the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Feb 2026
What can hydrological modelling gain from spatially explicit parameterization and multi-gauge calibration?
Abstract. Traditional hydrological modelling is facing transformative pressures from the rise of data-driven approaches and increasing demands for modelling realism. With improving data availability, enhancing the spatial representation of models while imposing stronger calibration constraints offers a promising pathway to reinvigorate the predictive capabilities of physically based distributed hydrological models. However, beyond their effects on aggregated simulated responses, the underlying mechanisms and interactions through which these approaches benefit hydrological modelling remain poorly understood. To bridge this knowledge gap, this study develops an Experiment Framework to evaluate the effect of Spatially explicit Parameterization and Multi-gauge calibration, termed EF-SPM. The framework is applied a representative nested catchment through a series of intensive comparative calibration experiments, in which multiscale parameter regionalization technique is integrated with the Variable Infiltration Capacity model.
Results indicate that, compared to simpler configurations, considering both spatially explicit parameterization with multi-gauge calibration leads to consistent improvements in streamflow simulations across all sub-basins. Controlled experiments isolating individual effects further show that spatially explicit parameterization is particularly effective in improving simulations under moderate-flow to high-flow conditions (with an 18 % improvement in %BiasFHV1), yet at the cost of degraded performance during low-flow periods (with %BiasFLV worsening by 8.6 %). On the other hand, multi-gauge calibration markedly enhances parameter identifiability by imposing stronger constraints on spatially shared parameters. This creates a trade-off with spatially explicit parameterization, which expands the parameter set, thereby reducing identifiability and subsequently increasing equifinality. Take them together, a cross-benefit can be clearly identified in the multidimensional objective space during calibration. We found that, under uniform parameterization, continuous and convex arc-shaped Pareto fronts emerged, reflecting pronounced competition among multi-gauge objectives. This competition is substantially alleviated under spatially explicit parameterization.
This study integrates two promising directions in contemporary hydrological modelling, highlighting the importance of pursuing more expressive parameterization and stronger calibration constraints in parallel, rather than prioritizing one over the other. In doing so, it provides a steppingstone for advancing distributed hydrological modelling toward a modern Model–Data Infusion framework.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-6543', Anonymous Referee #1, 27 Feb 2026
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AC1: 'Reply on RC1', Xudong Zheng, 01 Mar 2026
Thank you for your constructive comments and valuable feedback. We have provided a detailed, point-by-point response in the attached document "response_RC1.pdf". Your suggestions have significantly improved the quality of our manuscript. We also deeply appreciate your recognition of our work, and your input has been instrumental in refining and strengthening our study.
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AC1: 'Reply on RC1', Xudong Zheng, 01 Mar 2026
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RC2: 'Comment on egusphere-2025-6543', Anonymous Referee #2, 17 Mar 2026
Overall, I thought this was a well-designed study with a well written manuscript. The results demonstrated that spatially explicit parameterization and multi-gauge calibration increased overall accuracy of the VIC model simulated streamflow.
I have a few suggestions below:
Introduction:
The introduction needs a justification and explanation of the VIC model at the beginning or after line 70. The introduction, as it is currently, provides a specific, detailed explanation of spatial explicit parameterization without discussion, in detail, the implementation within VIC, despite the objectives detailing the application of MPR and VIC-refinements. I recommend at least one paragraph specifically justifying the use of VIC as the hydrologic model in this study.
I think the explanation of multi-gauge in nested catchment systems needs more explanation than the one sentence provided in line 105. I recommend expanding this to a full paragraph.
In objective 3 – Its unclear what you mean by cross-benefits between the two approaches. Can you expand on this by specifically defining the two approaches and generally discussing the expected cross-benefits?
Study Area
Can you provide a land use analysis on the Upper Han River Basin to visualize the amount of anthropogenic vs natural landscape?
Please include an explanation of the presence or absence of impoundments, dams, or reservoirs in the watershed.
Methods
Figure 2: Could you add the additional steps of RVIC parameter refinement using MPR technique here?
Results
Figure 4: The regression plot between the observed and simulated streamflow makes it hard to visualize the patterns of the majority flow observations below 100m3/s, and appears to rely on a few of the larger flow metrics. I recommend a random thinning to effectively visualize the patterns in the majority of below 1000 m3/s.
