the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Sep 2026
Integration of physics-informed deep learning with a distributed hydrological model (PIDL-DHM): A hybrid model for runoff simulation
Abstract. Climate change and vegetation restoration have altered hydrological processes, but quantifying vegetation-runoff interactions remains challenging due to complex feedback and data scarcity. We developed a physics-informed deep learning hybrid model that couples process-based hydrology with deep learning to improve runoff prediction in vegetation-altered basins. The model explicitly represents transpiration, interception, snow dynamics, dual runoff generation, water-balance constraints, and distributed spatial heterogeneity. Evaluations in three Chinese basins spanning hydroclimatic and vegetation gradients show that the hybrid models outperform pure deep learning, with the strongest improvements in semi-arid and vegetation-transition basins. Correlation coefficients exceeded 0.8 at monthly/annual scales and 0.75 at daily scales in the most responsive basins. Compared with GR4J, the added complexity is most beneficial in heterogeneous semi-arid and ungauged sub-basins. These results demonstrate that physical constraints improve extrapolation reliability and support hybrid models for sustainable basin management under climate change.
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Status: open (until 10 Nov 2026)
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CEC1: 'Comment on egusphere-2026-5146 - No compliance with the policy of the journal', Juan Antonio Añel, 23 Sep 2026
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AC1: 'Reply on CEC1', Junping Wang, 24 Sep 2026
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Dear Prof. Añel,
Thank you very much for your comments and for clarifying the GMD Code and Data Policy. We sincerely appreciate your guidance and fully understand the importance of code and data accessibility for scientific reproducibility.
In response to your comments, we have updated our Zenodo repository to provide the PIDL-DHM source code, pretrained model parameters, and simulated runoff and evapotranspiration data. These materials are publicly available at:
https://zenodo.org/records/22928140
The meteorological forcing data used in this study were obtained from the publicly available China Meteorological Forcing Dataset (CMFD):
https://doi.org/10.11888/AtmosphericPhysics.tpe.249369.file
We would also like to clarify that the runoff observational data is subject to third-party data-sharing restrictions and cannot be publicly redistributed by the authors. We will revise the Code and Data Availability section of the manuscript accordingly.
We will revise the Code and Data Availability section accordingly and would be grateful for your consideration and guidance regarding the restricted observational data.
Thank you again for your time and consideration.
Best regards,
Junping Wang
On behalf of all co-authors-
CEC2: 'Reply on AC1', Juan Antonio Añel, 24 Sep 2026
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Dear authors,
Thanks for your reply. Unfortunately, it does not solve the outstanding issues. We can not accept that you cite as source for your data the China Meteorological Forcing Dataset web page. Also, we can not accept your claims about problems with third-party distribution without adequate documentation that justify it.
Therefore, please, respond to this comment with a new text for the Code and Data availability section containing a citation to the acceptable repositories containing the requested data. Also,if you want that we study an exception to your obligation to share part of the data due to rules imposed on you, please, provide documentary evidence of the laws, rules or licenses that prevent you of sharing any data.
Therefore, the situation regarding your manuscript has not changed, and as it is right now, we can not consider your manuscript for publication or peer review in the journal.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2026-5146-CEC2 -
CEC3: 'Reply on CEC2 - remainder - non compliance with the code and data policy', Juan Antonio Añel, 12 Oct 2026
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Dear authors,
I would like to remind you that we continue waiting for a new Code and Data Policy for your manuscript. We can not continue the peer review process for your manuscript until this situation has been solved. Please, reply to this comment with any new information regarding this issue.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2026-5146-CEC3 -
AC2: 'Reply on CEC3', Junping Wang, 14 Oct 2026
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Dear Prof. Añel,
Thank you for your patience and for the clear explanation of GMD’s Code and Data Policy.
Due to legal prohibitions in China, we cannot publicly release the hydrological runoff data. We therefore request an exemption from the data-sharing requirement. If the journal cannot grant such an exemption, however, we request that the public discussion for this manuscript be closed.
We sincerely apologize for the time and effort you and the editorial team have spent on this submission, and we appreciate your guidance.
Best regards,
Junping Wang
Citation: https://doi.org/10.5194/egusphere-2026-5146-AC2 -
CEC4: 'Reply on AC2', Juan Antonio Añel, 14 Oct 2026
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Dear authors,
Thanks for your reply. In order to study and grant the requested exception we need that you share official documentation, a license, official webpage, or similar, that proves the restricted character of the data, are that you are forbidden to share them. Therefore, please, reply to this comment with such information so that we can evaluate it.
Juan A. Añel
Geosci. Model Dev. Executive Editor
Citation: https://doi.org/10.5194/egusphere-2026-5146-CEC4
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CEC4: 'Reply on AC2', Juan Antonio Añel, 14 Oct 2026
reply
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AC2: 'Reply on CEC3', Junping Wang, 14 Oct 2026
reply
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CEC3: 'Reply on CEC2 - remainder - non compliance with the code and data policy', Juan Antonio Añel, 12 Oct 2026
reply
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CEC2: 'Reply on AC1', Juan Antonio Añel, 24 Sep 2026
reply
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AC1: 'Reply on CEC1', Junping Wang, 24 Sep 2026
reply
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RC1: 'Comment on egusphere-2026-5146', Anonymous Referee #1, 13 Oct 2026
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The manuscript presents PIDL-DHM, a hybrid hydrological model combining a physics-based recurrent module, vegetation-related dynamic parameterization, and distributed routing. The topic is relevant to GMD, and the improvement associated with the vegetation module in HRB deserves acknowledgment. However, the methodological contribution is insufficiently established, several conclusions exceed the evidence, and inconsistencies in the model description prevent an independent assessment of its physical validity. It therefore can not be considered in its current form
Major comments:
1. authors identify dual-mechanism runoff generation, vegetation coupling, and spatial distribution as their principal innovations. Much of the underlying framework follows earlier work. Zhong et al (2024), already included in the references, developed a distributed differentiable hydrological model with routing and upstream evaluation using downstream training data, but the manuscript does not discuss its differences from that study.
