Relative contribution of uncertainties to standardized drought index calculation using a linear mixture model

Abstract

Standardized Precipitation Index (SPI) is widely used for monitoring drought due to its simplicity and effectiveness. However, various uncertainties arise from multiple factors in SPI calculation including the length of precipitation data, accumulation periods, probability distributions, and parameter estimation methods. This study aims to quantify the relative contribution of these factors to SPI uncertainty using a linear mixed model (LMM). In this study, various SPI calculation scenarios were considered by combining three data lengths (20, 30, and 50 years), four accumulation periods (1, 3, 6, and 12 months), five probability distributions (gamma, normal, log-normal, logistic, and generalized extreme value), and two parameter estimation methods (maximum likelihood estimation and L-moment). In our study, reference precipitation was defined as the amount of precipitation corresponding to a target SPI value (e.g., –1.0 or –2.0), determined by inverting the standard SPI calculation process. The uncertainty was quantified by calculating the root mean square error (RMSE) between the reference SPI and calculated SPI from various SPI calculation scenarios. The results showed that uncertainty decreased with longer accumulation periods and data lengths, while the RMSE was substantially higher and more variable under SPI = –2.0 than SPI = –1.0. The LMM was then used to assess the contribution of each uncertainty factor. The results revealed that for moderate drought conditions (SPI = –1.0), the primary contributors to uncertainty were sample size and accumulation period. However, under extreme drought conditions (SPI = –2.0), probability distribution accounted for over 50% of the total variance, reaching up to 84% in some cases. The impact of parameter estimation methods was relatively nonsignificant under all conditions, consistently accounting for less than 3% of the total variance. These findings suggest that selecting an appropriate distribution and using long-term precipitation data are critical for improving the reliability of SPI-based drought assessments. This study highlights the critical need for long-term precipitation records (at least 50 years), appropriate accumulation periods, and rigorous selection of probability distributions, particularly under extreme drought conditions.