1 Introduction

Coastal zones, although they comprise only 17 % of the US land area (http://coastalmanagement.noaa.gov/impacts.html), are home to more than half of the population as well as a wealth of natural and economic resources in the United States. Some of the most important energy and transportation infrastructures, ports and pipeline systems, and prestigious ecosystems are located on the northern coast of the Gulf of Mexico (GoM). Thousands of offshore oil and gas platforms exist off the Gulf coast, and about 30 % of the US oil supply and 20 % of the natural gas supply are produced in the GoM region (Minerals Management Service 2006; Staudt and Curry 2011). The low-lying areas of the Gulf coast are heavily populated and are experiencing a population shift from rural to urban and suburban areas (Burkett et al. 2008). Because many of the vital economic sectors, energy, and transportation infrastructures and large populations are located in the low-lying areas of the Gulf coast with little topographic relief, the Gulf coast is at high risk of storm surge and coastal inundation under climate change-related extreme events (Burkett et al. 2008; Needham et al. 2012).

Over the last six decades, more than 170 tropical storms have made landfall along the Gulf coast and nearly 60 of them were hurricanes (National Oceanic and Atmospheric Administration [NOAA] National Hurricane Center, http://www.nhc.noaa.gov/pastall.shtml). Storm surges induced by hurricanes and tropical cyclones pose significant threats to the coastal zones around the world. Hurricane-induced storm surge and coastal inundation can be significantly exacerbated by other factors such as astronomical tides, land subsidence, and climate change-related sea-level rise (SLR). Coastal vulnerability assessment studies in the GoM (Thieler and Hammar-Klose 2000; Pendleton et al. 2010) indicated that the Gulf coasts of the States of Mississippi, Louisiana, and Texas are at high to very high risk of SLR based on the “Coastal Vulnerability Index.” While high uncertainty exists in the projections of exact rates of future global SLR, it is clear that SLR at global and regional scales will result in potential impacts on coastal infrastructure, marine ecosystems, and cultural and natural resources (Nicholls et al. 2007). Land subsidence could also affect coastal inundation area and depth significantly in low-lying regions such as the northern GoM. An early study by Gornitz et al. (1991) using a hazard database indicated that the Louisiana coast and parts of the Texas coast are potentially the most vulnerable to SLR in the United States, due to anomalously high relative SLR, erosion, and land subsidence. Dixon et al. (2006) reported a maximum subsidence rate of 29 mm/year in the New Orleans area based on 2003–2005 Canada RADARSAT satellite data. Therefore, there is a strong need to study the variability of hurricane-induced storm surge and coastal inundation in the Gulf coastal regions as well as the effects of SLR and land subsidence on the surge levels under future climate conditions.

Numerical modeling has been shown to be a powerful tool for predicting storm surge and coastal inundation at desired temporal and spatial scales and resolutions. The rich data set generated from numerical models under different climate change and land subsidence scenarios can be used to assess the risk of storm surge and provide guidance for coastal emergency management, mitigation, and adaptation. Numerous research articles have studied hurricane-induced coastal storm surge and inundation using advanced numerical models as well as statistical analysis approaches, especially since the Hurricane Katrina disaster in 2005 (Shen et al. 2006; Weisberg and Zheng 2006, 2008; Irish et al. 2008; Westerink et al. 2008; Xu etal. 2010; Dietrich et al. 2010, 2011; Mousavi et al. 2010; Tebaldi et al. 2012; Warner and Tissot 2012).

This paper presents a modeling study that simulates tides and hurricane-induced storm surges in the GoM and evaluates the effects of SLR and subsidence on the storm surge level and coastal inundation with a focus on the Mississippi River delta and the Louisiana coast. The structure of the paper is as follows. Section 2 describes the model setup, grid development, forcing mechanisms, and projections of SLR and coastal subsidence for model simulations of tide and hurricane-induced storm surge. Model results, discussion of tides, and hurricane-induced storm surges, as well as sensitivity analysis of future SLR and subsidence on storm surge, are presented in Sect. 3. Finally, a summary is provided in Sect. 4.

2 Methods

2.1 Coastal storm surge model

Unstructured-grid models have demonstrated a great advantage in simulating coastal inundation processes that require not only high grid resolution near the surge zone in the coastal region, but also a large model domain to represent the large scale and long-period forcing of hurricane wind fields (Luettich et al. 1992; Weisberg and Zheng 2006, 2008; Shen et al. 2006; Westerink et al. 2008; Bunya et al. 2010; Dietrich et al. 2010, 2011; Dawson et al. 2011; Cho et al. 2012; Kennedy et al. 2012). The storm surge model used in this study is the unstructured-grid finite-volume coastal ocean model (FVCOM) developed by Chen et al. (2003). FVCOM is a free-surface, three-dimensional primitive equations model that fully couples ice-ocean-wave-sediment-ecosystem models with options for various turbulence closure schemes, generalized vertical terrain-following coordinates, wetting–drying treatment, and data assimilation under hydrostatic and non-hydrostatic approximations. The finite-volume approach in FVCOM combines the geometric flexibility of finite-element methods with the simple and efficient computational structure of finite-difference methods. The finite-volume approach also provides better mass conservation for momentum and transport processes. The flexible unstructured-grid and mass-conservative nature make FVCOM ideally suited for interdisciplinary application in coastal oceans. FVCOM has been used to simulate tidal and estuarine circulation (Xing et al. 2011; Zheng and Weisberg 2012; Yang et al. 2012; Yang and Wang 2013), storm surge predictions (Weisberg and Zheng 2006, 2008), tidal energy extraction (Karsten et al. 2008; Yang et al. 2013), and biogeochemical processes and internal waves (Lai et al. 2010a, b; Ji et al. 2011; Wang et al.2013).

