Influence of the Long-Range Dependence in Rainfall in Modelling Oueme River Basin (Benin, West Africa)

Abstract

Nowadays, there is evidence that hydrological processes exhibit long-range dependence (LRD), i.e. power-type decay of autocorrelation also known as the Hurst phenomenon. This means that the stationarity assumption of hydrological time series, which has been widely used in the past, cannot be further advocated. The objective of this paper is to detect the long-range dependence in rainfall in Oueme River basin and to understand how the Hurst coefficient influences the river discharge dynamics. To this end, this paper formulated the Hurst phenomenon that characterized hydrological and other geophysical time series. Then, the fractional generalization of the triple relationship between the fractional Brownian motion, the corresponding stochastic differential equations (SDE) describing the river basin and the deterministic fractional Fokker- Planck equations (FPE) is analysed for the modelling of the river discharge dynamics. This fractional FPE provides an essential tool for the study of the dynamics of the river discharge in Oueme River basin.