Changes between Version 249 and Version 250 of DevelopmentActivities/ORCHIDEE-DOFOCO


Ignore:
Timestamp:
2020-01-22T21:47:20+01:00 (4 years ago)
Author:
luyssaert
Comment:

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  • DevelopmentActivities/ORCHIDEE-DOFOCO

    v249 v250  
    7474== Functionalities (alphabetical order) == 
    7575 
    76 === Age classes (as in r6470) === 
     76=== Age classes (since r6470) === 
    7777Age classes were introduced to better handle heterogeneity at the landscape level. The feature allows us to distinguish between different successional stages of the same PFT (e.g., a newly grown forest vs. a mature forest). Age classes are independent of the number of diameter classes. Using age classes adds a lot of details to both the biophysics and the biogeochemistry following natural disturbances, forest management and land cover change. If half of a grassland is afforested with a PFT that already exists in the pixel, previous versions of ORCHIDEE will combine this newly forest land and the existing forest in a single PFT. This will result in, for example, a low albedo, a high roughness, and other properties.  When age classes are used, the newly afforested and the existing forest will end up in separate PFTs. One will have a high albedo, the other a low albedo, and other properties may differ significantly as well. In CAN with age classes, PFTs are only merged if the youngest age class for a PFT already has biomass. 
    7878 
     
    128128}}} 
    129129 
    130 === Albedo ((as in r6470) === 
     130=== Albedo (since r6470) === 
    131131ORCHIDEE-CN-CAN makes use of a two stream radiative transfer scheme through the canopy, extended to multiple canopy levels (https://doi.org/10.5194/gmd-2016-280). The scheme is based on Pinty et al 2006. This approach accounts not only for the leaf mass but also for the vertical and horizontal distribution of the leaf mass (=canopy structure), calculating an effective LAI based on the solar angle. Light from collimated (black sky) and diffuse (white sky) sources are used, and both are weighted equally as information about this partitioning is not yet available in forcing data.  In ORCHIDEE-CN-CAN the same scheme is used to simulate the reflected, transmitted and absorbed light, of which the absorbed light as a function of canopy level is passed to the photosynthesis routines and used in place of the exponential LAI layering found in older versions of the TRUNK (see the section Photosynthesis). This implies that albedo and photosynthesis are now fully consistent as well as the light reaching the forest floor (the latter is used in for example recruitment). ORCHIDEE-CN-CAN cannot revert to previous approaches for calculating albedo. 
    132132  
     
    135135When snow is present in a pixel, all snow is assumed to reach the ground and the background albedo and the snow albedo (calculated as a function of snow age) are weighted according to their cover fractions (see Background albedo).  
    136136 
    137 === Background albedo (CHECK) === 
     137=== Albedo (background) (CHECK) === 
    138138If covered by snow, the background albedo is calculated by the snow module and accounts for snow age and snow density (needs to be checked – last time snow did not account for NIR). If not covered by snow, the background albedo is not simulated but prescribed by the parameters '''bgrd_ref_vis''' and '''bgrd_ref_nir'''. If the background is partly covered by snow, the snow albedo and the background albedo are merged, which allows snow to settle under the canopy, reflecting In deciduous forest, grasslands and croplands, the background albedo is known to be strongly affected by the phenology and senescence of the understory vegetation. ORCHIDEE-CN-CAN has two options to prescribe the background albedo: 
    139139* The background albedo is prescribed per PFT but is constant throughout the year. This is the option that has been used in ORCHIDEE-CAN and is the option that has been validated over Europe. Set '''alb_bg_modis''' = n. 
    140140* The background albedo is constant across PFTs. This option reads background maps. Given that those maps are based on the JRC TIP product, they should be compatible with the new albedo scheme. This option, however, has not been validated yet. Set '''alb_bg_modis''' = y. 
    141141  
    142 === Snow albedo (CHECK) === 
     142=== Albedo (snow) (CHECK) === 
    143143The snow albedo could be either prescribed (in condveg_init.f90) or calculated following Chalita and Treut (1994) '''do_new_snow_albedo = n ''' or calculated following CLM3 '''do_new_snow_albedo = y'''. The difference between the latter two methods has not been tested yet. The CLM method was added to CN-CAN, the Chalita and Treut method was added in parallel to the runk. When merging both versions we ended up with two options. 
