi and
Eagleson, 1989).
Imax = ks (vxg − v + 1)
(39)
where v = −bψe /103 eg is an infiltration parameter.
Fg (mm s−1 ), the effective infiltration of water into
the soil, is the minimum between Imax and Pg and
SR = Pg − Imax is the surface runoff. The soil water
299
flux between layers d and g is calculated using the
expression obtained by Bonan (1996), pp.98).
2.8. Soil heat flux
The temperature of the soil g layer is calculated
as a function of the energy balance at the surface
(Section 2.6). Soil temperature in the d layer is calculated as a prognostic variable (Bonan, 1996) using
Cd
Td − Tg
dTd
=
= Gg
dt
(eg /2κg ) + (ed /2κd )
(40)
where κ is the soil thermal conductivity (W m−1 K−1 ).
The volumetric heat capacity of the soil (J m−2 K−1 )
depends on the volumetric fractions and the specific
heat capacity of each soil component (Campbell and
Norman, 1998):
Cg = ρm eg φm cm + mo φo co + cw wg
(41)
Cd = ρm ed φm cm + cw wd
(42)
where m, o, w are indexes related to the minerals,
organic materials and water present in the soil; mo =
2(Lu + Ls ) is the mass of organic matter of the soil
(kg organic matter m−2 ), as seen in Section 2.9—it is
assumed here that carbon accounts for half of the dry
biomass; and φm = 1 − φ is the volumetric fraction
of soil minerals. The thermal properties of the several
soil components are in Table 3.
Following Campbell and Norman (1998), soil thermal conductivity in the layer g, κg , and in the d layer,
κd (W m−1 K−1 ), is computed by the normalised sum
of the products of the volumetric fractions and the
thermal conductivities of the several soil components:
the mineral components (m), water (w) and gas phase
component (air).
κi =
θi ξw κw + φair ξair κair + φm ξm κm
ei (θi ξw + φarg ξi + φm ξm )
(43)
Table 3
Soil thermal properties and other values used for calculating the thermal capacity of the soil
Material
Density,
ρ (kg m−3 )
Specific heat capacity,
c (J kg−1 K−1 )
Thermal conductivity,
κ (W m−1 K−1 )
Correction factor, ξ
Organic matter (o)
Soil minerals (m)
Water (w)
Air
1300
2650
1000
–
1.92 × 103
0.87 × 103
4.48 × 103
–
–
2.50
0.596
0.025
–
0.54
0.92
1.75
Values derived from Campbell and Norman (1998), pp. 118.
300
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
where φair = φ − φi is the air volumetric fraction in
the g and d layers; ei is the thickness of the g and d
layers.
CO2a
NEE
2.9. Carbon balance
An
The parameterisation of the carbon balance, adapted
from the IBIS model (Foley et al., 1996), calculates the
carbon flux through prognostic equations. The carbon
fixed by photosynthesis can be allocated in four different reservoirs of the plants: leaves, stems, fine roots
and coarse roots (Eq. (44)). The amount of carbon allocated to each canopy reservoir is calculated using a
linear differential equation, assuming fixed fractions of
allocation in each reservoir and fixed residence times.
Fig. 8 presents a schematic representation of the distribution of carbon reservoirs and main fluxes.
dCi
Ci
= ai NPP −
(44)
dt
τi
where the subscript i can be equal to u, s, f and r,
that denote leaves, stems, fine roots and coarse roots,
respectively. The sum of the au , as , af and ar is equal
to 1. The initial values of the amount of carbon in each
reservoir are shown in Table 4.
The net primary production (NPP, kg C m−2 s−1 )
is expressed as a function of the gross photosynthesis
(Ag , mol CO2 m−2 s−1 ) and the canopy autotrophic
respiration (leaves, stems and roots).
NPP = 0.012(1 − n) (Ag − Ru − Rs − Rf − Rr )dt
(45)
where n = 0.3 is the fraction of carbon lost due
to growth (Amthor, 1984); 0.012 is the conversion
Cu Cs
Rsoil
Cs
Cu Cf
Fig. 8. Schematic representation of the carbon reservoirs and fluxes.
The direction of the arrows represents the positive direction of the
flux.
factor from mol CO2 to kg C; Ru is the respiration
rate of the leaves (mol CO2 m−2 s−1 ); Rs = 3.17 ×
10−10 Cs f(Ts )λ is the respiration rate of the stems (mol
CO2 m−2 s−1 ); Rf = 3.17×10−8 Cf f(Tg +Td /2) is the
respiration rate of the fine roots (mol CO2 m−2 s−1 );
Rr = 3.17 × 10−10 Cr f(Tg + Td /2)λ is the respiration
rate of the thick roots (mol CO2 m−2 s−1 ); λ = 0.10
is the sapwood fraction of the stem and coarse root
biomass, Cs , Cf and Cr are the carbon mass stored in
stems, fine roots and coarse roots.
The leaf area index (LAI) is calculated as a function
of the carbon biomass in the leaves (Cu ) and the leaf
specific area (Sl ) (Table 1).
LAI = Cu Sl
(46)
Table 4
Initial values of the storage parameters of carbon in the canopy and of carbon mass in litter
Reservoir
(τ)a
Residence time
Gross photosynthesis allocation fraction (a)a
Carbon mass (L, D)a
Carbon biomass (C)
a
b
c
Kucharik et al. (2000).
Calibrated to obtain the initial value of LAI.
Measured on site.
