Global Evaluation of Optimal Probability Distribution Functions for RDI Assessments

Abstract

Drought is caused by an imbalance between precipitation and evapotranspiration. A prolonged lack of precipitation and/or excess evapotranspiration results in insufficient replenishment of runoff and groundwater. Choosing an appropriate drought index is crucial for managing water resources effectively. The Reconnaissance Drought Index (RDI) which considers both precipitation and potential evapotranspiration is recommended for identifying droughts in a changing climate. Standardising the index involves using a probability distribution, and choosing the correct distribution is important for accurate assessments of drought characteristics. Furthermore, identifying the optimal distributions for RDI assessments ensures reliable evaluations of subsequent hydrological processes. Based on a regional study, the index developers suggest using gamma or log-normal probability distributions to compute the index using real observations. Furthermore, there is a lack of research on suitable distributions for RDI calculation using GCMs projections (simulated data) in drought projection studies. This global study aims to address these gaps in research by evaluating the performance of probability distributions in calculating RDI. The study consists of two phases: The first phase involves identifying the appropriate distribution for historical observed data, whilst the second phase does the same for future projections from GCMs. To achieve this, 17 probability distributions are applied. The 0.5° × 0.5° gridded CRU data from 1950 to 2018 and projections of 18 GCMs from 2006 to 2080 are utilised. The analysis identified the log logistic, inverse Gaussian and gamma distributions as the best fits for the historical period. For future projections, the gamma, inverse Gaussian and Nakagami distributions are recommended. Finally, the findings revealed for both periods, Fitting to the Best Distribution of any Grid (FBDG) performs the best for large-scale drought studies using gridded data.