加权马尔科夫链在鄂尔多斯市年降水量预测中的应用  

Application of Weighted Markov Chain in Prediction of Annual Precipitation in Ordos Region

作　　者：梁显丽[1] 宝秋利[1] 代海燕[2] LIANG Xian-li;BAO Qiu-li;DAI Hai-yan(Vocational Technology College,Inner Mongolia Agricultural University,Baotou 014109,China;Inner Mongolia Ecology and Agricultural Meteorology Centre,Hohhot 010051,China)

机构地区：[1]内蒙古农业大学职业技术学院,内蒙古包头014109 [2]内蒙古生态与农业气象中心,内蒙古呼和浩特010051

出　　处：《数学的实践与认识》2021年第4期161-171,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(41461102);林业公益性行业专项(201304206);内蒙古自治区自然科学基金(2017MS0359)。

摘　　要：鄂尔多斯市是内蒙古自治区重要的农牧渔业生产区.本文采用样本均值—标准差分级法,将鄂尔多斯市11个气象站1961-2019年的年降水量序列划分为丰水年、偏丰水年、平水年、偏枯水年,枯水年5个状态;以年降水量序列各阶自相关系数rk为权值,建立了加权马尔科夫预测模型,对鄂尔多斯市2017年、2018年、2019年的年降水量数值和所处状态进行预测.结果显示相对误差分别为1.3%,6.9%,4.5%,预测精度较高,方法得当.于是利用精度检验后的加权马尔科夫模型预测了鄂尔多斯市2020年降水量为312.81mm,划分为平水年.同时利用马尔科夫模型的遍历性,讨论了鄂尔多斯市年降水量的极限分布和丰枯状态重现期.研究结果表明,鄂尔多斯市59a来降水过程中枯水年、偏枯水年、平水年、偏丰水年、丰水年5种状态出现的概率分别为0.1358、0.1941、0.3693、0.1926、0.1083,即出现平水年的可能性最大,重现期为2.71a;出现丰水年的可能性最小,重现期为9.23a.上述研究结果与降水量序列及所处状态是保持一致的,由此可见利用加权马尔科夫链预测鄂尔多斯地区的年降水量是可行且有效的.Ordos region is an important agricultural,animal husbandry and fishery production area in Inner Mongolia Autonomous Region.In this paper,by using of sample meanstandard deviation grading method,the annual precipitation series of 11 meteorological stations in Ordos region from 1961 to 2019 are divided into five States:wet year,partial wet year,normal water year,partial dry year and dry year.The weighted Markov forecasting model is established with the autocorrelation coefficientsof each order of annual precipitation series as the weights,and the annual precipitation and their states in Ordos Region in 2017,2018 and 2019 are predicted.The results show that the relative errors are 1.3%,6.9%and4.5%,respectively,the forecasting accuracy is high and the method is proper.For this reason,the weighted Markov chain after accuracy test is used to predict the annual precipitation in Ordos region in 2020,its value is 312.81 mm and divided into normal water year.At the same time,by using the ergodicity of Markov chain,the limit distribution of annual precipitation and the recurring period of abundant and withered state in Ordos region are discussed.The research results show that the probabilities of five kinds of conditions,wet year,partial wet year,normal water year,partial dry year and dry year,in the precipitation process of Ordos region in the past 59 years are 0.1358,0.1941,0.3693,0.1926 and 0.1083,respectively,that is to say,there is the greatest possibility of a normal water year,the recurring period is 2.71 years;with the least possibility of a wet year,the recurring period is 9.23 years.The above research results are consistent with the precipitation series and its state,and consequently it is feasible and effective to predict the annual precipitation in Ordos region by using the weighted Markov chain.

关 键 词：加权马尔科夫链 鄂尔 多斯市 年降水量 预测 丰枯状态重现期 

分 类 号：P426.613[天文地球—大气科学及气象学] O211.62[理学—概率论与数理统计]