# Dynamic vegetation processes

#### Maximum canopy storage <a href="#toc147754705" id="toc147754705"></a>

SPHY allows the user to use the dynamic vegetation module in order to incorporate a time-variable vegetation cover and corresponding rainfall interception. In order to calculate the rainfall interception, the canopy storage needs to be calculated, using a time series of NDVI (Carlson and Ripley 1997). The first step involves the calculation of the fraction photosynthetically active radiation (FPAR). FPAR can be calculated using a relation between NDVI and FPAR, which was found by Peng et al. (2012) and described by Sellers et al. (1996), according to:

*Equation 4*

$$
FPAR = min\Bigg(\frac{(SR-SR\_{min})(FPAR\_{max}-FPAR\_{min})}{SR\_{max}-SR\_{min}}+FPAR\_{min},0.95\Bigg)
$$

with

*Equation 5*

$$
SR = \frac{1+NVDI}{1-NVDI}
$$

and $$FPAR\_{max}$$(-) and  $$FPAR\_{min}$$(-) having values of 0.95 and 0.001, respectively. An FPAR of 0.95 is equivalent to the maximum LAI for a particular class, and an FPAR of 0.001 is equivalent to a minimum LAI. In order to calculate FPAR, an NDVI time series is required.

The second step is the calculation of the leaf-area index (LAI), which is eventually required to calculate the maximum canopy storage (). According to Monteith (1973), LAI for vegetation that is evenly distributed over a surface can be calculated using a logarithmic relation between LAI and FPAR, according to

*Equation 6*

$$
LAI = LAI\_{max} \*\frac{log(1-FPAR)}{log(1-FPAR\_{max})}
$$

with LAI (–) the leaf-area index, and $$LAI\_{max}$$ (-) the maximum leaf-area index (vegetation type dependent). This means that the maximum and minimum LAI values are related to the maximum and minimum of FPAR. Table 2 shows the $$LAI\_{max}$$values for a certain number of vegetation types.

For vegetation that is concentrated in clusters, the linear relation from Goward and Huemmrich (1992) is often used. However, since SPHY is generally applied using grid-cell resolutions between 250m and 1km, we can assume that the effect of having vegetation concentrated in clusters is negligible. Therefore, the calculation of LAI in SPHY is done using the logarithmic relation of Monteith (1973) (Equation 6).

The next step involves the calculation of the maximum canopy storage ( (mm)). Many different relations between and LAI can be found in the literature, depending on the vegetation type (Jong and Jetten 2010). The best results for crop canopies are shown by Kozak et al. (2007) and are archived by Von Hoyningen-Huene (1981), who derived the following relation between and LAI:

*Equation 7*

$$
Scan\_{max} = 0.935 + 0.498LAI-0.00575LAI^2
$$

#### Interception <a href="#toc147754706" id="toc147754706"></a>

Interception is calculated on a daily basis if the dynamic vegetation module is used, and consists of the daily precipitation plus the intercepted water remaining in the canopy storage from the previous day. First, the canopy storage is updated with the amount of precipitation of the current day:

*Equation 8*

$$
Scan\_t=Scan(t-1)+P\_t
$$

with $$Scan\_{t} (mm)$$ the canopy storage on day $$t$$,  $$Scan\_{t-1} (mm)$$ the canopy storage on day $$t-1$$, and $$P\_{t} (mm)$$ the amount of precipitation on day $$t$$. The portion of precipitation that cannot be stored in the canopy storage is known as precipitation throughfall, or effective precipitation, according to:

*Equation 9*

$$
Pe\_t=max(0,Scan\_t-Scan\_{max,t})
$$

with  $$Pe\_{t} (mm)$$ the effective precipitation on day $$t$$, and $$Scan\_{t} (mm)$$ the canopy storage on day $$t$$. This equation shows that precipitation throughfall only occurs if the water stored in the canopy exceeds the maximum canopy storage. After the effective precipitation has been calculated, the canopy storage is updated as:

*Equation 10*

$$
Scan\_t=Scan\_t=Pe\_t
$$

The remaining amount of water stored in the canopy is available for interception, and the amount of water that will be intercepted depends on the atmospheric demand for open water evaporation. A commonly used value for the atmospheric demand for open water evaporation is 1.5 (Allen et al. 1998), which is derived from the ratio between 1 and the mean pan evaporation coefficient Kp(\~0.65). The interception can now be calculated using

*Equation 11*

$$
Int\_t=min(1.5ET\_{r,t},Scan\_t)
$$

with $$Int\_{t} (mm)$$ the intercepted water on day $$t$$, and $$ET\_{r,t} (mm)$$ the reference evapotranspiration on day $$t$$. Finally, the canopy storage is updated by subtracting the interception:

*Equation 12*

$$
Scan\_t=Scan\_t-Int\_t
$$
