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Effect of Wave Forces on Storm Surge


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EFFECT OF W A VE F OR CES ON STORM SUR GE By R OBER T J. WEA VER A THESIS PRESENTED TO THE GRADUA TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQUIREMENTS F OR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2004

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Cop yrigh t 2004 b y Rob ert J. W ea v er

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I dedicate this to Jacqueline, Mo ose and Chaos.

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A CKNO WLEDGMENTS I w ould lik e to thank m y paren ts for encouraging me to pursue m y goals, giving their supp ort, and b eing there when I needed an ear to b end. Thanks to Jacqueline for k eeping me on trac k, and tolerating me when I w ould go o on a tangen t. I w ould lik e to ac kno wledge m y adviser, Donald Slinn, and m y committee mem b ers Rob ert Dean and Max Sheppard for their supp ort and advice. I w ould lik e to thank the National Oceanographic P artnership Program, NOPP partners for their help and con tributions. Sp ecial ac kno wledgmen ts to Rob ert Jensen at Engineer Researc h and Dev elopmen t Cen ter, ERDC, for his help with the w a v e elds, Scott Hagen at the Univ ersit y of Cen tral Florida, UCF, for his help in understanding the Adv anced Circulation Mo del for Coasts, Shelv es, and Estuaries (ADCIR C) and grid generation, as w ell as pro viding the tides for our use in the prediction. I w ould also lik e to credit Vince Cardone and Andrew Co x at OceanW eather, Inc. for pro viding the wind and pressure elds for our mo del prediction. iv

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T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . iv LIST OF T ABLES . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . viii ABSTRA CT . . . . . . . . . . . . . . . . . . x 1 INTR ODUCTION . . . . . . . . . . . . . . . 1 1.1 Surge Mo del . . . . . . . . . . . . . . . 2 1.2 Air{Sea Coupling . . . . . . . . . . . . . 3 1.3 A tmospheric Pressure . . . . . . . . . . . . 4 1.4 Coastal Bath ymetry . . . . . . . . . . . . . 5 1.5 Hurricane Sim ulation . . . . . . . . . . . . 7 2 METHODOLOGY . . . . . . . . . . . . . . . 9 2.1 Numerical Mo del . . . . . . . . . . . . . 9 2.2 Bath ymetric T ests . . . . . . . . . . . . . 13 2.2.1 Domain . . . . . . . . . . . . . . 13 2.2.2 F orcings . . . . . . . . . . . . . . 14 2.2.3 Implemen tation . . . . . . . . . . . . 17 2.3 Hurricane Georges Hindcast . . . . . . . . . . 18 2.3.1 Domain . . . . . . . . . . . . . . 19 2.3.2 F orcing . . . . . . . . . . . . . . 20 2.3.3 Implemen tation . . . . . . . . . . . . 22 3 RESUL TS . . . . . . . . . . . . . . . . . 24 3.1 Wind Stress . . . . . . . . . . . . . . . 24 3.2 Bath ymetric Sensitivit y . . . . . . . . . . . . 26 3.3 Hurricane Georges . . . . . . . . . . . . . 32 4 CONCLUSIONS . . . . . . . . . . . . . . . 45 4.1 Bath ymetry . . . . . . . . . . . . . . . 45 4.2 Hindcast . . . . . . . . . . . . . . . . 46 4.3 Signicance of W a v e Set-Up . . . . . . . . . . 47 v

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APPENDIXA BA THYMETR Y TEST-INPUT FILES . . . . . . . . . 48 A.1 W a v e Mo del Inputs . . . . . . . . . . . . . 48 A.2 Circulation Mo del Inputs . . . . . . . . . . . 51 B HINDCAST TEST CIR CULA TION MODEL INPUT FILES . . . 57 REFERENCES . . . . . . . . . . . . . . . . . 62 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . 64 vi

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LIST OF T ABLES T able page 2{1 Drag co ecien t form ulations to test mo del sensitivit y . . . . 10 2{2 Wind strength and w a v e heigh t for bath ymetric sensitivit y tests . 15 2{3 Mo del input domains . . . . . . . . . . . . . 22 3{1 Surge generated b y forcing comp onen ts o v er eac h b ottom prole . 28 3{2 Co ordinates of selected lo cations . . . . . . . . . . 35 vii

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LIST OF FIGURES Figure page 2{1 Proles created for bath ymetric sensitivit y tests . . . . . 14 2{2 Finite Elemen t Grid created for bath ymetric sensitivit y tests . . 15 2{3 W a v e elds from SW AN . . . . . . . . . . . . 16 2{4 F x from SW AN . . . . . . . . . . . . . . 17 2{5 North-W est A tlan tic Domain . . . . . . . . . . 19 2{6 Gulf Coast region of mo del domain . . . . . . . . . 20 2{7 Nested domains for w a v e eld data . . . . . . . . . 21 3{1 Drag co ecien ts plotted vs. wind sp eed . . . . . . . 24 3{2 Wind stress plotted vs. wind sp eed . . . . . . . . . 25 3{3 Surge proles for wind stress form ulations . . . . . . . 26 3{4 F output from SW AN . . . . . . . . . . . . 27 3{5 Surge lev els for eac h forcing group o v er eac h bath ymetry . . . 28 3{6 Comparison of Mo del results with analytic solution . . . . 30 3{7 Surface con tour plots as Georges crosses Gulf . . . . . . 32 3{8 Surface con tour plots for eac h forcing com bination at t=82 hours 33 3{9 Time series of maxim um surface elev ation . . . . . . . 34 3{10 Maxim um surge predicted at selected lo cations . . . . . 36 3{11 Surge at No de{13266:P erdido Ba y FL . . . . . . . . 37 3{12 Surge at No de{11043:Lak e Borgne, LA . . . . . . . . 38 3{13 NO AA station data for P ensacola Ba y FL . . . . . . . 39 3{14 Mo del results at P ensacola Ba y FL . . . . . . . . . 40 3{15 NO AA station data for W a v eland, MS . . . . . . . . 41 viii

