A time fractional model to represent rainfall process

• Main Authors: Jacques Golder, Maminirina Joelson, Marie-Christine Neel, Liliana Di Pietro
• Format: Article
• Language: English
• Published: Elsevier 2014-01-01
• Series: Water Science and Engineering
• Subjects: 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
• Online Access: http://www.sciencedirect.com/science/article/pii/S1674237015302647

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.