The primitive governing equations for Reynolds-averaged turbulent flows with Boussinesq and hydrostatic approximations are represented in the following form in FVCOM:

$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$
(1)
$$\frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} + w\frac{\partial u}{\partial z} - fv = - \frac{1}{{\rho_{\text{o}} }}\frac{{\partial (p_{\text{h}} + p_{\text{a}} )}}{\partial x} + \frac{\partial }{\partial z}\left( {K_{\text{m}} \frac{\partial u}{\partial z}} \right) + F_{\text{x}}$$
(2)
$$\frac{\partial v}{\partial t} + u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} + w\frac{\partial v}{\partial z} + fu = - \frac{1}{{\rho_{o} }}\frac{{\partial (p_{\text{h}} + p_{\text{a}} )}}{\partial y} + \frac{\partial }{\partial z}\left( {K_{\text{m}} \frac{\partial v}{\partial z}} \right) + F_{\text{y}}$$
(3)
$$\frac{{\partial p_{h} }}{\partial z} = - \rho g$$
(4)

where (x, y, z) are the east, north, and vertical axes in the Cartesian coordinates; (u, v, w) are the three velocity components in the x, y, and z directions; (F x , F y ) are the horizontal momentum diffusivity terms in the x and y directions; K m is the vertical eddy viscosity coefficient; ρ is water density; p h is hydrostatic pressure; p a is atmospheric pressure; g is the gravitational acceleration; and f is the Coriolis parameter. To properly simulate storm surge and inundation in coastal wetland and intertidal zones, it is important to include the wetting and drying process in a storm surge model. The wetting and drying process in FVCOM is simulated using the point treatment technique based on the following criterion (Chen et al. 2008): For any given node, the node is

$$\left\{ {\begin{array}{*{20}c} {{\text{wet, }}\quad {\text{if }} D = h + \eta > D_{ \hbox{min} } } \\ {{\text{dry, }}\quad {\text{if }}D = h + \eta \le D_{ \hbox{min} } } \\ \end{array} } \right.$$
(5)

and for any given triangular cell, the cell is

$$\left\{ {\begin{array}{*{20}c} {{\text{wet, }}\quad {\text{if }} D = { \hbox{min} }(h_{N1} , h_{N2} ,h_{N3} ) + { \hbox{max} }(\eta_{N1} ,\eta_{N2} ,\eta_{N3} ) > D_{ \hbox{min} } } \\ {{\text{dry, }}\quad {\text{if }} D = { \hbox{min} }(h_{N1} , h_{N2} ,h_{N3} ) + { \hbox{max} }(\eta_{N1} ,\eta_{N2} ,\eta_{N3} ) \le D_{ \hbox{min} } } \\ \end{array} } \right.$$
(6)

where h and η are the bathymetric height and water level related to the referenced datum (North American Vertical Datum of 1988, NAVD88) in the model, respectively; N1, N2, and N3 are the three node numbers of a triangular cell; and D min is the minimum depth criterion for wetting and drying simulation. When a triangular cell is treated as dry, the cell velocity and the fluxes across the three sides of the cell are set to zero. The total water depth in the dry cell is kept the same until the cell becomes wet again. A minimum depth (D min) of 0.05 m was used as a dry cell criterion in all simulations in this study.

In FVCOM, the wind stress is calculated as follows:

$$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\tau } = C_{d} \rho_{a} \left| {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{U_{w} }} } \right|U_{w}$$
(7)

where \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\tau }\) is wind stress, ρ a is air density, \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{U_{w} }}\) is wind velocity at 10 m height above sea surface, and C d is the drag coefficient as a function of wind speed (Large and Pond 1981):

$$C_{d} = \left\{ {\begin{array}{*{20}c} {1.2 \times 10^{ - 3} } & {\left| {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{U_{w} }} } \right| < 11.0\,{\text{ms}}^{ - 1} } \\ {\left( {0.49 + 0.065\left| {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{U_{w} }} } \right|} \right) \times 10^{ - 3} } & { 11.0\,{\text{ms}}^{ - 1} \le \left| {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{U_{w} }} } \right| < 25.0\,{\text{ms}}^{ - 1} } \\ {\left( {0.49 + 0.065 \times 25} \right) \times 10^{ - 3} } & { \left| {\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{{U_{w} }} } \right| > 25.0\,{\text{ms}}^{ - 1} } \\ \end{array} } \right.$$
(8)

2.2 Model grid for the Gulf of Mexico

The GoM is a large semi-enclosed ocean basin with two narrow openings connected to the Atlantic Ocean (Fig. 1). It is connected to the Atlantic Ocean through the Straits of Florida between the United States and Cuba, and with the Caribbean Sea via the Yucatan Channel between Mexico and Cuba. Because of the circular shape of the Gulf, the shallow continental shelf occupies a significant portion of the surface area in the GoM. The Gulf coastal zones consist of large areas of wetlands, bays, barrier islands, and estuaries. Approximately, 38 % of Gulf waters are shallow intertidal areas. The deepest part of the Gulf, in the southwestern quadrant, is over 4,300 m deep, and the average water depth of the Gulf is about 1,600 m (US Environmental Protection Agency, http://www.epa.gov/gmpo/about/facts.html). The Gulf coast is generally low-lying with more than 80 % of the population living within 10 m of mean sea level (Gornitz et al. 1991).