    144144 
    145 === Allocation (CHECK) === 
    146 ORCHIDEE-CN-CAN uses the allometric allocation as developed in OCN. In ORCHIDEE-CAN the approach was adjusted to work for more than one diameter class. Since it was developed this allocation has been used in ORCHIDEE-CN, and ORCHIDEE-CNP. In those branches only a single diameter class was used. Except for the way the reserves and labile pools are calculated, the allocation scheme is identical between all aforementioned versions. The model is, however, very sensitive to the way the reserves and labile pools are calculated. The allocation makes use of a labile pool for which the activity is calculated based on the temperature. As such the model addresses the sink/source discussion initiated by Körner. Whereas this approach resulted in an acceptable interannual variability in for example NPP in ORCHIDEE-CAN, adding N seems to have dampen the interannual variability too much. This dampening was observed in ORCHIDEE-CN  and ORCHIDEE-CN-CAN. IN ORCHIDEE-CNP this temperature relationship was removed because the interannual variability became unrealistic.  
     145=== Allocation (since r6470) === 
     146ORCHIDEE-CN-CAN uses the allometric allocation as developed in O-CN. In ORCHIDEE-CAN the approach was adjusted to work for more than one diameter class. Since it was developed this allocation has been used in ORCHIDEE-CN and ORCHIDEE-CNP. In those branches only a single diameter class was used. Except for the way the reserves and labile pools are calculated (incl. the pseudo sugar loading), the allocation scheme remained rather similar between the aforementioned versions. The model is, however, very sensitive to the way the reserves and labile pools are calculated. The allocation makes use of a labile pool for which the activity is calculated based on the temperature. This sensitivity is important at the start and the end of the growing seasons when temperatures may be low. As such the model addresses the sink/source discussion initiated by Körner. Whereas this approach resulted in an acceptable interannual variability in for example NPP in ORCHIDEE-CAN, adding N seems to have dampen the interannual variability a lot/too much. This dampening was observed in ORCHIDEE-CN  and ORCHIDEE-CN-CAN. IN ORCHIDEE-CNP the temperature relationship was removed (hence NPP and GPP are strictly coupled) because the interannual variability became unrealistic.  
    147147 
    148148ORCHIDEE-CN-CAN calculates the number of individuals and uses this as a criterion to initiate a stand replacing disturbance. This approach, guided by the self-thinning relationship, avoids the need for a stand-level turnover time. ORCHIDEE-CN, and ORCHIDEE-CNP still make use of stand-level turnover. 
    149149 
    150 There are no options to revert to the allocation based on resource limitation. All references and parameters for allocation based on resource limitation have been removed from the code (those that were overlooked can be removed). Allometric allocation makes use of the following PFT-specific parameters: '''sla''', '''tau_root''', '''tau_leaf''', '''tau_sap''', '''pipe_density''', '''tree_ff''', '''pipe_tune_x''', '''k_latosa_max''', and '''k_latosa_min'''. In addition to this set of parameters that mainly describe the allometric relationships and the longevity of the different tissues, the calculation of the allocation coefficients makes use PFT-specific tissue conductivities, i.e., '''k_sap''', '''k_root''', and '''k_leaf''' (see also plant water stress). As such there is a functional link between C and N-allocation and the hydraulic architecture of a plant. Details on the parameters can be found in the SI of Naudts et al 2015 in GMD or in src_parameters/constantes_mtc.f90. 
    151  
    152 === Anthropogenic species change (CHECK) === 
    153 Following a disturbance (which could be a clear cut), tree species changes and forest management change can be prescribed or read from a map in ORCHIDEE-CAN. Set '''ok_change_species''' = y, '''read_species_change_map''' = y, and '''read_desired_fm_map''' = y and specify the paths of those maps in the COMP/stomate.card. This functionality replaces the DGVM in areas where humans rather than nature govern species distribution, for example, Europe. Note that there are some constraints on the possible species changes. If the forest is unmanaged (fm=1), the code assumes that nature will determine the species rather than humans. Anthropogenic species change has not been developed to work together with land cover change. For the moment it is one or the other. When testing this functionality read_species_change_map and/or read_desired_fm_map could be set to n. The new forest management strategy can then be simply prescribed by setting the parameter '''fm_change_force''' to one of the four fm strategies. Likewise the new species can be prescribed by setting the parameter '''species_change_force''' to the desired PFT number. 
