Validation of an Integrated Coastal Processes Model by Simulating Storm- Surge and Wave in the Mississippi/Louisiana Gulf Coast

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1 Validation of an Integrated Coastal Processes Model by Simulating Storm- Surge and Wave in the Mississippi/Louisiana Gulf Coast Yan Ding 1, Andi Rusdin 1, Soumendra N. Kuiry 1, Yaoxin Zhang 1, Yafei Jia 1, and Mustafa S. Altinakar 1 1 National Center for Computational Hydroscience and Engineering, The University of Mississippi, University, MS ding@ncche.olemiss.edu Abstract This study is to validate an integrated coastal processes model by simulating storm surges and waves in the Mississippi and Louisiana Gulf Coast. In the model, two coupled processes modules for simulating wave actions and storm surges are operating over one computational grid so that there is no need for steering operation to switch wave and hydrodynamic modules and interpolating computed variables in between if two modules are using two different grids. This integrated model can simulate coastal processes induced by tides, waves, and storms, as well as riverine process such as river inflows into estuaries and coasts. This integrated model is validated by simulating waves and storm surges created by Hurricane Gustav (2008) in the Southern Louisiana and Mississippi coast. Computed results for storm surges and wave parameters are in good agreement with the observations provided by NOAA s gage stations. 1. Introduction The Mississippi and Louisiana Gulf Coast bears the brunt of attacks by storm surges and ocean waves during tropical storm seasons. In the past decade, Hurricanes Katrina (2005) and Gustav (2008) made a tremendous damage in properties and caused hundreds of human causalities. Katrina reached category 5 on the Saffir Simpson scale in the Gulf of Mexico before weakening to category 3 before making landfall on the northern Gulf coast near Buras, Louisiana at 1110 UTC 29 August (Knabb et al. 2005). Katrina continued northward and made its final landfall near the mouth of the Pearl River at the Louisiana/Mississippi border, still as a Category 3 hurricane with an estimated intensity of 105 kt. Considering the scope of its impacts, Katrina was one of the most devastating natural disasters in United States history. Gustav (2008) was the first major hurricane to track through the northern Gulf of Mexico after Katrina. It briefly became a category 4 hurricane on the Saffir-Simpson Hurricane Scale and caused many deaths and considerable damage in Haiti, Cuba, and Louisiana. Gustav made its final landfall near Cocodrie, Louisiana, around 1500 UTC 1 September with maximum winds near 90 kt (Category 2) (Beven and Kimberlain 2009). Gustav was much weaker than Katrina, and its landfall was farther west to New Orleans. For those reason, the waves and surges by Gustav should be less threatening to the New Orleans and the Mississippi Gulf coast. However, Gustav increased in size as it approached Louisiana, and its outer, tropical-storm-strength winds impacted the system for hours. Gustav generated waves that damaged infrastructure in southern Louisiana and offshore, and its surge nearly overtopped large sections of the levee/floodwall system throughout metropolitan New Orleans (Dietrich et al. 2011).

