Uncertainty Analysis of Standardized Precipitation Index Due to the Effects of Probability Distributions and Parameter Errors

Abstract

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.

Probabilistic Evaluation of Drought in CMIP6 Simulations

“…Here we use the parametric approach by fitting a Gamma ( E  ) distribution to the monthly precipitation at each grid. Although alternative distributions could have been used the Gamma distribution is the most widely used for SPI calculations (Zhang & Li, 2020). The Gamma cumulative distribution function is given by…”

Performance evaluation of different probability distribution functions for computing Standardized Precipitation Index over diverse climates of Iran

“…(1993), it is commonly thought that the two‐parameter gamma best fits any precipitation time series aggregated at any time scale. However, the later studies showed that this is not always the case in many areas of the world (Guttman, 1999; Angelidis et al ., 2012; Sienz et al ., 2012; Blain and Meschiatti, 2015; Stagge et al ., 2015; Svensson et al ., 2017; Zhang and Li, 2020), particularly in dry and semi‐dry climates (Guttman, 1999; Stagge et al ., 2015).…”

“…In this study, the performances of a dozen PDFs listed in Table 2 are evaluated over different climatic areas of Iran. These distributions are widely used in hydrological analysis and have already been examined for SPI calculation in different areas of the world (Guttman, 1999; Lloyd‐Hughes and Saunders, 2002; Ntale and Gan, 2003; Vicente‐Serrano, 2006; Wu et al ., 2007; Quiring, 2009; Angelidis et al ., 2012; Vicente‐Serrano et al ., 2012; Guenang and Kamga, 2014; Blain and Meschiatti, 2015; Stagge et al ., 2015; Zhang and Li, 2020). Table 2 introduces the selected distributions, the number of their parameters, and the methods used for their parameter estimation.…”

“…(2012), Stagge et al . (2015), Blain and Meschiatti (2015), Zhang and Li (2020), just to name a few. Seven of the selected distributions, including W, two‐parameter Gamma (Gama2), Log logistic (LLogist), Logistic (Logist), N, LN, and Extreme value (EV) have two parameters while the remaining five distributions, namely the General Pareto (GP), Pearson Type III (PE3), General Logistic (GLO), General extreme value (GEV), and Log logistic 3‐parameters (LLogist3) have three parameters.…”

Meteorological Drought and its Relationship with Southern Oscillation Index (SOI)

“…Harisuseno [5] demonstrated that the SPI showed good reliability in assessing drought characteristics when compared with the RAI, while [6] utilized TRMM satellite data and SPI for monitoring and developing the spatiotemporal map of meteorological drought. Zhang and Li [7] examined the implications of different probability functions and parameter estimation on the SPI index, including drought intensity, duration, and frequency. The Standardized Precipitation Index (SPI) is more frequently applied to drought analysis regarding owing effortless calculation since the method is recommended by the World Meteorological Organization [8,9].…”