عنوان مقاله [English]
Background and objectives: In hydrology, the frequent ill-posed Inverse problems suffer from overfitting which leads to omitting the model parameters with less outputs fitness to observations. These parameters might have better fitting during other periods. They should not be rejected but should be considered in some way. Generalized Likelihood Uncertainty Estimation (GLUE) is one solution.
Materials and methods: In this study, GLUE has been used for uncertainty estimation of two rainfall-runoff model. In the method, an informal likelihood function with a subjective threshold is used for selecting a set of behavioral parameters and then predictive uncertainty bounds are estimated from these parameter outputs. The GLUE is applied for ChehelChai Catchment, located in North east of Iran, Golestan province. HyMod (HYdrologic MODel) and HBV (Hydrologiska Byråns Vattenbalansavdelning) lumped models were used for catchment modeling with six likelihood functions including Inverse Variance (IV), Nash-Sutcliff (NSE), Kling-Gupta (KGE), Whittle, Normal with homoscedastic error variance and Normal with heteroscedastic error variance.
Results: For appraisal of the GLUE method, the best likelihood function was selected and sensitivity analysis of different factors on the method was done. For the case study catchment, Inverse Variance (IV), Kling-Gupta (KGE) and Normal with homoscedastic error variance likelihood functions, regarding to their relative answers, was selected for subsequent assessments. The sensitivity analysis of the partitioning threshold between behavioral and non-behavioral parameters showed the 5 percent of simulations are suitable. Increasing shape factor devotes more weight to parameters with better goodness of fit and makes the GLUE to act more like an optimization method. Parameter uncertainty analysis showed low correlation among parameters which implies that both model parameters are well defined, but high coefficient of variation implies that identifiability of the parameters are low. Uncertainty bounds calculated by applying the GLUE method covered 62 percent of observation foe HyMod model and 55 percent for HBV model. For base-flows, the prediction bounds were widest among other components of hydrograph.
Conclusion: Considering the results, it can be indicated that the GLUE method is sensitive to likelihood function, the partitioning threshold between behavioral and non-behavioral parameters and also the assessed model because by changing from case to case, different results could be achieved. For Chehelchai catchment, the Kling-Gupta likelihood function was the best among other assessed likelihood functions, the best threshold was 5 percent of number of simulations and among applied models, HyMod had better results compared to HBV model. Parameter uncertainty estimated by the GLUE method is high, because total uncertainty of different elements of model is projected to parameter uncertainty. Simplicity and relatively preventing from overfitting are some advantages of the method.