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SurgeGen: A Hybrid Generative Diffusion Framework for Storm Surge Scenario Synthesis

Shunan Zheng, John J. Hasenbein

arXiv:2609.03382v1math.DScs.LG

TL;DR

Repeated physics-based simulations are costly, and storm-surge generative surrogates remain relatively unexplored. SurgeGen combines a coarse regression estimate with conditional diffusion, generating realistic scenarios both within and beyond the training conditions.

  • Problem

    Repeated numerical simulations are computationally expensive, while deterministic surge surrogates do not represent diverse scenarios for uncertainty analysis and risk assessment.

    Source: §1 · p. 1

  • Method

    SurgeGen predicts a coarse storm-surge map from storm and spatial conditions, then conditions a diffusion model on that estimate to generate refined scenarios.

    Source: §1 · p. 2, §2.3 · p. 3

  • Results

    SurgeGen generates realistic scenarios beyond the discrete simulator scenarios used for training, and the ablation reports single-stage diffusion MSEs of 2.574 for ID scenarios and 7.469 on OOD scenarios.

    Source: §1 · p. 2, §3.3 · p. 5

  • Takeaways & Limitations

    The results indicate potential for efficient storm-surge scenario exploration and downstream coastal risk applications such as evacuation planning and infrastructure assessment.

    Source: §5 · p. 5

    The current dataset does not capture the natural variability present in real storm events.

    Source: §4 · p. 5

Abstract

from arXiv · show

Predicting storm surge induced by landfalling tropical cyclones is crucial for flood mitigation and coastal risk management. Traditionally, physics-based numerical models simulate storm surge by solving the Navier--Stokes equations using numerical methods, but these simulations are computationally expensive. Generative models are promising for storm surge emulation because they can generate diverse realizations rather than producing a single deterministic prediction. However, their use for storm surge emulation remains largely unexplored. In this paper, we leverage diffusion models for storm surge surrogate modeling, combining a baseline prediction stage with conditional generation to provide a more interpretable modeling framework. We develop SurgeGen, a two-stage generative framework for generating storm surge scenarios conditioned on hypothetical storms with parameters defined in a continuous space. First, a baseline model produces a coarse estimate of the storm surge height. This estimate then conditions a diffusion model, which generates refined storm surge scenarios that better capture spatial patterns and variability. We demonstrate that our approach can generate realistic and diverse storm surge scenarios under conditions both within and outside the training distribution.

1 Introduction

Storm-surge models support coastal risk decisions but can be computationally expensive, while existing deterministic surrogates do not represent scenario variability. SurgeGen combines regression and conditional diffusion to generate realistic surge scenarios, including beyond the discrete training conditions.

1 Introduction

  • Repeated SLOSH runs for MEOW maps and discretized storm combinations constrain efficient, continuous scenario exploration for time-sensitive risk assessment.These limits motivate data-driven surrogates for realistic and continuous storm-surge samples.Source: §1 · p. 1
  • Existing surge surrogates primarily predict surge or peak levels, while deterministic maps limit representation of output variability for uncertainty analysis and risk assessment.Diffusion-based storm-surge surrogate modeling remains largely unexplored, including for zero-inflated surge maps.Source: §1 · pp. 1–2
  • SurgeGen first predicts a coarse map from storm and spatial conditions, then conditionally refines it with diffusion to generate detailed maps with diverse spatial patterns.The framework targets high-dimensional surge fields, limited simulator-generated data, and hypothetical conditions beyond the training data.Source: §1 · p. 2
  • SurgeGen generates realistic surge scenarios and explores conditions beyond the discrete simulator scenarios used for training.This supports scenario generation without repeatedly running the numerical simulator.Source: §1 · p. 2

2 Problem formulation and methodology

The method predicts peak-surge scenarios conditioned on storm and spatial information, then uses a coarse regression estimate to guide conditional diffusion. The two stages operate on MEOW data transformed from a curvilinear basin grid into a standardized image representation.