2 Storm surges and waves induced by hurricanes in the northern Gulf of Mexico have been studied by using integrated coastal/oceanic processes models. Bunya et al. (2010) have used two models: ADCIRC (a finite elemental model) for simulations of storm surges and STWAVE (a finite differential model) for waves, to hindcast Hurricane Katrina (2005). Chen et al. (2008) have also used ADCIRC and SWAN (a curvilinear mesh version) to compute the surges and waves induced by Hurricanes Ivan (2004) and Katrina (2005). Apparently, the above two coupled models used two different grids, one finite elemental unstructured mesh for ADCIRC and one or a few rectilinear meshes for STWAVE. A so-called steering operation has to be applied to switch the two models on and off. And the computed results have to be interpolated into other mesh grids. Without consideration of wave effect, Forbes et al. (2010) simulated the storm surges in the north Gulf coast by using an asymmetrical gradient wind model (AWM), the North American Mesoscale (NAM) model, and NOAA s Hurricane Research Division (HRD) H*Wind. Dietrich et al. (2011) adopted ADCIRC and SWAN to simulate the storm surges and waves induced by Hurricane Gustav (2008). The integrated model called SWAN+ADCIRC employs the same unstructured mesh on the same computational cores, passing information between models through local memory/cache, and thus it can simulate the propagation of waves from deep water to the nearshore with accuracy and efficiency. However, in the above coupled models, an explicit numerical scheme of ADCIRC restricts the time step size to one second (Bunya et al. 2010, Dietrich et al. 2011). Moreover, most numerical simulations of flooding and inundation along the Mississippi and Louisiana coastlines during hurricane events mainly concentrated on surges and waves from oceans. Even though some models included the Mississippi and Atchafalaya Rivers in computational domains, apparently, there is lack of investigations on the effect of river inflows on coastal flooding and inundation resulting from rainfalls during a hurricane. A part of the reasons is the lower resolution of the computational meshes over the inland side. In this study, to have a better assessment on the impact of storm surges, waves, and river flood inflows by hurricanes in the Mississippi and Louisiana coastal region, a large-scale simulation domain is taken to cover the Louisiana and Mississippi Gulf Coast, the detailed bathymetry in the watershed of the Pearl River, the lower Mississippi River and the Atchafalaya River. An integrated model, CCHE2D-Coast, developed by the National Center for Computational Hydroscience and Engineering (NCCHE) at the University of Mississippi is applied to simulate storm surges and waves over this large area due to hurricanes. Model validations have been made by simulating storm surges driven by Hurricane Gustav in By adopting a high-resolution mesh for watersheds in the land area, the model is able to study the setup of storm surges in the watershed region of the Pearl River in Mississippi. 2. Model Descriptions This study uses CCHE2D-Coast, which is an integrated coastal processes model developed in NCCHE (Ding et al. 2006, Ding and Wang 2008). It is built on the CCHE2D model and is enhanced to simulate coastal/ocean/riverine processes driven by tides, waves, storm surges, river inflows, etc. CCHE2D is a well-established simulation software package for modeling hydrodynamic and morphodynamic processes in rivers, estuaries, and lakes (Jia and Wang 1999, Jia et al. 2002). Based on the same numerical methodologies and the same software development platform, CCHE2D-Coast has been developed by integrating a multidirectional

3 wave spectral model, a coastal hydrodynamic model, and a sediment transport model (Ding et al. 2006). It has the following major capabilities for simulating hydrodynamic and morphodynamic processes in coasts, estuaries, rivers, and oceans: Non-orthogonal mesh that can model complex coastlines Irregular wave deformations with optional offshore wave spectrum inputs Tidal currents and river flows Surges and Waves driven by tropical storms, typhoons, and hurricanes Nearshore currents induced by short waves Sediment transport due to a combination of waves and currents Morphological changes in coastal and estuarine areas Morphological changes around coastal structures, e.g., groins, offshore breakwaters, artificial headlands, jetties, artificial reefs (submerged dikes on coasts) In the wave-action model, the breaking wave height is calculated based on the breaking wave criterion proposed by Goda (1970), or the one extended by Sakai et al. (1988). When the wave model is applied for simulating waves induced by winds, The energy input by wind forcing can be modeled as separated sink and source terms (Lin and Lin 2004a,b). The energy loss by bottom friction is calculated by a drag law model (Collins 1972). It is important to note that the hydrodynamic model and the wave model in CCHE2D-Coast are integrated seamlessly so that all the modules share one grid system for simulating coastal processes in sequence. Thus, unlike the model steering operation used in some models, CCHE2D-Coast does not need to switch executable codes of the modules. As a result of this advantage, CCHE2D-Coast avoids possible errors and loss of information resulting from interpolation and extrapolation of the results between two grid systems for two different computational models. All the coastal process modules in CCHE2D-Coast share the same non-orthogonal mesh which allows general quadrilateral grids. This non-orthogonal structural mesh can model irregular coastlines in a more flexible way, in comparison with the rectangular mesh used in some commercial and in-house wave simulation models. The temporal/spatial variations of atmospheric pressure and wind during a storm/hurricane period are simulated using a parametric storm wind model (Holland 1980) and NOAA s Hurricane Research Division (HRD) H*Wind fields (NOAA 2011). The multidirectional wave spectral model in CCHE2D-Coast is developed to consider wind energy input to wave spectral energy. Young s hurricane wave model is implemented to generate the offshore wave boundary condition for specifying wave spectrum (Young 1988, Young and Burchell 1996). The wave model is seamlessly coupled with the hydrodynamic model by sharing a single nonorthogonal mesh. Hence, the simulations for wave-current interactions do not need to switch models for waves and currents. The computational efficiency has been significantly improved by implementing advanced numerical simulation algorithms and implicit matrix solvers. The storm surge with wave effect and inland flooding during a multiple-day storm can now be simulated at the regional scale on a personal computer. Therefore, simulation results can be useful for better planning and management for flood/inundation protection in a wider area of the Mississippi Gulf Coast including the inland watershed. 3. Computational Conditions

