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Investigating Forecast Proficiency of Hurricane-Induced Compound Flooding With a Discontinuous Galerkin Shallow Water Equation Solver
Matthew Scarborough, Chayanon Wichitrnithed, Shintaro Bunya, Ethan Kubatko, Suranjan Nepal, Clint Dawson, Eirik Valseth
TL;DR
This paper addresses the challenge of forecasting compound flooding from interacting storm surge and rainfall runoff. It uses DG-SWEM with parametric rainfall forcing and Hurricane Beryl advisories and best-track data, finding that rainfall forcing substantially improves inundation and advisory agreement with the best-track hindcast.
Problem
Accurate real-time forecasting of compound flooding from synchronized storm surge and rainfall runoff remains a significant computational challenge.
Method
The study uses DG-SWEM with parametric rainfall models, including R-CLIPER, to incorporate rainfall directly into forecasting simulations for Hurricane Beryl using advisory and best-track data.
Results
Rainfall forcing greatly improves inundation of low-lying inland areas, with best-track hindcasts increasing water-column height by upwards of 50 centimeters in many wetland regions.
Takeaways & Limitations
Parametric rainfall produces more descriptive advisory forecasts and enables modeling of additional upstream and inland inundated areas despite differences in predicted storm trajectories.
Takeaways & Limitations
The analysis is limited by the small number of available high-water marks, leaving upstream-point RMSE above 0.5 meters.
Abstract
from arXiv · showhide
Recent severe storms on the U.S. Gulf coast have demonstrated the challenges presented by compound flooding, such as the interactions between rainfall runoff and storm surge. Historically, many studies have neglected these nonlinear interactions, but we propose to use a discontinuous Galerkin shallow water equation solver, which allows for incorporation of rainfall inputs directly onto the finite element mesh. In this work, we analyze the use of parametric rainfall for forecasting scenarios, using Hurricane Beryl (2024) as a case study. Beryl led to extensive flooding due to rainfall and storm surge along the Gulf. We use a collection of the National Oceanic and Atmospheric Administration's short-term advisories along with the best track data to demonstrate the efficacy of the parametric rainfall model for forecasting. Results show that the parametric rainfall input allowed for much more accurate inundation. Areas with heavy rainfall and low surge were affected the most, with many areas peaking over 50 cm above the baseline surge model. Almost none of the available high water marks from Beryl were captured by the standard models, but the compound flooding models capture many of them, the majority of which show relative errors under 10 percent. Results from the advisory forecast simulations were shown to be much closer to the best track hindcast simulation when rainfall forcing was used, even while early forecasts predicted the storm's trajectory much less accurately. The advisory simulations improved even further as Beryl neared the Texas coast, with sampled peak elevations most closely approximating the best track at Advisory 38, a few hours before landfall.
1. Introduction
Compound flooding from storm surge and rainfall runoff remains difficult to forecast accurately because loosely coupled models may miss their dynamic interaction. This paper investigates DG-SWEM for compound-flood forecasting using Hurricane Beryl as a case study.
- Hurricanes Harvey, Imelda, Beta, Allison, and Beryl illustrate compound flooding from interacting rainfall runoff and storm surge along the Texas coast.
- Loosely coupled atmospheric, ocean, and hydrologic models can fail to capture the synchronization of surge and runoff.
- 20–30%: Neglecting nonlinear surge–rainfall interaction can underestimate flood extent in transition zones.
- DG-SWEM solves the shallow water equations with a discontinuous Galerkin finite element method and has been extended to incorporate rainfall directly onto the finite-element mesh.
- The paper investigates DG-SWEM in a forecasting scenario for Hurricane Beryl (2024), with results and conclusions based on a simulation campaign.
2. Hurricane Beryl (2024) and Study Area
Hurricane Beryl intensified rapidly before crossing the Gulf and making landfall near Matagorda, Texas. Its rainfall, surge, wind field, and vulnerable low-lying coastal setting produced substantial compound-flooding impacts.
- 266 km/h: Beryl reached peak intensity with a minimum central pressure of 932 mbar on July 2 in the eastern Caribbean.
- 08:40 UTC on July 8, 2024: Beryl made landfall near Matagorda, Texas, after regaining Category 1 hurricane status.
- 1.66 meters above MHHW: Beryl produced the region’s highest storm surge since Hurricane Ike at Morgans Point.
- 15–36 centimeters: Beryl deposited this rainfall over the Houston metropolitan area, including a maximum 24-hour total of 30 centimeters.
