Skip to main content
Log in

Simulation of the Hurricane Dennis storm surge and considerations for vertical resolution

  • Original Paper
  • Published:
Natural Hazards Aims and scope Submit manuscript

Abstract

A high-resolution storm surge model of Apalachee Bay in the northeastern Gulf of Mexico is developed using an unstructured grid finite-volume coastal ocean model (FVCOM). The model is applied to the case of Hurricane Dennis (July 2005). This storm caused underpredicted severe flooding of the Apalachee Bay coastal area and upriver inland communities. Accurate resolution of complicated geometry of the coastal region and waterways in the model reveals processes responsible for the unanticipated high storm tide in the area. Model results are validated with available observations of the storm tide. Model experiments suggest that during Dennis, excessive flooding in the coastal zone and the town of St. Marks, located up the St. Marks River, was caused by additive effects of coincident high tides (~10–15% of the total sea-level rise) and a propagating shelf wave (~30%) that added to the locally wind-generated surge. Wave setup, the biggest uncertainty, is estimated on the basis of empirical and analytical relations. The Dennis case is then used to test the sensitivity of the model solution to vertical discretization. A suite of model experiments is performed with varying numbers of vertical sigma (σ) levels, with different distribution of σ-levels within the water column and a varying bottom drag coefficient. The major finding is that the storm surge solution is more sensitive to resolution within the velocity shear zone at mid-depths compared to resolution of the upper and bottom layer or values of the bottom drag coefficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • As-Salek JA (1998) Coastal trapping and funneling effects on storm surges in the Meghna Estuary in relation to cyclones hitting Noakhali-Cox’s Bazar Coast of Bangladesh. J Phys Oceanogr 28:227–249

    Article  Google Scholar 

  • Bye JAT (1965) Wind-driven circulation in unstratified lakes. Limnol Oceanogr 10(3):451–458

    Article  Google Scholar 

  • Chen C, Liu H, Beardsley RC (2003) An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. j atmos ocea techn 20:159–186

    Article  Google Scholar 

  • Chen CS, Beardsley RC, Cowles G (2006) An unstructured grid, finite-volume coastal ocean model: FVCOM user manual. SMAST/UMASSD University of Massachusetts-Dartmouth, Technical report-06–0602. New Bedford, Massachusetts

    Google Scholar 

  • Chen C, Huang H, Beardsley RC, Liu H, Xu Q, Cowles G (2007) A finite volume numerical approach for coastal ocean circulation studies: comparisons with finite difference models. J Geophys Res 112(C03018):34. doi:10.1029/2006JC003485

    Google Scholar 

  • Eckart C (1952) The propagation of gravity waves from deep to shallow water. National bureau of standards. Circular 20:165–173

    Google Scholar 

  • FDEP (2006) Hurricane Dennis and Hurricane Katrina. Final report on 2005 hurricane season impacts to Northwest Florida, Florida department of environmental protection division of water resource management bureau of beaches and coastal systems, Florida

  • FEMA (2005) Hazard mitigation Technical assistance program contract N0. EMW-2000-CO-0247, task orders 403 & 405, Hurricane Dennis rapid response Florida coastal high water mark (CHWM) collection, FEMA-1595-DR-FL, final report, 19 Dec 2005. Federal emergency management agency, region IV, Atlanta, GA

  • Francis JRD (1953) A note on the velocity distribution and bottom stress in a wind-driven water current system. J Mar Res 12:93–98

    Google Scholar 

  • Gill A (1982) Atmosphere-ocean dynamics. Academic Press Inc, New York

    Google Scholar 

  • Guza RT (1974) Excitation of edge waves and their role in the formation of beach cusps. Dissertation, University of California

  • Hedges TS, Mase H (2004) Modified Hunt’s equation incorporating wave setup. J Waterway Port Coastal Ocean Eng 130(3):109–113. doi:10.1061/(ASCE)0733-950X

    Article  Google Scholar 

  • Jelesnianski CP (1965) A numerical calculation of storm tides induced by a tropical storm impinging on a continental shelf. Mon Wea Rev 93:343–360

    Article  Google Scholar 

  • Jelesnianski CP (1970) Bottom stress time history in linearized equations of motion for storm surges. Mon Weather Rev 98:462–478

    Article  Google Scholar 

  • Large WG, McWilliams JC, Doney SC (1994) Oceanic vertical mixing: a review and a model with nonlocal boundary layer parameterization. Rev Geophys 32:363–403

    Article  Google Scholar 

  • Longuet-Higgins MS, Stewart RW (1963) A note on wave set-up. J Mar Res 21:4–10

    Google Scholar 

  • Longuet-Higgins MS, Stewart RW (1964) Radiation stress in water waves, a physical discussion with application. Deep-Sea Res 11:529–563