4 3.1. Computational Domain and Mesh As shown in Figure 1, the computational domain covers a regional area from southeast Louisiana to Mobile Bay in Alabama. The southern open sea boundary extends 440 km (273.4 miles) in a west-east direction. The area extends 323 km (200.7 miles) in a south-north direction. The entire Mississippi Gulf coast and most of the Louisiana coast are included in the computational domain. Four river basins, i.e. the Mississippi, the Atchafalaya, the Pearl River, and the Pascagoula Rivers, are considered as the sources of the river inflows into the Gulf coasts. Figure 1. Computed maximum water elevations in Hurricane Gustav (2008) The basic data for generating bed elevations in the study area was provided by an existing grid used in the ADCIRC storm-surge simulations, which is a finite elemental mesh data. This computational grid called SL15 was received from the USACE-ERDC. It has been used to study storm surges in the Gulf of Mexico (e.g. Bunya et al. 2010, Dietrich et al. 2011). It covers a very large area including Gulf of Mexico, Caribbean Sea and part of the Atlantic Ocean up to Maine and Nova Scotia. The SL15 mesh has 2,137,978 nodes and 4,184,778 triangular elements in total. It includes all the existing coastal structures such as dikes, seawells, etc. as of 2007 in the MS/LA Gulf coast. The grid resolution is higher near the structures. The sizes of the elements near the structures are about 40-50m. In fact, the computational domain used in the present study has been extended to the inland area in the north direction more than 100 km in order to include the Pearl River basin and most part of Mobile Bay. In addition to the existing bathymetric data in the SL15 mesh, other two data resources are used for generating high-resolution mesh for representing the rivers and coastal communities in Mississippi and Louisiana: One is from the USGS DEM tiles with 10m-resolution, another from surveyed channel cross sections for the navigable portion of the East Pearl River extending from the John C. Stennis Space Center to the coast. The river cross section data were described in McKay and Blain (2010). Upon request of NCCHE, the authors kindly provided the surved data for this research. The topography data for the entire computational domain including the inland DEM data and the river cross section data are used to generate the present computational mesh. The topography and bathymetry covering the computational domain are plotted in Figure 2.