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3{16 Mo del results at W a v eland, MS . . . . . . . . . . 42 3{17 Grid resolution comparison . . . . . . . . . . . 43 ix

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Abstract of Thesis Presen ted to the Graduate Sc ho ol of the Univ ersit y of Florida in P artial F ulllmen t of the Requiremen ts for the Degree of Master of Science EFFECT OF W A VE F OR CES ON STORM SUR GE By Rob ert J. W ea v er Ma y 2004 Chair: Donald N. Slinn Ma jor Departmen t: Civil and Coastal Engineering The disastrous eects of h urricanes on coastal comm unities are w ell kno wn, and there is a need to b etter understand the causes of storm surge to prepare for future ev en ts. T o b etter understand the mec hanisms, w e examine the inruence of individual factors that pro duce surge. The total surge dep ends on wind surface stress, in v erted barometer eects, and w a v e forcing, as w ell as tidal stage and bath ymetry in the path of the storm. W e are particularly in terested in the eect of w a v e stresses on o v erall surge. In the past, man y mo dels ha v e neglected the inruence of w a v e induced set-up. W a v e stresses could b e left out of n umerical mo dels for computational eciency when they are not a signican t pla y er. On the other hand, for conditions when w a v e stresses are signican t, it is of in terest to kno w if the total surge is a linear sup erp osition of the wind and w a v e set-up, or if there is a more complicated relationship. Our w ork is a comp onen t of a real-time wind, w a v e, and surge forecasting system for tropical cyclones b eing dev elop ed under the National Oceanographic P artnership Program. T o test the rise in surface elev ation, w e use the Adv anced Circulation Mo del for Coasts, Shelv es, and Estuaries in t w o-dimensional depth-in tegrated mo de x

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(ADCIR C 2DDI). W e conduct a suite of mo del studies including tests of wind stress form ulation, grid resolution, and b ottom friction. T o test sensitivit y to coastal bath ymetry w e generate three simple nite elemen t grids on idealized coastal top ographies. W e use these to test three dieren t strengths of storms. The storms range in in tensit y from a strong gust (10 m/s), to a medium strength tropical storm (30 m/s), to a Category 3 h urricane (56 m/s). Here, steady winds are applied on our coastal domain, and the asso ciated w a v e elds are predicted using SW AN (S im ulating W a v es N earshore). W e examine relationships b et w een bath ymetry and set-up due to wind and w a v es. These tests aid us in in terpreting more complicated results from historical storm ev en ts o v er real bath ymetry Our results indicate that for the same wind forcing and oshore w a v e conditions, w a v e generated surge can v ary for dieren t coastal bath ymetries. The shallo w er bath ymetric prole yields the greater lev el of wind-induced surge, and the steep er prole allo ws for a greater surge from w a v e set-up for the same forcing lev els. W e also note that the linear com bination of wind and w a v e forced set-up is sligh tly larger than the mo del prediction with com bined forcing. The nal application of our mo del system is a hindcast of h urricane Georges (1998). When Georges made landfall in the Bilo xi, Mississippi area, it w as a strong category 2 h urricane on the Sar-Simpson scale. W e use the North W est A tlan tic basin for the mo del domain. W e run the mo del three times, rst with wind and atmospheric pressure forcing. The second time w e force the mo del with w a v e radiation stresses from the predicted w a v e elds. The nal mo del run com bines wind and pressure elds with w a v e forcing. The resulting c hanges in surface elev ation are compared with eac h other and with NO AA station data. W e demonstrate that, in this case, to more accurately predict the surge it is necessary to include the w a v e forcing. Here, the w a v e forcing con tributes appro ximately 25% to 33% of the total rise in w ater lev el. xi

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CHAPTER 1 INTR ODUCTION T ropical cyclones are lo w-pressure systems that form in the tropics. In the northern hemisphere the wind will rotate around the lo w-pressure cen ter in a cyclonic pattern, coun ter-clo c kwise. As this lo w-pressure system mo v es o v er w armer w aters, it can in tensify A h urricane is a strong tropical cyclone. By the time the system is classied as a h urricane, there are maxim um sustained winds of 74 mph (33 m/s). The surface of the o cean under the storm will react to the pressure and wind. The threat to coastal comm unities from a h urricane includes high winds causing damage, as w ell as coastal ro o ding caused b y the storm tide. Storm surge is the rise in w ater lev el due to h urricanes. There are three main causes of storm surge: wind set-up, w a v e set-up, and the in v erse barometric eect of the lo w cen tral pressure of the storm. The tides will also pla y a role in the eect of the h urricane on the coast. Storm tide is the com bination of the surge with the tide. If the storm mak es landfall during high tide, the eect is a higher w ater lev el than if the surge hits the shore during lo w tide. The wind set-up is caused b y the wind blo wing across the surface of the w ater o v er h undreds of square kilometers. W a v e set-up is caused b y the generation and then release of w a v e momen tum (or radiation stress) in the w ater column as w a v es are formed, shoal, and then break. Radiation stress is the rux of momen tum due to w a v es ( Longuett-Higgins & Stew art 1964 ). It is the transfer of w a v e momen tum to the w ater column that forces a c hange in the mean w ater lev el. Near the coast, w a v e momen tum rux is balanced b y a pressure gradien t asso ciated with a c hange in the lo cal w ater depth. As w a v e momen tum increases in the presence of non breaking w a v es, the mean w ater lev el lo w ers. As breaking commences, the w a v e energy and momen tum decrease, 1

