Estimating uncertainty associated with the standardized precipitation index

Abstract

We investigate methodological uncertainties associated with the standardized precipitation index (SPI) that result from limited record length, trends, and outliers. We use long, homogenous records from 14 Italian stations to investigate how specific features in the precipitation record affect construction of an underlying gamma probability function. We apply a resampling scheme to the long records in order to estimate confidence intervals associated with a range of precipitation characteristics. Stability in parameter estimation increases nonlinearly as record length increases. The resulting SPI estimates for 30‐year reference periods have considerably more uncertainty than those made from 60‐year records. In general, increasing record length beyond 60‐years has limited benefits and, in the presence of a trend, may increase uncertainty. Extreme events also have significant influence on SPI estimates, even for records exceeding 60 years. Despite using stations from different geographic regions, each with unique precipitation characteristics, we find consistent confidence interval estimates across stations. These confidence intervals can be applied to specific time series to identify how trends, changes in variability, and outliers during a particular reference period influence SPI values.

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

“…In addition, the minimum length of record also depends on whether the precipitation pattern changes (Wu et al, 2005). Carbone et al (2018) found that extreme events also have a significant influence on SPI estimates, even over 60-years of records.…”

“…McKee et al (1993) regarded that a continuous period of at least 30-years seems ideal in the SPI calculation, while Guttman (1994) found that ∼40 to 60-years of record is needed for parameter estimation stability in the central part of the distribution and ∼70 to 80-years of record for stability in the tails. Carbone et al (2018) suggested that record lengths of 60-years are basically enough in general, which typically results in stable parameters and representative SPI values. In addition, the minimum length of record also depends on whether the precipitation pattern changes (Wu et al, 2005).…”

“…Beguería et al (2014) contrasted MLE and unbiased probability weighted moments method in estimating parameters in three-parameter log-logistic distribution and concluded that these two methods yield similar results, whereas the calculation of MLE is ∼2-fold more time consuming. Carbone et al (2018) discussed the relationship between the stability of parameter estimation and data record length and found that the stability in parameter estimation increases non-linearly as record length increases.…”

“…As to the input data, a large number of studies have concerned about the uncertainties associated with input data sources, data length, and sampling uncertainty in the calculation of drought index (e.g., Hao et al, 2014Hao et al, , 2016Liu et al, 2014;Hu et al, 2015;Katiraie-Boroujerdy et al, 2016;Vergni et al, 2017;Zambrano et al, 2017;Beyaztas et al, 2018;Carbone et al, 2018). Vu et al (2018) compared the performance of rain-gauge data and gridded precipitation data in the calculation of SPI over Vietnam.…”

“…Vu et al (2018) compared the performance of rain-gauge data and gridded precipitation data in the calculation of SPI over Vietnam. Carbone et al (2018) demonstrated that the SPI estimates derived from 30-year record have considerably more uncertainty than those from the 60-year record. Liu et al (2014), Hu et al (2015), Vergni et al (2017), and Beyaztas et al (2018) quantified the sampling uncertainties and their effects on the estimation of drought index.…”