## 2 Materials and Methods
### Data and Data Processing  
#### 2.2.1 Remote Sensing Data  
**MODIS VI Products:** MODIS VI products could provide consistent spatial and temporal comparisons of vegetation chlorophyll and canopy structure [27]. In this paper, the MODIS VI products (MOD13A1 C06) were generated with 16-day intervals and a spatial resolution of 500 m [28]. NDVI and EVI derived from atmospherically-corrected reflectance in the red, near-infrared and blue wavebands were used in this paper to assess the forest degradation. To minimize the impact of phenology, the mean NDVI and EVI from June to August from 2000 to 2010 were acquired in this paper. Ratio Vegetation Index (RVI) was well related to chlorophyll and biomass, which was defined as the ratio of the reflectance of near-infrared to the reflectance of red, was also obtained from MODIS VI products. **MODIS LAI/FPAR Products:** MODIS Leaf Area Index (LAI)/Fraction of Photosynthetically Active Radiation (FPAR) products (MOD15A2H C06) [29] were provided on an 8-day basis with a spatial resolution of 500 m. The LAI/FPAR retrieve algorithm consisted of a main algorithm that employed a biome-dependent look-up table based on simulations with a stochastic radiative transfer model that considered three-dimensional canopy  
Figure 1: Location of Three-North Forest Shelterbelt Program in China. The program locates in the semi-arid and arid lands in the northeastern, the northern and northwestern provinces of China. structure [30], and a back-up algorithm based on empirical relationships between NDVI and canopy LAI/FPAR [30]. Validation methods of the product included comparisons with in-situ data, comparisons with data from airborne and other space borne sensors, and analysis of trends [30]. The mean LAI/FPAR from June to August from 2000 to 2010 were calculated in this paper. _MODIS NPP Products:_ MODIS GPP/NPP products (MOD17A3 C06) with a spatial resolution of 500 m and temporal resolution of one year [31] were used to reflect the vegetation productivity of forest in this paper. NPP products were derived from the difference of the GPP and the maintenance respiration. The core science of the GPP algorithm is an application of the light use efficiency concept from MODIS LAI/FPAR product and NASA GMAO meteorological data [32]. A set of biome-specific radiation use efficiency parameters are extracted from the Biome Properties Look-Up Table [32]. The maintenance respiration was determined by the LAI and specific leaf area. NPP from 2000 to 2010 were used in this study to assess the vegetation productivity. _Landsat ETM+ Data:_ Landsat-7 Enhanced Thematic Mapper Plus (ETM+) images from June to August from 2000 to 2010 [33] were used to estimate high resolution (30 m) vegetation index. The data were first destriped, then surface reflectance was first obtained after radiometric correction and atmospheric correction. Relative radiometric normalization of multi-temporal satellite images was also the necessary process in detecting the forest change. _Climate Classification Map:_ As forest structure, function and degradation were closely related to the climate and climate changes, an improved Koppen-Geiger climate classification map (1980-2016) with the spatial resolution of 0.0083\({}^{\circ}\) (about 1 km) [34] was adopted in this paper when analyzing the degradation. The climate classification map was derived from an ensemble of high-resolution climatic datasets including WorldClim V1 and V2, CHELSA V1.2, and CHPclim V1. Validation with station observations data from Global Historical Climatology Network-Daily database and the Global Summary of the Day database demonstrated that the improved Koppen-Geiger climate classification map exhibited a high classification accuracy (80.0%) [34]. _Forest Map:_ The forest map was obtained from the \"Forest-Land one map\" database from the National Forestry and Grassland Admiration of China. This map was built from the forest resource inventory and forest resource planning and design.