Leaves (u)
Stems (s)
Fine roots (f)
Coarse roots (r)
1 year
0.45
0.50
0.360b
25 years
0.40
0.25
18.000a
1 year
0.10
0.44
0.100c
25 years
0.05
0.135
0.750c
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
The soil carbon module is based on the decomposition
of leaves and stems by bacteria, and is a function of soil
temperature, soil humidity and carbon mass in the litter, being similar to the IBIS model, with some modifications. The organic matter decomposition by the soil
respiration is proportional to the litter mass. The processes of soil carbon decomposition by heterotrophic
respiration are described by Eqs. (47) and (48).
dLi
Ci
− f g g g hi Li
=
dt
τi
(47)
(fg + fd ) (gg + gd )
dDi
Ci
=
−
h i Di
dt
τi
2
2
(48)
where Li is the carbon mass of leaf (i = u) or stem
(i = s) litter; Di is the carbon mass of dead fine root
(i = f) and coarse root (i = r) (kg C m−2 ) (the initial
values of carbon mass in the soil carbon reservoirs
are shown in Table 5); hi is the respiration rate of
leaves (i = u), stems (i = s), fine roots (i = f) and
coarse roots (i = r) litter (kg C kg−1 C s−1 ); f(Ti ) =
2((Ti −283.16)/10) is the soil temperature function in the
g and d layers (dimensionless); gg = 0.25 + 0.75xi
is the soil moisture function in the g and d layers
(dimensionless).
The parameterisation of the soil heterotrophic respiration (RH ) is solved by the sum of the products of the
temperature and moisture functions, and the decomposition rate for each reservoir of soil organic matter.
RH = fg gg (hu Lu
+ hs Ls ) +
(fg + fd ) (gg + gd )
(hf Df + hr Dr )
2
2
(49)
Table 5
Hydraulic properties of the soil at the micrometeorological site in
Caxiuanã, Pará State, Brazil (Cosby et al., 1984)
Variable
Symbol
Exponent of the moisture release
equation
Air entry water potential (mm)
Porosity (m3 m−3 )
Humidity content at field capacity
(m3 m−3 )
Wilting point of the soil (m3 m−3 )
Saturation water content (m3 m−3 )
Saturation hydraulic conductivity
(mm s−1 )
b
Used value
301
Finally, the net ecosystem production (NEP) is expressed by the difference between RH and the net
primary production (NPP). A negative value of NEP
indicates assimilation of carbon by the ecosystem.
NEP = RH − NPP
(50)
3. Description of the experimental area and site
specific biophysical parameters
The data used for the initial calibration and validation of SITE are part of the research conducted by the
large-scale biosphere–atmosphere experiment in Amazonia (LBA), which were collected at 30-min intervals
between April and September 1999, in the experimental area of the primary tropical evergreen forest in the
Caxiuanã Forest Reserve (latitude 01◦ 42 30 S, longitude 51◦ 31 45 W, altitude 60 m). The reserve has an
area of approximately 33,000 ha and is located about
400 km west of Belém, Pará, Brazil.
A series of 28 days of data, collected during the
dry season, from August 29 to September 25, 1999
(241–268 Julian day), was used to calibrate the model
and data collected from April 16 to May 27, 1999
(106–147 Julian day), a total of 41 days during the wet
season, were used to validate it. The measured data
used for calibration and validation of the model were
latent heat, sensible heat, and CO2 fluxes.
Tables 5 and 6 present some site-specific biophysical parameters. The distribution of the textural composition of the soil (sand, clay and silt fractions are
20, 37 and 23%, respectively) was obtained by Ruivo
et al. (2001). The hydraulic parameters of the soil
(Table 5) were calculated using Cosby et al. (1984)
and the biophysical parameters used for the studied
area are shown in Table 6.
4. Results and discussion
9.066
4.1. Sensitivity test
ψe
φ
θ cc
θ WILT
θs
ks
223.9
0.477
0.36
0.23
0.477
0.0032
Sensitivity analyses were performed to determine
the relative importance of variation in the main factors
controlling carbon, water vapour and energy fluxes in
a tropical rain forest. Below, we present results from
the analyses that showed the highest sensitivity for
CO2 and water vapour fluxes.
302
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
Table 6
Site-specific biophysical parameters used in the simulation
Variable
Symbol
Used value
Source
Height of data measurement (m)
Thickness of the superficial layer (m)
Thickness of the deep layer (m)
Depths of the center of the g layer (m)
Depths of the center of the d layer (m)
Typical dimension of leaves
Typical dimension of stems
Absorbed photosynthetically active radiation (W m−2 )
Leaves transmissivity
Stems transmissivity
za
eg
ed
zg
zd
du
ds
APAR
τu
τs
56
0.075
3.425
0.0375
1.75
0.072
0.10
0.44325 S
0.16
0.19
Measured on site
Section 2.7
Measured on site
eg /2
(eg + ed )/2
Measured on site
Measured on site
Oliveira (2000)
Moura et al. (2000)
Moura et al. (2000)
The CO2 flux simulated by the model is most
sensitive to the parameter Vmax (see Eq. (14)). We
run several simulations varying Vmax from 50 to
95 ␮mol m−2 s−1 , keeping the other parameters at
their baseline values. The CO2 flux calculated by the
model for two values of Vmax are plotted in Fig. 9,
along with the observed profile of CO2 . Using the
lowest Vmax (50 ␮mol m−2 s−1 ) underestimates CO2
flux, especially during night time, while the highest Vmax (95 ␮mol m−2 s−1 ) overestimates CO2 flux
(not shown). The optimum value found for Vmax was
75 ␮mol m−2 s−1 .
The water vapour flux simulated by the model is
most sensitive to the coefficient for stomatal angular
conductance, m (Table 2). We run several simulations
varying m from 5 to 15, keeping the other parameters at
their baseline values. The water vapour flux calculated
by the model for two values of m are shown in Fig. 10,
along with the observed fluxes. For m = 5, the model
underestimates the water vapour flux, while m = 10
results in a better fit between simulated and observed
data.
