## Data and Methods
### Data Use
The EVI and LSWI are calculated as:  
\[\text{EVI}\ =2.5\times\frac{\rho_{nir}-\rho_{red}}{\rho_{nir}+(6\times\rho_{ red}-7.5\times\rho_{blue})+1} \tag{1}\]  
\[\text{LSWI}=\frac{\rho_{nir}-\rho_{swir}}{\rho_{nir}+\rho_{swir}} \tag{2}\]  
where \(\rho_{blue}\), \(\rho_{red}\), \(\rho_{nir}\) and \(\rho_{SWIR}\) are the Landsat (5, 7 and 8) surface reflectance for the blue, red, NIR and SWIR bands, respectively. The relationship between the two indices from the primary and secondary Landsat datasets for the study site represented very good agreement, with correlation (\(r\)) values ranging from 0.90 to 0.96 for EVI and from 0.90 to 0.95 for LSWI, indicating that secondary data canbe used as a patch. The scatter plots between the indices from the primary and secondary Landsat datasets are presented in Figure 2.  
Topographic maps for 2003 and 2014 with a scale of 1:25,000, interpreted by the Japan International Cooperation Agency (JICA) [54] and Regional Planning and Development Board (Bappeda) of Depnasar city, were used to generate land use types for 2003 and 2014, respectively. However, due to the absence of land use data for 1995, the topographic maps in 1992 from the Indonesian Geospatial Information Agency (BIG, previously known as the Indonesian National Coordination for Survey and Mapping, BAKOSURTANAL) were used to produce land use types for 1995. Land use data from 1992 and 2014 were derived from a basic map that is used by stakeholders and policy makers published by the Indonesian government through central and local governments, respectively. Land use data for 2003 were interpreted by JICA based on Landsat data from 2003 that were utilized by the Public Works Department of Bali Province. Through the Indonesian Geospatial Information Agency, the Indonesian government has a regulation that when a map is used as a base map for the government, it should have an accuracy \(\geq\)85%. Therefore, all land use data used in this study have an accuracy level greater than or equal to that allowed. All land use data used in this study are in the form of vector data and are subsequently converted into raster data with the same spatial resolution as the Landsat data. To address the complexity of land use types, land use was labelled, and the clusters were combined into five land use types, similar to the classification scheme used by [PERSON] et al. [25], i.e., settlement, forest, agriculture and grass, others, and water (Table 1). Water and other land use types were not included for analysing changes in GPP values due to land use conversion in the current study as these cover types were assumed to be relatively constant with respect to GPP [25]. Figure 2: Scatter plots of the Landsat base index from the main data with the data used for patching the no-data regions caused by clouds and their shadows. Top panels present enhanced vegetation index (EVI) and bottom panels present land surface water index (LWSI). (**a**,**b**) for Landsat 5 on 3 February 1995 with 26 May 1995; (**c**,**d**) for Landsat 7 on 21 March 2003 with 28 March 2003 (black dots) and for 21 March 2003 with 22 April 2003 (red dots); and (**e**,**f**) for Landsat 8 on 27 March 2014 with 11 March 2014.