Fig. 1
figure 1

Tide stations and selected hurricane tracks for model validation in the Gulf of Mexico

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An unstructured grid with triangular elements was constructed for the entire GoM using the spherical coordinate system. Because of the semi-enclosed shape of the GoM, the model open boundaries were specified at the Straits of Florida in the southeast and the Yucatan Channel in the south. The NOAA 1-arc-minute Global Relief Model (ETOPO1) bathymetric data were used to define the model water depths in the main basin of the Gulf model grid. Model bathymetry in the low-lying coastal areas and nearshore regions was interpolated from the US Geological Survey’s (USGS’s) 10-m resolution Digital Elevation Model (DEM) database. The solid land boundaries of the model are primarily defined based on the 10-m topographic contour of the USGS DEM database. There are a total of 280,667 triangular elements and 143,697 nodes in the model grid. The element sizes vary from around 300 m in the Louisiana coastal region to about 30,000 m in the center part of the Gulf (Fig. 2). Five uniformly distributed vertical layers were specified for all the model simulations.

Fig. 2
figure 2

FVCOM model grid and bathymetry for the Gulf of Mexico

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2.3 Model forcing and boundary conditions

In this study, we focused on the coastal inundation induced by tide, relative SLR, and hurricane-induced storm surge. Flooding caused by river runoff was not considered. Salinity and temperature and their effect on density-induced circulation were also not considered. Therefore, the hydrodynamic model was run in the barotropic mode only. The model was driven by water level (i.e., tides and SLR) at the open boundaries along the Straits of Florida and the Yucatan Channel and wind and pressure fields at the water surface.

The wind field for tropical cyclones was constructed primarily based on the wind field (H*Wind) and hurricane track data from NOAA’s Hurricane Research Division (HRD) (http://www.aoml.noaa.gov/hrd/) (Powell et al. 1998, 2010). The hurricane track data included hurricane center location, central atmospheric pressure, maximum sustainable wind speed, and radius of maximum wind. Because the H*Wind field only occupies a region centered on the hurricane eye and has a radius ranging between 400 and 500 km, the wind field for the rest of the model domain outside the 500 km radius was filled with the prototypical hurricane wind field based on Holland’s method (Holland 1980). The tangential wind speed and atmospheric pressure relative to the center of a storm are determined as (Holland 1980):

$$V\left( r \right) = \sqrt {\frac{{AB\left( {P_{n} - P_{c} } \right){ \exp }^{{\left( { - \frac{A}{{r^{B} }}} \right)}} }}{{\rho_{a} r^{B} }} + \left( \frac{rf}{2} \right)^{2} } - \frac{rf}{2}$$
(9)
$$P\left( r \right) = P_{c} + \left( {P_{n} - P_{c} } \right){ \exp }^{{\left( { - \frac{A}{{r^{B} }}} \right)}}$$
(10)
$$V_{\text{m}} = \sqrt {\left( {\frac{B}{{\rho_{a} e}}} \right)\left( {P_{\text{n}} - P_{\text{c}} } \right)}$$
(11)

where r is the radial distance from the hurricane center; V(r) and P(r) are the tangential wind speed and atmospheric pressure at a distance of r from the hurricane center, respectively; P n and P c are the ambient atmospheric pressure and hurricane central pressure, respectively; A and B are hurricane shape parameters with A = R Bmax , where R max is the radius of maximum winds; and f is the Coriolis factor. In Eq. (11), V m is the maximum sustained wind speed and e is the base of the natural logarithm.

Following an approach similar to that of Weisberg and Zheng (2008), a linear weighting function was used to smoothly merge the H*Wind data with the Holland wind field such that the innermost region (within a radius of 400 km) near the hurricane eye was purely forced by the more accurate H*Wind data, while the outer region (beyond the H*Wind coverage radius of 500 km) was purely Holland wind. Since only atmospheric pressure data at the hurricane eye are available along the hurricane track from HRD, the hurricane pressure field was constructed using the Holland method (Eq. 10) for the entire domain based on the hurricane track data obtained from NOAA/HRD.

For tidal simulation in the GoM, eight major tidal harmonic constituents (M2, S2, N2, K2, K1, O1, P1 and Q1) were specified along the open boundaries based on XTide stations Cabo San Antonio and Key West, which are located at the Yucatan Channel and the Straits of Florida, respectively (Fig. 1). Tidal potential was included in the simulation. A 40-day period simulation was conducted so that the model had a sufficiently long spin-up time, with the last 30 days of that simulation period used for harmonic analysis.

For hurricane-induced storm surge simulation, a 20-day simulation was conducted, including at least 10 days before the storm made landfall. For the purpose of model validation, observed water levels at Key West station, which is maintained by the NOAA Center of Operational Oceanographic Products and Services, were used to specify the southeastern open boundary condition in the Straits of Florida. No observations are publically available near the Yucatan Channel. Therefore, XTide predictions at Cabo San Antonio station were used in the south open boundary.

2.4 Projections of future sea-level rise and subsidence

One of the most direct impacts of global warming is the change in global mean sea level (Meehl et al. 2007). Some regional and local physical processes also contribute to the relative sea-level change. The potential impacts of relative SLR include coastal inundation, storm surge, flooding, wetland loss, saltwater intrusion, rising water table, and impeded drainage (Nicholls et al. 2011).

