the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Feb 2026
Physically Coherent Machine Learning for Tropical Cyclone Storm Surge Emulation
Abstract. Climate change is projected to impact tropical cyclone magnitude and frequency, with high magnitude events becoming more common. The destructive nature of event derived storm surges and associated coastal flooding necessitates risk management. However, the historic record is too short and too sparse to assess risk effectively, resulting in incomplete probability distributions of surge heights, particularly for distribution tails. Hydrodynamic simulation can fill these gaps, but the number of simulations required, both spatially and under diverse climates, coupled with their high computational cost, is prohibitive. To address this, we present an Artificial Neural Network storm surge emulator, deployed in the northwest Gulf of Mexico. This is trained on a database of hydrodynamic simulations, and outputs spatially coherent time series of surge. Our model achieves an R2 of 0.91, with a RMSE of 13 cm when compared to an independent test set of hydrodynamic simulations, while exhibiting a computational gain factor of over 1500. Our approach is novel in its use of feature engineering to improve performance. Here variables which are physically relevant to surge are derived from commonly used features, such as wind and pressure, allowing us to maintain a simple model architecture, while steering the model towards physically coherent learning. Shapley Values are utilised for model interpretation and demonstrate that the model is making physically justified inference. Success is demonstrated by comparing our feature engineered model to a control, which engages in minimal feature engineering. The control achieves an R2 of 0.71 and a RMSE of 23 cm only.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-781', Anonymous Referee #1, 24 Jun 2026
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RC2: 'Comment on egusphere-2026-781', Anonymous Referee #2, 29 Jun 2026
The paper presents a point-wise feedforward ANN that emulates ADCIRC storm surge over the NW Gulf of Mexico. SHAP is used for interpretation and feature selection, and a feature-engineered Fullset is benchmarked against a Naive control with about 688 to 1535 claimed speed-up. The manuscript is a clean, well-written study, and the coordinate-ablation experiment is a nice piece of design. My concerns are mostly about a gap between the framing and what the experiments actually establish. I'd see this as a solid contribution after a substantial revision of claims, not necessarily of method.
Major comments
1. The test set is not independent in the way the headline metrics imply. The 40 storms are split using a ration of 7/2/1, leaving only about 4 test storms. Note that the arithmetic doesn't match with 7/2/1 of 40, since 28/8/4 produces 36 train+val, but Table 2’s caption says 37. More importantly, all 40 are perturbations of just 5 primary synthetic tracks. So a held-out storm is almost certainly a near-neighbour in feature space of a training storm. R^2 computed over millions of spatially/temporally autocorrelated nodes from 3~4 storm realisations has a tiny effective sample size, and no uncertainty is attached to any headline number. At minimum I'd want leave-one-track-out cross-validation and error bars on R^2/RMSE before the 0.91-vs-0.71 contrast is presented as definitive.
2. Generalization is the central motivation but is never tested. The abstract, intro and conclusion are built around global deployability and extrapolation beyond the training domain, but every evaluation is in-domain on the same synthetic family. Removing coordinates and retaining performance shows the model isn't memorizing location. The paper concedes “extrapolating beyond the training domain is the next step,” which I agree with, but that concession is in tension with the title and framing. I guess adding a real out-of-domain test (another region) would be necessary.
3. “Physically coherent” is partly undercut by your own SHAP results. Depth shows an inverse-to-theory relationship in the Fullset model, which you attribute to unspecified “feature interaction” and frame as “encouraging.” That reading is charitable. Given that SHAP's additivity assumes feature independence, and you've engineered many features from shared roots, the SHAP-based physical-coherence argument is the shakiest load-bearing claim in the paper. I'd recommend softening “physically coherent” to something like “broadly consistent with surge physics,” and acknowledging the correlated-feature caveat at the point where SHAP physics conclusions are drawn, not only in Section 2.6.2.
4. The tool is weakest exactly where the stated application needs it most. The entire motivation is filling distribution tails for return periods. However the models under-predict high extremes and over-predict low extremes, and the Fullset over-predicts negative surge in bays. RMSE of 13 cm is dominated by the enormous mass of near-zero/moderate points. Tail skill is what matters for probabilistic approach (e.g., PTHA-style) use and is where performance is worst. This trade-off deserves to be foregrounded in the abstract/conclusion rather than emerging gradually through Figs 4 to 8.
5. The speed-up accounting is one-sided. 688 to 1535 times speed-up compares single-GPU inference to 1024-core ADCIRC wall-clock, but excludes the cost of the 446 ADCIRC runs needed to create the training set, and the admitted hidden per-storm feature-generation cost, and preprocessing, which you show scales with feature-set size. For the stated use case (10^5+ runs) amortization is favorable, but the headline number should be stated as inference-only and the training-data cost acknowledged.
Minor comments
1. Eq. 4 is missing a closing parenthesis.
2. Many typos were found. “ADCRIC” for ADCIRC (several places), “Fullest” for Fullset, “final output later” for “layer”, and “Long-Term-Short-Term Networks” should be “Long Short-Term Memory.”
3. The 1013 mb inclusion threshold is essentially standard SLP, so “minimum pressure never falls below 1013 mb” is a very weak filter. It is worth a sentence justifying it.
4. Table 1 leads with R^2=0.93 (with XY) while the abstract uses 0.91 (no XY). Fine given your no-coordinate focus, but state the convention once up front.
5. Tides and waves are correctly flagged as omitted, but given the “risk management” framing and your own citations on nonlinear tide-surge interaction, I'd soften “risk management” to “a step toward risk-relevant emulation.”
6. “Novel in its use of feature engineering” overstates. Coastal geometry/bathymetric predictors appear in prior surge-ML work. The contribution is better cast as a systematic feature-engineering blueprint with interpretability, which is defensible.
Citation: https://doi.org/10.5194/egusphere-2026-781-RC2
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The manuscript presents a timely and practically relevant study on storm-surge emulation using physically motivated feature engineering within an artificial neural network framework. The work addresses an important computational bottleneck in hydrodynamic storm-surge modelling and demonstrates clear improvement over a naive machine-learning baseline. The manuscript is generally well motivated and has publication potential; however, the following points should be addressed before publication.