Numerical Models of Storm Surge, Wave, and Coastal Flooding

Storm surge models are a useful scientific tool for predicting real-time storm surge and future planning. These models provide real-time forecasting of the water level and potential inundation under storm conditions. Storm surge models are also used to hindcast the flooding generated by past hurricanes, assess future flood risks, and produce potential flooding maps for planning purposes.

Aerial photo of a portion of the Mississippi coastline after Hurricane Katrina (2005). The area was heavily damaged by Katrina's storm surge. In the image on the left, one can clearly see a "debris line", which marks the furthest extent of the surge (and everything that was carried with it). The photo on the right shows a zoomed-in image of the area in the red box on the left. Here, one can see the empty slabs from which houses were pushed and the sea of debris which surrounds those houses left standing. Image credit: NOAA

Although there are differences between every storm surge model, they all share a common set of required data to generate storm surge simulations. A basic recipe for running a storm surge model to generate wind-driven storm surge includes:

• computational mesh that covers the area of interest,
• bathymetry data for the area,
• hurricane information (position or storm track, wind strength) and atmospheric pressure; and
• tidal information.

Most storm surge models are two-dimensional, meaning that the current variation with depth is not resolved in these models. Researchers have shown that a well-tuned two-dimensional model is sufficient to produce an accurate estimate of the abnormal rise in water level due to storms. However, for some applications such as pollutant transport, a three-dimensional model is necessary for accurate results.

The SLOSH model was developed by the National Weather Service (NWS) in the 1990s (Jelesnianski et al. 1992, Glahn et al. 2009 ) and is still the operational model used by National Hurricane Center (NHC) due to its computational efficiency. The SLOSH model separates the coastline into 32 basins which cover the entire U.S. Atlantic and Gulf of Mexico coastlines as well as Hawaii, Puerto Rico, Virgin Islands, and the Bahamas. These model basins are centered particularly susceptible features, such as inlets, large coastal centers of population, low-lying topography, and ports. Each basin is represented by a mesh or grid (see Research Models - http://www.hurricanescience.org/science/forecast/researchmodels/) which can resolve ocean bathymetry and land features in great detail, but does not extend to the open ocean.

SLOSH model coverage. Image Credit NOAA NWS NHC

The Advanced Circulation (ADCIRC) model was developed at the University of North Carolina by Dr. Rick Luettich. It is a more complex and capable and more time-consuming storm surge model than the SLOSH model. ADCIRC makes use of a highly flexible mesh system to produce storm surge simulation. The model can better simulate tides propagated from the open ocean and is also capable of resolving very detailed bathymetry in the coastal region. After Hurricane Katrina, the Interagency Performance Evaluation Taskforce (IPET) used the primarily a two-dimensional ADCIRC model to simulate Katrina’s storm surge and produce coastal flood maps for a storm with a 1% and 0.2% annual chance of occurrence in a given year for the New Orleans region. ADCIRC is also being used by the U.S. Federal Emergency Management Association (FEMA) to produce Flood Insurance Rate Maps (FIRMs) in several coastal regions. A storm surge and wave guidance system is being developed based on the ADCIRC model that can be used for coastal emergency risk assessment (https://cera.coastalrisk.live).

The North Carolina v6c ADCIRC mesh (Source: http://adcirc.org/products/grids/)

Differences between surge models: SLOSH and ADCIRC
Differences between the SLOSH and ADCIRC models are mainly in the following three areas: mesh shape and resolution, mathematical methods to solve equations in the model (numerics), and the physics contained in the model. A comparison between the SLOSH and ADCIRC storm surge models is given in the table below.

The two models are computed on different mesh system. SLOSH utilizes a curvilinear grid system, which is by default a structured grid because there is a fixed relationship between grid points. The spatial resolution in the curvilinear grid can vary a little bit with latitude, but not drastically. In contrast, ADCIRC implements its computation on an unstructured grid system, which can be concentrated near the coast for higher resolution at the coast. Due to major differences in the mesh system, the mathematical methods used to solve the physical equations computationally in the models are also different (explained in the table above). However, the method used in SLOSH is not superior to the other one. Both of them can produce optimized results with their associated grid systems. The physics that is included in the model are different. In SLOSH, the ocean surface wave component of storm surge is not included. However, the ADCIRC model is bundled (coupled) with a wave model called SWAN (Simulating WAves Nearshore) to include the ocean surface wave component in the surge. Through the comparisons above, it is evident that the ADCIRC model is more complicated than the SLOSH model. Hence, it is not a surprise that running the ADCIRC model require a lot more computational resources and time than running the SLOSH model.