    154  
    155 === Bare soil (CHECK) === 
    156 The flag '''ok_bare_soil_new''' controls how the bare soil is perceived and calculated. If set to FALSE the total bare soil is still calculated as a function of veget. When a deciduous PFT sheds its leaves, the gaps in the forest will contribute to bare soil fraction in the grid. Although this approach was introduced a long time ago to get acceptable evaporation estimates from forest, the approach also resulted in using the albedo of deserts as the background albedo of forest gaps. The new albedo scheme (see Albedo and Background albedo) considers a specific background albedo for each PFT and calculates the albedo of the PFT including the canopy gaps. Moving gaps to the bare soil is no longer needed. So, if '''ok_bare_soil_new''' is set to TRUE, canopy gaps no longer contribute to the bare soil. It needs to be tested what will happen with the evaporation in the single-layer model. The multi-layer energy budget should be able to correctly deal with the gaps in the canopy because the diffusivity will increase when the canopy is becoming sparser.  
    157  
    158 === Bark beetles (CHECK) === 
     150There are no options to revert to the allocation based on resource limitation (Friedlingstein et al. 1999). All references and parameters for allocation based on resource limitation have been removed from the code (those that were overlooked can be removed). Allometric allocation makes use of the following PFT-specific parameters: '''sla''', '''tau_root''', '''tau_leaf''', '''tau_sap''', '''pipe_density''', '''tree_ff''', '''pipe_tune_x''', '''k_latosa_max''', and '''k_latosa_min'''. In addition to this set of parameters that mainly describe the allometric relationships and the longevity of the different tissues, the calculation of the allocation coefficients makes use PFT-specific tissue conductivities, i.e., '''k_sap''', '''k_belowground''', and '''k_leaf''' (see also plant water stress). Details on the parameters can be found in the SI of Naudts et al 2015 in GMD or in src_parameters/constantes_mtc.f90.  
     151 
     152Previously there was a functional link between C and N-allocation and the hydraulic architecture of a plant because both approaches used the same parameter k_root. In DOFOCO k_root described the conductivity of the fine roots and the soil. In ORCHIDEE-CN-CAN this joined conductivity has been split in a fine root conductivity and a soil to root conductivity. Allocation should make use of both conductivities but soil to root conductivity cannot be easily calculated when needed in the allocation. This is subject to future developments. Accounting for the soil to root conductivity in the allocation would imply an adaptation of plant growth to its environment.   
     153 
     154=== Anthropogenic species change (since r6470) === 
     155Following a disturbance (which could be a clear cut), tree species changes and forest management change can be prescribed or read from a map in ORCHIDEE-CN-CAN. Set '''ok_change_species''' = y, '''read_species_change_map''' = y, and '''read_desired_fm_map''' = y and specify the paths of those maps in the COMP/stomate.card. A example of such a configuration can be found in config/ORCHIDEE_OL/OOL_SEC_STO_FG5. This functionality replaces the DGVM in areas where humans rather than nature govern species distribution, for example, Europe. Note that there are some constraints on the possible species changes. If the forest is unmanaged (fm=1), the code assumes that nature will determine the species rather than humans. Anthropogenic species change has not been developed to work together with land cover change. For the moment it is one or the other. When testing this functionality read_species_change_map and/or read_desired_fm_map could be set to n. The new forest management strategy can then be simply prescribed by setting the parameter '''fm_change_force''' to one of the four fm strategies. Likewise the new species can be prescribed by setting the parameter '''species_change_force''' to the desired PFT number. 
     156 
     157=== Bare soil (since r6470) === 
     158The flag '''ok_bare_soil_new''' controls how the bare soil is perceived and calculated. If set to FALSE the total bare soil is still calculated as a function of veget. When a deciduous PFT sheds its leaves, the gaps in the forest will contribute to bare soil fraction in the grid. Although this approach was introduced a long time ago to get acceptable evaporation estimates from forest, the approach also resulted in using the albedo of deserts as the background albedo of forest gaps. The new albedo scheme (see Albedo and Background albedo) considers a specific background albedo for each PFT and calculates the albedo of the PFT including the canopy gaps. Moving gaps to the bare soil is no longer needed. So, if '''ok_bare_soil_new''' is set to TRUE, canopy gaps no longer contribute to the bare soil. It needs to be tested what will happen with the evaporation in the single-layer model. The multi-layer energy budget should be able to correctly deal with the gaps in the canopy because the diffusivity will increase when the canopy is becoming sparser. 
