Analysis of the Likelihood Function and Cutoff Threshold in the GLUE Procedure for Calibration of the Resistance Parameters of Mountain Rivers

Abstract

Generalized Likelihood Uncertainty Estimation (GLUE) is a widely used methodology for propagating uncertainty through models. However, GLUE has been criticized because of the random selection of two components: i) the likelihood function, which is used to determine the probability that a given set of parameters reflects the observed data, and ii) the cutoff threshold, which is used to divide models into behavioral and nonbehavioral groups. In this research, a GLUE procedure is implemented based on three mountain river morphologies (cascade, step-pool, and plane bed) with different flow characteristics (high, moderate and low flow) located in the Quinuas River basin. Geometry, flow, bed material, and field roughness data are available for the studied reaches. The simple Fuzzy-rule provides different results than metric-based likelihood functions, so a modification of the simple fuzzy-rule is suggested. The metric-based-likelihood functions influence likelihood curve shape and uncertainty values for a certain threshold when the system under study do not meet the model simplifications. The cutoff threshold is proven necessary for reducing uncertainty; however, this value cannot be too stringently set because there are many cases in which observations fall outside the 5% and 95% confidence intervals, producing outliers. A reasonable cutoff threshold seems to be 12%, which is the uncertainty in the water depth estimated with the continuity equation