Impact of runoff measurement error models on the quantification of predictive uncertainty in rainfall-runoff models

Abstract

The development of a robust framework for quantifying the parametric and predictive uncertainty of conceptual rainfall runoff (CRR) models remains a key challenge in hydrology. For practical purposes, reliable and robust characterization of predictive uncertainty is important for comparing the impact of management options on key variables of interest (e.g. reservoir yield, meeting low flow criteria for ecological purposes). For research purposes, robust identification of the sources of uncertainty is essential for understanding how to reduce predictive uncertainty, and thereby enhance model predictions. Both these tasks are recognized as a major challenge for hydrological modelling science. It is generally recognized that CRR modelling is affected by three main sources of uncertainty: (i) input uncertainty, e.g., measurement and sampling errors in the estimates of areal rainfall; (ii) output uncertainty, e.g., rating curve errors affecting runoff estimates; and (iii) structural uncertainty (sometimes referred to as "model uncertainty"), arising from lumped and simplified representation of hydrological processes in CRR models. Various approaches in the literature have aimed to quantify the individual contributions of input, output and structural uncertainties to the total predictive uncertainty. The beneficial impact of quantifying input errors on CRR parameter estimates and the reliability of model predictions has been established and techniques for evaluating model structural errors have begun to appear. However, almost all these studies make assumptions regarding the output (runoff measurement) errors. This study evaluated whether there is any beneficial impact in utilizing rating curve data to fit a runoff measurement error model. This was undertaken by incorporating this fitted output error (OE) model into the Bayesian total error analysis (BATEA) methodology. BATEA provides a comprehensive framework to hypothesize, infer and evaluate probability models describing input, output and model structural error. BATEA was used to calibrate the GR4J model to the ephemeral Horton catchment. To evaluate the impact of the fitted OE model the calibration results were compared to two other OE models; one representing a commonly assumed OE model and the other representing a conservative "overestimate" of the OE model. The estimated predictive uncertainty was more consistent with the observed runoff data for the fitted OE model than the assumed OE (which systemically under predicted the observed runoff) and the conservative OE (which overestimated the predictive uncertainty). This result was consistent in model calibration and validation. This illustrates for this case study there was beneficial impact in incorporating a fitted OE model. Comparison of the posterior distributions of parameters showed that the different OE model produced significantly different parameter estimates. This has implications for regionalizing parameters estimations to produce predictions in ungauged basins. Comparison of the estimated input/structural errors also showed substantial differences for different OE. This suggests an interdependency between the error sources, where reliable estimates of input/structural errors will be dependent on reliable estimates of the output error.