Uncertainty Analysis of Standardized Precipitation Index Due to the Effects of Probability Distributions and Parameter Errors - Zhang, Ying; Li, Zhanling (Frontiers in Earth Science, 2020)
The standardized precipitation index (SPI) is widely used in drought assessments due to its simple data requirement and multiscale characteristics. However, there are some uncertainties in the process of its calculation. This study, taking the Heihe River basin in northwest of China as the study area, mainly focuses on the uncertainty issues both in SPI calculation and in drought characteristics associated with the probability distributions and parameter estimation errors. Ten probability distributions (two- and three-parameter log-logistic and log-normal, generalized extreme value, Pearson type III, burr, gamma, inverse Gaussian, and Weibull) are employed to estimate the SPI. Maximum likelihood estimation is used to estimate distribution parameters. Randomly generating parameters based on the normality assumption is applied to quantify the uncertainty of parameter estimations. Results show that log-logistic–type distribution presents quite close performance with the benchmark gamma distribution and thus is recommended as an alternative in fitting the precipitation data over the study area. Effects of both uncertainty sources (probability distribution functions and parameter estimation errors) are more reflected on extreme droughts (extremely dry or wet). The more extreme the SPI value, the greater uncertainties caused by both sources. Furthermore, the drought characteristics vary a lot from different distributions and parameter errors. These findings highlight the importance of uncertainty analysis of drought assessments, given that most studies in climatology focus on extreme values for drought analysis.