    Google Scholar 

  • Luther ME, Merz CR, Scudder J, Baig SR, Pralgo LJ, Thompson D, Gill S, Hovis G (2007) Water level observations for storm surge. Marine Technol Soc J 41(1):35–43

    Article  Google Scholar 

  • Mattocks C, Forbes C (2008) A real-time, event-triggered storm surge forecasting system for the state of North Carolina. Ocean Model 25(3-4):95–119. doi:10.1016/j.ocemod.2008.06.008

    Article  Google Scholar 

  • Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problem. Rev Geophys Space Phys 20:851–875

    Article  Google Scholar 

  • Morey SL, Bourassa MA, Davis XJ, O’Brien JJ (2005) Remotely sensed winds for episodic forcing of ocean models. J Geophys Res 110:C10024

    Article  Google Scholar 

  • Morey SL, Baig S, Bourassa MA, Dukhovskoy DS, O’Brien JJ (2006) Remote forcing contribution to storm-induced sea level rise during Hurricane Dennis. Geophys Res Lett 33(19):L19603

    Article  Google Scholar 

  • Munk WH (1949) The solitary wave theory and its applications to surf problems. Ann N Y Acad Sci 51:376–462

    Article  Google Scholar 

  • Murty TS (1984) Storm surges - meteorological ocean tides. Friesen Printers Ltd., Ottawa

    Google Scholar 

  • Nihoul JCJ (1977) Three-dimensional model of tides and storm surges in a shallow well mixed continental sea. Dyn Atmos Oceans 2:29–47

    Article  Google Scholar 

  • Platzman GW (1958) A numerical computation of the surge of June 26, 1954, on Lake Michigan. Geophysica 6:407–438

    Google Scholar 

  • Powell MD, Houston SH, Amat LR, Morisseau-Leroy N (1998) The HRD real-time hurricane wind analysis system. J Wind Engineer Indust Aerodyn 77(78):53–64

    Article  Google Scholar 

  • Rao AD, Jain I, Ramana Murthy MV, Murty TS, Dube SK (2009) Impact of cyclonic wind field on interaction of surge–wave computations using finite-element and finite-difference models. Nat Hazards 49(2):225–239. doi:10.1007/s11069-008-9284-9

    Article  Google Scholar 

  • Resio DT, Bratos SM, Thompson EF (2002) Meteorology and wave climate. In: Vincent L, Demirbilek Z (eds) Coastal engineering manual part II, hydrodynamics, engineer manual 1110–2-1100, updated 2006, US. Army Corps Engineers, Washington

    Google Scholar 

  • Sherman D (2005) Dissipative beaches. In: Schwartz ML (ed) Encyclopedia of coastal science. Springer, The Netherlands, pp 389–390

  • Shewchuk JR (2002) Delaunay refinement algorithms for triangular mesh generation. Comput Geom 22(1–3):21–74

    Article  Google Scholar 

  • Smagorinsky J (1963) General circulation experiments with the primitive equations I. The basic experiment. Mon Wea Rev 91:99–164

    Article  Google Scholar 

  • Smith JM (2002) Surf zone hydrodynamics. In: Vincent L, Demirbilek Z (eds) Coastal engineering manual part ii, hydrodynamics, engineer manual 1110–2-1100, updated 2006, US. Army Corps of Engineers, D.C

    Google Scholar 

  • Smith ER, Kraus NC (1991) Laboratory study of wave-breaking over bars and artificial reefs. J Waterway Port Coastal Ocean Eng 117(4):307–325

    Article  Google Scholar 

  • Wang P, Kirby JH, Haber JD, Horwitz MH, Knorr PO, Krock JR (2006) Morphological and sedimentological impacts of Hurricane Ivan and immediate poststorm beach recovery along the northwestern Florida barrier-island coasts. J Coastal Research 22(6):1382–1402

    Article  Google Scholar 

  • Weggel JR (1972) Maximum breaker height. J Waterways Harbor Coast Eng Div 98(WW4):529–548

    Google Scholar 

  • Weisberg RH, Zhang LY (2008) Hurricane storm surge simulations comparing three-dimensional with two-dimensional formulations based on an Ivan-like storm over the Tampa Bay, Florida region. J Geophys Res 113(C12):C12001. doi:10.1029/2008JC005115

    Article  Google Scholar 

  • Weisberg RH, Zheng L (2006) Hurricane storm surge simulations for Tampa Bay. Estuaries Coasts 29(6A):899–913

    Google Scholar 

  • Welander P (1957) Wind action on a shallow sea: some generalizations of Ekman’s theory. Tellus 9:45–52

    Article  Google Scholar 

  • Young IR (1988) Parametric hurricane wave prediction model. J Waterways Harbor Coast Eng Div 114(5):637–652