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2 resulting in a reduction of the radiation stress carried b y the w a v es. These stresses (force p er unit area) are imparted in to the w ater column. The rapid reduction of w a v e radiation stress near the coast forces a rise in mean sea lev el. The disc harged momen tum from the w a v es pushes against the w ater column, and pro duces an opp osing h ydrostatic pressure gradien t. During storm ev en ts, the resulting rise in w ater lev el can pla y a ma jor role in storm surge. According to linear theory the eectiv e c hange in w ater lev el from a steady train of linear w a v es approac hing normal to the shore on a gen tly sloping b ottom is ab out 19% of the breaking w a v e heigh t ( Dean & Dalrymple 1991 ). This ma y increase or decrease as w e tak e in to accoun t nonlinear eects, dissipativ e forces, and w a v e obliquit y The amoun t of w a v e set-up is also aected b y the b ottom con tour of the near-shore and b eac h face. W e examine the eect of w a v e radiation stress on sea surface elev ation for complex forcing conditions. Our goal is to increase understanding of the role that w a v es pla y in storm surge. Our w ork is a comp onen t of a real-time wind, w a v e, and surge forecasting system for tropical cyclones b eing dev elop ed under the National Oceanographic P artnership Program (NOPP). This partnership in v olv es four academic institutions and six go v ernmen t agencies, sharing data, mo dels, and resources. 1.1 Surge Mo del The h ydro dynamic mo del w e use to predict the sea surface elev ation is the Adv anced Circulation Mo del for Coasts, Shelv es, and Estuaries in t w o-dimensional depth-in tegrated mo de (ADCIR C 2DDI) ( Luettic h et al. 1992 ). It is a nite elemen t mo del that solv es the conserv ation la ws for mass and momen tum through a Generalized W a v e Con tin uit y Equation in nonconserv ativ e form. W e predict w ater lev el c hanges b y driving the h ydro dynamics with Wind stress and atmospheric pressure only W a v e radiation stress only A com bination of wind and w a v e stresses and atmospheric pressure elds.

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3 F rom this series of predictions w e determine the signicance of including w a v e stresses in our mo del system. As a test case, w e p erform hindcasts of h urricane Georges (1998) with eac h of the forcing options. W e compare the results with w ater-lev el data for that time p erio d, and ev aluate the predictiv e v alue of including the w a v e forces in the mo del inputs. Domain sensitivit y studies ha v e b een p erformed using the ADCIR C mo del ( Blain 1997 ; Blain et al. 1994 ; Brebbia et al. 1995 ; Blain et al. 1998 ). It w as found that selecting an appropriate sized domain w as an imp ortan t factor in the dev elopmen t of an accurate prediction. With a large enough domain, the k ey features of resonance and circulation are captured (in our case, the domain includes the North w est A tlan tic Basin with the Caribb ean and the Gulf of Mexico). A b enet to suc h a large domain is the simplicit y of the b oundary conditions. The op en b oundaries are primarily lo cated in the deep o cean, minimizing b oundary eects on the coastal region of in terest. Hagen et al. ( 2000 2001 ) sho w ed that sucien t grid resolution o v er regions of v arying bath ymetry is imp ortan t. In these regions, a ner mesh is required to capture the ev olution of the w ater elev ation. 1.2 Air{Sea Coupling Storm surge is dep enden t on wind surface stress, in v erted barometer eects, tidal stage, bath ymetry and c hanges in w a v e radiation stresses. Momen tum transfer at the air-sea in terface pro duces wind-generated w a v es and has b een studied extensiv ely ( Geernaert & Plan t 1990 ; Donelan et al. 1993 ; Donelan 1998 ). The wind stress is usually appro ximated as = C d j U j U where is the densit y of air, U is the mean wind sp eed tak en at 10 meters ab o v e the surface, and C d is the drag co ecien t. The drag co ecien t dep ends on sea surface roughness and atmospheric stratication, and has a magnitude on the order of 10 3 There are man y dieren t recommended forms for the drag co ecien t, C d The range of v alidit y of the dieren t form ulas for C d dep end on wind conditions, and other

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4 factors. There has b een relativ ely little researc h, ho w ev er, in to what form ulation w ould b est suit h urricane wind and sea conditions. It is dicult to mak e op en o cean measuremen ts during h urricane conditions. Most equations pro duce (b y extrap olating from data) an increasing drag co ecien t with increasing wind sp eed. This form ulation ts data sets at lo w er wind sp eeds. But, when the strength of the winds b ecomes large, the tops of the w a v es can b e sheared and the relativ e w a v e surface roughness c hanges. This is analogous to a slip b oundary condition. One p ossibilit y curren tly b eing debated, is that at higher wind sp eeds the drag co ecien t ma y lev el o as the w a v es are sheared o at the crests, and the net momen tum imparted to the w ater column b egins to lev el o. With suc h complicated p ossible scenarios, one m ust b e a w are of the sensitivit y of the surge predictions to the c hoice of the co ecien t of drag in the wind stress form ulation. W e pursue suc h sensitivit y tests b elo w and then pro ceed with our hindcasts using one of the standard ADCIR C form ulas ( Garratt 1977 ) for drag co ecien t (Eq. 1{1 ), with a maxim um allo w able drag co ecien t of 0.003. The corresp onding form ulas for wind stress are giv en b y Eqs. 1{2 1{3 C d = 0 : 001 (0 : 75 + 0 : 067 U ) (1{1) w s x = C d 0 : 001293 v x ( n ) U (1{2) w s y = C d 0 : 001293 v y ( n ) U (1{3) whereU = [ v x ( n ) 2 + v y ( n ) 2 ] 1 2 | wind sp eed w s x | horizon tal wind stress in x{direction w s y | horizon tal wind stress in y{direction v x ( n ) | horizon tal wind v elo cit y in x{direction v y ( n ) | horizon tal wind v elo cit y in y{direction 1.3 A tmospheric Pressure Am bien t atmospheric pressures are around 1012 m b. The lo w-pressure cen ter of a tropical storm causes a lo cal rise in the sea surface. This in v erted barometer

