Optimal Probability Distribution and Applicable Minimum Time-Scale for Daily Standardized Precipitation Index Time Series in South Korea

Abstract

The Standardized Precipitation Index (SPI) is a standardized measure of the variability of precipitation and is widely used for drought assessment around the world. In general, the probability distribution used to calculate the SPI in many studies is Gamma. In addition, a monthly time-scale is applied to calculate the SPI to assess drought based on atmospheric moisture supply over the medium-to-long term. However, probability distributions other than Gamma are applied in various regions, and the need for a daily time-scale is emerging as concerns about fresh drought increase. There are two main innovations of our work. The first is that we investigate the optimal probability distribution of daily SPIs rather than monthly SPIs, and the second is that we address the issue of determining the minimum time-scale that can be applied when applying a daily time-scale. In this study, we investigate the optimal probability distribution and the minimum-applicable time-scale for calculating the daily SPI using daily precipitation time series observed over 42 years at 56 sites in South Korea. Six candidate probability distributions (Gumbel, Gamma, GEV, Log-logistic, Log-normal, and Weibull) and ten time-scales (5 day, 10 day, 15 day, 21 day, 30 day, 60 day, 90 day, 180 day, 270 day, and 365 day) were applied to calculate the daily SPI. A chi-square test and AIC were applied to investigate the appropriate probability distribution for each time-scale, and the normality of the daily SPI time series derived from each probability distribution were compared. The Weibull distribution was suitable for calculating the daily SPI for short time-scales of 30 days or less, while the GEV distribution was suitable for longer time-scales of 270 days or more. However, overall, Gamma was found to be the best probability distribution. While there were some regional variations, the minimum time-scales that could be applied per season were as follows: 15 days for spring and summer, 21 days for fall, and 30 days for winter. It is shown that the minimum time-scale depends on how many zero values are included in the moving cumulative-precipitation time series, and it is shown that it is appropriate to have less than about 2.5%. Finally, the applicability of the GEV distribution is investigated.