## 3 Results
### Comparison of VHI for Different Case Studies  
Three cases of documented [63; 64; 65] severe drought episodes over Iberia and Morocco are studied: (1) the winter drought over southern Iberia in 1998/1999; (2) the spring drought over Iberia in 2005; and (3) the spring drought of 2007 in Morocco. For this purpose, two areas inside Iberia and Morocco were chosen. Figure 6 shows the time-series of VHI estimated with the traditional rationale using equal weights (\(\alpha=0.5\)) for VCI and TCI (blue line) against the proposed SPEI-based approach (black line) with values of \(\alpha\) as presented in Figure 1. It may be noted that the time-series is based on values of pixels belonging to the dominant SPEI time-scale, namely 4 pixels out of 4 correspond to the 1-month SPEI scale in the case of Iberia and 8 pixels out of 16 correspond to the 9-month SPEI scale in the case of Morocco. It may be further noted that, for simplicity, we restrict to the case when VHI is computed with TCI as estimated with SMW LST. The grey vertical lines in Figure 6 identify the severe drought episodes as identified by months where the dominant time-scale of SPEI index is lower than \(-1.28\)[66]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\alpha\)} & \multirow{2}{*}{\(\frac{\text{\bf p25}}{\text{\bf p50}}\)} & \multicolumn{4}{c}{**p50**} & \multicolumn{4}{c}{**p75**} \\ \cline{3-10}  & & **PU** & **PMW** & **SMW** & **PU** & **PMW** & **SMW** & **PU** & **PMW** & **SMW** \\ \hline \multirow{6}{*}{_Biomes_} & 02 & 0.425 & 0.425 & 0.475 & 0.575 & 0.575 & 0.575 & 0.775 & 0.825 & 0.775 \\  & 03 & 0.425 & 0.425 & 0.400 & 0.525 & 0.575 & 0.525 & 0.625 & 0.775 & 0.725 \\  & 04 & 0.475 & 0.475 & 0.475 & 0.625 & 0.675 & 0.67 To ensure that results are comparable, the effect of the drought episodes on the traditional and new VHI is measured based on the difference of medians normalized by the interquartile range:  
\[\mu=\frac{\mathrm{P}_{50}^{\mathrm{drought\ dist}}-\mathrm{P}_{50}^{\mathrm{ total\ dist}}}{\mathrm{P}_{75}^{\mathrm{total\ dist}}-\mathrm{P}_{25}^{\mathrm{total\ dist}}}, \tag{6}\]  
where \(\mathrm{P}_{50}^{\mathrm{drought\ dist}}\) is the median of the distribution of values restricted to severe drought episodes as identified by SPEI (grey bars in Figure 6) and \(\mathrm{P}_{25}^{\mathrm{total\ dist}}\), \(\mathrm{P}_{50}^{\mathrm{total\ dist}}\), and \(\mathrm{P}_{75}^{\mathrm{total\ dist}}\) are the first quartile, the median, and third quartile of all values. This metric allows comparing the traditional VHI against the SPEI-based VHI since it assesses the capability of capturing a drought event as identified by the multi-scalar SPEI index. Results (Table 2) indicate that the SPEI-based VHI systematically presents larger absolute values of \(\mu\) than the traditional VHI, indicating that the drought episodes are best represented when using the new proposed approach. Figure 6: Comparison between time series of VHI estimated with: the traditional method (\(\alpha=0.5\)) previously introduced by [PERSON] (blue line); and the SPEI-based method (black line) for the Iberian (**top** panel) and Moroccan (**bottom** panel) regions. Vertical grey lines in the time-series represent severe drought events as estimated with the dominant time-scale of SPEI in each region: 1-month in Iberia and 9-month in Morocco. Figure 7 shows the spatial distribution of VHI computed using the SPEI-based approach (VHI\({}_{\text{SPEI}}\)) with \(\alpha\) as in Figure 1 (right panels) when deriving TCI with the SMW LST. The respective spatial distribution of baseline values estimated using the approach originally proposed by [PERSON] (VHI\({}_{\text{K}}\)) are also shown (left panels). The spatial patterns of the three cases clearly reflect that the SPEI-based VHI amplifies the drought episode in the two considered regions.