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by funding through the NOAA Applied Research Center grant to COAPS and by a grant from the Florida Catastrophic Storm Risk Management Center. Special thanks to Dr. J. Shewchuk (UC Berkeley) for providing the code of the triangular mesh generator “Triangle” and to Dr. C. Chen (UMass Dartmouth) for his assistance with FVCOM. NCEP-Reanalysis 2 data were obtained from the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at http://www.cdc.noaa.gov/. Sea level and wind observations are from the NOAA National Data Buoy Center; observations of the ocean currents are from the NOAA NGI Station A. Drs. M. Powell (NOAA AOML) and M. Bourassa (FSU) helped with preparing wind fields used in this study. The authors acknowledge Meredith Field and Kathy Fearon (COAPS FSU), for helping with materials on FEMA high-water mark survey and editing the manuscript. The authors thank HPC FSU staff for providing technical support for numerous simulations on HPC facility.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dmitry S. Dukhovskoy.

Appendix 1. Wave setup estimation

Appendix 1. Wave setup estimation

Setup at the shoreline is given by (Smith 2002):

$$ \bar{\eta }_{S} = \bar{\eta }_{\text{b}} + \left( {1 + {\frac{8}{{3\gamma_{\text{b}}^{2} }}}} \right)^{ - 1} H_{\text{b}} , $$
(5)

where \( \bar{\eta }_{\text{b}} \) is setdown, \( \gamma_{\text{b}} \) is the breaker depth index, and H b is the wave height at incipient breaking. Setdown for regular waves can be estimated from (Longuet-Higgins and Stewart 1963):

$$ \bar{\eta }_{\text{b}} = - \frac{1}{8}{\frac{{H_{\text{b}}^{2} \kappa }}{{\sinh \left( {2\kappa d_{\text{b}} } \right)}}}, $$
(6)

where κ is the wavenumber and d b is the water depth at breaking. The breaker depth index is

$$ \gamma_{\text{b}} = {\frac{{H_{\text{b}} }}{{d_{\text{b}} }}} . $$
(7)

Another important index that relates the wave height at incipient breaking and the wave height over the deep water, H 0, is the breaker height index:

$$ \Upomega_{\text{b}} = {\frac{{H_{\text{b}} }}{{H_{0} }}} . $$
(8)

The breaker indices Eqs. 7 and 8 depend on beach slope, which can be estimated as an average bottom slope from the break point to one wavelength offshore (Smith 2002), and characteristics of the wave (Weggel 1972; Smith and Kraus 1991). Detailed surveys of the surf zone are necessary for measuring this parameter as the available bathymetric data are not of sufficiently fine resolution. Wang et al. (2006) measured the beach slope (β) at St. George Island to be 0.05–0.06, but it is expected to be <0.01 over mud and seagrass flats near the St. Marks River entrance and Shell Point. The following wave setup estimates are derived for the beach slope of 0.01.

For calculating wave setup, characteristics of the waves generated by a storm in deep water are required. Ideally, measurements of the wave height and period from buoys could be used for estimating the wave setup. Unfortunately, there are no wave measurements available over the northern WFS during Hurricane Dennis. Therefore, Young’s model (Young 1988) for fetch-limited waves is used to estimate the deep-water wave height (H 0) and the spectral peak period of the wave (T0):

$$ H_{0} = 0.0016{\frac{{w_{10}^{2} }}{g}}\left( {{\frac{gF}{{w_{10}^{2} }}}} \right)^{0.5} $$
(9)
$$ T_{0} = 0.045{\frac{{2\pi w_{10}^{{}} }}{g}}\left( {{\frac{gF}{{w_{10}^{2} }}}} \right)^{0.33} $$
(10)

where w 10 is 10-m wind speed and F is wind fetch.

Wind fetch is estimated on the basis of the procedure outlined in Resio et al. (2002). Away from the coast, fetch is defined such that wind direction variations do not exceed 15 degrees and wind speed variations do not exceed 2.5 m s−1 from the mean. If distance to the upwind coastline is smaller than the fetch, the coastline limits the fetch. Estimates of wind fetch (Fig. 14) have been obtained when the hurricane center is close to Apalachee Bay when the winds reach their local maximum over the Bay. There is uncertainty about what region should be considered for estimating deep-water wave characteristics. In this study, the following logic has been used to define the region (shown in Fig. 14) where deep-water waves traveling to Apalachee Bay are generated. One criterion is the region should be deeper than the half-length of the wind waves generated during the storm. Wind waves generated during a storm in this region are O(100 m); thus, the deep region is deeper than the 100-m isobath. Another criterion is that the waves should travel to Apalachee Bay. It is assumed that the peak wave direction matches the local wind direction. The maximum surge at the Apalachee Bay coast occurred between 19 and 21 UTC (Fig. 4), about 3–4 h after the time shown in Fig. 14. Over this time, a gravity wave can travel about 200–300 km (assuming the average depth to be 50 m). From the above discussion, a possible region of deep-water generation is identified (Fig. 14). Over this region, the wind field exhibits very low curvature of the wind streamlines, resulting in a long fetch in the range from 80 to 120 km with an average of 100 km.

