the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 May 2026
Physically Anchored Multi-Resolution Neural Operator Framework for Flood Inundation Prediction
Abstract. Accurate flood inundation modeling using high-resolution hydrodynamic simulations is computationally demanding, limiting their use for large-scale analysis and rapid scenario evaluation. Although machine learning surrogates have been developed, many struggle to reproduce the full spatiotemporal evolution of flood dynamics while maintaining physical consistency across spatial scales. In particular, simultaneously capturing basin-scale wave propagation and fine-scale inundation boundaries remains challenging. This study presents a multi-resolution deep learning framework for dynamic flood prediction. The approach combines a coarse-resolution neural operator that captures large-scale hydrodynamic behavior with a terrain-aware refinement module that reconstructs a fine-scale boundary structure. The framework is trained on high-fidelity two-dimensional shallow-water simulations and evaluated across riverine, dam-break, and complex floodplain systems, including tests under structured bathymetric uncertainty. Results demonstrate accurate reconstruction of continuous water depth fields, wet-dry delineation, and peak flow magnitude and timing. The model preserves the evolution of domain-integrated water volume over time, ensuring physically consistent mass dynamics rather than purely geometric agreement, and maintains probabilistic consistency when input topography is uncertain. The framework, therefore, provides high-resolution flood predictions at substantially reduced computational cost relative to direct high-resolution simulation. These findings show that multi-resolution deep learning can approximate hydrodynamic flood processes with strong physical fidelity and robustness to geometric uncertainty, supporting scalable flood hazard assessment and rapid predictive modeling.
Competing interests: C. Shen and K. Lawson have financial interests in HydroSapient, Inc., a company that could potentially benefit from the results of this research. These interests have been reviewed and managed by The Pennsylvania State University in accordance with its conflict of interest policies to ensure the objectivity and integrity of the research. A.M. Behroozi declares no conflicts of interest for this manuscript.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 07 Aug 2026)
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RC1: 'Comment on egusphere-2026-1982', Anonymous Referee #1, 05 Jul 2026
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CC1: 'Reply on RC1', Abdolmehdi Behroozi, 06 Jul 2026
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Dear Reviewer,
We sincerely thank you for your thoughtful and encouraging assessment of our manuscript. We are grateful for your positive view of the study and for recognizing the usefulness of the proposed framework for large-ensemble flood simulations and uncertainty-aware analysis. Your constructive comments helped us improve the clarity, positioning, reproducibility, and technical completeness of the paper.
In particular, your suggestions helped us better frame the method as a fast surrogate for repeated hydrodynamic simulations rather than as a general replacement for high-fidelity solvers. They also motivated us to strengthen the hydrodynamic setup description, add more quantitative discussion, and improve the methodology explanation for a broader readership.
We have carefully considered each comment and will revise the manuscript accordingly. Below, we provide a point-by-point response.
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Concern 1: Positioning of the proposed method as a fast surrogate rather than a replacement for high-fidelity hydrodynamic solvers.
Response:
We agree with the reviewer. The proposed framework should be framed as a fast, physically anchored surrogate for repeated flood simulations, not as a general replacement for high-fidelity hydrodynamic solvers. Two-dimensional solvers such as ANUGA remain the reference standard for detailed hydraulic modeling because they directly solve the governing shallow-water equations. They are also essential for generating reliable training and validation data.We will revise the manuscript to make this distinction clearer. The motivation for using a surrogate model is not that high-fidelity hydrodynamic solvers are unnecessary, but that they can become impractical when the same type of model must be run repeatedly for many possible forcings, boundary conditions, roughness values, or topographic realizations. In such cases, the computational burden comes not only from one simulation, but from the need to explore a large scenario space for ensemble prediction, uncertainty quantification, sensitivity analysis, rapid screening, or probabilistic hazard assessment.
We also clarified that the proposed framework learns the relationship between inputs, such as hydrographs and terrain, and outputs, such as spatiotemporal flood-depth fields, using data generated from observations and/or high-fidelity hydrodynamic solvers. After this learning stage, the model acts as a fast emulator that can reproduce solver-like responses at much lower computational cost. In this sense, the framework complements physics-based solvers by making repeated simulations feasible, rather than replacing them for detailed hydraulic modeling.
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Concern 2: Advantage over GPU-accelerated and commercial hydrodynamic solvers.
Response:
We thank the reviewer for this helpful comment. We agree that modern GPU-accelerated hydrodynamic solvers, as well as advanced commercial CFD tools such as FLOW-3D, can substantially reduce the runtime of individual high-fidelity simulations. We will clarify that our framework is not intended to replace these solvers for a small number of detailed hydraulic analyses.The advantage of the proposed surrogate appears when many repeated simulations are required. GPU-accelerated and commercial solvers reduce the cost of each physics-based run, whereas the trained surrogate reduces the marginal cost of each additional scenario to approximately one forward pass. In our experiments, ANUGA simulations required about 3 hours per realization, while the trained surrogate required about 1 second per prediction.
We will revise the discussion to state that high-fidelity solvers, including GPU-accelerated and commercial tools such as FLOW-3D, remain essential for detailed hydraulic modeling, training-data generation, validation, and calibration. The proposed framework is most useful for large ensembles, uncertainty quantification, sensitivity analysis, and rapid scenario screening, where the training cost can be amortized over many predictions.
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Comment 1: Training-set size and learning-curve analysis.
