Reliability Analysis in Hydrological Modelling: Concepts and Applications to the GR3 Rainfall-Runoff Model
Reliability analysis is a method for evaluating the risk of failure of a system and this concept is widely used in structure design. The theory can be conveniently transposed to the field of water sciences so as to evaluate the quality of hydrologic models. Hydrological reliability of a model is defined as the probability that there will not be significant different performances between this model, with parameters assessed on the basis of a large sample including various hydrological conditions, and the same model running with ad hoc parameters estimated from the test sample. Consequently a tolerance threshold has to be introduced in reliability analysis for hydrological models. A number of conceptual differences between validation and reliability analysis are reviewed and categorized. This paper shows how to adapt the concepts of reliability to hydrology and gives details of the first two moment technique that can be implemented to compute the reliability of a rainfall runoff model. This technique is based on a Taylor series developed in the neighborhood of the model working point. This simplification allows for an explicit expression of the expectation and the variance of the hydrological model performance as functions of the marginal sensitivity of the criterion and the parameter uncertainties. A Student ratio can be easily computed to evaluate the quality of a hydrological model from a reliability-based point of view. The GR3 model is used to illustrate this technique. A reliability analysis of this three parameter conceptual rainfall-runoff model gives new insight into the performance of the model for short-term flood prediction in the Réal Collobrier river basin located in the French Côte d'Azur. Numerical results show that the reliability analysis approach is very simple and of practical interest. For 16 of the 18 samples used for validation, the GR3 rainfall runoff model proved to be reliable on the basis of the three criteria used in this paper to evaluate the quality of a hydrological model (general quadratic deviation loss of runoffs, flood volume error and flood peak error). Using reliability analysis, contributions of each parameter to the variance of the performance function can be conveniently identified. For the GR3 model and the Réal Collobrier case study, the impacts of each parameter on the model efficiency are as follows: - The contribution of a parameter varies from one criterion to another. This indicates that a parameter originally designed to play a specific role in the modeling of the rainfall runoff transformation process does contribute to the criterion that best describes this function, which confirms the conceptual "good sense" of GR3. - For each criterion, the cross contributions are very low: the GR3 model satisfies the principle of parsimony and each parameter adds something different to the general behavior of GR3. In this case study, the GR3 model exhibits a good balance between complexity and quality for hydrological models. Finally, reliability analysis can provide a multicriteria point of view of the model qualities by changing the various indices of performance. Extension of reliability analysis towards engineering risk would include the estimation of joint probability distributions for these multiple criteria of interest.