How standard are standardized drought indices? Uncertainty components for the SPI & SPEI case

Standardized drought indices such as the Standardized Precipitation Index (SPI) or the Standardized Precipitation and Evapotranspiration Index (SPEI) are frequently used around the world to assess drought severity across a continent or a larger region covering different meteorological regimes. But how standard are these standardized indices? In this paper we quantify the uncertainty of SPI and SPEI based on an Austrian dataset to shed light on what are the main sources of uncertainty in the study area. Five factors that either defy the control of the analyst (record length, observation period), or need to be subjectively decided during the steps of the calculation (choice of the distribution, parameter estimation method, and GOF-test of the fitted distribution) are considered. We use the root mean squared error (E-RMS) for estimating the typical error for different calculation algorithm of SPI and SPEI. The total and relative uncertainty components for each factor are analysed by a linear mixed model (LMM) and significance of each model parameter are tested by the Akaike information criterion (AIC) and the restricted likelihood ratio test. The E-RMS indicates that computational variations of standardized drought indices lead to highly variable results. From the LMM, the choice of the distribution and the observational window are the most important sources of uncertainty. They, on average, control between 19% and 63% (choice of distribution) and 24% to 70% (observation period) of the total variance of the SPI across all stations and month of the year, with similar values observed for the SPEI. The parameter estimation method and the GOF-tests, however, have almost no effect on the standardized indices. Total errors and observation period uncertainty are typically decreasing with the record length as one would expect, while the distribution uncertainty is almost independent from the record length. An additional assessment shows that the uncertainties are similar at the pan-European scale leading to uncertain characterizations of major events such as the drought of 2015. Overall, the uncertainty of standardized drought indices is substantial. Alternative approaches as nonparametric methods, ensemble approaches or probability-based indices based on established methods of extreme-value statistics should be considered, to make the indices more accurate.

Automated summary

This paper quantifies the uncertainty of standardized drought indices (SPI and SPEI) based on an Austrian dataset and finds that the computational variations of these indices lead to highly variable results. The choice of distribution and observational window are the main sources of uncertainty, while parameter estimation method and GOF-tests have almost no effect. Overall, the uncertainty of standardized drought indices is substantial.