Response:
We agree with the reviewer. Since the framework is motivated by large-ensemble simulation, the effect of training-set size should be evaluated more clearly.We have already prepared expanded hydrodynamic datasets with 1000 realizations for the case studies reported in the manuscript. In the revised paper, we will add a learning-curve analysis using different training sizes and realizations, while keeping the validation/testing set fixed.
We will report changes in relRMSE, NSE, POD, FAR, and CSI for completeness. However, our preliminary results show that increasing the training size beyond 100 realizations does not significantly improve performance. This is likely because the synthetic hydrographs already span the main range of flood-wave magnitudes, timing, and recession behaviors needed for the operator to learn the dominant input–output relationship. Additional realizations, therefore, mainly provide redundant samples within the same scenario space rather than substantially new hydraulic information. This analysis will be included in the revised manuscript to justify the selected training size and demonstrate the scalability of the framework.
Comment 2: Practical hydrodynamic setup details and reproducibility.
Response:
We thank the reviewer for this useful suggestion. We agree that adding more practical setup information will improve the reproducibility of the hydrodynamic simulations.In the revised manuscript, we will expand Appendix E to include a fuller description of the model setup, including mesh-generation criteria, spatial refinement strategy, timestep/CFL settings, output intervals, interpolation from the triangular ANUGA mesh to the raster grid, roughness assignment, boundary-condition implementation, and calibration or preprocessing steps. These additions will make the simulation workflow clearer and more reproducible.
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Comment 3: Coarse-mask dependency and Magnifier failure mode.
Response:
We thank the reviewer for this important comment. We would like to clarify that, in the proposed framework, the Magnifier is not designed to be applied to fully dry regions. This behavior is partly by design. The Magnifier acts as a local super-resolution and refinement operator for inundated regions already detected by the coarse FNO, rather than as an independent flood-detection model over the entire domain. Applying the Magnifier only to wet or non-dry coarse regions helps reduce computational overhead and makes the framework efficient for large-domain inference.We note that the manuscript already reports stage-wise inundation metrics for both the coarse FNO and the final Magnifier output. These results show that the coarse FNO has strong wet/dry detection skill before refinement, with POD values of 99.81%, 95.87%, and 97.72% for the Neuse River, Fall River dam-break, and Chowilla floodplain cases, respectively, along with low FAR values. This indicates that only a small fraction of inundated regions is excluded before the Magnifier is applied.
To make this point clearer, we will revise the Results/Discussion section to explicitly explain this distinction and clarify the intended role of the Magnifier.
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Comment 4: Strengthening the conclusion with quantitative findings.
Response:
We agree with the reviewer. In the revised manuscript, we will strengthen the conclusion by reporting the main quantitative findings rather than only summarizing the concept.Â
Comment 5: Need for an intuitive methodology explanation.
Response:
We thank the reviewer for this helpful suggestion. We agree that a short intuitive explanation will improve readability for readers outside machine learning. In the revised manuscript, we will add a brief plain-language explanation before the technical methodology.ÂÂ
We sincerely thank you again for your constructive and insightful comments. We believe that the revisions made in response to your suggestions improve the manuscript’s clarity, balance, reproducibility, and practical relevance. We appreciate your time and careful evaluation of our work.
Citation: https://doi.org/10.5194/egusphere-2026-1982-CC1
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CC1: 'Reply on RC1', Abdolmehdi Behroozi, 06 Jul 2026
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After going through many incremental works in this field, this study was a welcome reminder that we can still be pleasantly surprised. This study introduces a very useful tool for the handling a large number of simulations and where the uncertainty is a concern.
My specific comments are:
1-Since the main motivation is large-ensemble simulation, the use of only 150 hydrodynamic simulations per case study feels limited. The authors should either test a larger ensemble, for example 500 or 1000 scenarios, or provide a learning-curve analysis showing how model accuracy changes as the number of training simulations increases. This would help demonstrate whether 100 training cases are sufficient and whether additional simulations would meaningfully improve performance.
2-Although Appendix E explains the governing shallow-water equations, finite-volume discretisation, etc., more practical setup information would improve reproducibility. This could include mesh-generation criteria, numeric e.g., timestep settings, and interpolation from triangular mesh to raster grid, and any calibration steps.
3-The Magnifier is constrained to preserve the water volume implied by the coarse FNO prediction through a zero-sum residual correction, which is useful for mass consistency but may limit its ability to correct coarse-scale volume errors. In addition, the Magnifier is applied only to regions identified as wet or non-dry by the coarse model. Therefore, if the coarse FNO misses a shallow inundation pathway or incorrectly predicts a dry coarse cell, the refinement stage may not recover that flooding. The authors should quantify this failure mode by reporting stage-wise errors: coarse FNO wet/dry recall, missed inundated cells before refinement, and the sensitivity of final CSI/FAR/POD to the coarse wet-cell mask.
4-The conclusion is weak, use your numbers/values, rather than only summarising the concept. For example, the paper reports high NSE values for depth prediction, strong CSI values for inundation extent, low false-alarm rates compared with interpolation, and small peak magnitude/timing errors. REPORT THE QUANTITATIVE FINDINGS.
5-The current methodology is technically detailed, but a short intuitive explanation would help readers outside machine learning understand how the model learns the mapping from hydrographs and terrain to flood-depth fields. This explanation should be written in the authors’ own words rather than only relying on standard neural-operator terminology.