Fig. 14
figure 14

Wind fetch (km) estimated by the method of Resio et al. (2002). The wind field used for estimating the fetch is shown by the overlaid vectors. The location of NOAA NDBC station 42036 is shown. Anticipated region where deep-water waves that travel to the Apalachee Bay region are generated is marked by the white dashed box

Wind fields used in the model experiment reveal that the maximum sustained wind over the WFS during Hurricane Dennis was in the range 20–25 m s−1 in agreement with FDEP (2006). The maximum sustained wind measured in this area (NOAA NDBC, buoy 42036, 28°30′0″N 84°31′0″W, location is shown in Fig. 14) was 23.5 m s−1. Therefore, Eqs. 9 and 10 estimate that deep-water wave height in the studied region is in the range from 3.2 to 4.04 m and wave period is from 7.6 to 8.2-s.

Analytically derived estimates of the deep-water wave characteristics can be compared with simulated wave fields at 18:00 UTC 10 July 2005, (closest instant to the time shown in Fig. 14), from the regional North Atlantic Hurricane (NAH) NOAA WAVEWATCH III model (http://polar.ncep.noaa.gov/waves) shown in Fig. 15. The deep-water waves are considered to be the waves in the water at least 100 m depth. On the basis of the simulated significant wave direction, a possible region from where deep-water waves could travel to Apalachee Bay and contribute to the wave setup during the maximum storm surge (2–4 h later) is identified (marked by the white solid box in Fig. 15). Note that location of the area agrees with the earlier defined area for wind fetch. In this area, the significant height of the deep-water wave is 3.5–5 m with the period of 8–9-s. The analytical estimates of the deep-water wave height and period are close to the characteristics of the simulated waves. It is noteworthy that the region of maximum wave heights is not in the model domain. According to NAH simulation, on that date and time, waves greater than 10 m height with the period of 10-s were to the west of the Apalachicola Bay and did not contribute to the wave setup along the coast of Apalachee Bay.

Fig. 15
figure 15

Significant wave height (left) and peak wave period (right) on July 10, 2005, at 18:00 UTC, from the regional NAH WaveWatch III wave prediction model of NOAA National Weather Service. Overlaid gray arrows are significant wave direction vectors. The dashed box roughly delineates the Apalachee Bay model domain. The solid box indicates anticipated region from where deep-water waves might have travelled to Apalachee Bay by the time of maximum storm surge

Wave length is derived from the approximate dispersion relation for the surface gravity wave (Eckart 1952):

$$ L_{0} \approx {\frac{{gT^{2} }}{2\pi }}\sqrt {\tanh \left( {\omega^{2} \frac{d}{g}} \right)} , $$
(11)

where ω is wave frequency and L 0 is the length of the deep-water wave. The estimated deep-water wave length generated by Hurricane Dennis in Apalachee Bay is 90 m to 104 m.

The breaker height index is estimated as (Munk 1949):

$$ \Upomega_{\text{b}} = 0.3\left( {{\frac{{H_{0} }}{{L_{0} }}}} \right)^{{ - {1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}} , $$
(12)

which, together with Eq. 8, gives the wave height at incipient breaking to be from 2.9 to 3.6 m. Following Weggel (1972), for regions with slopes less or equal than 0.1 and H 0/L 0 < 0.06, the breaker depth index is found as:

$$ \gamma_{\text{b}} = b - a{\frac{{H_{\text{b}} }}{{gT^{2} }}} $$
(13)

where a and b are empirically determined functions of the beach slope:

$$ \begin{aligned} a =\, & 43.8\left[ {1 - \exp \left( { - 19\beta } \right)} \right] \\ b = \,& 1.56\left[ {1 + \exp \left( { - 19.5\beta } \right)} \right]^{ - 1} \\ \end{aligned} $$
(14)

The breaker depth index is 0.81. With this, Eq. 7 provides the depth of breaking from 3.6 to 4.4 m. After substituting all required values into Eqs. 5 and 6, one gets the estimated setup from 0.44 to 0.54 m.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dukhovskoy, D.S., Morey, S.L. Simulation of the Hurricane Dennis storm surge and considerations for vertical resolution. Nat Hazards 58, 511–540 (2011). https://doi.org/10.1007/s11069-010-9684-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-010-9684-5

Keywords

Navigation