Quantifying the relationship between drought and water scarcity using copulas: Case study of Beijing-Tianjin-Hebei metropolitan areas in China

Abstract

Making the distinction between drought and water scarcity is not trivial, because they often occur simultaneously. In this study, we used Copulas to quantify the relationship between drought and water scarcity. Beijing-Tianjin-Hebei Metropolitan Areas (BTHMA) was chosen as the study area. Standard Precipitation and Evapotranspiration Index (SPEI) and water exploitation index plus (WEI+) was chosen to represent metrological drought and water scarcity. Inverse Distance Weighted method was used for spatial analysis of SPEI and WEI+, and Archimedean Copula was used to establish two-dimensional joint probability distribution of SPEI and WEI+. The results are as follows: (1) The southern part of the study area was wetter. The middle part was drier, with moderate drought happened for most times. (2) WEI+ of Beijing and Tianjin showed significant decreasing trends from 2000 to 2015, while WEI+ of Hebei Province did not, which indicated that Hebei Province is facing much severer water scarcity situation than Beijing and Tianjin. (3) Gumbel copula was the best-fitting model to establish the joint probability distribution of SPEI and WEI+. The condition probability provided a probability distribution of water scarcity under different drought conditions, which can provide technical support for government managers during policy making.