The dual-mechanism formulation is not separately evaluated, and the description of hybrid-L does not clearly establish which runoff mechanisms it contains. Consequently, attributing improved transferability to the proposed mechanism is unsupported. The experiments need to isolate the contributions of the claimed innovations.2. As described, the vegetation LSTM in hybrid-P relies on meteorological inputs rather than independently observed, time-varying vegetation states. The improvement over hybrid-L therefore demonstrates the benefit of dynamic parameterization, but does not establish that the model captures vegetation change.
The process representation is also limited. Stomatal resistance is learned dynamically, interception reduces to a rainfall multiplier when canopy storage is zero, and infiltration uses an empirical formulation. A clearly specified root water uptake scheme is absent from the main text. Both stomatal resistance and the soil-water multiplier regulate ET, but their separate effects and physiological interpretation are not evaluated.3.The ET comparison is useful, but lacks results without the vegetation module. Agreement with PML-V2 and one flux tower cannot establish that vegetation coupling caused the improvement. A suitable control for additional network capacity and process-level evaluation are needed.
Table 4 shows that adding the distributed component changes NSE by -0.005, -0.001, and +0.002 in HRB, DRB, and GRB, respectively. This provides no consistent improvement over hybrid-P, despite jointly adding spatial discretization, grid attributes, and a delay kernel.
The claimed NSE improvement of up to 0.14 is unsupported by the table. Even relative to any lumped hybrid configuration, the largest increase is 0.099. A distributed model might improve internal processes without improving outlet discharge, but the manuscript does not demonstrate that benefit through comparative evaluation.4. Several equations are inconsistent with their physical interpretation. Eq. (7) gives qbase = qmax × (S1/Smax) raised to the power of minus beta. For positive beta, baseflow increases as storage decreases and diverges near zero storage, contradicting the stated meaning of qmax.
Let x = Prain - qsat. The first branch of Eq. (9) simplifies to qunsat = x - x squared/fmax, which becomes negative when x exceeds a positive fmax. The second branch, S1 - Smax, is also negative under unsaturated conditions. The switching condition needs clarification.
These may be manuscript errors rather than implementation errors. Nevertheless, correct state updates and numerical water-balance verification are necessary. The authors should also explain how changing Smax preserves water when capacity falls below current storage. Dynamic parameter definitions are inconsistent, spatial aggregation is missing from Eq. (17), and the reported grid resolution differs between sections.5.Testing five nested subcatchments after downstream training is useful, but does not establish transferability to independent ungauged basins. Their hydrological responses already contribute to the training discharge. In Table 6, hybrid-P-D has KGE values of 0.35-0.58 and biases near +38% at two stations. Its R2 is lower than DL at all five stations, contradicting lines 630-632. GR4J also has smaller absolute PBIAS at four stations. Likewise, temperature and precipitation bins within the evaluation period do not establish climatic extrapolation. Figure 10 lacks corresponding baseline comparisons and therefore cannot support the claimed superior robustness under drought or high temperatures.
6. Lines 453-454 explicitly treat KGE as a dependent correlation coefficient. Mengs Z-test compares correlation coefficients; it does not directly test differences in KGE or NSE. Even if applied to Pearson correlations, the results cannot establish significant improvements in those other metrics. Table 5 also needs to identify the tested statistic and explain the treatment of different basins, temporal dependence, and multiple comparisons.
7.Comparisons against a pure RNN and GR4J do not establish progress over the closest existing differentiable models. Baseline configuration needs clarification, particularly snow treatment in HRB and GR4J parameter transfer to subcatchments.
The authors should identify the data used for early stopping, since no separate validation period is specified. “Trained 150 times” also needs clarification. Without independent runs and uncertainty estimates, the stability of the small differences between hybrid-P and hybrid-P-D remains unknown.Minor comments:
1.Table 1, what is 'funtion'? training time is not necessary as architectural parameter.
2. Figure 8 repeated “(d), (e), and (f)”?
3. "Training year" should be validation data?
4. Lines 406-408 refer to 6 parameters but list 7.
5. Lines 689-690 correct the basin or station reference
6. line 235 “Holtan”?
7. Equation (17) and (18) are reused in the evaluation-metrics section after appearing in the routing and water-balance sections. renumber the equations consistently.Citation: https://doi.org/10.5194/egusphere-2026-5146-RC1
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Dear authors,
Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".
https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
in the Code and Data Availability section of your manuscript you state "The datasets used in this study are subject to confidentiality restrictions and cannot be publicly shared." The policy of the journal makes clear that all the data used in a work submitted to the journal must be published openly and without restrictions at the submission time in a repository. In your comment you mention confidentiality issues; however, you do not provide evidence of them. Therefore, as it is, we can not continue considering your manuscript for Discussions and peer review in the journal, and in fact it should have not been accepted for it due the mentioned issues.
The GMD review and publication process depends on reviewers and community commentators being able to access, during the discussion phase, the code and data on which a manuscript depends, and on ensuring the provenance of replicability of the published papers for years after their publication. Please, therefore, publish your code and data in one of the appropriate repositories and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible. We cannot have manuscripts under discussion that do not comply with our policy.
Later, if the Topical Editor decides to continue with the review or publication process of your manuscript and you are requested to upload a new version of it, then The 'Code and Data Availability’ section of your manuscript must also be modified to cite the new repository locations, and corresponding references added to the bibliography.
I must insist that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in GMD.
Juan A. Añel
Geosci. Model Dev. Executive Editor