# Satellite-Observed Global Terrestrial Vegetation Production in Response to Water Availability
## 2 Materials and Methods
### Lue Gpp  
The global GPP for the 1982-2015 period was calculated based on the LUE equation, as follows [31]:  
\[GPP=\varepsilon_{max}\times SOL\times 0.45\times fPAR\times f(T)\times f(W), \tag{1}\]  
in which \(\varepsilon_{max}\) is vegetation type related maximum light use efficiency, \(SOL\) is downward solar shortwave radiation, and \(fPAR\) represents the fraction of photosynthetically active radiation vegetation absorbs. \(ft\) and \(fw\) are temperature and water stress respectively to plant productivity. We adopted the meteorological data from the CRU-NCEPV6.1 dataset, which includes downward shortwave radiation, air temperature, specific humidity and air pressure, and so forth. We used \(fPAR\) [PERSON] et al. [27] developed. We calculated the temperature stress with Equation (2), as follows:  
\[ft=\frac{(T-T_{MIN})(T-T_{MAX})}{\left[(T-T_{MIN})(T-T_{MAX})\right]-\left(T-T _{opt}\right)^{2}}, \tag{2}\]  
in which \(T_{MIN}\) and \(T_{MAX}\) are the minimum and maximum temperature for plant's photosynthesis, with the specific parameters can be found in [PERSON] et al. [32]. In this study, we focused particularly on determining water stress (\(fw\)) in the LUE equation. The MODIS-GPP algorithm [33] calculates \(fw\) with the daily vapor pressure deficit (VPD) on consideration that leaf stomatal conductance is mainly restricted by cold stress and VPD, named VPDMOD expressed as in Equation (3):  
\[fw=f(VPD)=\left\{ \begin{array}{cc}1&\quad VPD\leq VPD_{open}\\ \frac{VPD_{close}-VPD_{open}}{VPD_{close}-VPD_{open}}&\quad VPD_{open}<VPD <VPD_{close}\\ 0&\quad VPD\geq VPD_{close}\end{array} \right., \tag{3}\]  
in which \(VPD_{close}\) represents VPD that induces full stomatal closure, while \(VPD_{open}\) represents VPD that results in full stomatal opening, all parameters are set based on the vegetation type. The GLO-PEM algorithm [34] considers each vegetation type's optimum growth temperature (\(T_{opt}\)). The algorithm calculates water stress with vegetation type, independently with Equation (4) named VPDGLO:  
\[fw=f(VPD)=\left\{ \begin{array}{cc}1-0.05\delta_{q}&\quad 0<\delta_{q}\leq 15 \\ 0.25&\delta_{q}>15\end{array} \right., \tag{4}\]  
in which \(\delta_{q}\) is the specific humidity deficit (g/kg), the difference between saturated and actual specific humidity. The CASA model provides a framework that considers water stress with a multidisciplinary algorithm [35], shown in Equation (5), as follows:  
\[W_{\text{s}}=\left\{\begin{array}{cc}fw=f(VPD)\times W_{s}\\ 1\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\in which \(ETR\) is the ratio of actual evapotranspiration to potential evapotranspiration. According to FAO 56 [36], \(ETR\) can be equal to \(K_{S}\), which is calculated based on root zone soil moisture (hereinafter \(SM\)) and soil and vegetation properties, written as Equations (6) and (7):  
\[K_{S}=\frac{SM-WP}{(1-p)\times TAW} \tag{6}\]  
\[p=p_{std}+0.04\times(5-ET_{0}), \tag{7}\]  
in which WP and \(TAW\) represent soil wilting point and total available soil water derived from the International Geosphere-Biosphere Programme Data and Information System (IGMP-DIS) dataset [37] and the World Inventory of Soil property Estimates (WISE) derived soil properties [38]. \(ET_{0}\) is calculated with Hagreeaves equation [39] while \(p_{std}\) is a vegetation type-specific depletion factor (allowable extent of soil water deficit before water stress) at \(ET_{0}\) of 5 mm per day. Actual evapotranspiration, potential evapotranspiration, and root-zone soil moisture data were all acquired from the GLEAM dataset. In this study, we provided a dataset of monthly plant productivity that spans the 34-year period from 1982-2015 at the global scale, composed by five LUE GPPs derived from the multidisciplinary framework in Equation (5). These five GPPs represent different considerations of water stress in the LUE equation, the VPD only model, VPD\({}_{\text{GLO}}\)-ETR model, VPD\({}_{\text{MOD}}\)-ETR model, VPD\({}_{\text{GLO}}\)-SM model, and VPD\({}_{\text{MOD}}\)-SM model.