By Karthika Swamy Cohen
Infrared Imagery of Hurricane Ike, which hit the Galveston-Houston area of Texas in 2008. Image credit: NOAA (Public domain, work of US Government)
Tropical and extratropical storms cause a great deal of flooding in coastal regions across the globe.
A storm surge or rise in sea level can occur during tropical cyclones and intense storms, such as hurricanes. Storms produce strong winds, pushing water into the shore, which can cause flooding and pose danger to coastal regions.
Storm surges increase risk of damage to coastal infrastructure, communities, and economies. Climate change, which can trigger increases in storm surge and sea level rise, are also of concern to coastal populations.
Hence, government and local organizations in these regions study potential mitigation systems to protect future generations from storm surge and the combined impact of surge, sea level rise and/or subsidence. Accurate and efficient forward models of coastal flooding are essential for such studies, as is the generation of synthetic hurricanes, which aid in analysis and prediction.
Clint Dawson (University of Texas at Austin) discussed various tools used in this type of study in the Houston-Galveston region of the Texas coast during a minisymposium at the SIAM Conference on Mathematics of Planet Earth. His group uses the Advanced Circulation (ADCIRC) model along with the Simulating Waves Nearshore (SWAN) model as a forward model for simulating storm surge.
Since hurricanes generally develop over the ocean—across the Atlantic or Pacific—they need to be modeled at a fairly large scale, Dawson explained. “But we also have to be able to account for what happens when the hurricane makes landfall,” he said. “There we are talking about modeling things on a regional scale.”
Modeling storm surge at regional scale involves waves at two spectra, with wave periods ranging from seconds to hours. Short waves, which are primarily wind-driven—the waves you actually see when you go out into the ocean—are in the order of seconds. Long wave periods in these models range from minutes to hours.
The physical processes that need to be accounted for in surge models include wind, pressure, and tides, as well as the Coriolis effect, a phenomenon which causes winds to move toward the right in the Northern Hemisphere and toward the left in the Southern Hemisphere due to Earth’s rotation. In addition, complex coastlines pose rough domains and complex boundary conditions in modeling equations. Another factor that affects models is the highly-variable topography and bathymetry (or depth) of oceans. Inundation and recession, as well as interaction of water with structures and vegetation as well as bottom friction are also factors.
Track of Hurricane Ike (2008). Image credit: Created using Wikipedia:WikiProject Tropical cyclones/Tracks. Background image is from NASA. Tracking data from the National Hurricane Center.
Long waves are modeled as shallow water equations since they have very long wavelengths compared to the water depth. For short wave equations, instead of modeling individual waves, the researchers obtain averages as governed by the action balance equation.
Dawson’s team first applied a circulation model, the Advanced Circulation (ADCIRC) modeling framework, to a hindcast study of Hurricane Betsy, which hit the Galveston region in 1965. In addition to this, several hurricanes in the 2000s were studied for extensive hindcasting and validation of the model. The model is now used worldwide to predict hurricane storm surge.
In addition to historical hurricanes, the group used a suite of synthetic storms generated for the Texas coast by probabilistic methods in order to validate the model.
The ADCIRC shallow-water circulation model was integrated with a wave model, the Simulating Waves Nearshore (SWAN) model, to generate a tightly-coupled SWAN+ADCIRC model.
This coupled model was then used to study Hurricane Ike, which swept through the Galveston-Houston area in 2008. Surge was dictated by geography, storm track, and bathymetry. In the Houston-Galveston area, frictional resistance is not a big factor since it’s a low-lying area.
A 10-day hindcast gave information on Hurricane Ike water levels. Researchers obtained good scatter plots when modeling peak surge of Hurricane Ike vs. measurements.
The group also evaluated various protection systems for major hurricanes within a 100-mile radius of Houston. Dawson described a recent study of the efficacy of the Houston Galveston Area Protection System (HGAPS), a proposed storm mitigation system, consisting of levees, berms, gates and a seawall.
General trends of storms in the area tend to be in the southeast to northwest and north to south directions. The group generated synthetic storm tracks based on the historical record, which were used to obtain statistics of surge probabilities and a flood insurance risk map.
Four storms were used for the evaluation including the 1900 and 1915 Galveston hurricanes, Hurricane Rita in 2005, and Hurricane Ike. Proxy storms were also included in the evaluation.
The simulation allows one to see how far inland the storm surge propagates. Increase in wind speed causes more devastating effects, as expected. The higher the population in the area, the higher the risk. Oil refineries and petrochemical plants in the region—which store oil and dangerous chemicals—increase risk.
The group evaluated HGAPS and the protection system known as the Mid-Bay Strategy to protect Galveston, Galveston Bay and surrounding cities.
They modeled surge reduction and evaluated the system for various barriers at different heights. “With this system, when we modeled the surge reduction, we can see that putting barriers at a certain height can reduce the surge almost to 0,” explained Dawson. “With Ike, had we had this in place, there would be no storm surge behind the barrier, [an area] which has a big population.”
This evaluation was then sent out for review/comment to each county and district. Unfortunately, these maps are generally challenged by local municipalities since it causes insurance rates in the area to rise when accepted. The group also evaluated another option called Ike Dike, which offered coastal protection with a gate and seawall. The latter is seriously being considered and being evaluated by the Army Core of Engineers.
Mathematical models are thus helping design very real protection strategies for our coastal communities.
|| Karthika Swamy Cohen is the managing editor of SIAM News.