## Data and Methods
### Methods  
GPP is estimated by the VPM. The VPM is an LUE model based on the conceptual partitioning of light absorption by chlorophyll pigments (FPAR\({}_{\rm chl}\)) and non-photosynthetic vegetation (NPV such as branches, trunks, stems or senescent leaves), where only FPAR\({}_{\rm chl}\) is used for photosynthesis [39]. A brief description of VPM is given below:  
\[\text{GPP }=\ \varepsilon_{g}\times\text{FPAR}_{\rm chl}\ \times\ \text{PAR} \tag{3}\]  
where \(\varepsilon_{g}\) is light-use efficiency (\(\mu\)mol m\({}^{-2}\) s\({}^{-1}\), photosynthetic photon flux density, PPFD); FPAR\({}_{\rm chl}\) is the fraction of photosynthetically active radiation (PAR) absorbed by chlorophyll; and PAR is the photosynthetically active radiation (\(\mu\)mol photosynthetic photon flux density, PPFD) calculated as 0.45 \(\times\) R (R, incoming global solar radiation). In the current study, daily PAR is summed in a year to obtain an annual PAR value; thus, annual GPP can be obtained. Light-use efficiency (\(\varepsilon_{g}\)) is a function of the maximum light-use efficiency (\(\varepsilon_{0}\)), temperature (\(T_{scalar}\)), water condition (\(W_{scalar}\)), and leaf phenology (\(P_{scalar}\)) and is defined as:  
\[\varepsilon_{g}=\varepsilon_{0}\times T_{scalar}\times W_{scalar}\times P_{ scalar} \tag{4}\]  
A maximum light-use efficiency, \(\varepsilon_{0}\), value of 0.40 gC mol\({}^{-1}\) PPFD [55] was used in this study. The parameter \(T_{scalar}\) represents the temperature sensitivity of photosynthesis and is calculated at each time step using the equation developed for the terrestrial ecosystem model [56]:  
\[T_{scalar}=\frac{(T-T_{\rm min})\times(T-T_{\rm max})}{\left[(T-T_{\rm min}) \times(T-T_{\rm max})\right]-(T-T_{opt})^{2}} \tag{5}\]  
where \(T\) is the monthly average air temperature (when PAR > 1 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\)) obtained from the Indonesian Meteorology, Climatology and Geophysics Agency (BMKG) and the parameters for \(T_{min}\), \(T_{max}\), and \(T_{opt}\) for photosynthesis were 0, 48, and 28 \({}^{\circ}\)C, respectively, based on [PERSON] et al. [43]. The \(W_{scalar}\) takes into account the complex impact of water stress on photosynthesis (i.e., changes in stomatal conductance, leaf water potential, etc.) caused by soil moisture and/or atmospheric water deficits [57]. \(W_{scalar}\) is calculated as follows [39]:  
\[W_{scalar}=\frac{1+\text{LSWI}}{1+\text{LSWI}_{\text{max}}} \tag{6}\]  
where \(\text{LSWI}_{\text{max}}\) is the maximum LSWI during the growing season for each pixel. In the VPM, \(P_{scalar}\) is included to account for the effect of leaf age on photosynthesis at the canopy level [58]. The calculation of \(P_{scalar}\) is dependent upon the longevity of leaves (deciduous, versus evergreen). For a canopy dominated by leaves with a life expectancy of one year, \(P_{scalar}\) is calculated in two different phases as a linear function [39]. Because urban areas have very complex and heterogeneous plant structures and always have new leaves emerging during the plant-growing season, \(P_{scalar}\) is set to be 1.0 in this study. \begin{table}
\begin{tabular}{c l} \hline \hline
**Land Use** & **Description** \\ \hline Settlement & Combines built-up areas, roads, backyards, and parking \\ Forest & Combines marroves, perennial plants, and shrubland \\ Agriculture and grass & Combines agricultural farmlands (irrigated paddy fields), \\  & dry land, grassy fields, golf courses, and parks \\ Others & Combines bare land and sand \\ Water & Combines rivers, fishponds, and dams \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definition of land use types for the current study.