     159 
     160At present the default settings combine the new albedo scheme with the single layer energy budget (enerbil) and '''ok_bare_soil_new''' = n. The consequences of this combination of settings should be evaluated against observations. 
     161 
     162=== Bark beetles (since r6470) === 
    159163The bark beetle module was developed such that it interacts with the windthrow module. If you want to activate it use the flag OK_PEST=y in the run.def. To specify which PFT may be affected by bark beetles use BEETLE_PFT_xxx= TRUE where XXX is the pft you interested in. Note that for the moment bark beetles in ORCHIDEE is parameterized only to work with Picea abies. 
    160164 
    161 === C13 (CHECK) === 
    162 The concentration of C13 in the leaves can be calculated by setting '''ok_c13''' to y in the run.def. This calculation follows Farquhar's approach and is currently limited to the fractionation in the leaves. 
    163  
    164 === Configuration (CHECK) === 
     165=== C13 (since r6470) === 
     166The concentration of C13 in the leaves can be calculated by setting '''ok_c13''' to y in the run.def. This calculation follows Farquhar's approach and is currently limited to the fractionation in the leaves. Following changes to the recalculation of GPP under plant water stress the calculation of Ci is no longer accurate. This may have broken the functionality to calculate C13. Needs to be tested. 
     167 
     168=== Configurations (since r6470) === 
    165169The model comes with the following configuration set-ups (config/ORCHIDEE_OL): 
    166 * SPINUP: under development. 
    167 * ENSEMBLE: under development. 
     170* SPINUP: used for single pixel FLUXNET runs. 
     171* ENSEMBLE: used for single pixel FLUXNET runs. 
    168172* SPINUP_ANALYTIC_FG1: 2x2 degrees CRU-NCEP forcing cycles over 1901-1910 between 1901 and 2240. Start from scratch. 15 PFTs, no land cover changes, nitrogen input for 1850, 1860 or 1900 depending on the species, and fixed CO2 concentrations.  
    169173* OOL_SEC_STO_FG1trans: 2x2 degrees CRU-NCEP forcing cycles over 1901-1910 between 1861 and 1900. Restart from SPINUP_ANALYTIC_FG1. 15 PFTs, no land cover changes, nitrogen input for 1900, and annual CO2 concentrations. 
     
    172176* OOL_SEC_STO_FG3nd: 0.5x0.5 degrees annual WFDEI_GPCC forcing between 1979-2013. Start from scratch. 15 PFTs, annual land cover changes, annual nitrogen input and annual CO2 concentrations. This configuration has been set-up and committed but has not yet been tested. Waiting for the new driver to be tested in CN-CAN. 
    173177* OOL_SEC_STO_FG4: ~0.5x0.5 degrees annual CRU-NCEP forcing between 1901 and 2010. Start from scratch. 64 PFTs, European forest are defined at the species level with 4 age classes, forests outside of Europe are defined at the MTC level with 1 age class, annual land cover and tree species changes, annual  input deposition, annual CO2 concentrations, annual forest management, and annual litter raking. 
    174 * OOL_SEC_STO_FG5: 1x1 degrees annual IPSL RCP 4.5 forcing between 1911 and 2100. Start from OOL_SEC_STO_FG4. XX PFTs, no land cover and changes, annual input deposition, annual CO2 concentrations, prescribed species and management changes following annual a stand replacing disturbance, litter raking for 2010. This configuration is under development. Waiting for the boundary files to be copied to orchideeshare. The species and management change functionality needs to be tested within CN-CAN.  
     178* OOL_SEC_STO_FG5: 1x1 degrees annual IPSL RCP 4.5 forcing between 1911 and 2100. Start from OOL_SEC_STO_FG4. XX PFTs, no land cover and changes, annual input deposition, annual CO2 concentrations, prescribed species and management changes following annual a stand replacing disturbance, litter raking for 2010.  
    175179* OOL_SEC: 2x2 degrees annual CRU-NCEP forcing between 1901 and 2010. Start from scratch. 15 PFTs prescribed by reading in a biomass map. Land cover changes, input deposition, CO2 concentrations, and all other biogeochemical and ecological processes are deactivated. This configuration is under development, waiting for a global LAI map (in case of CN-CAN this has become biomass map) to be tested. 
