## 3 Methods
### Estimation of GPP  
The GPP of urban vegetation was estimated using the MOD17 algorithm, which is based on the light-use efficiency (LUE) method [37]. GPP is related to the amount of photosynthetically active radiation (PAR) absorbed by the canopy through the use of a maximum radiation use conversion efficiency term (\(\varepsilon\)), such that [12]:  
\[\text{GPP}\left(\text{kg}\;\text{C}\;\text{m}^{-2}\text{day}^{-1}\right)\;=\; \varepsilon\;\left(\text{kg}\;\text{C}\;\text{MJ}^{-1}\right)\times\text{ fPAR}\times\text{PAR}\left(\text{MJ}\;\text{m}^{-2}\text{day}^{-1}\right), \tag{2}\]where fPAR is the fraction of incident PAR absorbed by the canopy, and PAR is the flux density of photosynthetically active radiation.  
The value of \(\varepsilon\) depends on the vegetation type, and is reduced by the daily minimum air temperature (T\({}_{\mathrm{MIN}}\)) and day-time vapor pressure deficit (VPD). \(\varepsilon\) is calculated as:  
\[\varepsilon\ =\ \mathrm{LUE}\left(\mathrm{kg}\ \mathrm{C}\ \mathrm{MJ}^{-1} \right)\times\mathrm{T_{MIN}scalar}\times\mathrm{VPDscalar}, \tag{3}\]  
The lack of flux towers within or around the study area made it inapplicable to calibrate \(\varepsilon\) using field data. The parameters for calculating LUE were taken from the modified biome property look-up table (BPLUT) provided by [PERSON] [PERSON] (2018). T\({}_{\mathrm{MIN}}\) and VPD scalars are multipliers that reduce the conversion efficiency when cold temperature and/or high VPD inhibit photosynthesis. The scalars are calculated as follows:  
\[\mathrm{T_{MIN}scalar}\ =\ \left(\mathrm{T_{MIN}}-\mathrm{T_{MIN}}\right)/ \left(\mathrm{T_{MIN}max}-\mathrm{T_{MIN}}\right), \tag{4}\]  
where T\({}_{\mathrm{MIN}}\) is the daily minimum temperature, T\({}_{\mathrm{MIN}min}\) is the daily minimum temperature at which LUE is 0, and T\({}_{\mathrm{MIN}max}\) is the daily maximum temperature at which LUE is maximum.  
\[\mathrm{VPDscalar}\ =\ \left(\mathrm{VPD_{max}}-\mathrm{daytime}\ \mathrm{average}\ \mathrm{VPD}\right)/\left(\mathrm{VPD_{max}}-\mathrm{VPD_{min}}\right), \tag{5}\]  
where VPD\({}_{\mathrm{min}}\) is the daily minimum VPD at which LUE is maximum, and VPD\({}_{\mathrm{max}}\) is the daily maximum VPD at which LUE is 0.  
fPAR was calculated with STARFM-derived synthetic NDVI, using the equation proposed by [PERSON] and [PERSON] [PERSON] and [PERSON] (2018):  
\[\mathrm{fPAR}\ =\ 1.1638*\mathrm{NDVI}-0.1426, \tag{6}\]  
The GPP values of built-up areas, water bodies, and bare land within the study area were set to zero.  
To minimize the effects of meteorological variations and emphasize the impacts of LUCC, GPP was estimated at 30-m resolution for every eight days under two scenarios. In the first scenario, GPP was estimated with the STARFM-generated NDVI, land cover maps, and ground-based meteorological measurements from 2000 to 2013. In the second scenario, GPP was estimated using the STARFM-generated NDVI from 2000 to 2013, the land cover maps from 2000 to 2013, and the meteorological data of the year 2000. The estimation of the first scenario (referred to as GPP_act) represented the actual dynamics of GPP in the study area, and was used for validation. The GPP estimated under the second scenario (referred to as GPP_ref) was used to quantify the impacts of LUCC on GPP in the urban areas.