Distributed Composite Drought Index Based on Principal Component Analysis and Temporal Dependence Assessment

A variety of drought indices were developed to monitor different types of drought, a significant natural hazard with multidimensional impacts. However, no single drought index can capture all dimensions of drought, necessitating a composite drought index (CDI) that integrates a range of indicators. This study proposes a CDI using principal component analysis (PCA) and a temporal dependence assessment (TDA) applied to time series of drought indices in a spatially distributed approach at the basin level. The indices considered include the Simplified Standardized Precipitation Index (SSPI), Simplified Standardized Precipitation-Evapotranspiration Index (SSPEI), soil moisture (SM), Normalized Difference Vegetation Index (NDVI), and streamflow (SF) from two climatically distinct small-sized basins in Portugal. Lag correlation analyses revealed a high contemporaneous correlation between SSPI and SSPEI (r > 0.8) and weaker but significant lagged correlations with SF (r > 0.5) and SM (r > 0.4). NDVI showed lagged and negligible correlations with the other indices. PCA was iteratively applied to the lag correlation-removed matrix of drought indices for all grid points, repeating the procedure for several SSPI/SSPEI time scales. The first principal component (PC1), capturing the majority of the matrix’s variability, was extracted and represented as the CDI for each grid point. Alternatively, the CDI was computed by combining the first and second PCs, using their variances as contribution weights. As PC1 shows its highest loadings on SSPI and SSPEI, with median loading values above 0.52 in all grid points, the proposed CDI demonstrated the highest agreement with SSPI and SSPEI across all grid cells, followed by SM, SF, and NDVI. Comparing the CDI’s performance with an independent indicator such as PDSI, which is not involved in the CDI’s construction, validated the CDI’s ability to comprehensively monitor drought in the studied basins with different hydroclimatological characteristics. Further validation is suggested by including other drought indicators/variables such as crop yield, soil moisture from different layers, and/or groundwater levels.