2.1 Problem formulation

  • The study uses Galveston Bay MEOW maps, which record maximum water level per grid cell for hypothetical storms defined by intensity, track direction, tide, and forward speed.The underlying SLOSH model solves hydrodynamic equations on basin-specific coastal grids with geographic features.Source: §2.1 · p. 2
  • The target is a conditional distribution of peak-surge maps given global storm parameters and spatial predictors such as elevation.The formulation distinguishes storm-wide conditions from grid-level spatial conditions.Source: §2.1 · p. 2

2.2 Data preprocessing

  • The curvilinear SLOSH grid is transformed into a standardized 64 × 64 image representation, then generated scenarios are transformed back to the geographic grid.The geographic-grid outputs support interpretation and downstream analysis.Source: §2.2 · p. 3

2.3 Two-stage conditional model

  • SurgeGen combines a coarse point estimate with SR3-style conditional diffusion, using the estimate to guide spatially coherent refinements.Figure 1 presents the framework and diffusion training and generation process.Source: §2.3 · p. 3, Figure 1 · p. 3
  • A hurdle-style baseline predicts surge occurrence and conditional depth from storm and spatial conditions, assigning zero depth to predicted non-inundated locations.Logistic regression models occurrence, while linear regression and gradient-boosted trees estimate depth; the resulting structured map conditions diffusion.Source: §2.3 · p. 3
  • Rather than modeling residuals, conditional diffusion generates the full surge map from noise, guided by the coarse prediction, topography, storm parameters, and noise level.The coarse map supplies large-scale structure, while spatial features provide topographic context for local refinement.Source: §2.3 · pp. 3–4
  • Training reconstructs the clean surge map with a noise-weighted MSE objective and penalties for negative and small-positive predictions.The additional penalties encourage non-negative outputs and separation between inundated and non-inundated regions.Source: §2.3 · p. 4

3 Experiments

SurgeGen is evaluated on held-out MEOW scenarios for magnitude, spatial accuracy, and distributional similarity, including tests on unseen storm conditions and framework ablations.

3 Experiments

  • The evaluation compares held-out maps using volume error, peak error, IoU, F1, and distributional measures at infrastructure locations.Distributional measures are Earth Mover’s Distance and Pearson correlation.Source: §3 · p. 4

3.1 Generation Quality

  • Generated maps visually resemble the test SLOSH scenarios, with inundation consistently increasing as storm intensity rises.Mean volume error is 0.057 ft and mean peak error is 0.484 ft; IoU and F1 are strongest at intermediate surge-height thresholds.Source: Figure 2 · p. 4, §3.1 · p. 4
  • At power-station locations, SurgeGen has higher marginal EMD but lower correlation error than NORTA, indicating better preservation of spatial dependence.The comparison uses generated storm-surge height distributions against original scenarios and the NORTA-based method.Source: §3.1 · p. 4

3.2 Out-of-Distribution Generation

  • Across Category 5 tests, generated responses vary smoothly as direction changes from WSW to ENE, with a mean RMSE of 2.116 ft.Other conditions are fixed at Category 5 intensity, 10 mph forward speed, and low tide; intermediate directions are also tested.Source: §3.2 · p. 4, Figure 3 · p. 5

3.3 Ablation Study

  • SurgeGen achieves the lowest MSE in both settings: 0.751 for ID and 5.050 for OOD generation.ID uses a random split across Categories 0–5; OOD holds out Category 5.Source: Table 1 · p. 5, §3.3 · p. 5

4 Limitations and Future Work

The framework has physical and data limitations that constrain fidelity and representation of natural storm variability.

4 Limitations and Future Work

  • The framework does not explicitly incorporate physical constraints because peak surge is defined as the maximum over simulated storm-surge maps.The authors identify incorporating such constraints as challenging under this definition.Source: §4 · p. 5
  • Richer geographic and physical information, including coastline geometry and land cover, could improve physical fidelity and robustness.Source: §4 · p. 5
  • The current dataset does not capture natural variability in real storm events, and adding physically meaningful simulation perturbations would be computationally expensive.The authors suggest purposefully designed perturbations as a direction for expanding the dataset.Source: §4 · p. 5

5 Conclusion

SurgeGen combines coarse regression prediction with conditional diffusion refinement to generate diverse peak-surge scenarios, including under conditions inside and outside the training distribution.