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5 eect is imp ortan t when attempting to predict w ater lev els. One can exp ect around 1 cm of w ater rise for eac h millibar of pressure drop in deep w ater ( An thes 1982 ). Though this eect ma y seem small, h urricane Georges had a minim um recorded cen tral pressure of 938 m b while in the A tlan tic, corresp onding to a 0.75 m rise in sea surface elev ation. Georges w eak ened b y the time it made landfall on the Gulf Coast. The cen tral pressure increased to 964 m b, corresp onding to an appro ximate 0.5 m rise in sea lev el in deep w ater. As a storm approac hes land, the heigh t of the sea lev el rise asso ciated with the in v erse barometer eect can increase due to the horizon tal con v ergence of the w ater. The con v ergence and rerection against the coastline can increase the surge lev el. If the barometric eect is neglected, the prediction of surge w ould b e less than the actual rise in elev ation measured at the coast. 1.4 Coastal Bath ymetry The bath ymetry of the shelf and near-shore region will also pla y a role in the lev el of storm surge measured at the coastline. The magnitude of the wind blo w-up is dep enden t on the depth and width of the con tinen tal shelf. Wind stress o v er a shallo w wide shelf will pro duce a larger set-up than the same wind stress o v er a narro w er or deep er shelf. The steady state, one-dimensional solution for wind-induced sea lev el rise ( Dean & Dalrymple 1991 ) is sho wn in Eq. 1{4 @ @ x = n z x ( ) g ( h + ) (1{4) whereh { mean w ater depth { displacemen t free surface ab out the mean x { cross-shore lo cation n = 1 z x ( h ) z x ( ) and n is greater than 1 z x ( ) { wind surface stress in x{direction z x ( h ) { b ottom shear stress in x{direction { reference densit y of w ater g { gra vit y

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6 As seen in Eq. 1{4 in the deep er w aters when h the set-up go es to zero. In the depth-a v eraged appro ximation, near a coast in steady state, the horizon tal v elo cit y is zero and the b ottom shear stress v anishes and n = 1. W e presen t results b elo w of exp erimen ts concerning w a v e set-up on a v ariet y of proles. The simplest b eac h mo del is a planar b eac h. Man y planar b eac h mo dels w ere used to deriv e the appro ximate form ulas for w a v e set-up ( Sa ville 1961 ; Longuett-Higgins 1983 ; Stiv e & Wind 1982 ; James 1974 ; Dean & Dalrymple 1991 ). F or a planar b eac h, the mean w ater surface displacemen t from small amplitude normally inciden t w a v es is ab out 0 : 19 H b ( Dean & Dalrymple 1991 ). Komar (1998) empirically ts a more complex relationship b et w een the slop e of the foreshore and the maxim um set-up elev ation at the shoreline, Eq. 1{5 based on the Irribaren n um b er, Eq. 1{6 (ratio of b eac h face slop e to w a v e steepness). max = 0 : 18 g 1 2 S H 1 2 1 T (1{5) 1 = S ( H 1 L 1 ) 1 2 (1{6) Where S is the slop e of the b ottom, H 1 and L 1 are the signican t w a v e heigh t and w a v elength of the inciden t w a v es in deep w ater, and T is the w a v e p erio d. Additional studies ha v e b een p erformed on b eac hes with a conca v e-up Equilibrium Beac h Prole, (EBP) ( Dean & Dalrymple 2002 ). h = Ax 2 3 (1{7) The results of these tests are compared to the case of a planar b eac h, and it w as found that the set-up on a conca v e-up b eac h will mirror the b ottom curv ature ( McDougal & Hudsp eth 1981 ). Smaller w a v es will break closer to the shoreline and the o v erall breaking pattern is in v ersely prop ortional to the w ater depth. T o a rst appro ximation, the maxim um surge lev el will b e the same at the shoreline as for a plane b eac h. F arther oshore, ho w ev er, the planar b eac h will allo w for a

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7 greater increase in elev ation, as the mean w ater lev el mimics the b ottom con tour. The EBP allo ws w a v es to propagate closer to the shoreline b efore breaking, imparting their momen tum to the w ater column closer to shore than on a planar b eac h. The rst set of tests describ ed b elo w w ere p erformed using the Equilibrium Beac h Prole as the bath ymetric con tour. Guza and Thorn ton (1981) dev elop ed a relation based on measuremen ts of irregular w a v e set-up on b eac hes in Southern California, Eq. 1{8 The study w as p erformed on a b eac h with a mild slop e (0.02), where the w a v es break across a wide surf zone. This w ould b e classied as a dissipativ e b eac h ( Komar 1998 ). The inciden t w a v e heigh ts ranged from 0.6 m to 1.6 m. max = 0 : 17 H 1 (1{8) This relation yields a result appro ximately 10% less than the linear solution. Our researc h fo cuses on m uc h more p o w erful w a v e ev en ts, with time v arying w a v e elds and complex shorelines. Our domain is the Gulf of Mexico shelf. This region has a m uc h milder sloping b eac h and near-shore region than that of California. W e exp ect more dissipation from nonlinear eects and b ottom friction in our test due to this bath ymetric dierence. 1.5 Hurricane Sim ulation F or our most comprehensiv e n umerical exp erimen t, w e p erform a hindcast of h urricane Georges. Hurricane Georges made landfall in the Bilo xi, Mississippi area on Septem b er 28, 1998 ( Guiney 1999 ). A t the time of landfall the storm w as rated a strong Category 2 h urricane on the Sar-Simpson scale, with estimated maxim um sustained one min ute winds of 90 knots (103.6 mph, 46.3 m/s). During previous da ys, as the storm made its w a y across the Caribb ean, Georges p eak ed as a Category 4 h urricane with estimated top wind sp eeds of 135 knots (155.4 mph, 69.5 m/s). The storm caused extensiv e damage and loss of life. The relief eort is

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8 estimated to ha v e cost $2.5 Billion and 602 liv es w ere lost, predominan tly in Puerto Rico, Cuba, and the Caribb ean islands. W e mo del the last 6 da ys of the storm, from the 25 th Septem b er, 1998 un til the 1 st of Octob er, 1998. After this time, the storm is w ell o v er land. The domain of our mo del predictions encompasses the North W est A tlan tic Basin. The nite elemen t grid w as pro vided b y Dr. Ric k Luettic h, of the Univ ersit y of North Carolina. Wind, w a v e, and barometric pressure data w as pro vided within the domain b y our NOPP partners, including NO AA, the National Hurricane Cen ter, the National W eather Service, and OceanW eather Inc. Our results will b e compared to tidal station data at dieren t lo cations on the Gulf Coast.

