Abstract:
The objective of this paper is to understand how the natural dynamics of a time-varying catchment, i.e.
the rainfall pattern, transforms the random component of rainfall and how this transformation influences
the river discharge. To this end, this paper develops a rainfall–runoff modelling approach that
aims to capture the multiple sources and types of uncertainty in a single framework. The main
assumption is that hydrological systems are nonlinear dynamical systems which can be described by
stochastic differential equations (SDE). The dynamics of the system is based on the least action principle
(LAP) as derived from Noether’s theorem. The inflow process is considered as a sum of deterministic
and random components. Using data from the Ouémé River basin (Benin, West Africa), the basic
properties for the random component are considered and the triple relationship between the structure
of the inflowing rainfall, the corresponding SDE that describes the river basin and the associated
Fokker-Planck equations (FPE) is analysed.
