Characterizing model error in conceptual rainfall-runoff models using storm-dependent parameters

Calibration and prediction in conceptual rainfall-runoff (CRR) modelling is affected by input, model and response error (Figure 1a). This study works towards the goal of developing a robust framework for dealing with these sources of error and focuses on model error. The characterization of model error in CRR modelling has been thwarted by poor conceptualizations of error propagation (Figure 1b) and the convenient but indefensible treatment of CRR models as deterministic descriptions of catchment dynamics. It is argued that CRR fluxes are fundamentally stochastic because they involve spatial and temporal averaging. Acceptance that CRR models are intrinsically stochastic paves the way for a more rational characterization of model error. The hypothesis advanced in this paper is that CRR model error can be characterized by storm-dependent random variation of one or more CRR model parameters that affect fluxes. A simple sensitivity analysis is developed to assist in identifying the parameters most likely to behave stochastically. A Bayesian hierarchical model is formulated to explicitly differentiate between input, response and model error - this provides a very general framework for calibration and prediction, as well as the testing of hypotheses regarding model structure and data uncertainty. A case study using daily data from the Abercrombie catchment (Australia) and employing a 6-parameter CRR model demonstrates the considerable potential of this approach. Figure 2 illustrates the excellent fit to the observed data. Of particular significance is the use of posterior diagnostics to test key assumptions about errors. The assumption that the storm-dependent parameters are log-normally distributed is only partially supported by the data, which suggests that the parameter hyperdistributions have thicker tails. Further research is aiming to refine this approach to characterizing model error. (Figure Presented).