3. Numerical Model and Proposed Forecasting Approach
The forecasting approach uses DG-SWEM to solve shallow-water equations with rainfall represented directly as a source term on the finite-element mesh, using parametric storm inputs to construct rainfall fields.
- 3. Numerical Model and Proposed Forecasting Approach: DG-SWEM models free-surface elevation, bathymetry, water-column depth, depth-averaged velocity, friction, rainfall, and other forces within conservative shallow-water equations.Rainfall enters through the continuity-equation source term R, while tidal elevation and zero-normal-flow conditions apply at ocean and land boundaries.
- 3.1. Discretization: The discontinuous Galerkin discretization approximates unknowns piecewise over mesh elements, permits interelement discontinuities, and uses numerical fluxes in boundary integrals.The formulation applies test functions elementwise, integrates by parts, and uses a Local Lax–Friedrichs flux with an orthogonal Dubiner basis.
- 3. Numerical Model and Proposed Forecasting Approach: Rainfall is added before wetting and drying checks, allowing forcing on both wet and dry elements without introducing instability through the primitive continuity equation.This implementation treats rainfall as the source term R and applies it directly to the finite-element mesh.
- 3.2. Forecasting with Rainfall: R-CLIPER and IPET construct rainfall rates from storm parameters and radial distance to the storm center for forecasting tropical-cyclone rainfall.The approach uses reported storm centers and maximum wind velocities, interpolates them to model time steps, and computes rainfall at finite-element mesh nodes.
- 3.2. Forecasting with Rainfall: R-CLIPER parameterizes rainfall using the radius of maximum rainfall, storm outer extent, central precipitation rate, and maximum precipitation rate at that radius.These parameters are fitted from global tropical-cyclone data through relationships with normalized maximum wind speed.
- 3.2. Forecasting with Rainfall: The study evaluates forecast advisories using a 1,947,485-node Gulf of Mexico mesh with 120-meter minimum resolution and simulations on 2000 processors.Forty-two National Hurricane Center advisories were issued, and seven selected advisories were analyzed in the simulation campaign.
4. Results
The study validates the forecasting setup by comparing best-track hindcasts with and without rainfall forcing, then evaluates selected advisory forecasts against those simulations and observations.
- 4. Results: The validation compares best-track hindcasts with and without rainfall forcing before analyzing advisory forecasts.The evaluation uses gauge data, high water marks, and the best-track hindcast model.
- 4. Results: Seven advisories are evaluated: 28 and 32 as earlier forecasts, 36–39 before Texas landfall, and 40 immediately afterward.The advisories span forecasts issued at different stages of Hurricane Beryl’s approach and passage.
4.1. Validation
The validation compares best-track hindcasts with and without rainfall forcing against gauges and high water marks. Rainfall improves agreement and captures inundation in inland and low-lying areas that surge-only modeling misses.
- Adding rainfall produced higher correlation with gauge data and slightly lower average RMSE than the no-rainfall hindcast.
- A rainfall-forced hindcast created a sustained gauge-elevation offset after Beryl’s strongest winds and rain, reaching about 10 centimeters at the Galveston Railroad Bridge.
- Rainfall most strongly affected upstream, higher-elevation areas beyond the traditional model’s storm-surge reach, where formerly dry nodes became wet.
- 40–50 centimeters of additional water occurred across low-lying coastal areas, while over three hundred nodes exceeded one meter of difference.
- Twenty-five high water marks were wet in the compound model, compared with only two in the best-track model without rainfall forcing.
- The best-track hindcast’s fit through the origin had slope 1.0009, while most wetted high water marks in compound runs had relative errors under 10 percent.
4.2. Advisories
Forecast performance improved as advisories approached landfall, and rainfall forcing substantially increased wet high-water marks and inland inundation relative to surge-only simulations.
- Advisory 28: Advisory 28’s forecast placed the storm over 250 kilometers from the actual landfall location, causing peak gauge elevations to be underpredicted.The simulation largely followed the pre-storm tidal pattern.
- Advisory 28: 17 HWMs were wet with rainfall forcing, compared with none without rainfall for Advisory 28.The distant predicted storm center reduced rainfall and surge in the Houston area; the highest relative error was 0.69.
- Advisory 32: 24 HWMs were wet for Advisory 32 with rainfall forcing, while surge-only simulations produced one wet HWM.The forecast storm center was still about 154 kilometers from the actual landfall location.
