Assessing the Uncertainty of the Xinanjiang Rainfall-Runoff Model: Effect of the Likelihood Function Choice on the GLUE Method

Abstract

In this paper, the generalized likelihood uncertainty estimation (GLUE) methodology, which is widely applied in the field of hydrology, is used for testing and predictive uncertainty estimation in the application of the Xinanjiang rainfall-runoff (XAJ-RR) model for estimating monthly stream flow (Nangao reservoir) catchment in China. However, one of the drawbacks of using the GLUE method is the definition of the likelihood function, which reflects the behavior of the hydrological model. Although there are different formulations of likelihood functions in the literature, most previous research focused on the application of the GLUE method with the likelihood function of Nash-Sutcliffe (NS) efficiency. In this respect, to illustrate the impact of the selection of likelihood functions on the results of the GLUE method, the authors adopted four likelihood functions: NS, normalized absolute error (NAE), index of agreement (IoA), and Chiew and McMahon (CM). The main findings of the study are that (1) the parameter uncertainty is more sensitive to the choice of the likelihood functions than the uncertainty in the model prediction by the GLUE method; (2) the parameters of the XAJ-RR model with NS had less uncertainty compared to those of NAE, IoA, and CM; (3) the uncertainty bounds showed slight differences from various likelihood functions; and (4) the computational efficiency of the GLUE method based on likelihood function IoA was much better because the IoA likelihood function corresponded to narrower uncertainty bounds, higher bracketing of observations, and the best maximum value of likelihood functions. Thus, this study confirms the importance of the likelihood function selection in the application of GLUE to the uncertainty assessment of the XAJ-RR model.