Estimating rainfall-runoff model parameters using the iterative ensemble smoother

Catchment water quality models are an important tool for understanding the impacts of land management practice on the water quality of the receiving waters of the Great Barrier Reef lagoon. As part of the Paddock to Reef program the Great Barrier Reef Catchment Loads Modelling Program estimates average annual loads of key pollutants (sediment, nutrients and pesticides) for each of the 35 catchments draining to the Great Barrier Reef. Since catchment models assume that constituent generation and transport within the catchment is largely controlled by rainfall and runoff, it is imperative that the hydrology calibration approach underpinning the catchment model is rigorous and achieves the best possible results. Because catchment models are conceptual representations of very complex landscape systems any forecasts and predictions they produce will be subject to uncertainty and quantifying uncertainty is an important aspect of analysing model performance. Various methods derived from a range of statistical frameworks have been applied to study uncertainty of rainfall-runoff models. Perhaps the most intuitive way of approaching uncertainty analysis is via the formalism of Bayes' theorem where some prior understanding of the model parameters is updated once exposed to relevant data. As elegant as Bayesian uncertainty analysis may be, there are practical limitations to implementing it. The equations defining Bayes' theorem often have no analytic solution, or at least one that is tractable, one must resort to numerical methods to complete the process. In practice, this usually involves a campaign of stochastically sampling from the Bayesian posterior distribution to construct a statistical facsimile. This can be a computationally exhausting process, particularly when an expensive model is used, the prior is significantly divergent from the posterior and a large number of parameters is involved. Ensemble methods such as the iterative ensemble smoother (IES) have been developed to alleviate much of the computational overhead demanded by the uncertainty quantification of environmental models, particularly those that involve high dimensional parameter spaces. On the face of it, the IES would seem to fit very well with the problem presented by catchment water quality models but to date, there is very little evidence of this. In this study, we apply a Gauss-Levenberg-Marquardt form of the IES to the calibration and uncertainty analysis of a rainfall-runoff model. The IES is found to be an efficient and powerful method for conditioning model parameters and providing robust uncertainty estimates adhering to the spirit of Bayesian statistics.