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Regional context

Indonesia (officially the Republic of Indonesia) is the largest archipelago country (over 17,000 islands) and the 14th largest country by area (about 2 million km2) in the world 19. The archipelago covers tropical rainforest, tropical monsoon, and tropical savanna climates, where there are more than 300 ethnic groups 19. Indonesia consists of 38 provinces, and the governance system is decentralized since the end of the twentieth century 19,20. In Indonesia, regencies (kabupaten) and representative cities (kota) are positioned at the same administrative level (level 2); the average size of regencies/cities is 3622 km2 (ranging from 10 to 44,013 km2). Regencies/cities are administratively separated by geographic conditions and historical (social, cultural, and political) backgrounds, with each regency/city having homogeneous environmental conditions and a socioeconomic status. 16.

The main drivers of the rapid deforestation in Indonesia were population growth and economic expansion, including the illegal clearance of forests 21,22. Indonesias economy has grown by>5% per year on average since 2000 until the Covid-19 pandemic; GDP PPP (international dollars) increased about three times from 1 Trillion USD in 2000 to 3.33 Trillion USD in 2019 23. Additionally, its population has increased by 1.14% annually, leading to an approximately 30% growth during this period (i.e., from 211 Million in 2000 to 273 Million in 2020), making it the most populous and prosperous country in Southeast Asia 19. Indonesia is also one of the largest emitters of greenhouse gases (GHG) 24.

In contrast, the Indonesian government is committed to unconditionally reduce its GHG emission by 29% and up to 41% if international assistance for finance, technology transfer, and capacity building are provided25. The land-use and energy sectors are to minimize the national GHG emission. Therefore, Indonesia first introduced moratorium on new forest clearance in 2011 26 and made it permanent in 2019 3. This moratorium mainly targeted Kalimantan, Sumatra, and Papua (New Guinea), which had been center of deforestation in the beginning of 2000s 3,27.

Meanwhile, agriculture has expanded in this century, with the primary export goods (e.g., oil palm and rubber plantations) coming from Sumatra and Kalimantan 5. Conversely, since the turn of the century, sustainable forestry policies in Java have caused a surge in the forestation of local smallholders 6. There are indications that forests on Java Island are recovering 7,8. Due to improved forestry policies and reforestation activities, the deforestation rate has decreased since 2011 9. Deforestation has been reported from all over Indonesia, but the causes of deforestation were different from one region to another because of geographic conditions and socioeconomic statuses 28.

Many studies have demonstrated that the NDVI is related to the leaf area, green biomass, percent green cover, and a fraction of absorbed photosynthetically active radiation (fAPAR) 18,29,30; moreover, NDVI is a global-based vegetation index. We utilized the product of NASA's MODIS Terra Program version 6.1. This product provides data at 16-day intervals (i.e., composite data for a 16-day period derived from images that are acquired almost every day) at 250m spatial resolution after correction for atmospheric effects (aerosols and gases) and sensor degradation, angular consideration, and minimization of the influence of daily cloud covers for consistent spatial and temporal comparisons of vegetation 17,18. The NDVI runs from1 to+1 (acceptable range for the NDVI of the MODIS: from0.2 to+1) and is determined from the visible and near-infrared light reflected by the quantity (biomass) and/or composition of vegetation.

The information used was from LP DAAC, a part of NASAs Earth Observing System Data and Information System run in cooperation between the US Geological Survey and NASA. We utilized the shapefile of Administrative Level 2 in April 2020 created by the Indonesian Bureau of Statistics (BPS). This was made available through the Humanitarian Data Exchange program (HDX) of the United Nations Office for Coordination of Humanitarian Affairs (OCHA) (https://data.humdata.org/) 31. The Administrative Level 2 consisted of 93 cities (kota), five administrative cities (kota administrasi), 415 regencies (kabupaten), and one administrative regency (kabupaten administrasi) (Supplementary Table 1). Each MOD13Q1 picture was dissected for the Administrative Level 2 and pixel reliability (1: no data; 0: excellent data; 1: poor data; 2: snow/ice; and 3: cloud). The coastal regions, where the pixels had recorded water cover, experienced the pixel reliability of MOD13Q1 with1 (no data). The NDVI was unreliable when the pixels were classified as level 2 (snow/ice). No NDVI was available for the pixels covered in clouds (pixel reliability=3). These cases were disregarded from further analysis. Hence, the average NDVI was determined for regions in each regency/city at each time point with a pixel reliability range of 0 or 1. Seribu Islands was the sole administrative regency, which was omitted from the studies because it was composed of a number of tiny islands, and all pixels covering it had some sea in them. Accordingly, further evaluations were conducted for 513 regencies and cities throughout a 20-year span (i.e., every 16days; 460 time points). We downloaded a total of 5520 pictures since 12 MOD13Q1 images at each time point cover the whole Indonesia.

