crowns and their leaf area in the canopy are calculated in horizontal canopy layers of 0.5 m.
The growth of an individual tree is based on its carbon balance. Calculations include photoproduction of the trees and assimilate losses due to respiration, litter-fall and fine root decay. Within a patch the light at-tenuation Ii downwards in the canopy is calculated from light intensity above the canopy I0 and the light extinction coeffi-cientkwith respect to the absorption of tree crowns. The dependence of specific pho-tosynthetic productivity Pi on irradiance is modelled using a Michaelis-Menten-type light response curve. Photoproduction ˜Pi is calculated from the tree’s leaf area and its specific productivityPi by integrating down the canopy of the tree in question (Monsi &
Saeki 1953). Differences between wet and dry seasony are considered in terms of dif-ferent light intensityI0y, the different length of daily photoactive periodSDy, and the dif-ferent length of seasonsSSy. We assume an increasing limiting effect of water transport deficiencies with increasing tree height. Ac-tual productivity is calculated by applying a size-dependent limitation factor q(di) ac-cording to q(di) = 1−(1 −qDM) ·(Ddi
M)2, whereDMis the maximum diameter of trees and qDM is the limitation factor at max-imum tree height (corresponds to the ag-ing factor cs of Landsberg & Waring 1997).
With the condition of no tree growth at maximum diameter, qDM can be calculated from the parameter set. Assimilate losses are estimated in relation to tree biomass (Kira 1978; Yoda 1983). Losses are com-posed of root decay, litter-fall and respira-tion of tree organs and leaves. We distin-guish between a biomass-dependent
main-tenance respiration Rm(B) and growth res-piration RG (Ditzer et al. 2000). This leads to our main growth equation
dBi
dt = ˜Pi·q(1−RG)−Rm(Bi) (6 .1) Water balance is not included in the model. The calculation of tree growth is performed in annual time steps.
Competition is modelled in terms of com-petition for light as described above and competition for space as described below concerning mortality.
Mortality
Mortality is modelled on an annual basis at a basic mortality rate MB. To this is added a diameter-dependent mortalityMD, which is zero above a threshold diameter dt = MD1. Thinning is assumed to occur in dense patches. Mortality is modelled as stochastic event. Senescent trees (≥ 10 cm d.b.h.) die and fall with probability W; they knock down smaller trees in neighbour-ing patches and create gaps. The number of trees NF destroyed from the total number Np in the target patch p is calculated from the crown projection area fF of the falling tree relative to patch size A (NF =NpfAF).
Regeneration
Seed germination depends on minimal light intensities IS on the forest floor. It is as-sumed that intact forest surrounding the simulation area supports a constant seed in-put NS. Incoming seeds are added to a seed pool, which takes into account the variance in the length of dormancy (MS) between plant functional types (cf. Garwood 1983, 1989).
Parameters and initial condi-tions
Table 6.3 contains the parameters used for the simulations. Data on the light environ-ment are drawn from Veillon (1989) and Kammesheidt (unpubl. data). Most allo-metric relations (h = f(d), cP) are based
Table 6.2: Description of parameters including functional relationships.
Parameter Description
Environmental parameters
k Light extinction coefficient
I0 Light intensity above canopy
SD Daylength
SS Length of wet/dry season
Establishment parameters DS Initial diameter of seedlings
ISs Minimal light intensity for germination NSs Ingrowth rate of seeds into seed pool
Mortality parameters
MB Basic mortality rate
MS Mortality rate of seeds
MDj Size dependent mortality rate (MD =MD0−MD0/MD1·d) W Probability of a dying tree to fall
Tree physignomic parameters
DM Maximum diameter
cP Crown length fraction
τ Fraction of stemwood biomass to total aboveground biomass h0h and h1h Height = f(diameter) (h=d/(1/h0h+d/h1h))
γj Form factor = f(diameter) (γ =γ0 ·exp(γ1·dγ2)) fj Crown diameter = f(diameter) (dc = (f0+f1 ·df2)·d) lj Leaf area = f(diameter) (l =l1·d+l2·d2+l3·d3) LAIM Maximal leaf area index of single tree
Biomass production parameters
PM Photosynthetic capacity in light response curve α Photosynthetic efficiency in light response curve
ρ Stem wood density
r0l and r1l Respiration = f(biomass) (Rm(Bi) =r0l·B2/3+r1l·Bi) RG Specific growth respiration rate ss
m Leaf transmittance
g Conversation factor gCO2 to godm
on data derived from Kammesheidt (1994, unpubl. data). The form factor γ, leaf and crown area to diameter relations are taken from measurements of Kato, Tadaki
& Ogawa (1978) and Kira (1978) in Pasoh,
Malaysia. Data on the photosynthetic re-sponse of plant functional types to different light levels are given in Oberbauer & Strain (1984). The wood density of species was de-termined at the Institute of Wood
Technol-Table 6.3: Parameter estimates for the simulation of the Caparo forest, Venezuela.Param-eters with subindex vary according to season(y), successional status (s), potential height (h) (corresponding to SS and HG in Table 6.1), or different functional coefficients (j).