- Advisory 36: 23 HWMs were wet for Advisory 36, whose forecast storm center was less than 10 kilometers from the actual landfall location.Its compound model had lower RMSE than Advisory 32 and the best track hindcast.
- Advisory 37: 25 HWMs were wet for Advisory 37, the most of any advisory, and its sampled results closely approximated the best track hindcast.Its best-fit line moved closer to y = x, although RMSE increased slightly from the previous advisory.
4.3. Best Track Analysis
Best-track comparisons show progressively improving forecast agreement and substantial differences between rainfall-forced compound flooding and surge-only modeling.
- Forecast agreement: The compound model’s best-fit slope improved from 0.5505 for Advisory 28 to 1.0339 for Advisory 40.Early advisories contained strong underpredictions and large overpredicting outliers, while Advisories 36–38 mostly slightly underpredicted.
- Forecast agreement: Forecasts performed successively better with each advisory when compared with the best track hindcast.Without rainfall, RMSE decreased for the first three advisories before increasing for Advisory 40, and the best fit approached y = x more slowly.
- Model comparison: The compound model captured upstream channels with relative errors less than 0.1, unlike the traditional model’s sparse wet-node distribution at higher elevations.Rainfall wetted additional nodes and expanded the effective modeling domain.
- Model comparison: NRMSE was remarkably lower for the compound flooding model, with the improvement increasing as rainfall wetted more inland elements.Rainfall increased mean peak elevations in the normalized comparison.
5. Concluding Remarks
For Hurricane Beryl, adding parametric rainfall substantially expanded and improved modeled inundation, including inland and upstream areas that surge-only simulations missed. Forecast performance improved across advisories, although limited high-water-mark coverage and the current mesh extent constrain evaluation.
- Concluding remarks: More than 50 centimeters of additional water-column height occurred in many low-lying wetland regions, especially near rivers, in the best-track compound hindcast.The rainfall forcing improved inundation even where storm surge was moderate.
- Concluding remarks: Seven advisory simulations increasingly approached the best-track results as forecasts improved, despite Advisory 28 placing the storm center over 200 kilometers from its landfall position.Rainfall-forced advisories produced more descriptive results and modeled many more upstream points.
- Concluding remarks: NOAA gauge peaks generally became closer to observations over time, although Advisories 39 and 40 overpredicted at some Galveston Island and Bolivar Peninsula stations.The earlier advisories severely underpredicted recorded peak elevations.
- Concluding remarks: Almost all available high-water marks were missed by the surge-only model, while successive advisories more closely approximated upstream measurements; however, RMSE remained above 0.5 meters.The available HWM sample was small compared with better-documented events such as Hurricane Harvey.
- Concluding remarks: 471 sampled points showed that the rainfall-free model rarely exceeded two meters, whereas the compound model reached elevations up to nine meters and penetrated farther inland.Rainfall contributed little in some deeper areas but enabled inundation of additional inland locations.
- Concluding remarks: A river gauge near Midfield recorded a stage increase exceeding 7.5 meters, but its location near or beyond the mesh boundary limited its use in this study.Extending the domain inland would improve future analysis capability.
- Concluding remarks: Applying river discharge farther upstream than rainfall could further improve modeling along rivers and in low-lying regions.This is identified as a potential extension for more effective inland-flood representation.
Appendix A. Simulated Advisories at Gauges
Appendix simulations compare each advisory with the best-track simulation and NOAA observations around Beryl’s U.S. landfall. The figures cover six named NOAA gauge locations along the Texas coast.
- Appendix A. Simulated Advisories at Gauges: The appendix plots compare simulated results from each advisory with the best-track simulation and NOAA gauge data and predictions.The comparisons span several days before and after Beryl’s U.S. landfall.
- Appendix A. Simulated Advisories at Gauges: Gauge locations include Manchester Houston, NOAA gauge 8770777.
- Appendix A. Simulated Advisories at Gauges: Gauge locations include San Luis Pass, NOAA gauge 8771972.
- Appendix A. Simulated Advisories at Gauges: Gauge locations include Galveston Bay Entrance North Jetty, NOAA gauge 8771341.
- Appendix A. Simulated Advisories at Gauges: Gauge locations include Galveston Railroad Bridge, NOAA gauge 8771486.
- Appendix A. Simulated Advisories at Gauges: Gauge locations include Rollover Pass, NOAA gauge 8770971, and Port Arthur, NOAA gauge 8770475.