    176 * TESTSTOMATE: Not maintained for ORCHIDEE-CN-CAN. Will be added back once teststomate.exe has been restored. 
    177180* FORCESOIL: Not maintained for ORCHIDEE-CN-CAN. Will be added back once forcesoil.exe has been restored. 
    178181 
    179 === Consistency checks (CHECK) === 
     182=== Consistency checks (since r6470) === 
    180183The code distinguishes between three options to check for mass and surface conservation. These options are controlled by the parameter '''err_act'''. Always use err_act = 3 when developing and testing the code. Note that in addition to checking for mass balance closure ORCHIDEE-CN-CAN will also check for the conservation of veget_max and frac_nobio. This is useful to make sure no surface area is lost when moving biomass from one PFT to another following natural disturbances, forest management, land cover changes and when using age classes. In some parts of the code, for example, modules that deal with disturbances, it is assumed that the tallest trees are stored in the last diameter class. When the difference in diameter between diameter classes becomes very small, this assumption could be violated. Therefore, the diameter classes are sorted to enforce the assumed order and where needed the order is checked. 
    181184* err_act = 1 is recommended when running global long-term simulations. Under this option, mass balance closure is checked for all biogeochemical processes but only at the highest level thus stomate.f90 and stomate_lpj.f90. Although the mass balance checks are not very expensive in terms of computer time, skipping the numerous lower level checks is expected to save some time. Under this option the total mass balance error is only written to the history file. No information is provided in which subroutine the problem occurred. 
     
    183186* arr_act = 3 is recommended when having a problem with mass balance closure. The mass balance is explicitly checked in stomate.f90, stomate_lpj.f90 and all its subroutines. If a mass balance error occurs, the model is stopped. 
    184187 
    185 === CWRR vs Choinel (CHECK) === 
    186 ORCHIDEE-CN-CAN was developed and tested with CWRR. The Choinel code is still available but was never used in ORCHIDEE-CN-CAN and can thus be removed. The hydrological schemes were not touched during the development of ORCHIDEE-CN-CAN. The hydraulic architecture in ORCHIDEE-CN-CAN relies on CWRR. 
     188=== CWRR vs Choinel (since r6470) === 
     189ORCHIDEE-CN-CAN was developed and tested with CWRR. The Choinel code is removed from ORCHIDEE-CN-CAN. The hydrological schemes were not touched during the development of ORCHIDEE-CN-CAN. The hydraulic architecture in ORCHIDEE-CN-CAN relies on CWRR. 
    187190 
    188191=== Diameter classes (CHECK) === 
     
    199202The above declaration implies that 9/15th of the trees will always be in the smallest diameter class, 5/15th will be in the medium class and 1 tree out of 15 will be in the largest diameter class. These ratios are kept throughout the simulations and the boundaries of the diameter classes are adjusted to respect this constraint. Consequently, an even-aged stand will be simulated with three diameter classes where the diameter of the first class may be, for example, 20.3 cm, the diameter of the second class 20.4 cm and the diameter of the third class 20.5 cm. The same code and set-up allows to simulate, in the same simulation, an uneven-aged stand for the same PFT but in a different pixel with, for example, the smallest diameter 7 cm, the medium diameter 25 cm and the largest diameter 45 cm. 
    200203 
    201 === Forced clear cut (CHECK) === 
    202 OK_CLEARCUT is a flag used to force ORCHIDEE-CN-CAN to clearcut a forest after one year of simulation. This flag is set to TRUE in order to restart a new stand at the beginning of the FIN step in ENSEMBLE runs. It helps us to control the stand age at the end of the HIST step. If you want to use this flag for other purposes, do not forget that a clearcut means that the majority of the living biomass is removed (circ_class_biomass for sapwood and heartwood), but the other pools are transferred in the litter pool (leaf, branches, fruit, fine root). 
