A universal Standardized Precipitation Index candidate distribution function for observations and simulations

Abstract

Abstract. The Standardized Precipitation Index (SPI) is a widely accepted drought index. Its calculation algorithm normalizes the index via a distribution function. Which distribution function to use is still disputed within the literature. This study illuminates that long-standing dispute and proposes a solution that ensures the normality of the index for all common accumulation periods in observations and simulations. We compare the normality of SPI time series derived with the gamma, Weibull, generalized gamma, and the exponentiated Weibull distribution. Our normality comparison is based on a complementary evaluation. Actual compared to theoretical occurrence probabilities of SPI categories evaluate the absolute performance of candidate distribution functions. Complementary, the Akaike information criterion evaluates candidate distribution functions relative to each other while analytically punishing complexity. SPI time series, spanning 1983–2013, are calculated from the Global Precipitation Climatology Project's monthly precipitation dataset, and seasonal precipitation hindcasts are from the Max Planck Institute Earth System Model. We evaluate these SPI time series over the global land area and for each continent individually during winter and summer. While focusing on regional performance disparities between observations and simulations that manifest in an accumulation period of 3 months, we additionally test the drawn conclusions for other common accumulation periods (1, 6, 9, and 12 months). Our results suggest that calculating SPI with the commonly used gamma distribution leads to deficiencies in the evaluation of ensemble simulations. Replacing it with the exponentiated Weibull distribution reduces the area of those regions where the index does not have any skill for precipitation obtained from ensemble simulations by more than one magnitude. The exponentiated Weibull distribution maximizes also the normality of SPI obtained from observational data and a single ensemble simulation. We demonstrate that calculating SPI with the exponentiated Weibull distribution delivers better results for each continent and every investigated accumulation period, irrespective of the heritage of the precipitation data. Therefore, we advocate the employment of the exponentiated Weibull distribution as the basis for SPI.

Accuracy Evaluation of Standardized Precipitation Index (SPI) Estimation under Conventional Assumption in Yeşilırmak, Kızılırmak, and Konya Closed Basins, Turkey

“…Sienz et al [32] showed that the Weibull-type distribution fts the monthly precipitation in Europe much better than the Gamma distribution. Pieper et al [43] recommended the exponential Weibull distribution as the basis for SPI calculations. Wang et al [52] investigated fve candidate distributions to describe cumulative precipitation series for SPI analysis for China.…”

“…Mahmoudi et al [42] highlighted that the generalized extreme value distribution at diferent time scales was a more accurate alternative for the SPI calculation compared to the default Gamma distribution. Pieper et al [43] argued for the use of exponentiated Weibull distribution when calculating SPI, instead of the default Gamma distribution.…”

Attribution of air temperature and precipitation to the future global drought events

“…Given the critical role of diverse meteorological and climatological features in the drought development, it is imperative for future studies to employ multiple drought metrics, such as runoff and soil moisture, to comprehensively understand the drivers of drought intensification across the globe. Reasonable assumptions can improve the robustness of the method, making it more resistant to outliers (Guttman 1999, Pieper et al 2020. Additionally, using a distribution function other than the normal distribution expands the method's applicability to non-normal data distributions.…”

Propagation in the Drought Cascade: Observational Analysis Over the Continental US

“…This is important for meteorological droughts since they are usually defined based on precipitation time‐series with different persistence of anomalies. For example, the Standardized Precipitation Index (SPI‐n) is widely applied to characterize meteorological droughts on a range of aggregation (n‐months) time scales (Pieper et al., 2020).…”