Geophysical Research Letters

On the importance of the forward speed of hurricanes in storm surge forecasting: A numerical study

Authors


Abstract

[1] A systematic investigation of storm surge along the coast of Louisiana was conducted by using the fully nonlinear Finite-Volume Coastal Ocean Model. FVCOM was first applied to Hurricane Rita and validated by in situ measurements. Experiments were conducted with different parameters to evaluate the impacts of each factor on inundation over a wide and shallow shelf. Results show that a hurricane's forward speed is a significant parameter which has been overlooked in previous studies. Resonance may occur for certain hurricane forward motion speeds: increasing this speed increases peak surge heights while decreasing inland volume of flood. The effects of wind intensity, Radius of Maximum Winds, tidal timing, amplitude, and wind inflow angle were also examined. It was concluded that varying a storm's forward motion may account for variations in flooded volumes equivalent to an upgrade or downgrade of about 1 category on the Saffir-Simpson scale.

1. Introduction

[2] A storm surge is an abnormal variation in the sea surface height caused by atmospheric forcing associated with extra-tropical cyclones or tropical storms such as hurricanes and typhoons [Flather, 2001]. Storm surges can cause severe damage to property and loss of lives. In the Gulf of Mexico (GoM), a hurricane flooded Galveston Island, Texas in 1900 with the loss of over 6000 lives [Blake et al., 2006]. Hurricane Katrina's storm surge in August 2005 exceeded 10 m in several locations along the Mississippi coast and became the costliest hurricane to ever strike the USA, resulting in the death of over 1000 people in Louisiana and 200 in Mississippi [Blake et al., 2006].

[3] Major destructive storm surges tend to occur when extreme storm winds act over extensive regions of shallow water. This is because in the governing equations the wind stress term is divided by the total depth, whereas the surface pressure gradient force is not – wind forcing thus increases in importance over shallower water [e.g., Flather, 2001]. Since it is the wind stress that generates most of the total hurricane-induced storm surge in coastal seas [e.g., Kohno et al., 2007], many numerical studies do not include the atmospheric pressure term at all [Chu et al., 2000; Dube et al., 2005]. We are only investigating the effects of the conventional long wave storm surge, and do not include short surface waves. Whereas faster surface flows reduce the air-sea momentum transfer rate (thereby reducing surge), bottom-layer return currents produce a shoreward bottom stress that adds to the wind stress (enhancing surge). These complex opposing effects due to waves depend strongly on local bathymetry [Resio and Westerink, 2008].

[4] Linear theory predicts that the ocean's response to an atmospheric traveling disturbance is proportional to (1-U2/gh)−1, i.e. when the speed of the traveling disturbance, U, is very close to that of the propagation of a long wave, there is resonance and the elevation becomes very large [Proudman, 1953]. Jelesnianski's [1972] numerical experiments with a standard hurricane over representative shelves suggested that a “critical speed” exists, greater than 30 mph (13.4 m/s), which gives the highest possible surge. Peng et al.'s [2004] numerical experiments on a North Carolina estuary suggested that both storm surge heights and inundation areas decreased as hurricane translation speed increased (for 1.74–13.88 m/s). Peng et al. [2006a], using a modified inundation scheme, concluded for Charleston Harbor in South Carolina that while slower hurricanes invariably induce greater inundation areas, whether or not they induce higher storm surges depends on their track and speed (only 5.07 and 10.14 m/s were tested). Irish et al. [2008] created an idealized, straight coastline basin representing the northern GoM with different slopes to investigate the effect of varying storm sizes on coastal peak surges. They also varied the storm motion (2.6–10.3 m/s) and concluded that for moderate bottom slopes a 50% increase in forward speed translates to a 15–20% increase in peak surge.

[5] Hurricane Rita attained Category-5 status and peak sustained winds of 280 km/h within 24 hours after entering the GoM. The barometric pressure reached 895 mbar, the third-lowest ever recorded for a tropical system in the Atlantic Basin at that time. It moved ashore as a Cat-3 hurricane near the Louisiana-Texas border at about 8am UTC, September 24, 2005 with sustained winds of 195 km/h. Hurricane Rita generated a substantial storm surge east of its landfall that reached 5–6 m, then weakened rapidly as it continued northward [Knabb et al., 2006].

[6] This paper applies the FVCOM to Hurricane Rita's storm tide (the total height of the surge plus the astronomical tide) over the Louisiana-Texas shelf with a successful validation. Hurricane Rita was chosen for two reasons: the relatively simple coastline and shelf geometry of the landfall area (allowing for a simplified, quasi-idealized look into surge results) and the unique dataset from the USGS, which recorded flooding along the southwest Louisiana coast (permitting the report of differences to a “base case” that is fully validated against observations). Our conclusions are thus representative of powerful hurricanes over mild slopes, impacting low-lying coasts consisting of marshes and inland lakes. Among other parameters, we focus on the impact of the forward speed of the hurricane, a factor that has been overlooked in previous studies.