     204=== Forced clear cut (since r6470) === 
     205'''OK_CLEARCUT''' is a flag used to force ORCHIDEE-CN-CAN to clearcut a forest after one year of simulation. This flag is set to TRUE in order to start a new stand at the beginning of the FIN step in ENSEMBLE runs. It helps us to control the stand age at the end of the HIST step. If you want to use this flag for other purposes, do not forget that a clearcut means that the majority of the living biomass is removed (circ_class_biomass for sapwood and heartwood), but the other pools are transferred in the litter pool (leaf, branches, fruit, fine root). Note that if '''OK_CLEARCUT''' is used, the model will clearcut at the end of every year. The typical set-up should be: 300 years of spin-up with '''OK_CLEARCUT''' set to FALSE, 1 year with '''OK_CLEARCUT''' set to TRUE, a simulation with the length similar to the age of the forest with '''OK_CLEARCUT''' set to FALSE.  
    203206 
    204207=== Forest management and management changes (CHECK) === 
     
    233236 
    234237=== Harvest (CHECK) === 
    235 All biomass harvest is recorded in a harvest variable Harvest_pool, this variable also stores the mass and dimensions of the harvest/mortality (absolute numbers!). Related variables were introduced: harvest_type,harvest_cut, and harvest_area. Wood product pools and fluxes from wood and biomass decomposition are calculated in a separate module dedicated to wood use. The dimension of the wood use pools were externalized and can be changed to better address regional differences when aiming for regional simulations. The default 1, 10 and 100 year pools should be replaced by 2, 17 and 50 years pools in Europe.  
     238All biomass harvest is recorded in a harvest variable '''harvest_pool''', this variable also stores the mass and dimensions of the harvest/mortality (absolute numbers thus accounting for the pixel area!). Related variables were introduced: '''harvest_type''', '''harvest_cut''', and '''harvest_area'''. Wood product pools and fluxes from wood and biomass decomposition are calculated in a separate module dedicated to wood use. The dimension of the wood use pools were externalized and can be changed to better address regional differences when aiming for regional simulations. The default 1, 10 and 100 year pools were replaced by 2, 17 and 50 years which is closer to the reality for Europe. For most parts of the world a 100 year wood pool is optimistic.  
    236239 
    237240=== Leaf area index map (CHECK) === 
    238 Four flags have been identified that control the model behavior in terms of lai: ok_stomate, ok_pheno, impose_veg and read_lai. There is a 5th implicit flag which is whether restart files are used or not. If a restart file is used, the lai values will come from the sechiba restart file which is read at t=48. Given that each flag can take two values, we have 32 configurations in total. Out of these 32 configurations 10 are defined of which about 5 to 7 seem to be intended (for more details see Start and restart - Table 1). Many of the remaining 22 settings are inconsistent (i.e. running stomate to calculate a lai and reading an lai_map to prescribe lai), duplicate other settings, or would require further developments to work properly. Furthermore, the current code does not stop or warn when inconsistent settings are selected. The table (see Start and restart) proposes a scheme with 2 flags which can run with our without restart files, thus resulting in 8 different ways to control the lai in sechiba or the initial lai in stomate. The remaining 2 combinations are inconsistent and will stop the model. 
     241Four flags have been identified that control the model behavior in terms of lai: '''ok_stomate''', '''ok_pheno''', '''impose_veg''' and '''read_lai'''. There is a 5th implicit flag which is whether restart files are used or not. If a restart file is used, the lai values will come from the sechiba restart file which is read at t=48. Given that each flag can take two values, we have 32 configurations in total. Out of these 32 configurations 10 are defined of which about 5 to 7 seem to be intended (for more details see Start and restart - Table 1). Many of the remaining 22 settings are inconsistent (i.e. running stomate to calculate a lai and reading an lai_map to prescribe lai), duplicate other settings, or would require further developments to work properly. Furthermore, the current code does not stop or warn when inconsistent settings are selected. The table (see Start and restart) proposes a scheme with 2 flags which can run with our without restart files, thus resulting in 8 different ways to control the lai in sechiba or the initial lai in stomate. The remaining 2 combinations are inconsistent and will stop the model. 
    239242 
    240243In the ORCHIDEE and ORCHIDEE-CN, canopy structure is prescribed by a single variable lai and the assumption of a turbid medium (Lambert-Beer). Consequently reading an lai value suffice to prescribe the entire canopy. In ORCHIDEE-CN-CAN, however, canopy structure has become a 3D property that can be calculated from the leaf biomass, stem biomass, the number of individuals and the assumptions that the trees follow a Poisson distribution in the horizontal plain, that the crowns are spherical and that the leaf biomass is uniformly distributed within the crowns.