4.2. Carbon flux
The simulated mean values of the carbon flux (NEP)
from April 16 (106) to May 27 (147), used in the validation, and from August 29 (241) to September 25
(268) of 1999, used in the calibration of the model,
were −0.69 and −0.79 kg C per m2 per year, respectively. These results present an error of −6.5% for the
validation period and 6.8% for the calibration period,
when compared to the observed mean values. (In this
study, negative values of NEP refer to assimilation
-2
-1
CO2 Flux (kgC m yr )
15
10
5
0
-5
-10
-15
255
256
257
258
259
260
261
262
-6
Day of the year
Simulated(Vmax=75.10-6 )
Simulated(Vmax=50.10 )
Observed
Fig. 9. Sensitivity analyses for Vmax (maximum Rubisco enzyme capacity) parameter on CO2 flux.
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
303
-2
-1
Water vapour flux (kg H2 O m h )
1,00
0,80
0,60
0,40
0,20
0,00
255
256
257
258
259
Day of the year
260
261
262
Simulated(m=10)
Simulated(m=5)
Observed
Fig. 10. Sensitivity analyses for m (coefficient for stomatal angular conductance for broadleaf trees) parameter on water vapour flux.
of carbon and positive indicates release to the atmosphere).
Carswell et al. (2002) found an observed value
of −0.54 kg C per m2 per year for the site in study,
based on a longer data collection period; Malhi et al.
(1998) found a NEP of −0.57 kg C per m2 per year for
Cuieiras, Manaus, for the period from 13 to November 21, 1995; Rocha et al. (1996), doing simulations
with the SiB2 model, found −0.63 kg C per m2 per
year in the Ducke Reserve, Manaus, for the period
from September of 1983 to August of 1985.
According to Goulden et al. (1996), the eddy correlation system does not provide good values of CO2
during calm nights. In addition, Miller et al. (2004)
found a strong dependence between nighttime NEP
and turbulence above the canopy, showing a reduction in NEP for friction velocity (u∗ ) smaller than
0.2 m s−1 . Therefore, in a few comparisons in this
study, the raw CO2 data collected during the night
were eliminated when u∗ < 0.2 m s−1 . The root mean
square error (RMSE) for raw and filtered CO2 flux data
are 0.15 and 0.13 kg C per m2 per year, respectively.
In the remaining discussion in this paper, the elimination of data is not considered except when noted.
Figs. 11 and 12 show the profile of selected processes associated to the CO2 flux, and simulated and
observed NEP. In Figs. 11a and 12a, Je has a null
value during the night, and a maximum close to noon,
local time. On the other hand, Jc presents a maximum value during the night, due to the dynamics of
carbon through the stomata. In addition, the inverse
dependence of Kc and Ko with air temperature also
contributes, in a secondary way, for the profile of Jc .
Figs. 11b and 12b show the net primary productivity (NPP) and the soil heterotrophic respiration (RH ).
While NPP basically follows the Ag pattern, in the
peaks during the afternoon it is possible to see the
dependence of RH with the soil temperature. The difference between RH and NPP is the net ecosystem
production (Figs. 11c and 12c), where negative values
indicate assimilation of CO2 by the ecosystem. The
model does not simulate the transport of CO2 in the
atmosphere—only the production of CO2 due to the
carbon balance is simulated. Thus, in spite of the reproduction of the general profile of the CO2 flux by
the model, some variations at the hourly scale cannot
be captured.
Fig. 11 shows that the photosynthesis rate rises
quickly after sunrise. In the second half of the morning, the activity of the Rubisco enzyme starts to limit
the photosynthetic activity, which reaches its peak before noon. The peak of the simulated NEP oscillated
between −7 and −8 kg C per m2 per year. Carswell
et al. (2002) obtained an average peak of −7.2 kg C
per m2 per year in the Caxiuanã forest for the period
from 108 to 114 for the same year in study, with peak
time at 11:00 a.m., local time. Malhi et al. (1998) observed an average peak of −6.8 kg C per m2 per year
in Cuieiras, central Amazonia. Williams et al. (1998),
using the SPA model (soil–plant–atmosphere canopy
304
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
Gross photosynthesis (kgC m
-2
-1
yr )
25
20
15
10
5
0
109
110
111
(a)
112
113
114
115
116
Ag
Je
Jc
Day of the year
12
-1
CO2 flux (kgC m yr )
10
-2
8
6
4
2
0
-2
109
110
111
(b)
112
113
114
115
116
RH
NPP
Day of the year
-2
-1
CO2 flux (kgC m yr )
15
10
5
0
-5
-10
-15
109
(c)
110
111
112
113
Day of the year
114
115
116
Simulated
Observed
Fig. 11. Profile of the processes associated to the observed and simulated CO2 fluxes: (a) gross photosynthesis (Ag) and its components
Je and Jc ; (b) soil heterotrophic respiration (Rsoil ) and net primary production (NPP); and (c) net ecosystem exchanges (NEP) from April
19 to 26 (109–116) of 1999. The negative sign corresponds to the accumulation of CO2 in the ecosystem.
305
25
Gross photosynthesis (kgC m
-2
-1
yr )
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
20
15
10
5
0
124
125
126
127
128
129
Ag
Je
Jc
Day of the year
(a)
12
-1
CO2 flux (kgC m yr )
10
-2
8
6
4
2
0
-2
124
125
126
127
128
RH
NPP
Day of the year
(b)
129
10
-2
-1
CO2 flux (kgC m yr )
15
5
0
-5
-10
-15
124
(c)
125
126
127
Day of the year
128
129
Simulated
Observed
Fig. 12. Profile of the processes associated to the observed and simulated CO2 flux: (a) gross photosynthesis (Ag) and its components Je
and Jc ; (b) soil heterotrophic respiration (Rsoil ) and net primary production (NPP); and (c) net ecosystem exchanges (NEP) from May 4
to 9 (124–129) of 1999. The negative sign corresponds to the accumulation of CO2 in the ecosystem.