Relative sea-level change at a specific location is defined as the water level variation relative to the sea bed over a specific time, which can be calculated based on the contribution factors on global, regional, and local time scales (Nicholls et al. 2011):

$$\varDelta {\text{RSL}} = \varDelta {\text{SL}}_{G} + \varDelta {\text{SL}}_{\text{RM}} + \varDelta {\text{SL}}_{\text{RG}} + \varDelta {\text{SL}}_{\text{VLM}}$$
(12)

where ΔRSL is the change in relative sea level; ΔSLG is the change in global mean sea level; ΔSLRM is the regional variation in sea level from the global mean due to meteorological and oceanographic factors; ΔSLRG is the regional variation in sea level due to changes in the earth’s gravitational field; and ΔSLVLM is the change in sea level due to the vertical land movement. Projection of change in SLR caused by the regional meteorological and oceanographic effects is a considerable challenge because of a lack of detailed technical guidance at the regional scale (Nicholls et al. 2011). Therefore, the regional effects of sea-level change are not considered in this study. Only contributions from the global sea-level change and land subsidence on relative sea-level change were considered in the sensitivity analysis of this paper.

Although a projected global SLR in the range of 0.18–0.6 m by the end of this century from the Intergovernmental Panel on Climate Change report has been widely cited in the past (Meehl et al. 2007), more recent research based on new future climate scenarios indicated that future global SLR could even reach 2 m by 2100 (Pfeffer et al. 2008; Vermeer and Rahmstorf 2009; Willis and Church 2012). The Coastal Protection and Restoration Authority of Louisiana (CPRA) projected 0.45 m of global SLR in the next 50 years (year 2060) and slightly above 1.0 m by the end of the century on the Louisiana coast under the less optimistic scenario developed in the Comprehensive Master Plan for a Sustainable Coast, based on information from a National Research Council study (CPRA 2012). For simplicity, we assumed 1.0 m global SLR by 2100 in the Gulf region in the SLR sensitivity analysis presented in the following section. Ranges of land subsidence rates in the Louisiana coastal region for the next 50 years were also projected by CPRA for the same less optimistic scenario, which indicated that the subsidence rate in the outer Mississippi River delta could reach as much as 25 mm/year. These land subsidence rates were used to estimate the land elevations in the Louisiana coastal region by year 2100 for the sensitivity analysis.

3 Results and discussion

3.1 Simulation of barotropic tides in the Gulf of Mexico

Tidal ranges in the Gulf of Mexico are small due to the narrow connections to the Atlantic Ocean. Tides on the Gulf coast are microtidal and mean tidal ranges are generally less than 2 m (Gornitz et al. 1991; Gouillon et al. 2010; Hill et al. 2011). Although tides are not the focus in this study, they are important in terms of coastal inundation, especially regarding interaction with storm surge in the low-lying areas of the Gulf coast. Tidal simulation in the GoM reached dynamic equilibrium after several days of spin-up, which is comparable to the spin-up time reported by Gouillon et al. (2010). Model results are presented in the form of horizontal two-dimensional (2-D) distributions of co-amplitude and co-phase in the entire Gulf basin.

Principal lunar semi-diurnal tide M2 and diurnal tide K1 are the two largest astronomical tidal constituents in the GoM (Hill et al. 2011). Distributions of co-amplitude and co-phase for M2 and K1 are shown in Fig. 3. In most of the central region of the Gulf, the M2 amplitude is very small. M2 amplitudes on the eastern coast of the GoM are generally greater than those on the western coast. There is an amphidromic point just north of the Yucatan Peninsula, and the phase difference around the amphidromic point varies by a complete M2 tidal cycle. In particular, model results show four distinct regions in the Gulf with large M2 amplitude: the southwest coast of Florida; the northwest coast of Florida; the west coast of Louisiana to the east coast of Texas; and the west coast of Yucatan Peninsula (Fig. 3), which are consistent with the model results by Hill et al. (2011) and Gouillon et al. (2010). In contrast to the M2 amplitude, the K1 amplitude is relatively uniform over the entire Gulf, with an average value of around 0.18 m except the regions near the open boundaries (the Straits of Florida and the Yucatan Channel) where the K1 amplitude decreases to around 0.05 m (Fig. 3). The phase difference for K1 tide in the GoM is relatively small as well, generally within 20°, except in the Straits of Florida and the Yucatan Channel where phase differences across the channels are over 100°. The distribution patterns of tidal amplitude and phase for M2 and K1 in the GoM are generally in good agreement with previous modeling studies (Hill et al. 2011; Gouillon et al. 2010). It is noted that although the distribution patterns of tidal amplitude and phase in both the Straits of Florida and the Yucatan Channel are consistent with previous studies (Hill et al. 2011; Gouillon et al. 2010), errors in these regions could be larger than those in the main basin of the Gulf because of the influence of open boundary conditions.