5 Figure 2. Topography and bathymetry of the Gulf coast included in the computational domain from three different data sources (i.e. SL15 mesh, DEM, and river cross section survey data). The stations are for the locations of the gages of NOAA and USGS. The preparation of the computational mesh is a very important and challenging process given the complicated coastline. The presence of various important features, such as rivers, coastal protection structures, roads, etc., should be accurately represented. The following general guidelines were adopted for the generation of the computational mesh: Cell sizes varying from 10 to 100m for representing levees, roads, coastal protection structures, etc. and the areas around them, Cell sizes varying from 10 to 100m to represent the Pearl River, Cell sizes of about 50 to 1,000m to represent Mississippi River, and Cell sizes equal to or larger than 1,000m to represent the deep water. The computational mesh was created using the CCHE-MESH program (Zhang and Jia 2009). The multi-block methodology was employed to decompose the computational domain into 17 subdomains, which were meshed separately. This was necessary to be able to accurately represent various features at various scales. The final mesh shown in Figure 3(a) has a total of 2,288,064 nodes (2103 grid points in the longitudinal direction and 1088 grid points in the latitudinal direction). The enlarged views of the computational mesh around Lake Pontchartrain and the Pearl River are shown in Figure 3(b) and Figure 4(a). Figure 3(b) provides a good example of the level of detail achieved around the coastal protection structures, roads, etc. Figure 4(a) clearly shows the level of resolution used in the present simulations to represent the meandering river course with sufficiently high accuracy. Figure 4(b) shows magnification of a portion of the final computational mesh around the Pearl River to give a better idea on the element sizes. The bottom roughness coefficients, i.e. Manning s n values, are obtained by interpolating the values from the SL15 mesh data. The values in the SL15 have considered the sea bottom roughness, coastal structures (i.e. dikes, roads, sea walls etc.), and vegetation at wetland. The roughness values at the inland area are set as 0.03.

6 (a) (b) Figure 3. (a) Computational mesh consisting of 2,288,064 nodes; (b) Enlarged view showing the Lake Pontchartrain and the Pearl River (a) (b) Figure 4. (a) Enlarged view showing the high-resolution topography in the Pearl River, (b) enlarged view showing the mesh in the Pearl River 3.2. Storm Track This hindcast of Hurricane Gustav in 2008 is performed to validate CCHE2D-Coast by simulating the waves and storm surges driven by the combined hydrological forcing from tides, waves, winds, river inflows, etc. The storm track is the best track of Hurricane Gustav from the National Center for Environmental Prediction (NCEP) Automated Tropical Cyclone Forecasting best track data. The track at the time around its landfall at the south Louisiana coast is shown in Figure 1. A hurricane cyclone model by Holland (1982) is used to generate the wind fields based on the hurricane parameters such as the central pressure, storm size (radius of cyclone), and the coordinates of the hurricane eyes Tides Based on the observations of tides at NOAA s tide gages at the south Louisiana Coast ( the tidal elevations at the Pilots Station East, SW Pass, LA is used as the tidal boundary condition at the south open sea boundary. Even though

7 there should be a time lag between this inland gage and the south open boundary, several preliminary tests have shown that the time lag is negligible Waves Wave set-up induced by storm winds can cause an additional increase in water surface elevation and increases the extent of inundation area and depth. By using the wave model in CCHE2D-Coast, the wind-induced wave fields are computed over the entire computational domain as shown in Figure 1. In the simulations of storm surge by coupling the wave model with the hydrodynamic model, the wave field was recomputed every one hour based on the latest flow results. On the offshore boundary, wave parameters as the wave boundary conditions are computed by a deep water wave model, Young s hurricane wave model (Young 1988, Young and Burchell 1996). The model assumed that the JONSWAP (Hasselmann et al, 1973, 1976) relationship, originally developed for fetch limited conditions, could also be applied in hurricane wind fields with the specification of a suitable equivalent fetch. Therefore, the significant wave height (Hs) and peak period (Tp) are computed by the JONSWAP spectrum. As long as the wave parameters are computed on the offshore boundary, the multidirectional wave spectral density at every offshore boundary node is calculated based on the given hurricane wind directions and the Bretschneider-Mitsuyasu (B-M) spectrum (Mitsuyasu 1970) River inflows The present study for the model validation considers the Mississippi and the Atchafalaya Rivers and the East Pearl River in the computational domain. The daily average discharges for the first two rivers are available from the USGS website Water Data for the Nation ( The stream gage USGS Mississippi River at Baton Rouge, LA, provided the daily average discharges for the Mississippi River. For the Atchafalaya River, the daily discharges were obtained from USGS Atchafalaya River at Simmesport, LA. The discharges measured at these two stations during Hurricane Gustav (2008) are used as river inflow boundary conditions along the northern boundary of the computational domain. In this validation of the model, no inflow from the Pearl River in Mississippi is considered. For the effect of the Pearl River discharge on the storm surge, one may further refer to Ding et al. (2012) Model Spin-up and Initial Conditions Before a storm surge simulation starts, the model has to be initialized, or spun up, so that a well-developed sea state is created for flow dynamic simulations driven by tides and dotrm winds. The spin-up consists of two steps: the first step is to generate a steady state flow condition, for which the constant river discharges are given to the rivers including in the domain, and the water surface elevation at the offshore boundary (the south boundary) is assumed to be at the datum NAVD88. The two discharges are m 3 /s for the Mississippi River, m 3 /s for the Atchafalaya River, which are from the USGS website at the Mississippi and Atchafalaya Rivers at UTC 0:00, Aug. 15, The steady flow condition is developed by running the model for sufficiently long time (approximately 10 days) before introducing tide at the offshore boundary. The second step is to spin up the model by running 10-day tidal flow simulation from Aug. 15 to Aug. 25, 2008 so that a wellestablished tidal flow condition is developed in the offshore area and the results at UTC 0:00,