We split the NDVI changes in the MOD13Q1 data into trends, seasonal changes, and residuals using a stochasticlevel and deterministic seasonal state space model (SSM). We performed time-series studies based on SSM 32 using two steps 16: (1) the NDVI data were averaged for each geographic unit (regency or city); and (2) stochasticlevel and deterministic seasonal models were used. The time-series change in this model was divided into trends, cycles, and residuals while excluding noises. The slopes and the levels were determined by a stochastic process, seasonal changes (annual cycle), and irregular changes with interporation of missing datasmoothed by the Kalman filter. The maximum likelihood estimation was made for the following equations:

$${y}_{t}={mu }_{t}+ {gamma }_{t}+ {varepsilon }_{t}, {varepsilon }_{t}sim mathrm{NID} left(0, {sigma }_{varepsilon }^{2}right)$$

$${mu }_{t+1}={mu }_{t}+{xi }_{t}, { xi }_{t}sim mathrm{NID}(0,{sigma }_{xi }^{2})$$

$${gamma }_{1, t+1}= {-gamma }_{1, t} {-gamma }_{2, t}dots {-gamma }_{22, t}$$

$${gamma }_{2, t+1}= {gamma }_{1, t}$$

$${gamma }_{22, t+1}= {gamma }_{21, t}$$

for t=1, n, where ({y}_{t}) is the observation (NDVI) at time t; ({mu }_{t}) is the unobserved level at time t; ({gamma }_{t}= {gamma }_{1, t}) denotes the seasonal component; ({varepsilon }_{t}) is the observation disturbance term at time t; and ({xi }_{t}) is called the level disturbance term at time t. The level ({mu }_{t}) was allowed to vary over time in the stochasticlevel and deterministic seasonal model. The seasonal changes, trends, and residuals are represented by , , and , respectively. R Software version 4.1.2 with dlm package was used for the analysis 33.

The USGS Earth Resources Observation and Science Center and the Climate Hazard Center of the University of California in Santa Barbara developed climate hazards group infrared precipitation with station (CHIRPS) v2p0, which provide data on rainfall estimates from rain gauge and satellite observations and is available for the entire world, including areas with sparse surface data 34. CHIRPS provide moderate resolution (0.05) gridded precipitation information. We obtained the CHIRPS monthly data for Indonesia from 2001 to 2020 and masked them at the administrative 1 (province) level (data compiled by Indonesian Statistical Office and available at OCHA HDX) because the resolution of CHIRPS is coarser than that of MOD13Q1. Using the same SSM model with the NDVI data, we decomposed the precipitation data into trends and seasonal cycles while excluding noises.Furthermore, the monthly average precipitation for each province over the course of 20 years was calculated from this dataset (rainfall level).

We used the population density data and the GDP at the regency/city level issued by the Ministry of Internal Affairs of the Republic of Indonesia 35. However, we were unable to study the time-series changes in socioeconomic development over a 20-year period because the administrative units increased from 397 in 2001 to 514 in 2020 due to the administrative reforms brought about by population and economic growth. The data used in this study were (1) the population densities in 2020, (2) GDP proportion from agriculture, forestry, and fisheries (as an indicator of the land-use intensities for agricultural and forestry development), and (3) GDP proportion from financial and insurance activities (as urban development). These indicators reflected the socioeconomic conditions of Indonesia, where the inequality in development among regions is very high. The total GDP was not used because it was closely correlated with the three variables used in this work.

After obtaining results of time-series analyses, we also conducted field observations in 2022 in North Sumatra, the Special Capital Region of Jakarta, Central Java, the Special Region of Yogyakarta, and South Sulawesi. We visited regencies and cities showing very consistent increases or decreases in NDVI, rapid loss or growth in NDVI, or dramatically irregular changes (e.g., disasters); furthermore, we observed the reasons behind such changes. In addition, we observed vegetation changes between 2014 and 2017 in parts of East Nusa Tenggara 16.

We defined the Pearsons correlation coefficients of the NDVI trend (after noise and cycle elimination) with time (every 16day) as the NDVI consistent trend. Furthermore, we defined the NDVI variation between 2001 and 2020 (in other words, differences in the average NDVI between 2020 and 2001) as the NDVI value change. Pettitts Test was used to identify the trend change-points 36. For precipitation, the correlation of the trend with time and the difference in the NDVI between 2020 and 2001 were also computed (CHIPRS data).

We used classification and regression trees (CART), a decision tree model data mining method that explains how a target variable is predicted by other variables based on categorizing samples into binary classes 37; exponential was used for NDVI consistent trend. The decision tree regression analysis was conducted to explore factors contributing to the consistent trend of the NDVI and the NDVI value changes. To minimize overfitting, the complexity parameter (cp) value for the biggest cross-validated prediction error of less than the minimal relative error plus the cross-validated prediction standard deviation was used as the cut-off (pruning tree model). To reflect the differences in agricultural intensities and main tree crops, all regencies and cities were classified into Sumatra, Western Kalimantan, Eastern Kalimantan, Western Java, Eastern Java, Nusa Tenggara, Northern Sulawesi, Southern Sulawesi, Maluku, and Papua (Supplementary Fig.1). QGIS 3.22.4 Biaowiea (QGIS Development Team) (https://qgis.org/) was utilized for the map creation.

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