Author : Biao I. Eliézer, Gaba Charlene, Alamou A. Eric and Afouda Abel

Rainfall is very often considered as the driving force of hydrological models. If the rainfall changes, the model output (i.e. flow) is also expected to change. The objective of this paper is to study the impacts of the uncertainties related to the random component of rainfall inflow in the Ouémé river basin. The inflow process is considered as a sum of deterministic and random components. Hydrological systems are considered as non – linear dynamical systems which can be described by stochastic differential equations (SDE). The dynamics of the system is here derived from the Least Action Principle (LAP) considerations. Using data from Ouémé river basin (Benin, West Africa), the modelling of the random component using an ARMA model is investigated. The generalized Fokker – Planck equation (FPE) that corresponds to the SDE describing the river basin is derived in terms of the transition probability distribution and characteristic function of the noise generating process. This generalized FPE is used to examine the effects of different type of uncertainties related to the random component of rainfall inflow on the dynamics of river discharge. The form of the FPE is found to be particularly sensitive to the uncertainty properties of the inflowing rainfall.

Keywords: ARMA model, Fokker – Planck equation (FPE), Least Action Principle (LAP), random component of inflow rainfall, stochastic differential equation (SDE), uncertainty.

Article published in International Journal of Current Engineering and Technology, Vol.5, No.3 (June-2015)