Separately accounting for uncertainties in rainfall and runoff: Calibration of event-based conceptual hydrological models in small urban catchments using Bayesian method

Abstract

[1] Uncertainty analysis of hydrological models is usually based on model calibration, and the Bayesian method is a popular way to evaluate the uncertainty. The traditional Bayesian method usually uses lumped model residuals to form the likelihood function, where uncertainty in inputs (rainfall) is not explicitly addressed. This paper compares three approaches based on Bayesian inferences, considering rainfall uncertainty either implicitly or explicitly in calibration. Consistent parameter estimation and reliable quantification of predictive uncertainty are mainly examined. When rainfall uncertainty is explicitly treated in calibration, several rainfall observations at one-minute time steps are grouped to share one multiplier to consider the possible observation errors. The appropriate grouping strategy that balances the representativeness and the complexity of the problem is suggested. The application of the methods considered in this study focuses on small urban catchments (<200 ha) with a small temporal scale (1 min time step), in contrast to most literature studies dealing with larger catchments monitored at larger time steps. It is found that uncertainty in rainfall has a minor contribution to the total uncertainty in runoff estimation, and this minor role can be explained by the low pass filter effect of the linear reservoir model. However, the approach explicitly accounting for input uncertainty results in more informed knowledge for uncertainties related with hydrological model calibrations, which can possibly provide an estimation of uncertainty attributed to rainfall records. It should be noted that rainfall error estimates can compensate model structural uncertainty that is not explicitly addressed in this study.Citation: Sun, S., and J.-L. Bertrand-Krajewski (2013), Separately accounting for uncertainties in rainfall and runoff: Calibration of event-based conceptual hydrological models in small urban catchments using Bayesian method, Water Resour. Res., 49, 5381-5394,

Urban hydrologic trend analysis based on rainfall and runoff data analysis and conceptual model calibration

“…For instance, errors in areal rainfall (represented by point measurements) and runoff measurements lead to biased calibration results, as in calibration, the model parameters are adjusted to make the lumped model outputs match the measurements. Additionally, the model parameters are correlated (e.g., Sun & Bertrand‐Krajewski, ). The initial loss and proportional loss are negatively correlated; the reservoir constant and the time shift are also negatively correlated.…”

Describing the catchment‐averaged precipitation as a stochastic process improves parameter and input estimation

“…Inferring σ β leads to a hierarchical parameter estimation problem. While some applications of RM kept σ β fixed [ Sun and Bertrand‐Krajewski , ], making the error model nonhierarchical, we prefer to infer this hyperparameter to learn about the overall input variance detected during calibration [ Li et al ., ; Sikorska et al ., ]. Despite using the same likelihood function as for the LS method, the replacement of the input description (2) by (6) leads to the consideration of input uncertainty at the level of whole storm events and augments the parameter vector with the parameters of the rainfall error model.…”

“…A more satisfying approach for considering input errors is to make the input uncertain and to propagate it through the model [ Honti et al ., ; McMillan et al ., ]. A simple way of doing so, which has become popular in hydrology, is the use of so‐called rainfall multipliers [ Kavetski et al ., ; Sun and Bertrand‐Krajewski , ]. These are event‐specific random variables multiplied with the observed rain to provide the input to the model.…”

Comparison of two stochastic techniques for reliable urban runoff prediction by modeling systematic errors

“…In both methods, structural and input uncertainties are aggregated into one term. Approaches that, instead of just describing the output errors, focus on identifying the causes of model inadequacies. To quantify input uncertainty, rainfall multipliers have been proposed [ Kuczera et al ., ; Sun and Bertrand‐Krajewski , ]. Structural uncertainty, instead, has been dealt with by inferring the model equations [ Bulygina and Gupta , ], the behavior of dynamic parameters [ Reichert and Mieleitner , ], or the value of model parameters and states [ Vrugt et al ., ].…”