Abstract. Parameter uncertainty estimation is one of the major challenges in hydrological modeling. Here we present parameter uncertainty analysis of a recently released distributed conceptual hydrological model applied in the Nea catchment, Norway. Two variants of the generalized likelihood uncertainty estimation (GLUE) methodologies, one based on the residuals and the other on the limits of acceptability, were employed. Streamflow and remote sensing snow cover data were used in conditioning model parameters and in model validation. When using the GLUE limit of acceptability (GLUE LOA) approach, a streamflow observation error of 25 % was assumed. Neither the original limits nor relaxing the limits up to a physically meaningful value yielded a behavioral model capable of predicting streamflow within the limits in 100 % of the observations. As an alternative to relaxing the limits, the requirement for the percentage of model predictions falling within the original limits was relaxed. An empirical approach was introduced to define the degree of relaxation. The result shows that snow- and water-balance-related parameters induce relatively higher streamflow uncertainty than catchment response parameters. Comparable results were obtained from behavioral models selected using the two GLUE methodologies.

Abstract. Parameter uncertainty estimation is one of the major challenges in hydrological modelling. Here we present parameter uncertainty analysis of a recently released distributed conceptual hydrological model applied in the Nea catchment, Norway. Two variants of the generalized likelihood uncertainty estimation (GLUE) methodologies, one based on the residuals and the other on the limits of acceptability, were employed. Streamflow and remote sensing snow cover data were 10 used in conditioning model parameters and in model validation. When using the GLUE limit of acceptability (GLUE LOA) approach, a streamflow observation error of 25 % was assumed. Neither the original limits, nor relaxing the limits up to a physically meaningful value, yielded a behavioural model capable of predicting streamflow within the limits in 100 % of the observations. As an alternative to relaxing the limits; the requirement for percentage of model predictions falling within the original limits was relaxed. An empirical approach was introduced to define the degree of relaxation. The result shows that 15 snow and water balance related parameters induce relatively higher streamflow uncertainty than catchment response parameters. Comparable results were obtained from behavioural models selected using the two GLUE methodologies.

Remote sensing fractional snow cover area (fSCA) has been increasingly used to get an improved estimate of the spatiotemporal distribution of snow water equivalent (SWE) through reanalysis using different data assimilation (DA) schemes. Although the effective assimilation period of fSCA is well recognized in previous studies, little attention has been given to explicitly account for the relative significance of measurements in constraining model parameters and states. Timing of the more informative period varies both spatially and temporally in response to various climatic and physiographic factors. Here we use an automatic detection approach to locate the critical points in the time axis where the mean snow cover changes and where the melt-out period starts. The assimilation period was partitioned into three timing windows based on these critical points. A fuzzy coefficient was introduced in two ensemble-based DA schemes to take into account for the variability in informational value of fSCA observations with time. One of the DA schemes used in this study was the particle batch smoother (Pbs). The main challenge in Pbs and other Bayesian-based DA schemes is, that most of the weights are carried by few ensemble members. Thus, we also considered an alternative DA scheme based on the limits of acceptability concept (LoA) and certain hydrologic signatures and it has yielded an encouraging result. An improved estimate of SWE was also obtained in most of the analysis years as a result of introducing the fuzzy coefficients in both DA schemes. The most significant improvement was obtained in the correlation coefficient between the predicted and observed SWE values (site-averaged); with an increase by 8% and 16% after introducing the fuzzy coefficient in Pbs and LoA, respectively.

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.

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 get 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 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 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; and the models identified using the coupled ML emulators and the limits of acceptability approach have performed very well in reproducing the median streamflow prediction both during the calibration and validation periods.