the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical Note: Benefits of Bayesian estimation of model parameters in a large hydrological model ensemble
Abstract. Quantifying and mitigating parametric and structural uncertainties in hydrological models are crucial to accurately understand and predict the rainfall-runoff process. Despite recent advances in Bayesian approaches for quantifying structural uncertainty using very large hydrological model ensembles, the simultaneous quantification of both parametric and structural uncertainties has yet to be implemented since previous works on large model ensembles have relied on deterministic optimization of parameters. Here we present the potential benefits of Bayesian estimation of parametric uncertainty within a large hydrological model ensemble. We find that Bayesian estimation of model parameters (more generally, change in calibration methods) potentially influences the interpretation of model comparisons. Specifically, Bayesian parametric uncertainty quantification greatly benefits complex models with many parameters, thereby affecting discussions of the appropriate level of model complexity. We also find that Bayesian parametric uncertainty quantification does not substantially improve multi-model hydrological predictions. The adverse effects of parameter misspecification in individual models are effectively mitigated by combining models with diverse structures. Thus, the high computational cost of Bayesian parameter estimation is not paid for to improve rainfall-runoff analysis in a large hydrological model ensemble.
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Status: closed
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RC1: 'Comment on egusphere-2025-4984', Anonymous Referee #1, 06 Jan 2026
- AC2: 'Reply on RC1', Yohei Sawada, 18 Mar 2026
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RC2: 'Comment on egusphere-2025-4984', Anonymous Referee #2, 16 Feb 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4984/egusphere-2025-4984-RC2-supplement.pdf
- AC1: 'Reply on RC2', Yohei Sawada, 18 Mar 2026
Status: closed
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RC1: 'Comment on egusphere-2025-4984', Anonymous Referee #1, 06 Jan 2026
General comments
This manuscript investigates the roles of parametric and structural uncertainties in hydrological models. Specifically, the study evaluates the scientific and practical benefits of Bayesian parameter estimation within a large ensemble of models. Overall, Bayesian parameter estimation improves the analysis of individual models but provides little additional predictive skill when compared to Bayesian model averaging across the full ensemble. The study tackles an important problem with impacts with operational hydrological forecasting and in the interpretation of hydrological model research. The study is well designed, and the manuscript is clearly written and structured. The manuscript would benefit from clearer figures to more effectively support the conclusions, as well as minor clarifications and typographical corrections.
Specific comments
- Lines 116-117: How was this model selection made? I understand the motivation to “preserve diversity in model complexity while minimizing the total computation cost” but what process was used to select, for example, model ID 07 instead of model ID 09 etc?
- Line 192: How were the 51 basins selected out of the 135 in MERV-Jp?
- Lines 211-213: Does this mean that for the 1-year calibration scenario and a typical station, the spin-up was performed from 1986 to 1990, calibration was then done for 1986, and then the timeseries was for evaluation was started from 1991? If so, from what set of initial conditions was the evaluation timeseries generated as it would have been the uncalibrated parameters that were used for the spin-up? Please clarify.
- Figures: Some figures are too small or cluttered to see the point the authors are making.
- Figure 2: The subplots are quite small and it is difficult to see the authors main point (that the BPA surpasses the deterministically optimized models particularly for data-sparse scenarios) due to the clutter within the axes and the broad scales used on the y-axes.
- Figure 3: It is not easy to see that more complex models benefit more from BPA partly because many model-basin pairs have near-white squares due to the colormaps. It would also be beneficial to add some indication of whether a model/basin benefits from BPA or not as currently the reader has to count the squares to find this information.
- Lines 286-287: “BPA achieves 0.8 KGE for nearly all models, while some deterministically optimized models (i.e., ID 7, 24, 30, and 31) perform poorly.” ID 31 deterministic performs as well as ID 21 BPA so this sentence may be misleading.
Technical corrections
- Line 52-53: “we refer <to> these approaches.”
- Lines 159-169: Something is off with this sentence. Pleas check the grammar for readability. “where N is the total number of models (=17 in this case). 𝒚 should be recognized as river discharge observation in a calibration period.”
- Line 210: “resulting <in> a 10-year”
- Line 219: “we have 17 hydrological predictions by 17 models in 51 river basins” implies 17 predictions from each of the 17 models (17 x 17 x 51). Please clarify.
- Line 226: “by <the> parameter estimation method”
- Line 240: “which leads <to> higher robustness to unseen data”
Citation: https://doi.org/10.5194/egusphere-2025-4984-RC1 - AC2: 'Reply on RC1', Yohei Sawada, 18 Mar 2026
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RC2: 'Comment on egusphere-2025-4984', Anonymous Referee #2, 16 Feb 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-4984/egusphere-2025-4984-RC2-supplement.pdf
- AC1: 'Reply on RC2', Yohei Sawada, 18 Mar 2026
Data sets
Dataset of "Benefits of Bayesian estimation of model parameters in a large hydrological model ensemble" Yohei Sawada and Shinichi Okugawa https://doi.org/10.5281/zenodo.17282833
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General comments
This manuscript investigates the roles of parametric and structural uncertainties in hydrological models. Specifically, the study evaluates the scientific and practical benefits of Bayesian parameter estimation within a large ensemble of models. Overall, Bayesian parameter estimation improves the analysis of individual models but provides little additional predictive skill when compared to Bayesian model averaging across the full ensemble. The study tackles an important problem with impacts with operational hydrological forecasting and in the interpretation of hydrological model research. The study is well designed, and the manuscript is clearly written and structured. The manuscript would benefit from clearer figures to more effectively support the conclusions, as well as minor clarifications and typographical corrections.
Specific comments
Technical corrections