306
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
model), simulated peaks between −7.6 and −9.5 kg C
per m2 per year.
Correlation coefficient between simulated and observed hourly CO2 fluxes for Caxiuanã Reserve in the
period from April 16 to May 27 (106–147) of 1999
is 0.88. Despite the good correlation, the model is
not able to simulate high values of CO2 flux during
night time (Fig. 12). Williams et al. (1998), using the
SPA model, obtained a correlation coefficient of 0.73
between simulated and observed hourly fluxes, while
Zhan et al. (2003), using two versions of the SSiB
model, obtained hourly fluxes correlation coefficients
of 0.73 and 0.79.
The average conditions around noon indicate a
slight closing of the stomata and the decrease of the
gross photosynthesis, causing a reduction in the loss
of water by evaporation and in the CO2 assimilation
rates. It is observed that between peak time and late
afternoon (period called the dark phase) the gross
photosynthesis fluxes are no longer determined by
the solar energy, but are limited by the activity of the
Rubisco enzyme. In late afternoon, the CO2 assimilation becomes limited by solar energy again (Figs. 11a
and 12a).
NPP has a mean value of approximately 2 kg C per
m2 per year (Figs. 11b and 12b). The NPP simulated
by the model is close to the simulated by Kucharik
et al. (2000) who, using the IBIS model, obtained a
mean value of 1.9 kg C per m2 per year for tropical
rainforests. In Figs. 12a and 12b, some oscillations in
the peaks of Ag and NPP close to noon can be verified in days 125 and 129, consequently altering the
NEP profile (Fig. 12c). These oscillations are related
to the presence of cloudiness (not shown), demonstrating consistency in the simulated values of Je . Clark
et al. (2001) reviewed the estimates of NPP from 39
tropical forests experimental sites around the world. In
these sites, the lower limit of NPP ranged from 0.17 to
1.18 kg C per m2 per year, while the upper limit ranged
from 0.31 to 2.17 kg C per m2 per year. In Amazonia,
NPP estimates ranged from 0.67 to 0.92 kg C per m2
per year (lower limit) and 1.22 to 1.68 kg C per m2 per
year (upper limit).
Our simulated values of soil heterotrophic respiration (averaging 1.3 kg C per m2 per year) are also
close to the observed values. Trumbore et al. (1995)
and Davidson et al. (2000) obtained mean values of
1.5 and 2 kg C per m2 per year in the Victoria farm,
Paragominas, Eastern Amazonia. Most of the references available in the literature report the total soil
respiration (autotrophic and heterotrophic). Carswell
et al. (2002) verified a seasonal variation for the night
respiration from 2.7 to 3.5 kg C per m2 per year, for
the Caxiuanã Reserve Forest. Rocha et al. (1996), using the SiB2 model, simulated a mean value of approximately 2.4 kg C per m2 per year in the Ducke
Reserve, corresponding to the period from September
1983 to August 1985, having also verified that the soil
contributes with approximately 70–80% of the total
carbon emitted to the atmosphere. Malhi et al. (1998)
obtained a mean value around 2.5 kg C m−2 h−1 for
the soil respiration in Cuieiras, Manaus. Grace et al.
(1996) reported values of night respiration ranging
from 2.3 to 2.6 kg C per m2 per year in the Jaru Reserve, Rondônia.
Fig. 13 shows the variation of the simulated canopy
conductance through the period 109–116, with mean
peak around 0.8 mol H2 O m−2 s−1 , which is similar
to the value observed in the same site by Carswell
et al. (2002), who found a maximum peak ranging
seasonally from 0.7 to 0.8 mol H2 O m−2 s−1 . Grace
et al. (1996) reported gs ranging from 0.4 to 1.0 mol
H2 O m−2 s−1 in the morning, and a decrease along
the day in the Jaru Reserve, Rondônia, in 1993.
However, Roberts et al. (1996), obtained peak values ranging from 0.35 to 0.4 mol H2 O m−2 s−1 , for
the experimental areas of forests of the ABRACOS
project. The difference among gs values is possibly due to the strong influence of the specific humidity deficit that exists in different experimental
areas.
4.3. Water vapour flux
The average simulated water vapour flux (E) ranged
from 0.14 kg H2 O m−2 h−1 (for the period from 106
to 147) to 0.19 kg H2 O m−2 h−1 (for the period from
241 to 268). The RMSE for raw and filtered water
vapour flux were 0.006 and 0.005 kg H2 O m−2 h−1 ,
respectively.
Although the simulated values of E overestimate the
observed values by approximately 17%, the simulated
mean values are in the range estimated for other areas
of the Amazon forest, such as at the Ducke Reserve,
in Manaus, where Shuttleworth (1988), Rocha et al.
(1996) and Hodnett et al. (1996) obtained mean values
Stomatal conductance (mol H2O m-2 s-1)
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
307
1.20
1.00
0.80
0.60
0.40
0.20
0.00
109
110
111
112
113
114
Day of the year
115
116
Fig. 13. Temporal variation of the stomatal conductance.
of 0.15, 0.15, and 0.16 kg H2 O m−2 h−1 , respectively.
Nepstad et al. (1994) found a mean rate of 0.15 kg H2 O
m−2 h−1 in the dry season in Pará, and Costa and Foley
(1997), using a modified version of the LSX model,
estimated a mean value of 0.18 kg H2 O m−2 h−1 for
the tropical Amazonian rainforest.