2. Methods

[7] We use the time-dependent FVCOM [Chen et al., 2003] to simulate tide and storm surge. FVCOM uses a non-overlapping unstructured triangular grid in the horizontal to resolve dynamics in complex regions, and solves the primitive equations by using a flux calculation integrated over each model grid control volume, ensuring mass, momentum, energy, salt, and heat conservations in individual control volumes and over the entire computational domain. The flooding/drying process in FVCOM is simulated using an unstructured wet/dry point treatment technique in which a viscous boundary layer is added into the model at the bottom to avoid the occurrence of singularity when the local water depth approaches zero. The bottom stress is computed using equation imageB = Czρwequation imageBequation imageB, where ρw is the water density, equation imageB is the near-bottom water velocity, and Cz is a bottom drag coefficient determined by matching a logarithmic bottom layer to the model at a height of the first sigma level above the bottom [Chen et al., 2003]. FVCOM has been tested against other well-established models and is being widely used in coastal ocean circulation studies [Li et al., 2008; Huang et al., 2008] and also in surge applications [Weisberg and Zheng, 2008; Rego and Li, 2009].

[8] Our model domain extends from the Mexico-U.S.A. border to Apalachicola Bay in Florida. A total of 178,675 triangular cells comprise the horizontal, with 2 sigma layers in the vertical. Mesh resolution increases from 10 km on the open boundary toward the region of Hurricane Rita's impact; the finest resolutions (200 m) are on coastal passes that connect the area's major lakes to the GoM. Bathymetry data is a combination of the NGDC's US Coastal Relief Model, the ETOPO-2 Global Relief model and Louisiana State University's (LSU) LIDAR Atlas. The model was forced by wind stress and tides.

[9] Following J. L. Rego and C. Li (The effect of tides and shelf geometry on storm surge: Numerical model experiments for Hurricane Rita, submitted to Journal of Geophysical Research, 2009), we use the parametric wind model by Holland [1980] fitted to NOAA's observed wind speed data [Powell et al., 1996]. Jelesnianski's [1972] “correction” accounts for the asymmetry due to the forward motion of a hurricane (increasing the wind speed in the right quadrants). Another parameter is the inflow angle, which previous authors have argued to have negligible [Johns et al., 1985], important [Peng et al., 2006b], or complex effect on storm surge [Phadke et al., 2003]. Here we set this angle to 10° on the “standard” hurricane simulations. A wind vector is then assigned to all cells in the domain as a function of the radial distance. The surface wind stress is computed from equation imageS = Cdρaequation imageWequation imageW, where ρa is the air density, equation imageW is the wind speed at 10 m height, and Cd is a drag coefficient dependent on wind speed, assumed constant when equation imageW > 25m/s [Large and Pond, 1981]. Powell et al. [2003] and Jarosz et al. [2007] suggest that Cd decreases for equation imageW > 40m/s, by about 15–20%. However, these authors recommend conflicting values for Cd with 20 < equation imageW < 40m/s winds. Given this lack of consensus, and given that our sensitivity analyses using Powell et al.'s [2003] strong winds correction showed little effect on surge results, Large and Pond [1981] is used.

[10] Tidal constituent were obtained from 14 NOAA tidal stations and three Coastal Studies Institute (CSI-LSU) WAVCIS stations. The model was initially forced at its open boundary by 9 tidal constituents obtained from Mukai et al. [2002] and run without wind forcing for 36 days. Calibrating FVCOM for this application consisted of varying the bottom friction coefficient, constant in the entire domain; the best results are obtained with Cz = 0.0040 (Rego and Li, submitted manuscript, 2009). The errors for tidal phase are small and rarely exceed one hour for all stations and all constituents, in a region where tides have a 24 h period. Typical amplitude prediction error is about 0.01 m for the largest constituents, O1 and K1. Overall the tidal predictions are very satisfactory.

[11] Observations by McGee et al. [2006] provided data for Hurricane Rita's storm tide validation. Comparison between FVCOM results and USGS water levels for coastal stations on central Louisiana demonstrated very good matches (Rego and Li, submitted manuscript, 2009). Peak amplitude errors are typically ± 0.20 m, for a storm tide of 3.5–4.5 m, suggesting a 5% error. With respect to timing, coastal results are also very good and the typical situation is a ± half hour shift. Inland stations have slightly larger errors; either peak elevations are overestimated or the peak arrives too early, but in most stations only one of these issues is a problem. Hindcast simulations of Hurricane Rita using SLOSH and ADCIRC had similar inland issues, which were attributed to the inability of models to account for differences in bottom friction between water and marsh [URS Group, 2006]. Our results also show good agreement with other published work on Hurricane Rita's inundation [Federal Emergency Management Agency, 2008; Berenbrock et al., 2009].

