Plant biomass dynamics

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The change in the biomass $B$ from day $t$ to $t+1$ of species $s$ in patch $x,y$ [kg ha⁻¹] is calculated based on the actual growth $G_{act,txys}$ [kg ha⁻¹], and the losses by senescence $S_{txys}$ [kg ha⁻¹] and management $M_{txys}$ [kg ha⁻¹]:

$$B_{t+1xys}=B_{txys}+G_{act,txys}-S_{txys}-M_{txys}$$

The change in the total biomass $B_{txys}$ is divided into the change in above-ground $B_{A,txys}$ [kg ha⁻¹] and below-ground biomass $B_{txys}$ [kg ha⁻¹]. We assume that plants aim to achieve a similar level of above-ground biomass per total biomass similar to the time-invariant trait above-ground biomass per total biomass $ab{p}_s$ [-]. We therefore calculate $A_{txys}$ [-] the ratio between the actual biomass ratio and the trait $ab{p}_s$:

$$A_{txys}=\frac{\left(\frac{B_{A,txys}}{B_{txys}}\right)}{ab{p}_s}$$

$A_{txys}$ is less than one if the above-ground biomass per total biomass is less than expected by the trait $ab{p}_s$, for example after a mowing event. This variable can be used to allocate biomass changes by growth and senescence to above-ground and below-ground biomass. Biomass loss by mowing and grazing affects only the above-ground biomass:

$$\begin{array}{rl}{B}_{A,t+1xys}& =B_{A,txys}+A_{txys}\cdot G_{act,txys}-(1-A_{txys})\cdot S_{txys}-M_{txys}\\ B_{B,t+1xys}& =B_{B,txys}+(1-A_{txys})\cdot G_{act,txys}-A_{txys}\cdot S_{txys}\end{array}$$