State variables
Table 16: Geometrical state variables.
| Symbol | Description | Unit |
|---|---|---|
| $D$ | Stem diameter at breast height | $\text{m}$ |
| $H$ | Height | $\text{m}$ |
| $C_{D}$ | Crown diameter | $\text{m}$ |
| $C_{L}$ | Crown length | $\text{m}$ |
| $C_{A}$ | Crown projection area | $\text{m}^2$ |
| $B$ | Aboveground biomass | $t_{\text{ODM}}$ |
| $LAI$ | Leaf area index | - |
| $\Delta B$ | Biomass increment per time step | $t_{\text{ODM}}$ |
| $\Delta D$ | Diameter increment per time step | $\text{m}$ |
Table 17: Recruitment and establishment state variables.
| Symbol | Description | Unit |
|---|---|---|
| $N_{\text{pool}}$ | Seed pool (i.e number of seeds) | $\tfrac{1}{\text{patch}}$ |
| $N_{\text{germ}}$ | Number of successfully germinated seeds | $\tfrac{1}{\text{patch}}$ |
| $N_{\text{est}}$ | Number of successfully established seedlings | $\tfrac{1}{\text{patch}}$ |
| $x_{\text{ind}}$, $y_{\text{ind}}$ | Random position of a mother tree on a patch | - |
| $x_{\text{seed}}$, $y_{\text{seed}}$ | Position of a dispersed seed | - |
| $I_{\text{floor}}$ | Percentage of incoming irradiance at floor | $\%$ |
Table 18: Mortality state variables.
| Symbol | Description | Unit |
|---|---|---|
| $M_{D}$ | Mortality rate dependent on stem diameter | $\tfrac{1}{\text{yr}}$ |
| $M_{I}$ | Mortality rate dependent on stem diameter increment | $\tfrac{1}{\text{yr}}$ |
| $M$ | Mortality rate affecting individuals each time step | $\tfrac{1}{\text{yr}}$ |
| $m_{\text{frag}}$ | Factor changing the mortality rate $M$ due to fragmentation | - |
| $CCA_{i}$, $i = 1$, $...$, $\#_{\text{layer}}$ | Cumulative crown area per height layer | - |
| $l_{\text{min}}$, $l_{\text{max}}$ | Lower and upper height layer covered by the crown of a single individual | - |
| $R_{c}$ | Individual crowding reduction factor | - |
| $N_{C}$ | Number of individuals dying due to crowding | $\tfrac{1}{\text{cohort}}$ |
| $N_{Y}$ | Number of individuals dying due to mortality per time step | $\tfrac{1}{\text{cohort}}$ |
| $N$ | Number of alive individuals | $\tfrac{1}{\text{cohort}}$ |
| $\Delta _{rM}$ | Auxillary variable | - |
| $N_{F}$ | Number of individuals affected by a falling tree | - |
Table 19: Light climate and growth state variables.
| Symbol | Description | Unit |
|---|---|---|
| $\overline{L_i}$ | Individual leaf area contribution to height layer $i$ | $\text{m}^2$ |
| $\widehat{L_i}$ | Patch-based leaf area index | - |
| $I_{\text{ind}}$ | Incoming irradiance on top of an individual | $\tfrac{\mu\text{mol}_{\text{photon}}}{{\text{m}^2}\text{s}}$ |
| $I_{\text{leaf}}$ | Incoming irradiance on top of the leaf surface (absorbable radiation) | $\tfrac{\mu\text{mol}_{\text{photon}}}{{\text{m}^2}\text{s}}$ |
| $P_{\text{ind}}$ | Gross photosynthetic rate of an individual | $\tfrac{\mu\text{mol}_{\text{CO}_2}}{\text{yr}}$ |
| $P_{\text{leaf}}$ | Gross photosynthetic rate of a single leaf | $\tfrac{\mu\text{mol}_{\text{CO}_2}}{\text{m}^2\text{s}}$ |
| $GPP$ | Gross productivity of an individual (possibly reduced) | $\tfrac{t_{\text{ODM}}}{\text{yr}}$ |
| $R_{m}$ | Maintenance respiration | $\tfrac{t_{\text{ODM}}}{\text{yr}}$ |
| $r_{m}$ | Maintenance respiration rate | $\tfrac{1}{\text{yr}}$ |
Table 20: Water module state variables.