In terms of performance, it is hard to say which model is better because parameters can always be tuned differently to produce accurate simulations. However, the less complex SLOSH model, tuned to run in operational mode, can perform badly under some unusual hurricane cases. For example, when the storm size (defined by the radius of gale-force wind (~17m/s)) is large and the hurricane moves slowly, water will be transported from the open ocean and the so-called forerunner surge due to the Coriolis force (basically the earth rotation) can be generated hours prior to the hurricane landfall. In this case, the ADCIRC model can do a better job than SLOSH mainly because of a larger computational domain size. Hurricane Ike in 2008 is a good example. Ike’s wind field was among the largest observed for a landfalling hurricane in the Atlantic over the past 30 years. (For more details of the forerunner surge in Ike, see Kennedy et al. 2011.) Discrepancies between the SLOSH model and the observations are reported to be significant. (see comments in https://texas.resiliencesystem.org/fr/comment/1325#comment-1325) The highest recorded surge is 22 feet coming ashore at Sabine Pass, which almost doubles the SLOSH prediction.

The SLOSH model is still the model used for real-time forecasting because the forecast has to be made in a short time period (a few hours); and the SLOSH model output is accurate enough, in most conditions, for decision making as a storm approaches. Care needs to be taken when the hurricanes share characteristics similar to Hurricane Ike (2008).

The SLOSH model is generally accurate within plus or minus 20 percent given a perfect track, intensity, and size of the hurricane. For example, if the model calculates a peak 3 m (~10 ft) storm surge for the event, one can expect the observed peak to range from about 2.4-3.6 m (~8 -12 ft).

Deterministic prediction
In this type of prediction, the forecast of storm surge is based on only one single simulation performed by solving physics equations. The accuracy of a deterministic prediction strongly relies on the accuracy of the meteorological input, because the location and timing of a hurricane’s landfall is crucial in determining the areas susceptible to storm surge. Unfortunately, there could be large uncertainties in the hurricane track information when an emergency manager must make an evacuation decision. (Lean more about forecast track error for Atlantic tropical cyclones HSS page). Hence, a single simulation from either SLOSH or ADCIRC is not capable of depicting the true storm surge vulnerability of an area. For this reason, a deterministic approach is typically used for hindcast, where the hurricane track is already available and the purpose of the modeling is to learn more about a past storm, conduct research or improve a model parameter (such as bottom drag).

Probabilistic Prediction
Probabilistic prediction will show the overall chances that the specified storm surge height will occur at each individual location. The probabilities are computed by statistically evaluating a large set of model simulations based on the current NHC official forecast information, while taking into account historical errors in official NHC track and intensity forecasts. An example of this type of prediction is the Probabilistic Surge (P-Surge) product from SLOSH model (https://www.nhc.noaa.gov/surge/psurge.php). Probabilistic products are encouraged by the National Research Council’s Fair Weather Report. https://www.nap.edu/read/10610/chapter/8?term=+Probabilistic+#105. This type of prediction is used for forecasting surge in real-time from a storm. The Tropical Cyclone Storm Surge Probabilities product https://www.nhc.noaa.gov/surge/psurge.php from the National Hurricane Center is an example of the output from this type of prediction.

Composite/Ensemble Prediction
A composite or ensemble prediction is made by running the storm surge model multiple times (hundreds to thousands of times) with hypothetical hurricanes under different storm conditions. In the SLOSH model, the products generated from this approach are the Maximum Envelopes of Water (MEOWs) and the Maximum of MEOWs (MOMs). These two results are regarded by NHC as the best approach for determining storm surge vulnerability for an area. Because this method incorporates a large number of possibilities, it takes into account forecast uncertainty and storm variability in terms of intensity, pressure, and size. The MEOWs and MOMs play an integral role in emergency management, as they provide the worst-case estimate and form the basis for the development of the nation's evacuation zones.

Probabilistic prediction and composite/ensemble prediction are the model outputs that the public and emergency managers use. The deterministic approach is more commonly used for research (model improvement) and past storm analysis.

Resio, D.T. & Westerink, J.J., 2008. Modeling the physics of storm surges. Physics Today

Glahn et al. 2009, the role of the slosh model in national weather service storm surge forecasting

Kennedy, A. B., Gravois, U., Zachry, B. C., Westerink, J. J., Hope, M. E., Dietrich, J. C., … Dean, R. G. (2011). Origin of the Hurricane Ike forerunner surge. Geophysical Research Letters, 38(8), n/a-n/a. http://doi.org/10.1029/2011GL047090

National Research Council. 2003. Fair Weather: Effective Partnership in Weather and Climate Services. Washington, DC: The National Academies Press. https://doi.org/10.17226/10610.

Committee on FEMA Flood Maps, Board on Earth Sciences and Resources/Mapping Science Committee, National Research Council (NRC), 2009, "Mapping the Zone: Improving Flood Map Accuracy." http://www.nap.edu/catalog.php?record_id=12573

Jeffrey Masters, Ph.D., "Storm Surge Inundation Maps for the U.S. Coast." Weather Underground. http://www.wunderground.com/hurricane/surge_images.asp

NOAA, "Hurricane Preparedness- SLOSH Model." http://www.nhc.noaa.gov/HAW2/english/surge/slosh.shtml

NOAA/NHC, "Storm Surge Overview." http://www.nhc.noaa.gov/ssurge/ssurge_overview.shtml

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