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The Influence of Domain Size on the Response Characteristics of A JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 99, NO. C9, PAGES 18,467-18,479, SEPTEMBER 15, 1994 The influence of domain size on the responsecharacteristics of a hurricane storm surge model C. A. B lain and J. J. Westerink Departmentof Civil Engineeringand Geological Sciences, Universityof Notre Dame, Notre Dame, Indiana R. A. Luettich Jr. Universityof North Carolinaat ChapelHill, Instituteof Marine Sciences,Morehead City Abstract. The influenceof domainsize on boundarycondition specification and on computedstorm surge response is investigated.Storm surge response along the Florida shelf in the Gulf of Mexico dueto HurricaneKate is examinedover three domains using two differentopen oceanboundary forcing functions, a still water (or zero elevation)condition andan inverted barometer condition which accounts for the atmosphericpressure component of themeteorological forcing. The firstdomain is relativelysmall and is situatedprimarily on the continentalshelf in the regionof intensestorm surge generation. A seconddomain includesthe entire Gulf of Mexico basin. The final domain covers the Gulf of Mexico, contiguousbasins, and extends out into the deepAtlantic Ocean. The computedstorm surge responseindicates that the smalldomain is inadequate,since cross-shelf boundaries are in regionsof significantstorm surge generation where surge and therefore boundary conditions are not known a priori. Also, the behaviorof resonantmodes that are physicallyexcited within the Gulf of Mexico dueto the passageof the hurricaneis unknownat the boundaries of this smalldomain. The domainthat includes the entireGulf of Mexico capturesthe primary stormsurge well but may not correctlymodel resonant modes. In general,these resonantmodes are difficultto accuratelyset up by boundarycondition specification, since theymay be dependenton interactionsbetween the Gulf andcontiguous basins. The primary stormsurge response as well asresonant modes excited by the stormare bestrepresented usinga domainwhich encompassesthe westernNorth Atlantic Ocean,the CaribbeanSea, andthe Gulf of Mexico. This domainwith deepAtlantic Ocean boundaries facilitates simple boundarycondition specification and minimizes the influenceof boundaryconditions on stormsurge generation in coastalregions. Basin resonant modes and basinto basin interactionsare alsocaptured. Introduction systematicgrid convergencestudies for tidal, wind-driven,and large-scale baroclinic circulation [Le Provost and Vincent, Numerical modeling has become a widely used tool for 1986; Bennett and Campbell, 1987; Dietrich et al., 1990; assessingthe physicsof continentalmargin waters. It is impor- Piacsek and Allard, 1993; Dietrich, 1993; Westerink et al., tant to recognizethat the computedresponse of thesewaters is 1994]. The primary focus of this brief report is to investigate controlledby the variouscomponents which makeup a model, the influence of domain size on hurricane storm surge including the governingequations, the boundaryconditions, response. the forcing functions,the numerics,the grid structure,and the For this study,an actual hurricanethat made landfall on the computationaldomain itself. A major shortcomingin coastal Florida shelf in the Gulf of Mexico is applied over three oceanmodeling work is the lack of adequatestudies to prove domains.Each domain has a different size fanning out from convergencewith regard to grid structure,grid spacing,and the pointof hurricanelandfall and covering successively larger domainsize. As a result,it is oftenunclear whether computed regions.The first domain is a relatively small coastaldomain water body responsesare significantlyaliased due to inade- which extends mainly over the continental shelf. A second quate grid resolution or are overwhelmedby the imposed domain covers the entire Gulf of Mexico basin. The final boundaryconditions and their interactionswith the selected domain extends well into the deep Atlantic Ocean. Two domain. Only recently have there been efforts to establishthe different elevation boundaryconditions are consideredin the level to which the computedphysics has convergedby doing simulations, a still water condition and a condition that incor- porates the atmosphericpressure component of the meteoro- logical forcing. Comparisonsare made betweenstorm surge Copyright 1994 by the AmericanGeophysical Union. elevations computed over all three domains using both boundaryconditions to determinethe influenceof domain size Papernumber 94JCO 1348. and the sensitivity to boundary condition specificationon 0148-0227/94/94JC-O 1348505.00 storm surge response. 