| Symbol | Description | Unit |
|---|---|---|
| $\Theta_{\text{soil}}$ | Soil water content | $\tfrac{\text{mm}}{\text{h}}$ |
| $IN$ | Interception | $\tfrac{\text{mm}}{\text{h}}$ |
| $RO$ | Run-off | $\tfrac{\text{mm}}{\text{h}}$ |
| $RO_{\rightarrow}$ | Surface run-off | $\tfrac{\text{mm}}{\text{h}}$ |
| $RO_{\downarrow}$ | Sub-surface run-off | $\tfrac{\text{mm}}{\text{h}}$ |
| $TR$ | Transpiration | $\tfrac{\text{mm}}{\text{h}}$ |
| $\phi_{W}$ | Reduction factor of $GPP$ due to limited soil water | - |
Table 21: Temperature state variables.
| Symbol | Description | Unit |
|---|---|---|
| $\phi_{\text{act}}$ | Length of vegetation period | $\text{d}$ |
| $\phi_{T}$ | Limitation factor of $GPP$ by temperature | - |
| $\phi_{T,l}, \phi_{T,h}$ | Inhibition factors for low and high temperatures | - |
| $\kappa_{T}$ | Factor affecting maintenance respiration rate $r_{M}$ by temperature | - |
Table 22: Carbon cycle state variables.
| Symbol | Description | Unit |
|---|---|---|
| $S_{\text{dead}}$ | Carbon stock of deadwood | $\tfrac{t_C}{\text{patch}}$ |
| $S_{\text{slow}}$ | Carbon amount of slow decomposing soil stock | $\tfrac{t_C}{\text{patch}}$ |
| $S_{\text{fast}}$ | Carbon amount of fast decomposing soil stock | $\tfrac{t_C}{\text{patch}}$ |
| $S_{\text{mort}}$ | Carbon amount of individuals dying within the current time step | $\tfrac{t_C}{\text{patch}}$ |
| $t_{S_{\text{dead}}\rightarrow A}$ | Transition rate of carbon from deadwood stock $S_{\text{dead}}$ to atmosphere $A$ | $\tfrac{t_C}{\text{patch}}$ |
| $t_{S_{\text{slow}}\rightarrow A}$ | Transition rate of carbon from slow decomposing soil stock $S_{\text{dead}}$ to atmosphere $A$ | $\tfrac{t_C}{\text{patch}}$ |
| $t_{S_{\text{fast}}\rightarrow A}$ | Transition rate of carbon from fast decomposing soil stock $S_{\text{dead}}$ to atmosphere $A$ | $\tfrac{t_C}{\text{patch}}$ |
| $t_{S_{\text{dead}}\rightarrow}$ | Transition rate of carbon from deadwood stock $S_{\text{dead}}$ to soil | $\tfrac{t_C}{\text{patch}}$ |
| $t_{S_{\text{dead}}}\rightarrow S_{\text{slow}}$ | Transition rate of carbon from deadwood stock $S_{\text{dead}}$ to slow decomposing soil stock $S_{\text{slow}}$ | $\tfrac{t_C}{\text{patch}}$ |
| $t_{S_{\text{dead}}}\rightarrow S_{\text{fast}}$ | Transition rate of carbon from deadwood stock $S_{\text{dead}}$ to fast decomposing soil stock $S_{\text{fast}}$ | $\tfrac{t_C}{\text{patch}}$ |
| $NEE$ | Net ecosystem exchange | $\tfrac{t_C}{\text{patch}}$ |
| $C_{GPP}$ | Carbon amount of gross productivity per patch | $\tfrac{t_C}{\text{patch}}$ |
| $C_{R}$ | Carbon amount released by total respiration per patch | $\tfrac{t_C}{\text{patch}}$ |
Table 23: Disturbances (fire, landslide) state variables.
| Symbol | Description | Unit |
|---|---|---|
| $N_{D}$ | Number of individuals dying due to disturbances | $\tfrac{1}{\text{cohort}}$ |
| $P_{F_1}, P_{F_2}, P_{F_3}, P_{F_4}$ | Burning probabilities for the 4 fire tolerance levels | - |
Table 24: Lidar state variables.
| Symbol | Description | Unit |
|---|---|---|
| $d_{\text{Lid}}$ | Number of vegetation voxels above a focal voxel, corresponds to distance that the laser beam traveled within tree canopy space | $\text{m}$ |
| $P_{\text{Lid}}$ | Probability of a voxel to contain a Lidar return | - |