Effect of different likelihood measures on parameter conditioning and model uncertainty

This study investigates the impact of different likelihood measures on parameter conditioning within the Generalized Likelihood Uncertainty Estimation (GLUE) framework for the parameter identification, calibration and uncertainty analysis of a conceptual NAM (Nedbor Afstromnings Model) rainfall-runoff model. Hydro-meteorological data of the Ilgaz catchment from 2012 to 2017 was used for the current study. Root Mean Square Error (RMSE) with a threshold of 0.45 and Nash–Sutcliffe Efficiency (NSE) with a threshold of 0.55 as comparative likelihood measures are used. The findings reveal distinct variations in parameter likelihoods, notably with the runoff coefficient showing considerable differences under RMSE compared to NSE when extra data is included. Specifically, RMSE facilitated a higher encapsulation of uncertainty, leading to a P-factor of 0.6, unlike NSE, which yielded a narrower uncertainty bound, indicated by a P-factor of 0.4 and an R-factor of 0.44. Further analysis using an alternative likelihood measure that allows for adjusting the exponent N revealed its significant influence on prediction limits and efficiency measures. Moreover, leveraging prior samples from the MIKE-NAM AutoCal function demonstrated a substantial enhancement in computational efficiency. By utilizing constrained prior distributions, the study achieved highly constrained posterior distributions with markedly less computational effort, maintaining the robustness of model predictions evidenced by a close match between observed and estimated flows and reasonable containment within prediction bounds. Notably, the additional data led to a highly constrained parameter distribution, especially when using NSE, with the study showing a maximum NSE value of 0.69 for the 2013–2017 period compared to 0.53 for 2013 alone. This indicates a more stringent posterior distribution of parameters under the scrutinized conditions. The NSE value of 0.69, RMSE of 0.24, and a correlation coefficient of 0.89 further affirm the accuracy of the hydrological model’s predictions under likelihood measure with exponent N. These findings underscore the importance of selecting suitable likelihood measures and the effectiveness of tuning prior sample distributions in enhancing the efficiency and accuracy of the GLUE methodology in hydrological modeling. The research contributes valuable insights into improving uncertainty estimation in hydrological predictions, advocating for tailored approaches to likelihood measures and adjustments in prior distribution settings.