8 Aug. 25, 2008 are used as initial condition for simulating storm surges driven by the storm conditions of Hurricane Gustav (2008). 4. Model Validation Results Simulations of storm surges were done by computing sequentially hurricane wind fields, wind-induced waves, and flows driven by waves, winds, and tides. By means of an implicit scheme implemented in the CCHE2D-Coast flow model, a large time-step size, 120 seconds, is allowed to simulate the flows. The wave fields were computed every 1 hour by updating the latest hydrodynamic variables such as currents and water elevations. CCHE2D-Coast provides two options for modeling wave actions driven by the cyclonical storm winds: a halfplane wave model and a full-plane wave model. The former is only to compute the wave fields from the upwinding direction to the downwind direction. Namely, the wave computations in the direction-frequency plane are preceded from the south to the north, following the hurricane track direction. The later one is to compute the wave fields by sweeping back and forth at the north and south directions. Holland s wind model is used to generate wind fields at every time step of the hydrodynamic simulations. All the simulations were performed on a PC with Intel quad core TM i7 GHZ. Only a single CPU was used for the simulations. A 10-day hurricane simulation with wave computations took approximately 40 CPU hours. A current-wave interaction simulation with the full-plane wave simulation during the 10-day hurricane period took about 88 CPU hours. Even though the computing performance can be further improved by implementing parallel computing in a supercomputer, in terms of a single CPU, CCHE2D-Coast is efficient. In the near future, a parallel computing version of this model by using multi cores or graphic processing units (GPUs) will certainly make this model capable of quickly simulating a regional scale hurricane in an ordinary PC with a very attractive cost-benefit performance. To verify the quality of the wind fields generated by the parametric wind model, the calculated wind speeds and directions have been compared with the data of the winds at the NOAA gages. As examples, Figure 5 presents the comparisons of wind speeds at three NOAA gages as shown in Figure 2. The wind speeds are slightly overestimated at the station, NDBC 42040, located at the offshore. Others are in good agreement with the observations of winds at the ground stations. Figure 5. Comparisons of wind speed between observations at three NOAA gages (St. 1, 2, and 27 as shown in Figure 2) and simulations by using Holland s model and the best track parameters of Hurricane Gustav. During the simulations, the wave and flow models were working with the same computational mesh, which is a non-orthogonal structural grid. Therefore, the wave and flow models were running on the same computational cores, passing information between models through local memory/cache, and thus it could simulate the propagation of waves from deep water to the nearshore without any interpolations between the wave and the flow fields. The wave model

