## 3 Results
### Regional Drought Patterns Derived from NDVI and VIUPD-Derived VCI  
The months of April to October 2011 were selected to exemplify the spatial variation of the indices for that in 2011, the U.S experienced one of the typical severe droughts in the history of the country. The drought map in Figure 2 shows a variation among the indices. In Figure 2, the VIUPD-derived VCI was compared against NDVI-derived VCI using only those months from April to October. This was done because these months represent the maximum vegetation growth and VCI is only useful for monitoring drought condition during the growing-season for it measures vegetation health. Another reason for choosing April to October is to exclude some noise effects in winter, such as snow. In Figure 2, the first column displays the observed USDM drought data for the period of April to October 2011, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dropout Indices**} & \multicolumn{8}{c}{**RMSE (\(n\) = 24,080)**} \\ \cline{2-9}  & **PDSI** & **Z** & **SPI-1** & **SPI-3** & **SPI-6** & **SPI-9** & **SPI-12** & **SPI-24** \\ \hline VIUPD-VCI & 2.658 * & 2.244 & 1.159 & 1.075 * & 1.082 * & 1.058 * & 1.068 * & 1.074 * \\ NDVI-VCI & 2.782 & 2.384 & 1.681 & 1.145 & 1.326 & 1.344 & 1.368 & 1.370 \\ PCI & 3.440 & 0.865 & 0.801 * & 2.559 & 2.598 & 2.650 & 2.703 & 2.811 \\ TCI & 2.709 & 2.289 & 1.166 & 1.145 & 1.271 & 1.223 & 1.379 & 1.278 \\ TCI-VUA & 2.774 & 2.567 & 1.026 & 1.057 & 1.071 & 1.059 & 1.085 & 1.099 \\ SMCI-VUA & 2.856 & 2.234 & 1.183 & 1.324 & 1.245 & 1.255 & 1.265 & 1.278 \\ SMCI-NSIDC & 3.374 & 3.237 & 3.291 & 3.122 & 3.140 & 3.155 & 3.156 & 3.202 \\ \hline \hline \end{tabular}  
\end{table} 
Table 4: Comparisons of RMSE between VIUPD-derived VCI and other commonly used remote sensing-based single drought indices. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dropout Indices**} & \multicolumn{8}{c}{**MAE (\(n\) = 24,080)**} \\ \cline{2-9}  & **PDSI** & **Z** & **SPI-1** & **SPI-3** & **SPI-6** & **SPI-9** & **SPI-12** & **SPI-24** \\ \hline VIUPD-VCI & 0.622 * & 0.313 & 0.234 & 0.564 * & 0.582 * & 0.584 * & 0.548 * & 0.390 * \\ NDVI-VCI & 0.382 & 0.284 & 0.217 & 0.354 & 0.326 & 0.344 & 0.318 & 0.237 \\ PCI & 0.440 & 0.806 & 0.865 * & 0.559 & 0.398 & 0.350 & 0.303 & 0.211 \\ TCI & 0.542 & 0.589 & 0.487 & 0.515 & 0.471 & 0.423 & 0.379 & 0.278 \\ TCI-VUA & 0.215 & 0.241 & 0.147 & 0.182 & 0.168 & 0.155 & 0.126 & 0.072 \\ SMCI-VUA & 0.370 & 0.451 & 0.426 & 0.389 & 0.331 & 0.297 & 0.259 & 0.197 \\ SMCI-NSIDC & 0.074 & 0.237 & 0.291 & 0.222 & 0.140 & 0.085 & 0.056 & 0.002 \\ \hline \hline \end{tabular}  
\end{table} 
Table 3: Comparisons of the r-value between VIUPD-derived VCI and other commonly used remote sensing-based single drought indices. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dropout Indices**} & \multicolumn{8}{c}{**MAE (\(n\) = 24,080)**} \\ \cline{2-9}  & **PDSI** & **Z** & **SPI-1** & **SPI-3** & **SPI-6** & **SPI-9** & **SPI-12** & **SPI-24** \\ \hline VIUPD-VCI & 1.592 * & 1.819 & 0.871 & 0.892 * & 0.897 * & 0.873 * & 0.885 * & 0.887 * \\ NDVI-VCI & 1.682 & 1.984 & 1.217 & 1.354 & 1.366 & 1.368 & 1.378 & 1.437 \\ PCI & 1.840 & 0.963 & 0.665* & 0.959 & 1.198 & 1.350 & 1.403 & 1.511 \\ TCI & 1.642 & 1.967 & 0.987 & 0.915 & 0.971 & 0.923 & 0.979 & 0.978 \\ TCI-VUA & 2.198 & 1.767 & 0.867 & 0.885 & 0.897 & 0.879 & 0.901 & 0.910 \\ SMCI-VUA & 2.656 & 2.451 & 1.326 & 1.339 & 1.381 & 1.297 & 1.259 & 1.197 \\ SMCI-NSIDC & 3.074 & 3.267 & 2.991 & 2.222 & 0.240 & 2.285 & 2.356 & 2.402 \\ \hline \hline \end{tabular}  
\end{table} 
Table 5: Comparisons of MAE between VIUPD-derived VCI and other commonly used remote sensing-based single drought indices. while the second, third and fourth columns show the NDVI-derived VCI, difference between the VIUPD-derived VCI and NDVI-derived VCI, and VIUPD-derived VCI respectively.