## 2 Materials and Methods
### Vegetation Condition Index  
The NDVI is widely used to estimate the density and health of vegetation. Because of the close relationship between vegetation vigor and available soil moisture, it has been used to monitor drought conditions. The maximum value composites (MVC) method was used to composite the eight-day images to monthly data. The VIUPD is computed based on the universal pattern decomposition approach [22]. It can be computed as a combination of four pattern decomposition coefficients: the patterns of vegetation, soil, and water, and the supplementary pattern.  
\[VIUPD=\frac{C_{V}-a\times C_{S}-C_{4}}{C_{W}+C_{V}+C_{S}}, \tag{4}\]  
where \(C_{V}\), \(C_{S}\), \(C_{W}\) and \(C_{4}\) represent the standard pattern reflectance of vegetation, soil, water, and the supplementary pattern, respectively. \(a\) is a empirical coefficient and defined as 0.1 according to the experiments conducted by [PERSON] _et al._[22]. In this study, eight-day MODIS surface reflectance data (MOD09A1) were used to calculate VIUPD based on the formula above. The \(C_{V}\), \(C_{S}\), \(C_{W}\) and \(C_{4}\) are determined by the formula below:  
\[R_{i}=C_{w}P_{iw}+C_{v}P_{iv}+C_{s}P_{is}+C_{4}P_{iA}, \tag{5}\]  
where, \(R_{i}\) is the reflectance of band \(i\) measured by MOD09A1, \(C_{V}\), \(C_{S}\), \(C_{4}\) and \(C_{W}\) are the decomposition coefficients for vegetation, soil, supplement and water respectively, and \(P_{iw}\), \(P_{iv}\), and \(P_{is}\) are the respective standard spectral patterns for water, vegetation and soil for MODIS sensor. \(P_{i4}\) is the supplementary standard pattern for \(i\) bands and a yellow-leaf spectrum is used in this study. Formula (5) can also be expressed using matrix notations as follow:  
\[R=PC+r, \tag{6}\]  
where \(R=(R_{1}\), \(R_{2}\),..., \(R_{n})^{\mathrm{T}}\) is the vector of reflectance, \(n\) is the number of spectral bands which in this study is 7. \(P=(P_{w}\), \(P_{v}\), \(P_{s}\), \(P_{4})\) is the 7 \(\times\) 4 matrix for band number 7, \(\mathrm{C}=(C_{w}\), \(C_{v}\), \(C_{s}\), \(C_{4})^{\mathrm{T}}\) is the column vector of coefficients and \(r\) is the residual column vector for band \(i\). By minimizing the sum-of-squared-error criterion function yields of Equation (6), we can get the values of \(C_{w}\), \(C_{v}\), \(C_{s}\) and \(C_{4}\).  
Eight-day images of VIUPD were composited into monthly data, weighted by the number of days recorded in each month, and based on the data generated after masking the cloud value pixels, using MODIS data quality flags.  
The VCI was developed to control for local differences in ecosystem productivity. The VCI is a pixel-wise normalization of VI that is useful for making relative assessments (e.g., pixel-specific) of changes in the VI signal by filtering out the contribution of local geographic resources to the spatial variability of VI. The _VCI_ is computed as:  
\[VCI_{ijk}=\frac{VI_{ijk}-VI_{i,\min}}{VI_{i,\max}-VI_{i,\min}}, \tag{7}\]where \(V_{ijk}\) represents the monthly VI for pixel \(i\) in month \(j\) for year \(k\), and \(V_{i,max}\) and \(V_{i,min}\) denote the multiyear minimum and maximum \(VI\), respectively, for pixel \(i\) in month \(j\). In this study, NDVI-derived VCI and VIUPD-derived VCI were computed based on the formula above wherein \(VI\) is replaced by NDVI and VIUPD, respectively. The VCI values were averaged spatially to climate division level to facilitate comparison with observation-based drought indices.