Recursive Bayesian Estimation of Conceptual Rainfall-Runoff Model Errors in Real-Time Prediction of Streamflow

Conceptual rainfall-runoff models account for the spatial dynamics of hydrological processes in a basin using simple spatially lumped storage-flow relations. Such rough approximations introduce model errors that are often difficult to characterize. Here, we develop and apply a methodology that recursively estimates and accounts for model errors in real-time streamflow prediction settings by adding time-dependent random noise to the internal states (storages) of the hydrological model. Magnitude of the added noise depends on a precision (inverse variance) parameter that is estimated from rainfall-runoff data. A recursive Bayesian technique is used for estimation: posteriors of hydrological parameters and states are updated through time with an ensemble Kalman filter, whereas the posterior of the precision parameter is updated recursively using a novel gamma density approximation technique. Applying this algorithm to different model error scenarios allows identification of the main source of model errors. The methodology is applied to short-term streamflow prediction with the Hymod rainfall-runoff model in a semi-cold, semi-humid basin in Iran. Results show that (i) streamflow prediction in this snow-dominated basin is more affected by model errors in the slow flow than the quick flow component of the model, (ii) accounting for model errors in the slow flow component improves both low and high flow predictions, and (iii) predictive performance further improves by accounting for Hymod parameter uncertainty in addition to model errors. Overall, accounting for model errors increased Nash-Sutcliffe efficiency (by 1–5%), reduced mean absolute error (by 2–43%), and improved probabilistic predictive performance (by 50–80%).