The Establishment Of SPI_GD Drought Index And The Research On Its Test And Application

SPI has advantages of simplicity in calculation,without the restrictions of seasons and topography and can be compared at various time scales.Thus,it has recently been widely used both at home and abroad.It is well known the two main uncertainties in calculation of SPI are the distribution function of cumulative precipitation and the length of precipitation record.SPI works under an assumption that cumulative precipitation is subject to Gamma distribution,and it was suggested that the data used in calculations should be longer than 30 years.Climate is complex and varied in different parts of the world,and the cumulative precipitation in different areas may not meet the requirement of the Gamma distribution.Besides the 30-year-long precipitation data may not be able to ensure the accuracy of SPI values.Therefore,the keys of the improvement of SPI are selecting the distribution function which meets the distribution features of cumulative precipitation in a certain area and makes calculation by using the data of precipitation with the best length.In recent years,many studies on the applicability of the gamma distributions using SPI are investigated,but existing studies only focus on the comparison and discussion of other distributions and Gamma distribution.The suitable way instead of the gamma distribution is desired to get more accurate and improved SPI.Moreover,there is no deep study on the stability of the length of precipitation data at different time scales.Therefore,we aimed at these two items by using the monthly precipitation data of 760 meteorological stations in China in the year of 1961-2013 on six time scales of one,three,six,nine,twelve,twenty-four months.We compared Generalized Extreme Value Distribution(GEV distribution),Weibull distribution,Log-normal distribution,Normal distribution and Rayleigh distribution with Gamma distribution.And we carried nationwide discussions and analyzed.The results are as follows:(1)On the one-month time scale,the K-S test of Gamma distribution and Weibull distribution has the highest pass rate.From the three-month time scale,the pass rate of the GEV distribution is the highest.Besides,the percentage of the optimal distribution of the GEV distribution is also the highest on each time scale.After a detailed discussion for every season on one-month time scale and three-month time scale,we found that on the one-month time scale,GEV distribution is better than Gamma distribution in spring,summer and autumn,while Gamma distribution is better than GEV distribution in winter.On the three-month time scale,GEV distribution is better in describing the distribution feature of cumulative precipitation in both summer and winter in China.(2)According to the results of K-S test,we gave a comprehensive score for every distribution,the GEV distribution is the best distribution both in the comprehensive score of all time scales and in the seasonal discussion.The score of the Gamma distribution is relatively high,its score ranks second.(3)We divided China into arid,semi-arid,semi-humid and wet areas according to annual precipitation.The detailed K-S tests were carried out in each climate area and in every season,then we found that the Gamma distribution only ranked first only in the arid area,and in the other three climate areas,the scores of the GEV distribution are the best,then followed by the Gamma distribution.(4)Take Pingliang station as an example,after the comparison of all SPIs calculated with each distribution,the results show that the deviation of all distribution function images is the biggest on one month time scale.And then the deviation in all images decreases with the increase of time scale.After comparing the SPI of each distribution of the deviation of numerical values and the judgment of the drought level,it was found that the SPI difference value is most significant between the Lognormal distribution and the Normal distribution in both cases.And Gamma distribution and the Weibull distribution have the smallest SPI difference value.The Gamma distribution and the Lognormal distribution have the smallest proportion in the judgment of drought level deviation.(5)A new drought monitoring index called SPI_GD was proposed after replacing the Gamma distribution which was used in SPI by GEV distribution,and formulas of the calculation of SPI_GD was given.After monitoring the drought condition of China in autumn,2009 as well as the drought condition of Wuwei,Gansu in 1986 with SPI_GD3,it turned out that SPI_GD could not only well describe the extent and degree of drought,but also accord with the actual drought conditions.Then SPI_GD1 and SPI1 were both used to analyze the drought condition of Henan Province in summer,1987,and it was found that SPI1 made some errors in the monitoring of the extent and degree of the drought condition in the west of Henan,while SPI_GD1 was more accurate in monitoring drought condition and has a higher correspondence with actual condition.(6)Go on taking Pingliang station as an example,the probability density function images and parameters of every distribution were obtained by using the data of 5-year to 50-year-precipitation respectively.It was found that the parameters and function images of all distributions changed drastically when using the shorter length of the data,and with the length of the data used gradually increasing,the parameters and images gradually became stable.(7)The SPI values of the Pingliang site in March 2012 were calculated by using the precipitation data of each length at each time scale.It was also found that all SPIs changed drastically at each time scale when using shorter length of precipitation data,and with the gradual increase in the length of precipitation data,SPI values gradually stabilized.Besides,as the time scale increases,the material length of precipitation data is needed for SPI values to reach the stability.Finally,we summarized the length of the precipitation data when the SPI values reached stability at each time scale,and recommendations were given on how long the precipitation data should be selected for calculations of SPI and SPI_GD at different time scales in practical applications.