Candidate Distributions for Climatological Drought Indices (SPI and SPEI)

Abstract

The Standardized Precipitation Index (SPI), a well-reviewed meteorological drought index recommended by the World Meteorological Organization (WMO), and its more recent climatic water balance variant, the Standardized Precipitation-Evapotranspiration Index (SPEI), both rely on selection of a univariate probability distribution to normalize the index, allowing for comparisons across climates. Choice of an improper probability distribution may impart bias to the index values, exaggerating or minimizing drought severity. This study compares a suite of candidate probability distributions for use in SPI and SPEI normalization using the 0.5° × 0.5° gridded Watch Forcing Dataset (WFD) at the continental scale, focusing on Europe. Several modifications to the SPI and SPEI methodology are proposed, as well as an updated procedure for evaluating SPI/SPEI goodness of fit based on the Shapiro-Wilk test. Candidate distributions for SPI organize into two groups based on their ability to model short-term accumulation (1-2 months) or long-term accumulation (>3 months). The two-parameter gamma distribution is recommended for general use when calculating SPI across all accumulation periods and regions within Europe, in agreement with previous studies. The generalized extreme value distribution is recommended when computing the SPEI, in disagreement with previous recommendations.