Fig. 3
figure 3

Simulated co-amplitude and co-phase for semi-diurnal tide M2 (a, b) and diurnal tide K1 (c, d) in the Gulf of Mexico

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To further validate the tidal model for the Gulf of Mexico, modeled and observed results for three largest tidal constituents (K1, O1, and M2) were compared at selected NOAA real-time tide stations along the northern coast of the Gulf (Table 1). Locations of the real-time tide gages are shown in Fig. 1. Observed values for the harmonic constituents were directly obtained from the NOAA real-time tide Web site. Root-mean-square-errors (RMSE) were calculated for both amplitude and phase. Overall, the modeled tidal amplitudes agree with observations reasonably well, with RMSEs of 0.04, 0.033, and 0.04 m for K1, O1, and M2, respectively. The RMSEs for tidal phase are 10.7°, 12.1°, and 30.1° for K1, O1, and M2, which roughly correspond to 1-h difference between model predictions and observations for both diurnal and semi-diurnal tides. Some large errors in tidal phase predictions were mainly caused by the limitation of model grid resolution that did not resolve the detailed complexity of the shoreline, barrier islands, and small bays and inlets in the Gulf (Gouillon et al. 2010). Because the main objective of the study is on the coastal inundation induced by storm surge, sea-level rise, and land subsidence, the accuracy of tide prediction is considered sufficient for the purpose of this study.

Table 1 Comparison of tidal amplitude (m)/phase (degree) between observations and model results (italics) at NOAA real-time tide gage stations in the Gulf of Mexico
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3.2 Simulation of storm surges induced by hurricanes

To demonstrate the model’s capability for simulating storm surges induced by hurricanes along the northern Gulf coast, model simulations of storm surges forced by historical hurricane wind and pressure fields were conducted. Four historical hurricanes, including Ivan (2004), Katrina (2005), Rita (2005), and Dolly (2008), which made landfalls along the northern Gulf coast, were selected for simulation based on the consideration of data availability, hurricane intensity, and landfall locations. The tracks and key characteristics of the four hurricanes are given in Fig. 1 and Table 2, respectively.

Table 2 Hurricane characteristics near the time of landfall
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Hurricane Ivan was a long-lived Category 5 hurricane, according to the Saffir-Simpson Hurricane Wind Scale (NOAA/NWS 2012), which made landfall three times along the US Coast. It made the first landfall near Gulf Shores, Alabama, as a strong Category 3 hurricane around 0700 Coordinated Universal Time (UTC) on September 16, 2004, with 195 km/h winds. The impact of the associated storm surge was magnified by its coincidence with high tide. Hurricane Katrina was the costliest hurricane in US history and the deadliest and most destructive hurricane of the 2005 Atlantic hurricane season. Katrina approached the Mississippi shelf as a Category 5 hurricane before degrading to Category 3 when it made landfall at 1110 UTC on August 29, 2005, along the southern reach of the Mississippi River in Louisiana. Due to its especially large size and unique landfall location, Katrina brought massive damage and flooding to the City of New Orleans. Hurricane Rita was another Category 5 hurricane of the 2005 hurricane season and struck the Gulf coast a few weeks after Katrina’s landfall. Rita made landfall near the border between Texas and Louisiana on September 24, 2005, as a Category 3 hurricane with winds at 195 km/h and quickly weakened after the landfall. Hurricane Dolly was one of the few hurricanes that made landfall along the northwestern coast of the GoM and the second most destructive US hurricane that occurred in the month of July. Dolly made landfall on South Padre Island, Texas, at 1800 UTC July 23, 2008, as a Category 1 hurricane, with 140 km/h sustained winds.

Simulations of the storm surge induced by all four selected hurricanes were compared to observed water levels at NOAA tide stations that are closest to the hurricane tracks (or landfall locations) (Fig. 1). Modeled and observed storm surge heights were compared at two NOAA tide stations on both side of the hurricane track for all four hurricanes. Time-series comparisons of water levels during hurricanes are provided in Fig. 4. It can be seen in general that simulated water levels match the field observations reasonably well. The model captured the peak surge heights at most of the stations. It should be noted that observed data and model results only show about 2 m surge height for Hurricane Katrina (Fig. 4a) because Pilot’s Station East is far offshore from the location of maximum surge height, which occurred near the mouth of Bay St. Louis. Maximum surge heights of 8.45 m and 7.83 m were recorded at Pass Christian and Long Beach, respectively (http://www.wunderground.com/hurricane/surge_us_records.asp?MR=1), where the model hindcasted maximum surge heights of 8.01 m at Pass Christian and 7.58 m at Long Beach. The model underpredicted the peak surge height by about 0.4 m at Pilot’s Station East during Katrina (Fig. 4a). The misfit was mainly caused by two factors. The first was that the channel of Southwest Pass and the nearby levee were not very well represented in the model because of the grid resolution. The tide gage was located at the southeast end of the Pass and was subject to strong onshore wind that resulted in higher water levels along the shore during Hurricane Katrina. However, the nearest model grid point near the gage was off the south end of Southwest Pass and therefore the model under-predicted the surge height. The other factor is the uncertainty of the wind field. In this study, wind forcing was constructed based on a combination of H*Wind for an inner core region of 400 km radius and Holland wind for the outer region. The approach may lack the accuracy in the merging area between the inner and outer regions for large hurricanes, such as Katrina, in which sustained tropical-storm-force wind extended outward up to 370 km from the hurricane center (Graumann et al. 2005, Powell et al. 2010). Furthermore, three-hourly intervals of wind field may not be sufficient to accurately represent the temporal variations of hurricane wind forcing, as shown in studies by Dietrich et al. (2010, 2011), in which 30-min intervals of Katrina wind field were used. Although observed data were missing during the period of peak surge at Calcasieu Pass station because the tide gage was damaged during Hurricane Rita (Fig. 4b), post-hurricane surge level records indicated that the maximum storm surge height during Hurricane Rita was 4.57 m near the city of Calcasieu Pass, LA (http://water.weather.gov/ahps2/crests.php?wfo=lch&gage=capl1), which is close to the hindcasted maximum surge height of 4.27 m. There was no distinct surge signal in the observed data at Galveston Pleasure Pier during Hurricane Rita, but the model showed a small surge. The misfit was likely caused by the model grid resolution that was not fine enough to revolve the complex shoreline of Galveston Bay. There is also a possibility of errors in the data because of the irregular time history as shown in the right panel of Fig. 4b. Similarly, the model failed to capture the slowly dropping water level after the landfall of Hurricane Ivan (Fig. 4c) because the model grid was not able to represent the tide gage location at the northeast side of Dauphin Island, which was subject to offshore wind after hurricane landfall. Clearly, model results can be further improved by refining the model grid, especially near the tide gage locations. But the resolution is sufficient for the purpose of this study, which emphasizes the effects of storm surge, sea-level rise, and subsidence on coastal inundation. Simulated storm surge heights during Hurricane Dolly matched the observed data well although model results were slightly lower than the data at Corpus Kristi Station (Fig. 4d).

