Uncertainty Analysis Of Two Typical Meteorological Drought Indexes

In recent years,extreme climates have occurred frequently around the world,and drought problems are very prominent.The drought index is an effective tool for drought researches;in order to conceptualize and abstract the complex drought process,some numerical equations and parameters are usually selected to determine the drought index and describe the actual drought.Due to the limitation of methods and data,there are some uncertainties in the process of determining drought index,and then in drought assessments.This paper takes the Heihe River Basin as a research area,based on the Standardized Precipitation Index(SPI)and the Standardized Precipitation Evapotranspiration Index(SPEI),selects four drought characteristic variables of drought intensity,peak value,drought maximum duration and total duration,and analyzes the uncertainty of drought index and drought evaluation of model structure,parameter estimation and input data.Selecting four three-parameter and five two-parameter probability distribution functions to calculate SPI,five three-parameter and four two-parameter probability distribution functions to calculate SPEI,to study the uncertainty caused by the model structure;using the maximum likelihood parameter estimation method,and randomly generating parameters based on the normality assumption is applied to quantify the uncertainty of parameter estimations;using non-parametric Bootstrap resampling method to quantify the uncertainty of data sampling,and studied the impact of different length sequences on the drought index value.The research results are as follows:The goodness of probability distribution fitting has an important impact on the reliability of drought assessment results;overall,the three-parameter probability distribution performs better than the two-parameter distribution.The fitting result of the three-parameter and two-parameter Log-logistic distribution is better than the recommended Gamma distribution,and can be used as an alternative distribution for calculating the SPI of the Heihe River Basin.From the influence of different probability distribution models on drought index,the more extreme the SPI and SPEI indexes are(SPI/SPEI?2,SPI/SPEI?-2),the greater the uncertainty caused by the distribution model;from the perspective of the influence of probability distribution models on drought characteristic variables,the influence of different probability distributions on drought characteristics is mainly reflected in the duration.(2)The influence of the parameter estimation error of the probability distribution model on the drought index is mainly manifested as the more extreme the SPI and SPEI index values(SPI/SPEI?2,SPI/SPEI?-2),the greater the uncertainty.and The width of the maximum confidence interval is almost twice the average width,all of which occur in extreme and severe events;the impact of parameter estimation errors on drought characteristic variables is mainly reflected in the duration;under the premise of ensuring the goodness of fitting,the uncertainty caused by parameter estimation error is larger than that caused by different probability distributions.(3)The impact of data sampling uncertainty on the two drought indexes is different.The effect on the SPI index is that the more extreme the SPI value(SPI?2,SPI?-2),the greater the uncertainty caused by sampling;but the impact on the SPEI index is that for not drought and mild events(-1<SPEI<1),the uncertainty caused by sampling is greater;the impact of data sampling uncertainty on drought characteristic variables is also mainly reflected in duration;in addition,the shorter the length of the time series,the greater the uncertainty of the drought index;in the Heihe River Basin,it is recommended to use at least 30 years of data to calculate the SPI index and at least 40 years of data to calculate the SPEI index.