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CHAPTER 2 METHODOLOGY 2.1 Numerical Mo del T o predict the rise in surface elev ation, w e use the Adv anced Circulation Mo del for Coasts, Shelv es, and Estuaries in t w o-dimensional depth-in tegrated mo de (ADCIR C 2DDI). ADCIR C w as dev elop ed b y the Arm y Corps of Engineers Dredging Researc h Program (DRP). The principal dev elop ers w ere J.J. W esterink and Ric k Luettic h ( Luettic h et al. 1992 ). One of the purp oses of the researc h w as to dev elop a mo del that could compute storm surge h ydrographs and pro vide surface elev ation data. There are four main inputs for the ADCIR C mo del. These include the nite elemen t grid and bath ymetry le, the n umerical parameter set, the meteorological forcing and the w a v e forcing les. The grid is dened b y no de n um b ers and lo cations, elemen t neigh b ors and b oundary information. The input parameters include the time step, duration of the mo del run, co ordinate system denitions, friction co ecien t, horizon tal eddy viscosit y output parameters, input le parameters, etc. ( Luettic h et al. 1992 ). Tw o other main input elds are necessary to force the mo del run, the meteorologic (wind stress and atmospheric pressure) and the w a v e stress forcing les. The meteorological forcing le con tains the wind stress and pressure data at sp ecied time in terv als. Wind stress is computed from the wind sp eed and direction using Eqs. 1{2 and 1{3 In order to mak e this con v ersion, w e m ust decide on the form ula to use for drag co ecien t. There are n umerous relationships that attempt to parameterize the drag co ecien t, C d W e tested sev en dieren t form ulations, six giv en in T able 2{1 ( Geernaert & Plan t 1990 ) and a constan t v alue of C d = 0 : 003. Garratt's (1977) form ula represen ts a compilation of results 9

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10 T able 2{1: Drag co ecien t form ulations used to test mo del sensitivit y Authors C d 10 3 Garratt (1977) 0 : 75 + 0 : 067 j U j Miller (1964) 4.0 Klapsto v (1983) 0 : 49 + 0 : 07 j U j + 2 : 58 j U j 1 : 06 ( T air T sf c ) j U j 2 Geernaert (1987) 0 : 58 + 0 : 085 j U j Smith (1980) 0 : 61 + 0 : 063 j U j Large & P ond (1981) 0 : 44 + 0 : 063 j U j calibrated for wind sp eeds b et w een 4 and 21 m/sec. The ADCIR C mo del uses Garratt's form ula; ho w ev er, the mo del puts a cap on the maxim um v alue at C d = 0 : 003. W e remo v e this maxim um requiremen t for the sensitivit y tests. Miller (1964) prop osed a maxim um drag co ecien t of 4 : 0 10 3 for wind sp eeds of 52 m/sec. The v alue w as inferred using the ageostrophic tec hnique. This metho d assumes a transfer of angular momen tum in a cyclonic system whic h results in a cross-isobaric ro w. Klapsto v (1983) pro vides a comprehensiv e form ulation determined from 214 records of data for wind sp eeds ranging from 2 to 21 m/sec. Geernaert's (1987) form ula, for wind sp eeds of 5 to 25 m/sec, w as t to 116 data p oin ts. The Large & P ond (1981) form ula is a t to 1001 data p oin ts, for wind sp eeds of 10 to 26 m/sec. Smith (1980) t 120 p oin ts for wind sp eeds ranging from 6 to 22 m/sec. There ha v e b een no direct measuremen ts of drag form ula for wind sp eeds o v er 26 m/sec. When Georges made landfall the estimated one min ute winds w ere 90 knots (46.3 m/sec). Holding all other v ariables constan t, w e ran the ADCIR C mo del for eac h of the drag co ecien t form ulations, and determined the sensitivit y of the mo del. Once w e ha v e decided on a satisfactory form ulation, w e generate the wind and pressure input le, fort.22. The w a v e forcing elds sp ecify the x and y directed w a v e stresses. These are also pro vided for ev ery no de at predetermined time in terv als. W e will discuss the generation of the w a v e elds in more detail for eac h test case b elo w. Once calculated, w e generate the w a v e forcing input le, fort.23.

