A Fokker–Planck–Kolmogorov equation-based inverse modelling approach for hydrological systems applied to extreme value analysis

Abstract

Abstract This paper takes a stochastic approach to identify uncertainties in hydrological systems that can be applied to the study of hydrological extremes. The system to be identified is supposed to be governed by a stochastic differential equation of the Langevin type, whose parameters are found through the inverse solution of the equivalent Fokker–Planck–Kolmogorov equation. The study presents the algorithmic and numerical implementation for the inverse modelling process, along with the implementation of this approach in three study areas. Results showed a flexible method that made it possible to consider hydrological variability and seasonality during system identification. The identified system parameters rely on the internal–external driving factors of the analysed river basin and provide indications about the behaviour of extreme events in possible future climate scenarios or situations where internal system parameters are altered. While the study cases presented refer to non-stationary Markov processes that allow for one-dimensional systems identification only, the proposed methodological approach is a step in the right direction when it comes to identifying n-dimensional Markov processes/systems.