Fig. 4
figure 4

Comparison of modeled and observed storm surge levels during hurricane events a Katrina; b Rita; c Ivan; and d Dolly. Note: Some data were not available due to damage of tide gage at Calcasieu Pass, LA, during Hurricane Rita and Pensacola, FL during Hurricane Ivan

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Figure 5 shows snapshots of wind fields and simulated water levels during Hurricane Katrina. As one can see, the spatial distributions of water level height are closely correlated with the wind field. For instance, higher storm surge tends to develop at the right side of the hurricane track where the wind speed is strongest and wind direction is toward the shore. In contrast to the left side of the hurricane track, water level is lowered as winds blow the water offshore. Figure 5a, b shows the Hurricane Katrina wind field and induced surge height at 0600 UTC August 29, 2005, 6 h before landfall. As Hurricane Katrina approached the shore, water level was elevated on the east side of the Mississippi River delta (right side of Katrina track) and decreased on the west side of the river (left side of Katrina track). When Katrina made landfall at 1200 UTC August 29, 2005 (Fig. 5c), strong onshore winds occurred in the coastal region east of the Mississippi River delta, resulting in storm surge height over 6 m during the landfall (Fig. 5d).

Fig. 5
figure 5

Hurricane Katrina wind field and induced storm surge along the eastern Louisiana coast at 0600 UTC, Aug 29, 2005 (a, b) and 1200 UTC, Aug 29, 2005 (c, d). Water level is referred to NAVD88

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Compared to Hurricane Katrina, the speed of Hurricane Rita was much slower as it approached the northern coast of the Gulf. Figure 6a, b shows the Hurricane Rita wind field and induced surge height at 1200 UTC September 23, 2005. Although it was about 20 h before landfall, water started to surge along the western Louisiana coast (Fig. 6b). During the landfall of Hurricane Rita around 0730 UTC September 24, 2005 (Fig. 6c), strong storm surge occurred in a broad area along the western Louisiana coast as a result of strong onshore (northward) winds (Fig. 6d). To the left side of the hurricane eye, water level along the coastline was actually suppressed by the offshore winds. It is also seen that large areas were inundated along eastern Texas and western Louisiana coasts during Hurricane Rita’s landfall (Fig. 6d) in comparison with the condition before landfall (Fig. 6b).

Fig. 6
figure 6

Hurricane Rita wind field and induced storm surge along the western Louisiana coast at 1200 UTC, Sept 23, 2005 (a, b) and 0730 UTC Sept 24, 2005 (c, d). Water level is referred to NAVD88

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3.3 Effects of SLR and land subsidence

To evaluate the effects of global SLR and localized land subsidence on coastal inundation during storm surge events in the GoM, sensitivity simulations were conducted based on the projections of SLR and subsidence rates described in Sect. 2.4. Three sensitivity runs were conducted, including SLR only, subsidence only, and combined SLR and subsidence. To simulate the effect of global SLR, we used the approach by Mariotti et al. (2010) and Mousavi et al. (2010) to superimpose the rate of 1-m rise by the end of the century on tidal elevations at the open boundaries. The effect of land subsidence was simulated by modifying the model bathymetry to reflect the land subsidence, with the assumption that subsidence rates along the Louisiana coast by the end of the century remain the same as those for the next 50 years estimated by CPRA (2012). Figure 7 shows the change of model bathymetry in the Mississippi River delta between the baseline and the subsidence condition. A substantial change in water depth and water coverage area as a result of land subsidence can be seen. This change could have broader impact on coastal inundation because it not only affects the subsidence areas but also makes adjacent upland regions more vulnerable to coastal flooding. For all the sensitivity runs, the same wind and pressure forcing of Hurricane Katrina used in the baseline condition were applied.

Fig. 7
figure 7

Comparison of bathymetry height between baseline (a) and subsidence condition (b). The circles labeled with A, B, and C denote the three sites for subsequent water level analysis in Figs. 10, 11, and 12

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Figure 8a–c shows the coastal storm surge height and inundation area for scenarios of SLR, subsidence, and combined SLR and subsidence under the same wind forcing as Hurricane Katrina. Compared to the baseline condition (Fig. 5c), water level and inundation area for the 1-m SLR scenario increase significantly in the entire Mississippi Delta region (Fig. 8a). However, for the subsidence scenario (Fig. 8b), although more areas are inundated due to land subsidence, water level on the west side of the delta and hurricane track (Fig. 1) actually becomes lower than the baseline condition because strong offshore wind blows the water offshore such that the water level is close to the subsided water bottom, which is lower than the baseline condition. For the combined SLR and subsidence scenario (Fig. 8c), water level on the east side of the delta and hurricane track increase even more than in the SLR scenario because more water is available to be pushed toward the shore by the onshore hurricane wind. On the other hand, water level on the west side of the delta and hurricane track is lower than the SLR scenario, similar to the result for the subsidence scenario due to the same mechanism of strong offshore wind.

