A time fractional model to represent rainfall process

作     者：Jacques GOLDER Maminirina JOELSON Marie-Christine NEEL Liliana DI PIETRO 

作者机构：Department of PhysicsUniversity of Avignon Mediterranean Environment and Agro-Hydro System Modelisation LaboratoryFrench National Institute for Agricultural Research 

出 版 物：《Water Science and Engineering》 (水科学与水工程（英文版）)

年 卷 期：2014年第7卷第1期

页      面：32-40页

核心收录：

学科分类：07[理学] 070601[理学-气象学] 0706[理学-大气科学] 

主　　题：rainfall process heavy-tailed probability distribution tempered a-stable probability law log-normal law Hurst exponent continuous time random walk model fractional Fokker-Planck equation 

摘      要：This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.