## 2 Materials and Methods
### Validation of the VIIUPD-Derived VCI  
We evaluated the VIUPD-derived VCI in three stages. During the first stage, we selected the growing season (April-October) in 2011 as the drought year with which to evaluate the indices. The US, and Texas in particular, experienced a harsh drought in the summer of 2011 [19]. The drought conditions monitored from VIUPD-derived VCI were compared to the drought conditions monitored from NDVI-derived VCI and USDM. USDM was used as a standard for the comparison. The widespread use of the USDM makes this choice feasible; additionally, USDM has a certain level of subjectivity due to individuals' reports. In this stage, we used the visual comparison method; the VIUPD-derived VCI are closer to USDM than NDVI-derived VCI in spatial distribution.  
In the second stage, we used the _in situ_ drought indices as the standard data, and evaluated the performance of the VIUPD-derived VCI and NDVI-derived VCI using three goodness-of-fit measures: the correlation values (r-value), the root mean square error (RMSE), and the mean absolute error (MAE). In the comparison between the VIUPD-derived VCI and NDVI-derived VCI, the correlation values were calculated between VIUPD-derived VCI, NDVI-derived VCI, and SPI-1, SPI-3, SPI-6, SPI-9, SPI-12, SPI-24, Z-index, and PDSI in 334 climate divisions from May to October (in total, \(2\times 8\times 7\times 344=38528\) r-values). The total RMSE, MAE and 38528 r-values were used to evaluate the performance of VIUPD-derived VCI. The r-value, RMSE and MAE were calculated using the formulas below:  
\[RMSE=\sqrt{N^{-1}\sum_{i=1}^{N}{(X_{i}-Y_{i})^{2}}}, \tag{8}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Drought Index** & **Data Source** & **Method** & **Source** \\ \hline TCI & MODIS, AMSR-E & \((LST_{i,max}-LST_{ijk})/(LST_{i,max}-LST_{i,min})\) & [17] \\ SMCL\_VUA & AMSR-E & \((SM_{ijk}-SM_{i,min})/(SM_{i,max}-SM_{i,min})\) & [2] \\ SMCL\_NSIDC & AMSR-E & \((SM_{ijk}-SM_{i,min})/(SM_{i,max}-SM_{i,min})\) & [2] \\ PCI & TRMM & \((TRM_{ijk}-TRM_{i,min})/(TRM_{i,max}+TRM_{i,min})\) & [2] \\ \hline \(LST_{ijk}\), \(SM_{ijk}\), \(TRMM_{ijk}\)—monthly LST, SM, TRMM for pixel \(i\), in month \(j\), for year \(k\), respectively. \(LST_{i,min}\), \(SM_{i,min}\), \(TRMM_{i,min}\)—multi-year minimum LST, SM, TRMM, respectively, for pixel \(i\). \(LST_{i,max}\), \(SM_{i,max}\), \(TRMM_{i,max}\)—multi-year maximum LST, SM, TRMM, respectively. & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Description of the remote sensing-based drought indices.  
\[MAE=N^{-1}\sum\limits_{i=1}^{N}{\left|{{X_{i}}-{Y_{i}}}\right|}, \tag{9}\]  
\[r=\frac{{\sum\limits_{i=1}^{N}{{{({X_{i}}-\overline{X})}({Y_{i}}-\overline{Y})}} }}{{\sqrt{{\sum\limits_{i=1}^{N}{{{({X_{i}}-\overline{X})}^{2}}}\sqrt{\sum \limits_{i=1}^{N}{{{({Y_{i}}-\overline{Y})}^{2}}}}}}}}, \tag{10}\]  
where \(X_{i}\) is the remote sensing-based drought index for point \(i\); \(\overline{X}\) is the mean value of the remote sensing-based drought indices; \(Y_{i}\) is the _in situ_ drought index for point \(i\); and \(\overline{Y}\) is the mean value of the _in situ_ drought indices.  
In the third stage, we used the _in situ_ drought indices as the standard data and compared the VIUPD-derived VCI with the commonly used remote sensing drought indices SMCI, TCI, PCI, and SMCI, derived from the Data and Information Services Center (NSIDC) and Vrije Universiteit (VUA). We calculated the overall RMSE, MAE as well as the r-values in each of the 344 climate divisions from May to October.