18,467 18,468 BLAIN ET AL.: INFLUENCE OF DOMAIN SIZE ON STORM SURGE RESPONSE Hydrodynamic Model Description whereps is thespatially and temporally varying pressure field, p is the pressure at the center or eye of the storm, eye _ The hydrodynamiccomputations were performed using Ap = p-p is the pressureanomaly with • taken as an eye ADCIRC-2DDI, the depth integratedoption of a set of two- average backgroundpressure, and r is the radial distance and three-dimensionalfully nonlinear hydrodynamiccodes outwardfrom the eye of the storm.The scaleradius, R, often named ADCIRC [Luettich et al., 1992]. ADCIRC-2DDI uses assumed equivalent to the radius to maximum wind, is the vertically averaged equationsof mass and momentum computedfrom an approximationof a nomographrelating R conservation,subject to the hydrostaticpressure approxima- to the maximum wind speedand the pressureanomaly, Ap tion. For the applicationsin this paper,we usedthe standard [Jelesnianskiand Taylor, 1973]. Wind speedcomputed within quadraticparameterization for bottomstress and neglected the the HURWIN model is obtained through a solution of the baroclinic terms, the finite amplitude terms, as well as the equationsof horizontal motion which have been vertically advectiveand lateral diffusion/dispersionterms, leading to the averagedthrough the depth of the planetaryboundary layer. following set of conservationstatements in primitive,noncon- Thesewind speedsare then convertedto surfacewind stresses servative form expressedin a spherical coordinate system usinga quadraticdrag law proposedby Garratt [1977]. [Kolar et al., 1994a]: For all simulationspresented in this brief report,Hurricane Kate is the historicalstorm that servesas the meteorological • + + ß = 0 (1) 3t Rcos0 [_•--•- (Vhcos0)1 forcing for the hydrodynamicmodel. The track of Hurricane Kate throughthe westernNorth Atlantic Oceanand the Gulf of 3U • - 2•sin 0V - Mexico is shown at 6 hour incrementsin Figure 1. The 3t Rcos•) 33• +g + HURWIN model simulationof HurricaneKate beganat 1800 UT November 15, 1985, and ended 8 days later at 1800 UT (2) November 23, 1985. During this periodthe forward speedof Poh HurricaneKate ranged from 1.5 m s-1 to 13.4m s-1 andthe radius to maximum wind varied between 80 km and 17 km. • +2f•sin•)U = +g + 3t R300 Throughoutthe HURWIN model simulation,a constantback- groundpressure of 1013 mbarwas assumed. All otherparame- s0 (3) ters pertaining to Hurricane Kate were obtained from the Poh HURDAT tape [Jarvinen et al., 1993] which documentsthe where t representstime, )•, 0 are degreeslongitude (east of movement and characteristics of historical hurricanes. Greenwichpositive) and degreeslatitude (north of the equator positive),• is the free surfaceelevation relative to the geoid, Hydrodynamic Domain Descriptions U, V are the depth-averagedhorizontal velocities, R is the Three hydrodynamicdomains of widely varied sizes are radiusof the Earth, h is the bathymetricdepth relative to the consideredin our investigation.The domainsizes are selected geoid,• is the angularspeed of theEarth, P s is the atmo- to clearly demonstratethe relationshipbetween the domain sphericpressure at the free surface,g is the accelerationdue to and open ocean boundaryelevation specification. The two gravity,P0 is the reference density ofwater, XsZ, Xs, are the smallerdomains are constructedto correspondwith domains appliedfree surfacestresses, and x. is givenby theexpression usedin recentstorm surge modeling efforts. All domainsused Cf(W2+V2) 1/2/h , whereCf equals the bottom friction here expandoutward from the landfall region of Hurricane coefficient. Kate nearPanama City, Florida,and cover increasingly larger Equations(1)-(3) are reformulatedinto a generalizedwave areas. The exact areal extent of each domain as well as other continuityequation (GWCE) and are subsequentlydiscretized characteristicspertinent to the domainsand their discretiza- using the finite element (FE) method[Lynch and Gray, 1979; tions are summarized in Table 1. Lynch, 1983; Kinnmark, 1984; Westerinkand Gray, 1991]. The smallest domain considered is the Florida coast domain ADCIRC-2DDI hasbeen implemented using linear, triangular picturedin Figure 2a. The Florida coastdomain is a semicir- finite elements. The details of ADCIRC-2DDI are described cular basin similar to the one used by the National Weather by Luettich et al. [1992], Kolar et al. [1994a,b], and Westerink Service at PensacolaBay in conjunctionwith the SLOSH et al. [1994]. It is notedthat shorelinewetting and/or drying is storm surge model [Jarvinen and Lawrence, 1985; not currentlyaccommodated in the code.In fact, near-drying Jelesnianski et al., 1992]. The Florida coast domain extends elementsrequire the linearizationswhich are appliedfor the radially outward into the Gulf of Mexico from the shoreline simulationsdescribed in this paper. surroundingPanama City, Florida, with a radiusof approxi- mately 175 km. The outer arc of the semicircularbasin forms Meteorological
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