5 Conclusion

  • SurgeGen combines regression-based coarse prediction with conditional diffusion refinement for storm-surge scenario generation.Source: §5 · p. 5
  • The framework generates spatially coherent and diverse peak-surge scenarios while avoiding repeated numerical simulation.Source: §5 · p. 5
  • Experiments demonstrate realistic generation under in-distribution and out-of-distribution conditions, including continuously varying storm directions.The paper identifies evacuation planning, infrastructure assessment, and flood mitigation as downstream coastal-risk applications.Source: §5 · p. 5

A Dataset and preprocessing

The study uses SLOSH-generated MEOW scenarios for Galveston Bay and preprocesses storm maps and spatial features for the model’s image representation.

A.1 MEOW dataset details

  • The Galveston Bay MEOW dataset contains 324 SLOSH scenarios formed from storm intensity, track direction, tide level, and forward speed.Intensity spans Categories 0–5; forward speeds are 5, 10, and 15 mph, with low- and high-tide conditions.Source: §A.1 · p. 8
  • A compact scenario label encodes storm conditions; for example, “ne510i1” denotes a northeast-approaching Category 5 storm at 10 mph and low tide.Source: §A.1 · p. 8
  • The original curvilinear basin grid has spatial density that varies across the basin, with finer representation near the coastline.SurgeGen’s target maps are derived from this grid after spatial transformation.Source: §A.1 · p. 8
  • Topo-bathymetric information for Texas and the Gulf of Mexico is represented as elevation-derived spatial features aligned to a 64 × 64 image grid.The construction of the feature channels follows the model implementation’s preprocessing.Source: §A.1 · p. 8

A.2 Data preprocessing

The preprocessing maps the Galveston Bay study region to a regular image grid and reconstructs geographic maps by resampling. The first stage supplies a coarse inundation-and-depth estimate, which conditions a diffusion model that generates the full storm surge map.

A.2 Data preprocessing

  • The Galveston Bay crop spans 95.7°W–94.8°W and 28.9°N–29.8°N, covering the populated areas, infrastructure, and surge locations in selected scenarios.The region is selected using a geographic bounding box.Source: §A.2 · p. 8
  • The curvilinear SLOSH grid is transformed to a regular 64 × 64 image grid with approximately uniform visual cell size and about 1.5 km nominal resolution.The raster is approximately 0.014° per pixel in the study region.Source: §A.2 · p. 8
  • Geographic reconstruction uses pull-based resampling: transform coordinates on the desired output grid, then interpolate the generated image at those locations.This avoids explicitly deriving an analytic inverse and aligns the reconstructed map with the original geographic domain.Source: §A.2 · p. 8

B.1 First-stage regression

  • The first-stage hurdle model predicts inundation with logistic regression and positive depth with a linear estimate corrected by gradient boosting.Its coarse map sets non-inundated cells to zero and provides large-scale extent and magnitude, leaving spatially structured residual variation and fine-scale detail to diffusion.Source: §B.1 · p. 9

B.2 Diffusion model

  • The diffusion stage generates the full 64 × 64 storm surge map, denoising it with the coarse regression guidance and spatial conditioning.The U-Net receives the noisy map, regression map, elevation-derived features, and valid-cell mask.Source: §B.2 · pp. 9–10

B.3 Conditioning and data augmentation

The conditioning combines embeddings for the diffusion noise level and global storm variables. Their fused representation is projected into residual blocks as additive channel-wise modulation.

B.3 Conditioning and data augmentation

  • The diffusion noise level is encoded from 0.25 log σ, while global storm variables are embedded separately and the two embeddings are summed.The storm condition comprises category, speed, tide, and sine/cosine direction; the noise embedding uses a sinusoidal encoding.Source: §B.3 · p. 10
  • For each residual block, a learned linear projection maps the fused embedding to the channel dimension and broadcasts it across spatial locations.The implementation uses additive channel-wise modulation, not the full affine scale-and-shift FiLM transformation.Source: §B.3 · p. 10

C Complete Training Hyperparameters

The complete model configuration is listed in Table 2, and the reported model uses the final epoch-100 checkpoint without checkpoint selection.

