Pragmatic methods for analysing performance and identifiability issues in rainfall-runoff modelling

Abstract

Uncertainty has become a primary issue for modellers and decision makers concerned about understanding the behaviour of natural systems. Characterising uncertainty is an important modelling step for assessing the options for managing it. Without an understanding of a model's strength and weakness and of model uncertainty we cannot judge if management interventions will cause significant change. Methods for characterising uncertainty range from empirical, through naive Monte Carlo to formal Bayesian methods. Most uncertainty methods are complex and difficult to implement. But uncertainty analysis can be so much simpler than this and lead to powerful insights and model improvements. This is illustrated in this thesis where it demonstrates that simple methods can provide useful insight into model uncertainty. This thesis uses four hydrological models of varying complexity applied to five catchments of differing characteristics. It shows that uncertainty analysis can be simple and provide crucial insights into the behaviour of environmental models. This thesis begins by showing how a simple global sensitivity analysis can identify parameters in a model that are unimportant in explaining model outputs, and that might improve identifiability either by checking which ones can be fixed or by changing the objective function. The results confirm that for the catchment examined a minimum of five years is required to characterise the sensitivities assuredly and that only the simpler models have well-identified parameters, but parameter sensitivities vary between catchments. The simple global sensitivity analysis is then complemented with an identifiability analysis of the four models. More complex models have more uncertain and poorly-identified parameters. Model structure is shown to be the major problem in obtaining a global solution, far outweighing data informativeness and the objective function selected. Moreover, the more complex models do not dominate the performance of the less complex, the best model depending on the catchment of interest and even the calibration period. This thesis then considers the issue of minimum acceptable model performance. It is argued that a typical hydrological model identification process of optimising the objective function and reporting the performance in a validation period is no longer sufficient practice. If models with lower objective function values are to be accepted, we need to know how bad a model will be considered as good enough. It proposes a generic approach that uses elimination of Pareto-dominated models and cross-validation to identify minimal criteria for which models should be accepted. Finally, this thesis investigated uncertainties introduced by variable time delays between rainfall events and hydrograph response, a response complexity not handled well by rainfall-runoff models. Smaller events tend to have larger time delays and variability compared to larger events. It proposes a simple solution for model calibration by shifting rainfall and/or modelled times series in events by the amount of observed time lag, as calculated by a cross-correlation function. A variable integer time delay method leads to general improvements in simulation on independent periods, when invoking performance metrics of a Shifted Nash-Sutcliffe Efficiency and absolute relative bias. Overall the variable integer time delay method also improved parameter identifiability.