Fig. 14 illustrates simulated and observed E profiles
for the periods from April 18 to 25 (108–115), from
April 30 to May 8 (120–128) and from May 13 to 20
(133–140), periods used to validate the model. The
mean simulated peaks of E were 0.50, 0.50 and 0.35 kg
H2 O m−2 h−1 for the three periods, respectively.
The peaks of the simulated E in the night of the
days 108, 111, 123, 136, and 138 were overestimated
by the model due to the effect of wind bursts that
happened during these periods. We believe that this
discrepancy found in the simulation is due to the following factors: (a) integration interval (dt) relatively
high (1 h) – models like LSX, LSM, and SiB2 generally use integration intervals of the order of 20 min or
less; (b) high sensitivity of E to the strong night wind
bursts, when the air inside of the canopy is saturated
or near saturation; (c) numerical instability in conditions of neutral atmosphere, similar to the observed in
other models with similar structure.
Although the referred problems could be solved
through the use of new numeric methods for the mass
and energy transport, the reduction of the integration
interval (dt) or the increase in the complexity of the
parameterisation of the atmospheric conductance, we
believe that the results are satisfactory (ρ = 0.64 for
the entire validation period), considering the desired
intermediate complexity of the code. More sophisticated models (SSiB, SPA) typically obtain values in
the range of 0.80–0.90 (Zhan et al., 2003; Williams
et al., 1998).
4.4. Energy balance and sensible heat flux
In general, the simulated sensible heat flux was
smaller than the observed in the two studied periods.
The underestimation of the sensible heat flux, is related
to the overestimation of the latent heat flux. Although
the mean simulated sensible heat flux is smaller than
the measured at the site, it was similar to the simulated
values found by Rocha et al. (1996) of 13.9 W m−2
for Ducke Reserve in the period from September of
1983 to August of 1985. Table 7 illustrates the comparison of the partition of the energy balance, showing
approximately 10 days in the periods used for validation and calibration. The model overestimates the latent heat flux and underestimates the sensible heat flux,
and the RMSE for the sensible heat flux (non-filtered)
is 3.8 W m−2 . The soil heat flux and the variation
in the energy stored in the ecosystem (G + :S) are
obtained by the difference between the other energy
fluxes (Rn − Lv E − H).
The partitions of energy between the sensible and
latent heat flux were different between the periods. In
the period from 106 to 116, the solar radiation was
attenuated by the high presence of cloudiness, presenting a mean value of approximately 145.3 W m−2 ,
where 75% of this value was used in the evapotranspiration, and 7% was used to heat up the atmosphere.
308
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
-2
-1
Water vapour flux (kg H2 O m h )
1,00
0,80
0,60
0,40
0,20
0,00
108
109
110
111
(a)
112
113
114
115
Simulated
Observed
Day of the Year
-2
-1
Water vapour flux (kg H2 O m h )
1,00
0,80
0,60
0,40
0,20
0,00
120
121
122
(b)
123
124
125
126
127
Day of the Year
128
Simulated
Observed
-2
-1
Water vapour flux (kg H2 O m h )
1,00
0,80
0,60
0,40
0,20
0,00
133
(c)
134
135
136
137
Day of the Year
138
139
140
Simulated
Observed
Fig. 14. Simulated (3-h running mean) and observed profile of water vapour flux (E) from April 18 to 25 (108–115), from April 30 to
May 8 (120–128) and from May 13 to 20 (133–140) of 1999.
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
309
Table 7
Mean values of the partition of the simulated and observed energy balance: net radiation (Rn), latent heat flux (Lv E), sensible heat flux
(H) and residue (G + :S), in periods from 16 to 26 of April (106–116) and from 11 to 20 of September (254–263) of 1999
Variable
(W m−2 )
Rn
Lv E
H
G + :S
Period 106–116
Period 254–263
Simulated (%)
Observed (%)
RMSE (non-filtered)
145.3
109.5
9.1
26.6
145.3
82.6
29.7
33.0
–
4.4
3.8
–
(100)
(75)
(7)
(18)
(100)
(57)
(20)
(23)
Simulated (%)
147.1
146.5
11.7
−11.1
The heat flux into the soil and the variation of the energy stored in the ecosystem removes approximately
18% of the radiation balance:
In the period from 254 to 263, the net radiation
was more intense and the CO2 flux and the canopy
conductance were higher. Consequently, the available
energy was almost totally used for the evapotranspiration. The simulated Lv E was approximately equal
to the net radiation, although 20% greater than the
Lv E observed. In general, it can be observed that the
values simulated by the model agree well to the values observed in the experimental area in study, being
in the range of uncertainty of the method of flux mensuration (∼20%). In this period, RMSE for latent and
sensible heat fluxes are 10.9 and 5.2 W m−2 , respectively. Delire and Foley (1999), using the IBIS model
at Reserva Jaru, Rondônia, obtained a RMSE of 43
and 31 W m−2 for the latent and sensible heat fluxes,
respectively.
(100)
(100)
(8)
(−8)
Observed (%)
147.1
122.3
31.9
−7.1
(100)
(83)
(22)
(−5)
RMSE (non-filtered)
–
10.9
5.2
–
Nobre et al. (1996) found mean values of 138.9,
112.3 and 26.1 W m−2 , for Rn, Lv E and H, respectively, for the Ji-Paraná forest, Rondônia, in the
period of July of 1993. Reviewing the measurements of energy balance in the Amazon tropical
forest, Pereira (1997) reported an average radiation
balance of 123.8 W m−2 , being 64% of Rn transformed in latent heat, and 29% transformed in sensible heat, for the rainy season. Galvão and Fisch
(2000) evaluated the energy balance in the area
of Ji-Paraná, Rondônia, finding a ratio of Lv E/Rn
and H/Rn of 79 and 17%, respectively. During the
dry season, Lv E and H corresponds to 62 and 18%
of Rn, respectively. Using the SiB2 model, Rocha
et al. (1996) found the approximate simulated ratios of Lv E/Rn and H/Rn of 82 and 18% for the
Reserva Ducke, 79 and 21% for the Reserva Jaru,
and 88 and 12% for the Reserva Vale do Rio Doce,
respectively.
