Response to comment on 'Candidate Distributions for Climatological Drought Indices (SPI and SPEI)'

Abstract

This response expands on the analysis performed in 'Candidate Distributions for Climatological Drought Indices (SPI and SPEI)' by explaining several topics in greater detail and by testing the conclusions of our original article against the claims made in the comment by Drs Vicente-Serrano and Begueria. Tests using the same 11 climate time series confirm the original findings from Stagge et al. (2015) that the Generalized Extreme Value (GEV) distribution produces consistently better fits. Claims that the GEV distribution exaggerates extreme SPEI values were found to be false by comparing Log-Logistic and GEV-generated SPEI values directly to the baseline normal distribution, rather than to one another. Once compared with the theoretical normal distribution, the GEV distribution was shown to better model the extreme tails, while the Log-Logistic distribution consistently underestimated these values. Analysis of the tails was shown to introduce significant uncertainty due to extrapolation regardless of the distribution. We thus strongly disagree with claims made in the comment by Vicente-Serrano and Begueria that their results clearly recommend the Log-Logistic distribution. Instead, we prove that differences tend to be small, but consistently support the use of the GEV distribution for SPEI analysis across multiple data sources and goodness of fit metrics.