Abstract
Abstract. Monte Carlo (MC) methods have been widely used in uncertainty analysis and parameter identification for hydrological models. The main challenge with these approaches is, however, the prohibitive number of model runs required to acquire an adequate sample size, which may take from days to months – especially when the simulations are run in distributed mode. In the past, emulators have been used to minimize the computational burden of the MC simulation through direct estimation of the residual-based response surfaces. Here, we apply emulators of an MC simulation in parameter identification for a distributed conceptual hydrological model using two likelihood measures, i.e. the absolute bias of model predictions (Score) and another based on the time-relaxed limits of acceptability concept (pLoA). Three machine-learning models (MLMs) were built using model parameter sets and response surfaces with a limited number of model realizations (4000). The developed MLMs were applied to predict pLoA and Score for a large set of model parameters (95 000). The behavioural parameter sets were identified using a time-relaxed limits of acceptability approach, based on the predicted pLoA values, and applied to estimate the quantile streamflow predictions weighted by their respective Score. The three MLMs were able to adequately mimic the response surfaces directly estimated from MC simulations with an R2 value of 0.7 to 0.92. Similarly, the models identified using the coupled machine-learning (ML) emulators and limits of acceptability approach have performed very well in reproducing the median streamflow prediction during the calibration and validation periods, with an average Nash–Sutcliffe efficiency value of 0.89 and 0.83, respectively.
Highlights
Conceptual hydrological models have a wide range of applications in solving various water quantity- and quality-related problems
The highest performance of the machine-learning models (MLMs) was observed in year 2014, with R2 values of 0.91, 0.76, and 0.92 for random forest (RF), K nearest neighbours (KNN), and neural network (NNET), respectively, and the lowest performance was observed in year 2013 with R2 values of 0.86, 0.7, and 0.85 for RF, KNN, and NNET, respectively
When using streamflow close to the observed values (Score) as a target variable and the test samples, RF, NNET, and KNN showed a decreasing order of performance based on the three evaluation metrics, i.e. root mean squared error (RMSE), R2, and MAE
Summary
Conceptual hydrological models have a wide range of applications in solving various water quantity- and quality-related problems. A conceptual model typically comprises one or more calibration parameters, as part of the user’s perception of the hydrological processes in the catchment, and the corresponding simplifications that are assumed to be acceptable for the intended modelling purpose (Beven, 1989; Refsgaard et al, 1997). Various uncertainty analysis techniques have been proposed to infer model parameter values from observations, including the generalized likelihood uncertainty estimation (GLUE) methodology (Beven and Binley, 1992), the dynamic identifiability analysis framework (DYNIA; Wagener et al, 2003), the Shuffled Complex Evolution Metropolis (SCEM) algorithm (Vrugt et al, 2003), and the Bayesian inference (Kuczera and Parent, 1998; Yang et al, 2007).
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