C Complete Training Hyperparameters

D Metric definitions

The section defines complementary measures for surge magnitude, spatial agreement, and distributional similarity, then reports additional threshold, extrapolation, geographic, and downstream comparisons.

D Metric definitions

  • Volume error is the absolute relative discrepancy in area-weighted total surge volume, while peak error is the discrepancy between scenario maxima averaged over evaluated scenarios.The volume calculation sums surge height over valid cells with spatial-area weighting when converting raster values to volume.Source: D Metric definitions · pp. 10–11
  • MSE is averaged over generated samples and scenarios, while IoU and F1 compare thresholded inundation masks using relative thresholds tied to each ground-truth map’s maximum.The mask metrics use predicted and ground-truth inundated regions; the MSE is calculated over valid grid cells.Source: D Metric definitions · pp. 11–12
  • EMD compares empirical surge-level distributions at infrastructure locations by minimum transport cost; Pearson correlation measures linear dependence, while the downstream table reports correlation error.The distributions are generated and reference surge levels; correlation is reported as an error in the downstream table.Source: D Metric definitions · p. 12

E.1 Threshold-based spatial agreement

  • IoU and F1 peak at intermediate relative surge thresholds; uncertainty bands span five generated samples per scenario.Agreement is weaker at low thresholds, where small prediction differences enlarge the predicted region, and at high thresholds, where local misalignment matters more.Source: Figure 5 · p. 12, §E.1 · p. 12

E.2 Out-of-distribution depth agreement

  • For Category 5 extrapolation, maps trained on Categories 0–4 are compared cellwise with SLOSH; Figure 7 plots predicted against true surge heights.Figure 8 is also cited as providing examples of out-of-distribution generation.Source: §E.2 · p. 12, Figure 7 · p. 13

E.3 Geographic visualization of generated scenarios

  • After mapping a generated field back to its geographic domain, the contour visualization shows coastal inundation concentration and inland surge-height decay.The earlier study compared the mapped scenario with a satellite basemap.Source: §E.3 · p. 13

E.4 Downstream power-grid comparison with NORTA

  • NORTA achieves lower marginal-distribution error according to EMD, while the diffusion model achieves lower correlation error, indicating stronger spatial-dependence agreement.Table 3 reports EMD and correlation error statistics for both methods in the power-grid task.Source: §E.4 · p. 13

E.5 Ablation Settings

The ablation variants alter the baseline, augmentation, or diffusion target, and the variants are evaluated under in-distribution and Category 5 holdout settings.

E.5 Ablation Settings

  • Single-stage Diffusion removes the baseline; XGBoost-guided swaps it, augmentation perturbs inputs with probability 0.5, residual diffusion predicts the baseline residual, and SurgeGen uses full-map refinement.For augmentation, the original continuous inputs are retained with probability 0.5; otherwise, small Gaussian perturbations are applied to continuous spatial features and selected conditioning variables.Source: §E.5 · pp. 13–14

Out-of-distribution generated samples

  • Figure 8 places original maps, generated samples, and errors in successive rows; some generated samples match the ground-truth surge map.The examples are out-of-distribution Category 5 hurricane scenarios.Source: Figure 8 · p. 14

Geographic visualization

  • Figure 9 shows a geographic overlay and contour visualization after a generated scenario is mapped back to the original geographic domain.Source: Figure 9 · p. 14

E.5 Ablation Settings

  • Variants are evaluated on a random split across Categories 0–4 and on a Category 5 holdout trained with Categories 0–4.All other experimental procedures are kept consistent across variants.Source: §E.5 · p. 14

Downstream comparison

  • Table 3 compares EMD and correlation error statistics for NORTA and the diffusion model in the power-grid downstream task.Source: Table 3 · p. 15
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