A time fractional model to represent rainfall process

Abstract

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 α-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation (FFPE) with tempered α-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered á-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered α-stable waiting times is more efficient in reproducing the observed behavior.

Keywords

• rainfall process
• heavy-tailed probability distribution
• tempered α-stable probability law
• log-normal law
• Hurst exponent
• continuous time random walk model
• fractional Fokker-Planck equation