[12] Upon a successful representation of Rita's storm tide, storm surge dynamics and coastal inundation are studied. Different scenarios are simulated in which 5 major parameters are varied: (1) wind intensity, (2) Radius of Maximum Winds (RMW), (3) landfall timing relative to the tide, also varying the tidal amplitude, (4) forward speed and (5) wind inflow angle (Table 1). In addition to these simulations, a “standard” simulation representing the observed Hurricane Rita (i.e., 100% intensity and RMW, ∼5 m/s forward speed, 10° inflow angle) without tidal forcing is run. Wind intensity is varied in 15% increments (used here to represent a one-category difference in the Saffir-Simpson scale); since Rita was a very powerful hurricane, a 7.5% increase is also tested. Hurricane Rita was a medium-size hurricane while over the shelf, and RMWs are varied in larger, 25% increments. Storm tide is simulated with hurricane landfalls forced at high and low tides, having the observed tidal amplitudes of about 0.33 m (B and C, respectively, on Table 1), and with tides having twice the observed amplitudes (A and D, respectively). The hurricane's forward speed is varied from very slow (2 m/s) to very fast (12 m/s). The tested inflow angles (0 to 40°) reflect typically used values. The mesh, bathymetry and hurricane track are the same in all 21 hurricane simulations.

Table 1. Parameters Used in the Experimentsa
 ABCD
  • a

    Changes relative to the base case.

Intensity (relative to H. Rita)70%85%107.5%115%
RMW (relative to H. Rita)50%75%125%150%
Tide: Landfall timing and forced amplitudeHigh, 2x Amp.High, Obs. Amp.Low, Obs. Amp.Low, 2x Amp.
Forward speed2 m/s3.5 m/s8 m/s12 m/s
Wind vector inflow angle20°40°

3. Discussion

[13] Total inundation volumes are computed using maximum inundation heights for each model cell in an area-weighted sum for all land cells affected by the hurricane. Given FVCOM's proven wetting and drying module, these volumes and maximum heights can be used to compare the effects of varying the parameters in Table 1. Maximum inundation maps (Figure 1) illustrate flooding extent and distribution of surge amplitudes. Total volumes are summarized on Figure 2a for all 5 × 4 simulations, compared to the “standard” run representing Hurricane Rita without tide (dashed line). Figure 2b shows peak surge heights, which depend to some extent on where the right-sided RMW hits land.

Figure 1.

Maximum inundation maps for hurricanes having forward speeds of (a) 2 m/s, and (b) 12 m/s. Track shown as dashed line. Inset shows location on regional map.

Figure 2.

(a) Total flooded volumes and (b) maximum surge heights. Bars show results for scenarios A, B, C and D (Table 1). Dashed line indicates “standard” run values.

[14] The effect on total flooded volumes of varying wind intensity and RMW is the largest (Figure 2a). They are also similar in magnitude, indicating that a 70–115% change in intensity is roughly equivalent to a 50–150% change in RMW (the chosen test range). For both parameters, scenarios A and D yield about 3 and 22 km3, respectively, whereas the standard case floods about 14 km3. Increasing each parameter also results in the increase of both volumes and peak heights (Figure 2b). Varying wind intensity has a more significant impact on peak surges (2.9–6.3 m) as compared to varying the RMW (3.6–5.6 m). Flooded volumes peak for about 125% of the observed Hurricane Rita's RMW. In this application, a 25% larger RMW means that the strongest winds act on an area of convergence (near Calcasieu Pass), enhancing local peak surges but having little influence on overall flooding. Tidal timing also affects flooded volumes and peak surges in the same manner: hurricanes landfalling at high tide yield both greater flooded volumes and peak surges than those landfalling at low tide. Variations in this case are only about ±16% of the “standard” volume (Figure 2a). Tide-surge nonlinearity decreases the impact of high- or low-tide landfalls: peak storm tides for high tide and double high tide should be greater than the no-tide case by about 0.33 and 0.66 m (the tidal amplitude) and they are not. This is because nonlinear tide-surge interaction is stronger during low-tide and peak surge, opposing the tidal signal by up to 70% on the Louisiana-Texas shelf (Rego and Li, submitted manuscript, 2009).