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11 The ADCIR C mo del output includes surface elev ation and depth a v eraged curren t v elo cities for ev ery no de at user sp ecied time in terv als. One can also prescrib e recording stations for time series of v elo cit y and sea lev el at predened time in terv als for an y lo cation in the domain. The mo del also has the abilit y to p erform harmonic analysis of the surface elev ation. This nite elemen t mo del solv es the conserv ation la ws for mass and momen tum. Conserv ation of mass is implemen ted b y w a y of the Generalized W a v e Con tin uit y Equation (GW CE) ( Luettic h et al. 1992 ) deriv ed from Eq. 2{1 The momen tum equations in nonconserv ativ e form are deriv ed from the turbulen t incompressible Na vier-Stok es (Reynolds a v eraged) equations. First the three dimensional equations are simplied using the Boussinesq appro ximation and the h ydrostatic pressure appro ximation, yielding Eqs. 2{2 2{4 @ u @ x + @ v @ y + @ w @ z = 0 (2{1) @ u @ t + u @ u @ x + v @ u @ y + w @ u @ z f v = @ @ x p 0 + 1 0 @ xx @ x + @ y x @ y + @ z x @ z (2{2) @ v @ t + u @ v @ x + v @ v @ y + w @ v @ z + f u = @ @ y p 0 + 1 0 @ xy @ x + @ y y @ y + @ z y @ z (2{3) @ p @ z = g (2{4) wheref = 2n sin = Coriolis parameter g = acceleration due to gra vit y = tide generating parameter = molecular viscosit y p ( x; y ; z ; t ) = time-a v eraged pressure ( x; y ; z ; t ) = densit y of w ater 0 = reference densit y of w ater t = time T = in tegration time scale for separating turbulen t and time-a v eraged quan tities xx ( x; y ; z ; t ) = [2 @ u @ x ] 1 T R T 0 u 0 u 0 dt { com bined viscous and turbulen t Reynolds stress y x ( x; y ; z ; t ) = [ @ u @ y + @ v @ x ] 1 T R T 0 u 0 v 0 dt { com bined viscous and turbulen t Reynolds stress

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12 z x ( x; y ; z ; t ) = [ @ u @ z + @ w @ x ] 1 T R T 0 u 0 w 0 dt { com bined viscous and turbulen t Reynolds stress xy ( x; y ; z ; t ) = [ @ v @ x + @ u @ y ] 1 T R T 0 v 0 u 0 dt { com bined viscous and turbulen t Reynolds stress y y ( x; y ; z ; t ) = [2 @ v @ y ] 1 T R T 0 v 0 v 0 dt { com bined viscous and turbulen t Reynolds stress z y ( x; y ; z ; t ) = [ @ v @ z + @ w @ y ] 1 T R T 0 v 0 w 0 dt { com bined viscous and turbulen t Reynolds stress = degrees latitude u ( x; y ; z ; t ) ; v ( x; y ; z ; t ) ; w ( x; y ; z ; t ) = time-a v eraged v elo cities in the x; y and z directionsu 0 ( x; y ; z ; t ) ; v 0 ( x; y ; z ; t ) ; w 0 ( x; y ; z ; t ) = departures of the instan taneous turbulen t v elo cities from the time-a v eraged v elo cities x; y = horizon tal co ordinate direction z = v ertical co ordinate direction n = angular sp eed of the Earth (7.29212x10 5 rad/s) After eliminating pressure as a dep enden t v ariable using 2{4 and dening the top and b ottom b oundary conditions, Eqs. 2{1 2{2 and 2{3 are v ertically in tegrated to yield t w o-dimensional equations for free surface displacemen t and depth-a v eraged v elo cit y The depth-in tegrated form of the con tin uit y equation is giv en b y Eq. 2{5 The v ertically in tegrated momen tum conserv ation equations are giv en b y Eq. 2{6 and 2{7 @ @ t + @ U H @ x + @ V H @ y = 0 (2{5) @ U @ t + U @ U @ x + V @ U @ y f V = @ @ x [ p s 0 + g ( )] + 1 H [ M x + D x + sx 0 bx 0 ] (2{6) @ V @ t + U @ V @ x + V @ V @ y + f U = @ @ y [ p s 0 + g ( )] + 1 H [ M y + D y + sy 0 by 0 ] (2{7) where = eectiv e Earth elasticit y factor ( = 0 : 69) D x @ D uu @ x @ D uv @ y | momen tum disp ersion D y @ D uv @ x @ D v v @ y | momen tum disp ersion D uu R h ^ u ^ u dz ; D uu R h ^ v ^ udz ; D uu R h ^ v ^ v dz ( x; y ; z ) | Newtonian equilibrium tidal p oten tial M x = @ @ x R h xx 0 dz + @ @ y R h y x 0 dz | depth-in tegrated, horizon tal momen tum diusion

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13 M y = @ @ x R h xy 0 dz + @ @ y R h y y 0 dz | depth-in tegrated, horizon tal momen tum diusionU ( x; y ; t ) 1 H R h udz | depth-a v eraged horizon tal v elo cit y V ( x; y ; t ) 1 H R h v dz | depth-a v eraged horizon tal v elo cit y ^ u ( x; y ; z ; t ) u U | departure of horizon tal v elo cit y from depth-a v eraged v elo cit y ^ v ( x; y ; z ; t ) v V | departure of horizon tal v elo cit y from depth-a v eraged v elo cit y H ( x; y ; t ) + h | total w ater depth to free surface | free surface h ( x; y ) | bath ymetric depth relativ e to geoid sx ; sy | applied free surface stresses bx ; by | applied b ottom stresses The b ottom stresses are replaced b y a quadratic friction term. The equations are dieren tiated and com bined to get the GW CE. DSRP-92-6, Rep ort 1: Theory and Metho dology ( Luettic h et al. 1992 ) giv es a complete deriv ation. 2.2 Bath ymetric T ests The rst set of tests w e p erform are a series of exp erimen ts examining set-up o v er idealized bath ymetric conditions for dieren t wind and w a v e conditions. Our purp ose is to determine the mo del resp onse to separate and com bined inruences of v ariations in wind sp eed, w a v e heigh t, and w ater depth. 2.2.1 Domain W e generate wind and w a v e elds o v er three bath ymetries. Con tours are created, Figure 2{1 using the equilibrium b eac h prole metho d ( Dean & Dalrymple 2002 ): h = Ax 2 3 A = 0 : 2 ; 0 : 1 ; 0 : 05 (2{8) Where A is a parameter based on the a v erage grain size of the near-shore sedimen t, x is the cross-shore distance and h is w ater depth. W e dene the a v erage near-shore slop e as the slop e from the shore, x = 0, to the w ater depth at x = 1 km. The b eac h proles ha v e a v erage near-shore slop es of 0.017, 0.0091 and 0.004, from steep est to mildest. F arther oshore, in the region 2 km to 20 km, the a v erage slop es are 0.0065, 0.0028 and 0.0017, resp ectiv ely The prole is uniform

