Uncertainty analysis of SPI calculation and drought assessment based on the application of Bootstrap

The Standardized Precipitation Index (SPI) has been widely used to monitor the drought status. In the estimation of SPI, an appropriate probability distribution function (APDF) is required to fit precipitation series with different timescales, such as 3-month, 9-month and so on. Then the standard normal distribution function is used to transform the cumulative probability derived from APDF to calculate the SPI value. Obviously, the estimation accuracy of SPI particularly depends on the sample that influences the selection of PDF and parameter estimation. However, the size of the observed sample is usually small, and it cannot perfectly present the statistical property of the population, which usually causes the uncertainty on calculation of SPI and in turn results in the uncertainty of drought assessment. Due to the existence of gap between the estimated SPI and the true SPI, when one obtains the estimation of SPI, it is necessary to know the reliability or uncertainty of the estimated SPI. In this article, a new method based on the Bootstrap method was put forward to analyse the impact of sampling uncertainty on the estimation of SPI and drought assessment. Through repeating samples from the original sample, a large number of Bootstrap samples are constructed, and based on each Bootstrap sample, the corresponding estimation of SPI for the given event can be obtained. Therefore, the sampling distribution of SPI for the given event can also be derived, on which both the point estimation and interval estimation of SPI for the given precipitation event can be provided, and the overall assessment of a drought event could be achieved. The case study shows that, compared with the original SPI calculation method, the proposed method not only provides equivalent assessment results, but also has the capability to assess the impact of sampling uncertainty on the uncertainty of SPI calculation and drought assessment.