[15] Conversely, varying a hurricane's forward speed and wind inflow angle have opposite effects on flooded volumes and peak surge elevations. Increasing the forward speed from the standard value decreases flooded volumes (by up to 40%) while increasing peak surges (by up to 7%); decreasing the forward speed from the standard value increases flooded volumes (by up to 9%) while decreasing peak surges (by up to 30%) in the range considered. The same pattern holds for different inflow angles, albeit with an influence of only about 15% (Figure 2).

[16] The impact a hurricane's forward speed has on coastal flooding had not been recognized before and is shown to be very interesting: consistent with theory it has a significant positive effect on peak surge heights, but a significant negative effect on total maximum flooded volumes. A slower storm produces lower peak surges (below 4 m) that travel far inland (Figure 1a), whereas a faster hurricane will move swiftly across the shoreline generating higher surges (above 5 m) but flooding a relatively narrower section of the coast (Figure 1b). Slower hurricanes (here represented by 2 and 3.5 m/s speeds) are usually feared the most because, having considerable more time to impact coastal waters they tend to produce heavier flooding – which is consistent with our results. But considering highest surge elevations alone, faster hurricanes are shown here to be more dangerous, causing higher surges. Local surge curves have considerably different shapes depending on the hurricane's forward speed. For the Louisiana-Texas shelf, 5–12 m/s moving hurricanes produce higher, narrower surge curves, compared to those by 2–3.5 m/s moving hurricanes. A threshold separating broad and narrow surge curves is identified between 3.5 and 5 m/s, implying a representative depth of about 2 m [Proudman, 1953]. On this coast the 2 m isobath is typically 1000–3000 m offshore.

[17] These are significant results, as the effect of hurricanes' forward speed is typically overlooked in surge studies. Previous analyses focus mostly on the two major parameters: wind intensity and RMW. Some authors describe wind inflow patterns with more or less validation, whereas the timing of landfall (relative to the tide) is commonly mentioned as a source of added uncertainty (and most studies fail to address it). Here we show how a storm's forward motion speed is more important than the latter two factors, with a distinct effect on the coast: the slowest tested hurricane yields greater flooded volumes than the fastest (by up to 49%) while producing reduced peak surges (by up to 37%).

4. Concluding Remarks

[18] A systematic investigation of storm surge impact to the coast of Louisiana was conducted using FVCOM [Chen et al., 2003]. An application to Hurricane Rita's storm surge event is described, and flooding along the Louisiana-Texas coast is used for model validation. We then conduct idealized experiments to quantitatively evaluate the impacts of each parameter influencing coastal inundation over a wide and shallow continental shelf. The effects on total flooded volumes of varying wind intensity and RMW are the largest, and our results indicate that a 70–115% change in intensity translates approximately to a 50–150% change in RMW. For both variables, extreme scenarios yield total flooded volumes of about 25 and 160%, respectively, compared to the standard case. Landfall timing is another factor for which flooded volumes and peak surges vary together: those hurricanes landfalling at high tide yield both greater flooded volumes and peak surges than those landfalling at low tide. The variations in this case are smaller, about ±16% of the base case volume.

[19] Conversely, varying a hurricane's forward speed has opposite effects on flooded volumes and peak surge elevations. Increasing the forward motion speed of the storm decreases flooded volumes while increasing peak surges, by about 40%. Regarding surge levels, this is consistent with Irish et al.'s [2008] results on a northern GoM continental shelf, while contradicting Peng et al. [2004], who studied surges for the much narrower North Carolina shelf. These authors have not investigated variations in flooded volumes. We show that a slower moving storm produces lower peak surges that travel far inland, whereas a faster hurricane moves swiftly across the shoreline generating higher surges that flood a narrower section of the coast. We conclude that varying a storm's forward motion may account for variations in flooded volumes equivalent to an upgrade or downgrade of about 1 category on the Saffir-Simpson scale (Figure 2a), providing new insight into coastal surge dynamics. This represents a larger impact than tidal timing, amplitude, or wind inflow angle, more likely to be the focus of previous studies.

Acknowledgments

[20] The first author was funded by the Portuguese “Fundação para a Ciência e Tecnologia”, Doctoral Fellowship 28815/2006. Changsheng Chen (UMASS-Dartmouth) kindly shared the FVCOM code. Imtiaz Hossain (LSU's Shell Coastal Environmental Modeling Laboratory), helped with computational resources. Data from CSI's WAVCIS stations were used in part of the model validation. We also acknowledge the support of NSF (OCE-0554674), NOAA (NA06NPS4780197) for NGoMEX, and NOAA (NA06OAR4320264-06111039) to the Northern Gulf Institute.

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