Fig. 8
figure 8

Simulated hurricane-induced coastal inundation for a SLR scenario, b subsidence scenario, and c combined effect of SLR and subsidence. Water level is referred to NAVD88

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To better illustrate the changes of coastal inundation between a sensitivity run and the baseline condition, the change of inundation depth (ΔD inund) at a model grid node was used in the analysis, and is defined as follows:

$$\varDelta D_{\text{inund}} = \left\{ {\begin{array}{*{20}c} {\varDelta D - \varDelta h} & {\text{if a node is wet in both runs}} \\ { 0 } & {\text{if a node is dry in both runs}} \\ {\varDelta D} & {{\text{if a node is dry in one of the runs}} } \\ \end{array} } \right.$$
(13)

where ΔD is the difference of total water depth between the sensitivity run and the baseline condition at the grid node; Δh is the difference of bathymetry height between the sensitivity run with subsidence effect and the baseline condition. Based on the definition (Eq. 13), one can see that ΔD inund represents the net change of inundation depth at a model grid node between the sensitivity run and the baseline condition.

The spatial distributions of change of inundation depth (ΔD inund) near the Mississippi River delta for the three sensitivity runs were calculated to illustrate the effects of SLR and land subsidence on coastal inundation (Fig. 9). Figure 9a, b shows the distribution of ΔD inund for the 1-m SLR scenario at 6 h before the landfall and at the time of landfall. In most of the areas, especially offshore, ΔD inund is very close to 1 m, which is primarily attributed to the 1-m SLR imposed at the open boundaries. However, in shallow areas near the delta, ΔD inund shows substantial spatial variations caused by the hurricane wind field and nonlinear effects. In general, water tends to pile up to the east side of the Mississippi River, corresponding to the onshore wind direction, as indicated by areas with ΔD inund > 1 m. In comparison with the west of the Mississippi River, water is pushed away offshore, as indicated by areas with ΔD inund < 1 m. As the hurricane approaches landfall (Fig. 9b), the change of inundation depth (ΔD inund) becomes even larger and occurs in more areas near shore, as compared to the condition 6 h before landfall (Fig. 9a). In contrast, the change of inundation depth (ΔD inund) for the subsidence scenario during the hurricane event is close to zero in most of the deep area in the Mississippi Delta (Fig. 9c, d). However, local variations of inundation depth are seen in the shallow region where inundation depth tends to increase on the east side of the hurricane track and decrease on the west side of the track.

Fig. 9
figure 9

Simulated change of inundation depth. Upper panels: 1-m SLR scenario at a 6 h before hurricane’s landfall and b during hurricane’s landfall. Middle panels: subsidence scenario at c 6 h before hurricane’s landfall and d during hurricane’s landfall. Lower panels: scenario with combined effect of 1 m SLR and land subsidence at e 6 h before hurricane’s landfall and f during hurricane’s landfall

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The change of inundation depth (ΔD inund) shows even stronger nonlinear response to the combined effect of SLR and land subsidence (Fig. 9e, f) in comparison with the SLR scenario (Fig. 9a, b). The combined effect of global SLR and subsidence substantially increased the total water depth in many areas that are either very shallow or even dry in the baseline condition (see also Fig. 7). The increase in water depths as well as in wetting areas intensify the storm surge potential and results in greatly increased inundation depth in shallow regions that are subject to strong onshore winds during the hurricane. As seen in Fig. 9e, f, inundation depths in the nearshore regions (e.g., Lake Pontchartrain) increase significantly both at 6 h before and during the hurricane’s landfall. It should be pointed out that the severity of inundation in the Lake Pontchartrain area may be over-predicted due to the lack of sufficient grid resolution to resolve the fine-scale levee structures in the model.

To evaluate the effects of SLR and subsidence on the temporal evolution of storm surge and coastal inundation, time series of water levels are compared between sensitivity runs and the baseline condition at three sites around the Mississippi River delta. As shown in Fig. 7, Site A is located offshore with water depth greater than 100 m. Site B is within the intertidal zone on the east side of the Mississippi River and the hurricane track, a region that experienced strong surge during hurricane landfall. In contrast, Site C is located in a shallow embayment to the west of the Mississippi River and experienced water set down during hurricane landfall.

Figure 10a–c shows the time series of water levels between baseline and SLR scenarios and their differences at Sites A, B and C. Clearly, at the offshore Site A (Fig. 10a), water level for the 1-m SLR scenario basically equals to the sum of the baseline water level and the 1-m SLR that was imposed at the open boundaries, indicating a linear relationship between SLR scenario and baseline conditions in the offshore region. In contrast, storm surge heights at Sites B and C show strong nonlinear responses to the effect of SLR. At Site B (Fig. 10b), there is a noticeable phase difference in the peak surge between the baseline and SLR conditions. Under the SLR condition, the surge wave propagated slightly faster than that in the baseline condition, presumably due to the increase in water depth from SLR. As indicated by the time-series difference of water levels in Fig. 10b, the effect of 1-m SLR also resulted in a greater increment of inundation depth (nearly 2 m) at Site B before the hurricane landfall, which is consistent with the horizontal 2-D plot of the change of inundation depth (ΔDinund > 1 m, as shown in Fig. 9a, b). Compared to Site B, the water level at Site C is reduced nearly to the baseline level because Site C is on the west side of the hurricane track where water mass is being blown away by the strong offshore wind, resulting in a water level close to the baseline condition despite the 1-m sea-level rise. Consequently, the water level differences between the baseline and SLR conditions were smaller than 1 m and even close to 0 during the landfall period.