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14 C r o s s s h o r e D i s t a n c e ( m e t e r s ) E l e v a t i o n ( m e t e r s ) 0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 1 4 0 1 2 0 1 0 0 8 0 6 0 4 0 2 0 0 2 0 h = 0 2 0 x ( 2 / 3 ) h = 0 1 0 x ( 2 / 3 ) h = 0 0 5 x ( 2 / 3 ) M W L Figure 2{1: Bath ymetric con tours created to test the w a v e and wind set-up in the alongshore. W e generate a nite elemen t grid, Figure 2{2 for the mo del domains using A CE/gredit ( T urner & Baptista 1999 ). Resolution at the shoreline is on the order of 20 meters, and decreases as the depth increases. 2.2.2 F orcings Three dieren t strength shore normal winds are c hosen. The w eak est wind forcing is a 10 m/s wind that corresp onds to a strong gust. The in termediate case is a 30 m/s wind, corresp onding to a medium strength tropical storm. The strongest wind used corresp onds to a Category 3 h urricane on the Sar-Simpson scale, with a 56 m/s wind sp eed. The asso ciated w a v e forces w ere generated using SW AN (S im ulating W a v es N ear-shore) ( Holth uijsen 2000 ). The oshore w a v e heigh ts sp ecied are 1.0 m, 5.0 m, and 7.0 m, corresp onding to the wind sp eeds of 10, 30 and 56 m/s resp ectiv ely (T able 2{2 ). These oshore w a v e heigh ts w ere selected after a series of iterations with SW AN, k eeping the wind sp eed constan t.

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15 C r o s s s h o r e ( m e t e r s ) A l o n g s h o r e ( m e t e r s ) 2 5 0 0 5 0 0 0 7 5 0 0 1 0 0 0 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 Figure 2{2: Finite Elemen t Grid created with A CE/gredit (resolution at the shoreline is 20 m) T able 2{2: Wind in tensit y and o-shore w a v e heigh t used to force the circulation mo del for the bath ymetry tests Strength Wind(m/s) W a v e(m) W eak 10 1.0 Medium 30 5.0 Strong 56 7.0 Our applied winds are uniform in time and space. The domain SW AN uses to compute the w a v e elds is 20 km cross-shore and 50 km along-shore. W e mak e sure that the along-shore direction is large enough that the cen ter line of the domain will b e unaected b y b oundary eects. SW AN uses a Cartesian computational grid with 5 m spacing. The w a v e elds generated in SW AN are based on a JONSW AP distribution with directional spreading of 5 degrees. Bottom friction is turned on, as is white-capping. The SET-UP function is also turned on. SW AN outputs the momen tum transfer from the w a v e eld to the depth a v eraged curren ts b y

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16 in tegrating the radiation stresses o v er the w a v e direction and frequency sp ectrum. The x and y comp onen ts of the momen tum transfer are F x = 1 [ @ S xx @ x @ S xy @ y ] (2{9) F y = 1 [ @ S y y @ y @ S y x @ x ] (2{10) whereS xx = g R ncos 2 + n 1 2 E d d S xy = S y x = g R nsin cos E d d S y y = g R nsin 2 + n 1 2 E d d n = C g C The w a v e heigh ts and forcings output b y SW AN are sho wn in Figure 2{3 and Figure 2{4 resp ectiv ely for the three bath ymetric con tours and three sp ecied wind elds. The wind sp eed is con v erted in to a wind stress for ADCIR C as 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 2 4 6 8 10 Crossshore Distance (meters)Wave Height (meters)A ) Steep SlopeMild SlopeShallow Slope 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 2 4 6 8 10 Crossshore Distance (meters)Wave Height (meters)B ) Steep SlopeMild SlopeShallow Slope 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 0.5 1 1.5 2 Crossshore Distance (meters)Wave Height (meters)C ) Steep SlopeMild SlopeShallow Slope Figure 2{3: The w a v e elds output b y SW AN o v er the three bath ymetric con tours. A) Strong forcing. B) Medium forcing. C) W eak forcing.

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17 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 0.2 0.4 0.6 0.8 1 1.2 Crossshore Distance (meters)Fx (m2/s2)A ) Strong ForcingMedium ForcingWeak Forcing 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0.01 0 0.01 0.02 0.03 0.04 0.05 Crossshore Distance (meters)Fx (m2/s2)B ) Strong ForcingMedium ForcingWeak Forcing 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0.01 0 0.01 0.02 0.03 0.04 0.05 Crossshore Distance (meters)Fx (m2/s2)C ) Strong ForcingMedium ForcingWeak Forcing Figure 2{4: The F x output eld from SW AN for eac h of the three forcing strengths (the v alue of the forcing is giv en b y Equation 2{9 ). A) Steep slop e. B) Mild slop e. C) Shallo w slop e. describ ed previously and then in terp olated to the nite elemen t grid, Figure 2{2 Using ADCIR C, w e test the c hange in sea lev el for three scenarios atmosphere forcing only w a v e forcing only com bined wind and w a v e forcing. 2.2.3 Implemen tation The time step for ADCIR C is determined b y the Couran t n um b er and is set suc h that C # < 1 : 5. The Couran t n um b er is giv en as C # = ( g h ) 1 2 t x (2{11) On the nely resolv ed grid, a time step of 0.10 sec is necessary to ensure reliable, stable results. With suc h a small time step, the total run length needs to b e as short as p ossible, but long enough for the system to reac h equilibrium. W e use