Figure 6: I find the pie chart hard to visualize, and I would recommend converting to nested barcharts.
Figure 7: I recommend adding the explanation of Case 1, 5, 7, and 8 in the caption so readers don’t have to refer to table 4 in order to interpret the results.
Citation: https://doi.org/10.5194/egusphere-2025-6543-RC2 -
AC2: 'Reply on RC2', Xudong Zheng, 18 Mar 2026
We sincerely appreciate your constructive comments and insightful feedback. A detailed, point-by-point response is provided in the attached document “response_RC2.pdf”. Your suggestions have highlighted aspects where the manuscript could be further clarified or strengthened, and we have carefully addressed these points to improve the quality and rigor of our study. We are grateful for your recognition of our work, and your input has been invaluable in enhancing the clarity and robustness of our manuscript.
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AC2: 'Reply on RC2', Xudong Zheng, 18 Mar 2026
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The manuscript presents a timely and highly relevant investigation into the combined effects of spatially explicit parameterization and multi-gauge calibration on hydrological modeling. The paper is well-written, logically structured, and provides a meaningful steppingstone for the advancement of modern Model-Data Infusion frameworks. However, there are several issues needed to be addressed before publication.
Specific comments:
1. In the parameter calibration, the authors did not consider three key VIC parameters that are commonly calibrated, namely Ds, Ws, and Dm. Although Gou et al. (2020) is cited in the manuscript, that study does not provide sensitivity analysis results for the specific basin investigated here. Including these parameters in the calibration process could potentially lead to different results. Therefore, the authors are encouraged to provide sensitivity analysis results for the study basin to justify the exclusion of these parameters. Otherwise, I believe that Ds, Ws, and Dm should be incorporated into the calibration.
2. The use of MPR is indeed an effective approach for deriving distributed parameters; however, one of its key limitations lies in the uncertainty associated with the transfer functions. Previous studies have shown that different transfer functions can lead to substantially different calibration results. For example, Gou et al. (2021) adopted transfer functions for D1–D3 that differ from those used in this study. It remains unclear whether such differences could lead to different conclusions. The manuscript currently lacks analysis and discussion on this issue, which should be addressed to strengthen the robustness of the study.
Gou, Jiaojiao, et al. "CNRD v1. 0: a high-quality natural runoff dataset for hydrological and climate studies in China." Bulletin of the American Meteorological Society 102.5 (2021): E929-E947.
3. The manuscript currently lacks sufficient statistical validation of the calibration experiments. Without statistical evaluation, it is difficult to determine whether the reported improvements reflect meaningful advancements or merely small fluctuations. For instance, an KGE difference between 0.715 and 0.716 in Table 6 is not necessarily meaningful without significance testing. The authors are encouraged to incorporate appropriate statistical tests, such as the Wilcoxon signed-rank test or paired t-tests for comparisons. In addition, reporting the standard deviation (you only showed ensemble mean) across ensemble runs would substantially strengthen the credibility of the results.
4. The description of the two-step mechanism for reconciling soil data with the VIC three-layer (VIC-3L) vertical structure is confusing. Since Table 2 already presents the transfer functions for D1–D3, it is unclear what additional role this two-step procedure plays. Because this component underpins the subsequent analysis, a more detailed and transparent explanation is essential.
5. The authors designed eight calibration experiments; however, the current numerical labeling makes it difficult for readers to remember the specific configurations during subsequent discussion. It is recommended that the authors adopt clearer and more descriptive naming conventions to distinguish the different experiments, which would improve readability and interpretability.
6. When applying the NSGA-II algorithm for multi-objective optimization, the implementation details are not sufficiently described. Given that the study basin includes five gauging stations, does this imply that five separate objectives were defined for calibration? The authors should clearly specify how the objective functions were formulated and aggregated, and how the multi-objective framework was structured in practice.
7. The authors should include, in Table 5, the ranges for all parameters to be optimized. Providing the parameter bounds would improve transparency and allow readers to better assess the robustness and reproducibility of the calibration procedure.
8. Although the authors provided a zoomed-in view in Figure 5, the differences remain unclear. From my perspective, the four schemes perform almost identically in the high-flow segment.