-2
-1
Water vapour flux (kg H2 O m h )
1,00
0,80
0,60
0,40
0,20
0,00
133
134
135
Day of the Year
136
137
138
139
140
Simulated(with moving average)
Simulated(without moving average)
Observed
Fig. 15. Simulated (with and without 3-h moving average) and observed water vapour fluxes profiles for 8-day period from May 13 to 20
(133–140) of 1999.
310
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
4.5. Numerical stability of the model
The results discussed in the previous section indicates that the SITE CO2 simulation is much more accurate than the water vapour and sensible heat flux
simulations. The major reason for the lower quality
of the water vapour and energy simulations is a weak
numerical instability of the model.
Eqs. (23), (24) and (30), when solved through finite
differences, are highly unstable numerically. To avoid
this problem, an implicit numerical method was used
through the solution of a system of four linear equations. We should note here, however, that even the solutions presented are somewhat unstable numerically,
especially for the time step of one hour. To avoid the
numerical instability, we should substitute Eqs. (9),
(20), (21) and (22) in Eqs. (23) and (32), introducing undesired mathematical complexities, caused by
the if-clauses associated to Eqs. (9), (20) and (21),
and to the iterative (two-step) calculations of Wu and
Ws . Were SITE coupled to an atmospheric model, this
instability would be unacceptable, as it would propagate into the atmospheric circulation. However, we
figured out that the effects of the instability in the output variables virtually disappear if a moving average
of the output variables is plotted. The numerical instability can be seen in Fig. 15, where simulated raw
and 3-hourly moving averages water vapour fluxes are
plotted.
5. Summary and conclusions
We have developed an intermediate complexity
model to simulate the carbon, energy and water fluxes
between a tropical ecosystem and the atmosphere.
The Simple Tropical Ecosystem Model (SITE) also
simulates the carbon dynamics in the ecosystem.
In SITE, we combined a realistic representation of
the processes involved in the ecosystem functioning
with a simple mathematical framework, keeping the
required mathematics at the linear differential equations and linear algebra level. In addition, the simple
structure of SITE makes it easy for users to implement parameterisations of processes that are not yet
represented.
Although the model was tested against data collected at an 150-year-old Amazon tropical forest site,
where species from families Sapotaceae, Chrisobalanaceae and Lauraceae dominated, it can be used in
several other situations, including tropical forests under different management strategies, young forests and
even other tropical ecosystems, provided that adequate
input data and parameters are available.
Even though SITE is considerably less complex
than other models of similar goals, it reproduces well
the hourly variability of the fluxes of CO2 and water vapour, and it simulates the balance of those elements in seasonal scale properly. In particular, SITE
CO2 flux simulations have a very good correlation
with the hourly-observed values. In most of the times,
the model reproduces well the hourly variability in the
fluxes, including some details usually difficult to reproduce, like the NEP peak that happens before noon,
and the transient water vapour flux during the night.
Nevertheless, the model is excessively sensitive to
wind bursts that happen during the evening, when the
canopy air is near saturation, overestimating the water
vapour flux in these situations.
SITE is available as a 1200-line FORTRAN code,
and as a computer spreadsheet. We believe the model
will be useful to help train the next generation of tropical ecologists in the use of ecosystem models.
Acknowledgements
The Brazilian agencies CAPES and CNPq, as well
as WWF–Brazil, provided funding for this research.
Data used for validation and calibration of the model
was collected by the project ECOBIOMA, also funded
by CNPq. We would like to thank the anonymous reviewers and the editor for their comments and recommendations.
References
Amthor, J.S., 1984. The role of maintenance respiration in plant
growth. Plant Cell Environ. 7, 561–569.
Bonan, G.B., 1996. A Land surface model (LSM version 1.0)
for ecological, hydrological, and atmospheric studies: technical
description and user’s guide. NCAR Technical Note TN417+STR, 150 pp.
Campbell, G.S., Norman, J.M., 1998. An Introduction to
Environmental Biophysics. 2nd ed. Springer-Verlag, New York,
286 pp.
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
Carswell, F.E., Costa, A.C.L., Palheta, M., Malhi, Y., Meir,
P., Costa, J.P.R., Ruivo, M.L., Leal, L.S.M., Costa, J.M.N.,
Clemente, R.J., Grace, J., 2002. Seasonality in CO2 and H2 O
flux at an eastern Amazonian Rain Forest. J. Geophys. Res.
v.107, 8076, doi: 10.1029/20001D000284.
Clark, D.A., Brown, S., Kicklighter, D.W., Chambers, J.Q.,
Thomlinson, J.R., Holland, J.eE.A., 2001. Net primary
production in tropical forests: an evaluation and synthesis of
existing field data. Ecol. Appl. 11, 371–384.
Collatz, G.J., Ball, J.T., Grivet, C., Berry, E.J.A., 1991.
Physiological and environmental regulation of stomatal
conductance, photosynthesis and transpiration: a model that
includes a laminar boundary layer. Agric. For. Meteorol. 54,
107–136.
Collatz, G.J., Carbo, M.R., Berry, J.A., 1992. Coupled
photosynthesis-stomatal conductance model for leaves of C4
plants. Aust. J. Plant Physiol. 19, 519–538.
