# Spatiotemporal Variations in Vegetation Canopy Interception in China Based on a Revised Gash Model
## 2 Materials and Methods
### The Revised Gash Model  
The analytical Gash model assumes that rainfall events separated by sufficiently long intervals and the intercepted water is completely evaporated before the next rainfall [45]. Three phases could be distinguished in each rainfall event: (1) the wetting phase, as rainfall reaches the canopy; (2) the saturation phase, as the canopy reaches its maximum water storage capacity; and (3) the drying phase after rainfall has ceased. Then, the model adds up the canopy interception of each phase to obtain the total canopy interception. The revised version considers leaves, branches, and crowns as a whole during the estimation of canopy interception [1; 21], and introduces additional parameters, such as canopy coverage to simplify the calculation. The calculation formula is:  
\[\left\{\begin{aligned} & I_{j}=c\sum_{j=1}^{m}P_{G,j},P_{G}\leq P_{G, j}^{\prime}\\ & Ij=(ncP_{G}^{\prime}-ncS_{c})+c\frac{\overline{E}}{R}\sum_{j=1} ^{n}\left(P_{G,j}-P_{G}^{\prime}\right)+ncS_{c}+(qS_{t}+P_{t}\sum_{j=1}^{n-q}P_ {G,j}),P_{G}>P_{G,j}^{\prime}\end{aligned}\right. \tag{1}\]  
where \(m\) and \(n\) indicate that the vegetation is not saturated for \(m\) times and is saturated for \(n\) times of the \(m+n\) precipitation events; \(I_{j}\) is the canopy interception of the \(jth\) of \(m\) rainfall events; \(c\) is the canopy density; \(q\) is the number of times that the trunk reaches saturation and produces stemflow; \(P_{G,j}\) is the gross rainfall (mm) of the \(jth\) of \(m\) rainfall events; \(S_{c}\) is the canopy storage capacity and \(S_{c}=S/c\); \(S_{t}\) is the trunk storage capacity (mm); \(\overline{E}\) is the averaged evaporation rate (mm/h) and \(E_{c}=\overline{E}/c\); \(\overline{R}\) is the average rainfall rate (mm/h); \(S_{t}\) is the trunk storage capacity (mm); and \(P_{t}\) is the stem runoff coefficient.  
Several studies have attempted to develop the remote sensing based Gash model, and successfully applied it to simulate canopy interception in large-scale regions [30; 32; 46]. The calculation formula is:  
\[\left\{\begin{aligned} I_{i}=F_{vc}\times P_{G},P_{G}\leq P^{\prime}_ {G,i}\\ I_{i}=F_{vc}\times P_{G,i}+(F_{vc}\times\frac{\overline{E_{v}}}{ \overline{R}}),P_{G}>P^{\prime}_{G,i}\end{aligned}\right. \tag{2}\]  
where \(I_{i}\) is the canopy interception of the _ith_ subpixel; \(F_{vc}\) is the vegetation coverage; \(P_{G}\) is the gross rainfall; \(P^{\prime}_{G,i}\) is the rainfall threshold for saturation; \(\frac{\overline{E_{v}}}{\overline{R}}\) is the ratio of the mean evaporation rate to the mean rainfall rate, which is selected on the assumption that the evaporation of the saturated canopy and trunk are the same. The calculation formula of \(P^{\prime}_{G,i}\) is as follows:  
\[P^{\prime}_{G,i}=-\frac{\overline{R}}{\overline{E_{v}}}\times\frac{S_{\text{ regg}}}{F_{vc}}\times\ln(1-\frac{\overline{E_{v}}}{\overline{R}}) \tag{3}\]  
where \(S_{\text{reg}}\) is the canopy and stem storage capacity, and it is assumed to be linearly related to the vegetation area index (_VAI_).