摘要
This paper aims at the spatiotemporal distribution of rainfall in Ethiopia and developing stochastic daily rainfall model.Particularly,in this study,we used a Markov Chain Analogue Year(MCAY)model that is,Markov Chain with Analogue year(AY)component is used to model the occurrence process of daily rainfall and the intensity or amount of rainfall on wet days is described using Weibull,Log normal,mixed exponential and Gamma distributions.The MCAY model best describes the occurrence process of daily rainfall,this is due to the AY component included in the MC to model the frequency of daily rainfall.Then,by combining the occurrence process model and amount process model,we developed Markov Chain Analogue Year Weibull model(MCAYWBM),Markov Chain Analogue Year Log normal model(MCAYLNM),Markov Chain Analogue Year mixed exponential model(MCAYMEM)and Markov Chain Analogue Year gamma model(MCAYGM).The performance of the models is assessed by taking daily rainfall data from 21 weather stations(ranging from 1 January 1984–31 December 2018).The data is obtained from Ethiopia National Meteorology Agency(ENMA).The result shows that MCAYWBM,MCAYMEM and MCAYGM performs very well in the simulation of daily rainfall process in Ethiopia and their performances are nearly the same with a slight difference between them compared to MCAYLNM.The mean absolute percentage error(MAPE)in the four models:MCAYGM,MCAYWBM,MAYMEM and MCAYLNM are 2.16%,2.27%,2.25%and 11.41%respectively.Hence,MCAYGM,MCAYWBM,MAYMEM models have shown an excellent performance compared to MCAYLNM.In general,the light tailed distributions:Weibull,gamma and mixed exponential distributions are appropriate probability distributions to model the intensity of daily rainfall in Ethiopia especially,when these distributions are combined with MCAYM.
本文针对埃塞俄比亚降雨的时空分布建立了随机日降雨模型。首先使用具有模拟年分量(AY)的马尔科夫链模型(MCAYM)来模拟日降雨的发生过程,模拟效果较为理想。然后,结合发生过程模型和数量过程模型,我们开发了马尔科夫链模拟年降雨的威布尔模型(MCAYWBM)、马尔科夫链模拟年降雨的对数正态模型(MCAYLNM)、马尔科夫链模拟年降雨的混合指数模型(MCAYMEM)和马尔科夫链模拟年降雨的伽玛模型(MCAYGM)。通过从埃塞俄比亚国家气象局(ENMA)的21个气象站获取每日(1984年1月1日至2018年12月31日)降雨数据来评估模型的性能。结果表明,MCAYWBM、MCAYMEM和MCAYGM在埃塞俄比亚日降雨过程的模拟中表现非常好,与MCAYLNM相比,它们的性能几乎相同但又略有差别。MCAYGM、MCAYWBM、MAYMEM和MCAYLNM四个模型的平均绝对百分比误差(MAPE)分别为2.16%、2.27%、2.25%和11.41%。因此,与MCAYLNM相比,MCAYGM、MCAYWBM、MAYMEM模型表现出更优异的性能,威布尔分布、伽马分布和混合指数分布是模拟埃塞俄比亚日降雨强度的合适概率分布,尤其当这些分布与MCAYM结合时,其模拟效果更好。
