Integration of three drought indices based on triple collocation and multi-scalar weighted amalgamated drought index

Several indices based on both single and multiple hydro-climatic factors have been established to monitor and evaluate droughts. However, no single drought indicator can accurately describe the density of the overall drought due to constraints caused by a number of factors. Therefore, combining many drought indices more properly into one instrument to better depict and manage droughts would be beneficial. This study differentiated and established two merging methods through Triple Collocation (TC) and Multi-scalar Weighted Amalgamated Drought Index (MWADI). Therefore, three individual standardized drought indices (SDIs), including the Standardized Precipitation Index (SPI), Standardized Precipitation Temperature Index (SPTI), and Standardized Precipitation Evaporation Index (SPEI), were used to fabricate a composite Merged Drought Index (MDI) based on TC and MWADI across six meteorological stations of Pakistan from 1971 to 2017. Their performance was analyzed through correlation, Taylor diagram, Kling Gupta Efficiency Criteria (KGE), Root Mean Square Error (RMSE), and Sen's slope. In addition, the performance of TC is also evaluated through Correlation Coefficient (CC’s) and Fixed Residual Mean Square Error (FRMSE) through Extended Triple Collocation (ETC). The exploratory analysis reveals that individual indices SPI and SPTI are closely related to both MDI relative to SPEI across the study area. However, TC-based MDI has a stronger correlation with the individual indices than MWADI. Sen's slope indicates a similar trend with a slight divergence in magnitude from both approaches. The estimated values of KGE suggest TC exhibits better efficiency than MWADI. RMSE shows a minute difference under both approaches. Overall, TC executes well with individual series in contrast with MWADI. Furthermore, the performance of TC is also evaluated through Correlation Coefficients (CC’s) and Fixed RMSE (FRMSE), where it shows high sensitivity. However, implicit presumptions place restrictions on the accuracy of TC comparison. MDI has the potential to be a useful tool for collaborating and making decisions concerning multiple kinds of droughts.