Description of the LUE-NDWI model
The NDWI, strongly related to vegetation water content (Murphy et al., 2018; )(50), can be a very good proxy for vegetation water stress. After examining measurements from many flux towers, we found that the following nonlinear function can be used to representWS , the regulation scalar of water stress on GPP:
\begin{equation} \mathbf{W}_{\mathbf{S}\_\mathbf{\text{NDWI}}}=\mathbf{a}*\left(-\mathbf{\text{NDWI}}+\mathbf{0}.\mathbf{5}\right)^{\mathbf{b}}+\mathbf{c}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\mathbf{7})\nonumber \\ \end{equation}
Using the NLS method of parameter optimization adjustment, the coefficients were determined to be a (=0.35), b (=2.14) and c (=0.086). The WS_NDWI values vary between 0 and 1, with values beyond the bounds set to 0 or 1, respectively. The use of WS_NDWI can be very convenient for applications from local to global scales as the NDWI fields can be directly derived from satellite observations.