Copula-based standardized precipitation evapotranspiration index and its evaluation in China

Abstract

The standardized precipitation evapotranspiration index (SPEI) lacks the assessment mechanism for the coupling relationship between the magnitudes of the precipitation (P), potential evapotranspiration (ETP), and water deficit, making it hard to predict the drought precisely. This paper selected the marginal and joint cumulative distribution functions (CDF) of P and −ETP to present their magnitudes and water deficit, respectively. We formatted the Frank copula-based SPEI (SPEIC) to combine the marginal CDFs at 3, 6, 9, and 12-month scales. It indicated that the two-parameter Gamma distribution was the best-fitted marginal CDFs of the P (CDFP) and −ETP (CDF–ETP). The CDFP exerted a slightly more significant marginal effect on the joint CDF than the CDF–ETP at 6 to 12-month scales, indicated by the steeper slope of the CDFP’s marginal curves vs joint CDF. The verified more significant marginal effect denied the implied assumption of the same marginal effects of the P and −ETP using SPEI. The new-constructed SPEIC temporally fluctuated highly consistent with the SPEI in the whole, energy- and water-limited regions of China, indicated by the higher 3 to 12-month-averaged Nash-Sutcliffe efficiency coefficient ≥ 0.63 and determination coefficient ≥ 0.75. The SPEIC had a more sensitive detectivity of the drought frequency, indicated by more events detected. Besides, it had a minor sensitive detectivity of the drought severity, indicated by the larger SPEIC under the same specified frequencies of the P and −ETP.