GTDI: a game-theory-based integrated drought index implying hazard-causing and hazard-bearing impact change

Abstract

Developing an effective and reliable integrated drought index is crucial for tracking and identifying droughts. The study employs game theory to create a spatially variable weight drought index (game-theory-based drought index, GTDI) by combining two single-type indices: an agricultural drought index (standardized soil moisture index, SSMI), which implies drought hazard-bearing conditions, and a meteorological drought index (standardized precipitation evapotranspiration index, SPEI), which implies drought hazard-causing conditions. In addition, the entropy-theory-based drought index (ETDI) is introduced to incorporate a spatial comparison with GTDI to illustrate the rationality of gaming weight integration, as both entropy theory and game theory belong to linear combination methods in the development of the integrated drought index and entropy theory has been applied in related research. Leaf area index (LAI) data are employed to confirm the reliability of GTDI in identifying drought by comparing it with SPEI, SSMI, and ETDI. Furthermore, a comparative analysis is conducted on the temporal trajectories and spatial evolution of the GTDI-identified drought to discuss GTDI's level of advancement in monitoring changes in hazard-causing and hazard-bearing impacts. The results show that GTDI has a very high correlation with single-type drought indices (SPEI and SSMI), and its gaming weight integration is more logical and trustworthy than that of ETDI. As a result, it outperforms ETDI, SPEI, and SSMI in recognizing drought spatiotemporally and is projected to replace single-type drought indices to provide a more accurate picture of actual drought. Additionally, GTDI exhibits the gaming feature, indicating a distinct benefit in monitoring changes in hazard-causing and hazard-bearing impacts. The case studies show that drought events in the Wei River basin are dominated by a lack of precipitation. The hazard-causing index, SPEI, dominates the early stages of a drought event, whereas the hazard-bearing index, SSMI, dominates the later stages. This study surely serves as a helpful reference for the development of integrated drought indices as well as regional drought prevention and monitoring.