9 uses 14 frequency bins that increase in bandwidth logarithmically so that the wave spectral energy is equally divided into the frequency bins, and 24 directional bins with a constant width of 15 o. By using the full-plane option for computing wave fields every one hours, as shown in Figure 6, the maximum significant wave heights (Hs) and wave periods (Ts) are obtained. The distributions of waves over the entire region show that the maximum Hs can reach more than 14 m at the offshore of the south Louisiana coast, and about 8 m at the offshore of the Mississippi Gulf coast. In Figure 7, comparisons of Hs and the peak(dominant) wave periods (Tp) at the NDBC station (or St. 1 in Figure 2) indicate that the computed time series of wave parameters are close to the observations at this NOAA gage, and the results after the hurricane landfall by the full-plane model are better than the half-plane model. Figure 6. Computed significant wave heights (left) and wave periods (right) Figure 7. Comparisons of significant wave heights and dominant wave period at St. 1, NOAA NDBC 42040, Luke Offshore Test Platform. The wave heights are computed by two options of CCHE2D-Coast, the half-plane and the full-plane models The distributions of the maximum water elevations above NAVD 88 are given in Figure 1. It shows that the highest water elevation during the period of Hurricane Gustav (2008) is about 5.0 meter around the Grand Isle, LA, and the storm surges induced more inundations in the wetland area at the south Louisiana, but the storm waters at the Mississippi coast rise up to 3.0 meter. Three time series of the computed water elevations at three NOAA gages ( , , and ) are compared with their observation data obtained from the NOAA website. The comparisons imply that the inclusion of wave effect (e.g. wave setup) can improve significantly the predictions of storm surges. And the wave setup at the three stations is about 0.5 m.

10 Figure 8. Comparisons of water elevations above NAVD88 at St. 3, 6 and Conclusions This study has validated an integrated coastal processes model, CCHE2D-Coast, by simulating storm surges and waves in the Mississippi and Louisiana Gulf Coast due to Hurricane Gustav in To have a better assessment on the impact of storm surges, waves, and river flood inflows by hurricanes in the Mississippi and Louisiana coastal region, a largescale simulation domain is taken to cover the Louisiana and Mississippi Gulf Coast, and the detailed bathymetry in the watershed of the Pearl River, the lower Mississippi River and the Atchafalaya River is included. Computed results for storm surges and wave parameters in Hurricane Gustav (2008) are in good agreement with the observations provided by NOAA gage stations. In the model, two coupled processes modules for simulating wave actions and storm surges are operating over one computational grid so that there is no need for steering operation to switch wave and hydrodynamic modules and interpolating computed variables in between if two coupled modules are using two different grids. This integrated model can not only simulate coastal processes induced by tides, waves, and storms, but also riverine process such as river inflow to estuaries and coasts. The implicit scheme for solving both wave energy equation and hydrodynamic equations allow the large-scale surge-wave simulation to use a large time step to make the computations highly efficient, even only using an ordinary PC with a single CPU. In the near future, parallel computing techniques for multi cores or GPUs will be implemented to further speed up the model computing efficiency. ACKNOWLEDGEMENTS The authors thank Ty Wamsley at USACE-ERDC for providing the SL15 mesh data, and Paul McKay and Cheryl Ann Blain at Naval Research Laboratory, Stennis Space Center, MS for providing the cross section data in the Pearl River. The authors also thank Xiaobo Chao, Marcus McGrath, and Vijay Ramalingam for collecting the river discharge data and providing the DEM data for modeling the Mississippi Coasts. References Beven II, J. L., and Kimberlain, T. B. (2009). Tropical Cyclone Report, Hurricane Gustav, 25 August 4 September NOAA/National Hurricane Center, 38 pp., Available at Bunya, S., Dietrich, J. C., Westerink, J. J., Ebersole, B. A., Smith, J. M., Atkinson, J. H., Jensen, R., Resio, D. T., Luettich, R. A., Dawson, C., Cardone, V. J., Cox, A. T., Powell, M. D., Westerink, H. J., Roberts, H. J. (2010). A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part I: Model Development and Validation, Monthly Weather Review, 138(2), pp

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