Autocorrelation Structure of SPI and Its Implication for Drought Forecasting

Abstract

Standardised precipitation index (SPI) with different accumulation periods (denoted as '') of monthly data, such as 3, 6, 12 and 24 months, has been popularly employed to monitor and forecast drought conditions. Its autocorrelation function (ACF) might contain an deterministic structure because the values are estimated with the sum of monthly precipitation for a certain period. If the ACF possesses a deterministic structure, then drought forecasting with SPI might be critically influenced. Therefore, we derived the ACF structure of SPI values with three assumptions for easy calculation. Three assumptions are (AS-I) normality of the variable without gamma and standard normal transformation; (AS-II) uncorrelation of monthly precipitation and (AS-III) the ignorance of seasonality. It was found that the AC structure of SPI- could be deciphered by for lag-, indicating a linear decrease of the accumulation period, then zero afterwards. This derivation was verified by simulation and case studies from the U.S. and South Korea. The stations in the northeast side of the U.S. presented higher autocorrelation structure than the theoretical one, indicating that long-term forecasting can be made. The first assumption (AS-I) is acceptable, since the accumulation of precipitation follows the normal distribution according to the central limit theorem. The second assumption (AS-II) was checked with the data simulated from the lag-1 autoregressive model as well as by deriving the related ACF structure. The derived equation and simulation data showed that the diminution of ACF was delayed with higher lag-1 autocorrelation. However, the long-term structure over the northeast side of the U.S. could not be explained. The third assumption of seasonality (AS-III) was checked from the ACFs of the SPI-1, -3, -6, and -9 months, illustrating the dominant annual cycle. The prevailing seasonality can be reproducible by just adding the mean of the corresponding months. Overall, results indicated that SPI possessed the deterministic structure, implying that drought forecasting through SPI should be carefully done due to the deterministic component.