Fig. 10
figure 10

Comparisons of water level time series at Sites A (a), B (b), and C (c) between baseline condition and 1-m SLR. The vertical black lines denote the hurricane’s landfall time around 11 a.m

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Figure 11a–c shows the time series of water levels between the subsidence scenario and baseline condition at Sites A, B, and C. Again, change in water level at Site A is nearly zero (Fig. 11a). At Site B (Fig. 11b), the peak of the surge level happens earlier than the baseline condition, likely caused by faster wave propagation speed in deeper water, resulting in a large increase in inundation depth right before landfall and decrease right after landfall. At Site C (Fig. 11c), water level drops even below the baseline condition because Site C is not only in the offshore wind region, similar to the condition of the 1-m SLR scenario, but also in the subsidence region where bathymetry height is lower than the baseline condition. Therefore, water level is further set down by the hurricane wind. These results are consistent with the 2-D distribution of water level (Fig. 8b) and change in inundation depth shown in Fig. 9c, d.

Fig. 11
figure 11

Comparisons of water level time series at Sites A (a), B (b), and C (c) between baseline condition and subsidence scenario. The vertical black lines denote the hurricane’s landfall time around 11 a.m

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Time-series distribution of water levels for the scenario of combined SLR and subsidence at Site A (Fig. 12a) has a pattern similar to that of the SLR-only and subsidence-only scenarios. However, water level at Site B is much more elevated, and the phase shift of peak surge becomes more evident due to the combined effects of SLR and land subsidence (Fig. 12b) in comparison with the SLR-only or subsidence-only scenarios (Figs. 10b, 11b). Water level differences are generally larger than 2 m at Site B for the period prior to the hurricane’s landfall. At Site C, although water level in the combined SLR and subsidence scenario is generally higher than the baseline condition due to the combined effect of SLR and land subsidence, it still drops below the baseline level after the hurricane’s landfall (hours 13–15 in Fig. 12c), as a result of lower bathymetry height and the strong offshore hurricane wind.

Fig. 12
figure 12

Comparisons of water level time series at Sites A (a), B (b), and C (c) between baseline condition and the scenario with combined effects of 1-m SLR and land subsidence. The vertical black lines denote the hurricane’s landfall time around 11 a.m

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Model results shown in Figs. 10 and 12 suggested that the effects of SLR and subsidence can exacerbate the storm surge height, the timing of the peak surge, and inundation areas in the nearshore regions during a hurricane. The response of storm surge and coastal inundation to these effects is nonlinear and varies temporally and spatially. However, in the offshore deep-water regions, the effect of subsidence on storm surge is negligible and the effect of SLR is just a linear addition to the storm surge height.

4 Summary

In an effort to understand the effects of global SLR and local subsidence on coastal inundation during extreme storm surge events, an unstructured-grid coastal ocean model, FVCOM, was applied to simulate tides and hurricane-induced storm surges in the northern GoM. A series of sensitivity runs were also conducted to further evaluate the effects of SLR and subsidence on coastal inundation. The comparisons of model results to field observations for four selected historical hurricanes (Katrina, Rita, Ivan, and Dolly) demonstrated that the model can simulate tides and storm surges reasonably well in the GoM. Model results suggested that storm surge height and coastal inundation induced by hurricanes could be exacerbated by future global SLR and land subsidence. Effects of global SLR and land subsidence on storm surge and coastal inundation are highly nonlinear and vary on temporal and spatial scales, which could either increase or reduce the inundation depth substantially, depending on the location of the coastal zone relative to the hurricane track.

While this study presents interesting and important findings about the effects of SLR and land subsidence on coastal inundation during storm surge events, the model can be improved to increase the accuracy of storm surge prediction in the northern Gulf coast and reduce the uncertainties of the findings. For example, the model grid resolution can be further refined to better represent the coastal features, such as channels, embayments, and barrier islands, which are important to the accuracy of prediction of storm surge height and inundation area (Dietrich et al. 2010). Wave effect was not included in this study. Consideration of wind-driven wave interaction with storm surge in model simulation would improve the prediction of storm surge as suggested by Sheng et al. (2010) and Dietrich et al. (2011). Tidal boundary conditions were specified using XTide in this study. It is necessary to explore different tidal models (such as ADCIRC and TPXO) for further improvement of boundary conditions and accuracy of tide prediction in the Gulf. Finally, hurricane track and wind field are the most important forcing mechanisms but also the major sources of uncertainty for storm surge prediction. The time intervals of NOAA/HRD H*Wind (3 h) and hurricane track data (6 h) are generally not fine enough to capture sufficient detail in temporal variations of wind fields and will affect the accuracy of storm surge simulations. In addition, although the Holland method has been widely used in hurricane-induced storm surge simulations, it may be overly simplified in the region outside the core of hurricane. Different methods for improving hurricane wind fields can be explored in future study, such as optimization and data assimilation techniques (Dietrich et al. 2011), atmospheric model simulations (Davis et al. 2008), and parametric hurricane wind models (Shen et al. 2006; Chen et al. 2011).