Cosby, B.J., Hornberger, R.B., Clapp, R.B., Ginn, T.R., 1984.
A statistical exploration of the relationships of soil moisture
characteristics to the physical properties of soils. Water Resour.
Res. 20, 682–690.
Costa, M.H., Foley, J.A., 1997. The water balance of the Amazon
basin: dependence on vegetation cover and canopy conductance.
J. Geophys. Res. 102, 23973–23990.
Davidson, E.A., Verchot, L., Cattânio, J.H., Ackerman, I.L.,
Carvalho, J.E.M., 2000. Effects of soil water content on soil
respiration in forests and cattle pastures of eastern Amazonia.
Biogeochemistry 48, 53–69.
Delire, C., Foley, J.A., 1999. Evaluating the performance of a land
surface/ecosystem model with biophysical measurements from
contrasting environments. J. Geophys. Res. 104, 16895–16909.
Dickinson, R. E., Sellers, A.-H., Kennedy, P. J., Wilson, M. F.,
1984. Biosphere-Atmosphere transfer scheme (BATS) for the
NCAR community climate model, NCAR Technical Note TN275+STR, 69 pp.
Entenkhabi, D., Eagleson, P.S., 1989. Land surface hydrology
parameterization for atmospheric general circulation models
including sub grid scale spatial variability. J. Climate 2, 816–
831.
Farquhar, G.D., Caemmerer, S.V., Berry, J.A., 1980. A biochemical
model of photosynthetic CO2 assimilation in leaves of C3
species. Planta 149, 78–90.
Farquhar, G.D., Sharkey, T.D., 1982. Stomatal conductance and
photosynthesis. Ann. Rev. Plant Physiol. 33, 317–345.
Foley, J.A., Prentice, I.C., Ramankutty, N., Levis, S., Pollard, D.,
Sitch, S., Haxeltine, A., 1996. An integrated biosphere model
of land surface processes. Global Biogeochem. Cycles 10, 603–
628.
Galvão, J.A.C., Fisch, G., 2000. Energy budget in forest and
pasture sites in Amazonia. Revista Brasileira de Meteorologia
15, 25–37.
Goulden, M.L., Munger, J.W., Fan, S.-M., Daube, B.C., Wofsy,
S.C., 1996. Measurements of carbon sequestration by long-term
eddy covariance: methods and a critical evaluation of accuracy.
Global Change Biol. 2, 169–182.
Grace, J., Lloyd, J., Mcintyre, J., Miranda, A.C., Meir, P., 1996.
Carbon dioxide flux over Amazon rainforest in Rondônia. In:
Gash, J.H.C., Nobre, C.A., Roberts, J.M., Victoria, R.L. (Eds.),
311
Amazonian Deforestation and Climate, 1st ed. John Wiley and
Sons, Chichester, pp. 307–318.
Haxeltine, A., Prentice, I.C., 1996. Biome 3: an equilibrium
terrestrial biosphere model based on ecophysiological
constraints. Global Biogeochem. Cycles 10, 693–709.
Hodnett, M.G., Tomasella, J., Marques Filho, A., De, O., Oyama,
M.D., 1996. Deep soil water uptake by forest and pasture in
central Amazonian: predictions from long-term daily rainfall
data using a simple water balance model. In: Gash, J.H.C.,
Nobre, C.A., Roberts, J.M., Victoria, R.L. (Eds.), Amazonian
Deforestation and Climate, 1st ed. John Wiley and Sons,
Chichester, pp. 81–99.
Hurtt, G.C., Moorcroft, P.R., Pacala, S.W., Levin, S.A., 1998.
Terrestrial models and global change: challenges for the future.
Global Change Biol. 4, 581–590.
Kucharik, C.J., Foley, J.A., Delire, C., Fisher, V.A., Coe, M.T.,
Gower, S.T., Lenters, J.D., Young-Molling, C., Norman, J.M.,
Ramankutty, N., 2000. Testing the performance of a dynamic
global ecosystem model: water balance. Global Biogeochem.
Cycles 14, 795–825.
Leuning, R., 1995. A critical appraisal of a combined stomatalphotosynthesis model for C3 plants. Plant Cell Environ. 18,
339–355.
Malhi, Y., Nobre, A.D., Grace, J., Kruijt, B., Pereira, A.C., Scott,
S., 1998. Carbon dioxide transfer over a central Amazonian
rain forest. J. Geophys. Res. 31, 31593–31612.
Medina, E., Cuevas, E., 1996. Biomass production in nutrientlimited rainforest: implications for responses to global change.
In: Gash, J.H.C., Nobre, C.A., Roberts, J.M., Victoria, R.L.
(Eds.), Amazonian Deforestation and Climate, 1st ed. John
Wiley and Sons, Chichester, pp. 221–239.
Melillo, J.M., Mcguire, A.D., Kicklighter, D.W., Moore III, B.,
Vörösmarty, C.J., Schloss, A.L., 1993. Global climate change
and terrestrial net primary production. Nature 363, 234–240.
Miller, S.D., Goulden, M.L., Menton, M.C., Rocha, H.R., Freitas,
H.C., 2004. Annual CO2 exchange by a tropical Forest.
Ecological Applications. In press.
Moura, R.G., Manzi, A.O., Nogueira, V.S., Mendes, D., 2000.
Comparação entre os perfis de radiação solar dentro de ambiente
de floresta para dias com diferentes coberturas de nebulosidade.
XI Congresso Brasileiro de Meteorologia, Rio de Janeiro-RJ.
Anais.
Neilson, R.P., 1995. A model for predicting continental scale
vegetation distribution and water balance. Ecol. Appl. 5, 362–
385.
