On the Impact of Uncertainty in Initial Conditions of Hydrologic Models on Prediction

Abstract:

Determining the initial conditions for predictive models remains a challenge due to the uncertainty in measurement/identification of the state variables at the scale of interest. However, the characterization of uncertainty in initial conditions has arguably attracted less attention compared with other sources of uncertainty in hydrologic modelling (e.g, parameter, data, and structural uncertainty). This is perhaps because it is commonly believed that: (1) hydrologic systems (relatively rapidly) forget their initial conditions over time, and (2) other sources of uncertainty (e.g., in data) are dominant.

This presentation revisits the basic principles of the theory of nonlinear dynamical systems in the context of hydrologic systems. Through simple example case studies, we demonstrate how and under what circumstances different hydrologic processes represent a range of attracting limit sets in their evolution trajectory in state space over time, including fixed points, limit cycles (periodic behaviour), torus (quasi-periodic behaviour), and strange attractors (chaotic behaviour). Furthermore, the propagation (or dissipation) of uncertainty in initial conditions of several hydrologic models through time, under any of the possible attracting limit sets, is investigated. This study highlights that there are definite situations in hydrology where uncertainty in initial conditions remains of significance. The results and insights gained have important implications for hydrologic modelling under non-stationarity in climate and environment.