Name Special Units Values
Environmental parameter
k [-] 0.7
I0y wet dry [µmol(p) m−2 s−1] a 816.0 1005.0
SDy wet dry [h] 12.0 12.0
SSy wet dry [-] 0.67 0.33
Establishment parameter
DS [m] 0.01
NSs s=1-4 [ha−1 y−1)] 500 200 25 50
ISs s=1-4 [fraction ofI0y] 0.05 0.01 0.01 0.01
Mortality parameter
MBs,h s=1; h=1-6 [y−1] 0.00 0.12 0.08 0.00 0.00 0.00
MBs,h s=2; h=1-6 [y−1] 0.06 0.05 0.035 0.03 0.00 0.00
MBs,h s=3; h=1-6 [y−1] 0.05 0.04 0.03 0.025 0.00 0.00
MBs,h s=4; h=1-6 [y−1] 0.00 0.00 0.00 0.00 0.01 0.01
MSs s=1-4 [y−1] 0.1 0.5 1.0 1.0
MDj j=0-1 [y−1, m−1] 0. 4 0. 2
W [-] 0.40
Tree physignomic parameter
DMs,h s=1; h=1-6 [m] 0.10 0.25 0.70 1.00 0.25 0.40
DMs,h s=1; h=2-3 [m] 0.13 0.35
cp [-] 0.358
τ [-] 0.7
h0h h=1-6 [cm m−1] 1.63 1.63 1.41 1.50 0.22 0.22
h1h h=1-6 [m−1] 19.9 19.9 35.7 45.4 325.7 325.7
γj j=0-2 [-, cm−1, -] 2.575 -1.409 0.0358
fj j=0-2 [-, -, -] 0.132 0.933 -0.6615
lj j=1-3 [cmm, cmm2, cmm3] 3.197 0.0684 -0.000379
LAIM [-] 2
Biomass production parameter
PMs s=1-4 [µmol(c) m−2 s−1] a 27.7 11.3 6.8 6.8 αs s=1-4 [µmol(c)µmol(p)−1] a 0.043 0.043 0.043 0.043
ρs s=1-4 [todmm−3] 0.24 0.69 0.69 0.75
r0s s=1-4 [t3/2odm] 0.20 0.06 0.05 0.04
r1s s=1-4 [-] 0.60 0.02 0.015 0.04
RG [-] 0.25
m [-] 0.1
g [godmg−1CO2] 0.63
ap: photons; c: CO2
ogy and Wood Biology of G¨ottingen Univer-sity. Parameters for respiration processes (r0sandr1s) were investigated using param-eter variation to gain realistic diamparam-eter in-crement values for different size classes and light conditions. Mortality and ingrowth rates correspond to typical values found in
literature (Swaine 1989; Condit et al. 1992;
1995a, b; Carey et al. 1994; Phillips & Gen-try 1994; Silva et al. 1995; van der Meer &
Bongers 1996). Mortality M is correlated to the diameter growth rate gd and maxi-mum size dmax such that ω = dmax/gd·M is roughly constant. Otherwise the
num-ber of large trees would be overestimated (ω << 1) or only small trees would occur (ω >>1) (Chave 1999b).
From data sets of the two stands cho-sen for simulations (MF, LG5), 25 patches (of 400 m2 each) — randomly chosen in the case of LG5 — were clustered to form the initial data set for one hectare. The functional groups were then aggregated into different cohorts regarding their diameter (d.b.h. class of 5 cm). To minimise stochas-tic effects in tree mortality, each simulation was performed for an area of 25 hectares.
The model was written in the program-ming language C++. Simulations were run on a PC (400 MHz, system Linux), taking on average 9 sec to simulate the growth of 1 ha of rain forest over 100 years.