Nepstad, D.C., Carvalho, C.R., Davidson, E.A., Jipp, P.H.,
Lefebvre, P.A., Negreiros, G.H., Silva, E.D., Stone, T.A.,
Trumbore, S.E., Vieira, S., 1994. The role of deep roots in
the hydrological and carbon cycles of Amazonian forests and
pastures. Nature 372, 666–669.
Nobre, C.A., Fisch, G., Rocha, H.R., Lyra, R.F., Rocha, E.P.,
Costa, A.C.L., Ubarana, V.N., 1996. Observations of the
atmospheric boundary layer in Rondônia. In: Gash, J.H.C.,
Nobre, C.A., Roberts, J.M., Victoria, R.L. (Eds.), Amazonian
deforestation and climate, 1st ed. John Wiley and Sons,
Chichester, pp. 413–423.
312
S.N. Monteiro Santos, M.H. Costa / Ecological Modelling 176 (2004) 291–312
Oliveira, J.B., 2000. Análise do Balanço de Radiação na Região
Amazônica. Viçosa, MG: UFV, M.S. thesis dissertation, Federal
University of Viçosa, Brazil, 79 pp.
Parton, W., Stewart, J., Cole, C., 1988. Dynamics of C, N, P and
S in grassland soils: a model. Biogeochemistry 5, 109–131.
Prentice, I.C., Cramer, W., Harrison, S.P., Leemans, R., Monserud,
R.A., Solomon, A.M., 1992. A global biome model based on
plant physiology and dominance. J. Biogeography 16, 117–
134.
Pereira, A.R., 1997. Radiation regime of tropical rain forest.
Revista Brasileira de Agrometeorologia, vol. 5. pp. i–viii.
Pollard, D., Thompson, S.L., 1995. The effect of doubling stomatal
resistance in a global climate model. Global Planet. Change
10, 129–161.
Raich, J.W., Rastetter, E.B., Melillo, J.M., Kicklighter, D.W.,
Steudier, P.A., Peterson, B.J., Grace, A.L., Moore, B.,
Vörösmarty, C.J., 1991. Potential net primary productivity in
South America: application of a global model. Ecol. Appl. 1,
399–429.
Roberts, J., Cabral, O.M.R., Costa, J.P., Mcwilliam, A.L.C.,
1996. An overview of the leaf area index and physiological
measurements during ABRACOS. In: Gash, J.H.C., Nobre,
C.A., Roberts, J.M., Victoria, R.L. (Eds.), Amazonian Deforestation and Climate, 1st ed. John Wiley and Sons, Chichester,
pp. 287–306.
Rocha, H.R., Sellers, P.J., Collatz, G.J., Wright, I.R., Grace, J.,
1996. Calibration and use of the SiB2 model to estimate water
vapour and carbon exchange at the ABRACOS forest sites. In:
Gash, J.H.C., Nobre, C.A., Roberts, J. M., Victoria, R.L. (Eds.),
Amazonian Deforestation and Climate, 1st ed. John Wiley and
Sons, Chichester, pp. 460–471.
Ruivo, M.L.P., Quanz, B., Sales, M.E.C., Meir, P., 2001. Solos
dos Sı́tios do Experimento esecaflor-Caxiuanã, Pa. In: Lisboa,
P.L.B. (Ed.), Caxiuanã. Populações Tradicionais, Meio Fı́sico e
Biodiversidade, Belém, Museu Paraense Emilio Goeldi, Belém,
pp. 206–213.
Running, S.W., Gower, S.T., 1991. Forest-BGC, a general model of
forest ecosystem processes for regional applications, II, dynamic
allocation and nitrogen budgets. Tree Physiol. 9, 147–160.
Sellers, P.J., Mintz, Y., Sud, Y., Dalcher, A., 1986. A simple
biosphere model (SiB) for use within general circulation
models. J. Atm. Sci. 43, 505–531.
Sellers, P.J., Bounoua, L., Collatz, G.J., Randall, D.A., Dazlich,
D.A., Los, S.O., Berry, J.A., Fung, I., Tucker, C.J., Field, C.B.,
Jensen, T.G., 1996. Comparison of radiative and physiological
effects of atmospheric CO2 on climate. Science 271, 1402–
1406.
Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., Moore, C.J.,
Roberts, J., Marques, A.D., Fisch, G., Silva, V.D., Ribeiro,
M.D.G., Molion, L.C.B., Sá, L.D.D., Nobre, C.A., Cabral,
O.M.R., Patel, S.R., Moraes, J.C., 1984. Eddy-correlation
measurements of energy partition for Amazonian forest. Quart.
J. R. Met. Soc. 110, 1143–1162.
Shuttleworth, W.J., 1988. Evaporation from Amazonian rainforest.
Proc. R. Soc. Lond. 33, BS321–346.
Trumbore, S.E., Davidson, E.A., Camargo, P.B., Nepstad, D.C.,
Martinelli, L.A., 1995. Below ground cycling of carbon in
forests and pastures of eastern Amazonia. Global Biogeochem.
Cycles 9, 515–528.
Williams, M., Malhi, Y., Nobre, A.D., Rastetter, E.B., Grace,
J., Pereira, M.G.P., 1998. Seasonal variation in net carbon
exchange and evapotranspiration in a Brazilian rain forest: a
modelling analysis. Plant Cell Environ. 21, 953–968.
Woodward, F.I., 1987. Climate and Plant Distribution. Cambridge
University Press, Cambridge.
Zhan, X., Xue, Y., Collatz, G.J., 2003. An analytical approach for
estimating CO2 and heat fluxes over the Amazonian region.
Ecol. Model. 162, 97–117.