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18 time w eigh ting factors for the free surface terms in the GW CE of 0.35, 0.30 and 0.35. The free surface terms at the K th time lev el are w eigh ted b y g (0 : 35 + 0 : 30). These terms at the K 1 time lev el are w eigh ted b y g 0 : 35. These factors are c hosen suc h that the sum is 1.0. The initial conditions are u = v = = 0. In order to damp out the w a v e created b y the initial o v ersho ot of the equilibrium p osition, the mo del is ramp ed up b y gradually in tro ducing the forcing o v er 6 hours and the b ottom friction is increased to 0.06. This is acceptable b ecause w e are in terested in obtaining a steady state solution in whic h the depth a v eraged curren ts and asso ciated b ottom stresses are zero. In SW AN, for the w a v e elds, w e used the more realistic default b ottom friction, the semi-empirical form ula deriv ed from the JONSW AP results ( Holth uijsen 2000 ). The factor that w eigh ts the w a v e and primitiv e con tin uit y con tributions to the GW CE is set to matc h the v alue of the friction co ecien t as recommended in the ADCIR C man ual, o = 0 : 06. Without these steps an o v ersho ot w a v e will seic he through the basin, p oten tially in tro ducing a n umerical instabilit y or requiring a smaller time step and tak e m uc h longer to ac hiev e steady state conditions. T aking the ramp-up time in to consideration, w e obtain a steady state set-up b y running the mo del for a p erio d of 1 da y F or this grid resolution, a mo del run tak es appro ximately 2 da ys of CPU time on a 3.0 GHz P en tium pro cessor. After insp ecting the output, w e notice that the system equilibrates after appro ximately 0.75 da y App endix A giv es sample ADCIR C input les for the bath ymetric test. 2.3 Hurricane Georges Hindcast W e conducted a hindcast of a historical storm ev en t. The landfall of h urricane Georges on the Mississippi coast w as c hosen as the sub ject storm. In order to accomplish this w e needed to decide on the prop er mo del domain and forcings to b e used. W e also obtained historical data to compare to our surge predictions from

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19 the NO AA National Ocean Service Cen ter for Op erational Oceanographic Pro ducts and Services, (NO AA NOS CO-OPS) w eb site. 2.3.1 Domain It is imp ortan t to ensure that the domain is large enough to capture the true resonan t c haracteristics of a basin ( Blain et al. 1998 ). W e also w an t to form ulate our mo deling system to accommo date the ma jorit y of tropical cyclones so w e can ha v e a general use domain for future mo del forecasts. The mo del domain is the North W est A tlan tic Basin, including the Caribb ean Sea and the Gulf of Mexico, Figure 2{5 This grid w as pro vided b y Ric k Leuttic h. With suc h a large domain, L o n g i t u d e L a t i t u d e 9 0 8 0 7 0 6 0 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 Figure 2{5: Finite Elemen t Grid of the North w est A tlan tic Domain consisting o v 31435 No des and 58369 Eleman ts. The no dal spacing is 0.03 to 0.06 degree at the coast, 0.016 degree in the inlets, and ab out 0.5 deg maxim um spacing in the Gulf of Mexico.w e ha v e the abilit y to mo del an y storm that en ters the w estern A tlan tic, not just the Gulf of Mexico. In addition, the only op en b oundary is at the easternmost

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20 w all. This is far enough from the coastlines of in terest that b oundary eects will b e minimized. In the case of h urricane Georges, our sim ulation starts as the storm en ters the Gulf of Mexico b et w een Florida and Cuba, and lasts un til after landfall. The region of landfall is sho wn in Figure 2{6 F rom this p ersp ectiv e w e are able to see the relativ ely high resolution in the coastal region. L o n g i t u d e L a t i t u d e 8 9 8 8 8 7 8 6 8 5 2 6 5 2 7 2 7 5 2 8 2 8 5 2 9 2 9 5 3 0 3 0 5 Figure 2{6: The Gulf Coast region of our mo del domain (Louisiana to Florida). This is where h urricane Georges made landfall in the Con tinen tal U.S. 2.3.2 F orcing Our forcings for h urricane Georges are pro vided b y the NOPP partners. The wind and pressure inputs are a pro duct of satellite, aircraft righ t lev el, and buo y data from the National Hurricane Cen ter, assimilated b y OceanW eather Inc. (Cardone and Co x). The data are giv en o v er the whole domain, 5N{53N and 99W{50W, in 30 min ute in terv als, on a 0.20 degree Cartesian grid. The wind and pressure elds are then in terp olated on to the nite elemen t grid, Figure 2{5 The

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21 wind sp eed is con v erted in to a wind stress as describ ed previously The wind stress and pressure are then written out to the meteorological forcing le, fort.22, to b e read b y ADCIR C. W a v e elds w ere generated b y Rob ert Jensen at the US Arm y Corps of Engineers, Engineer Researc h and Dev elopmen t Cen ter (ERDC). The assimilated wind and pressure data are used to force W AM-3G (W a v e A ction M o del, Third Generation) ( Komen et al. 1996 ). W a v e elds are calculated at t w o resolutions o v er the p ortion of the domain sho wn in Figure 2{7 The coarser resolution data set, L o n g i t u d e L a t i t u d e 9 5 9 0 8 5 8 0 7 5 2 0 2 5 3 0D e p t h 1 0 0 0 9 0 0 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 Figure 2{7: The w a v e elds are pro vided at t w o lev els of resolution. Near the region of landfall the w a v es are giv en at ev ery 0.1 degree. In the Gulf of Mexico basin the w a v es are giv en at ev ery 0.2 degree. 0.2 degree, is giv en o v er a basin domain consisting of the Gulf of Mexico, p ortions of the Caribb ean and North w est A tlan tic. A ner resolution grid, 0.1 degree, is pro vided for the region of in terest near landfall along the Gulf Coast, including the coastal regions of Louisiana, Mississippi, Alabama, and Florida. The domains

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22 T able 2{3: Mo del and forcing domains Domain SN WE NW A tlan tic FE Grid 8N-46N 98W-60W Wind and Pressure 5N-53N 99W-50W W a v e Basin 18N-31N 98W-75W W a v e Region 28N-30.4N 97W-82W for the inputs are giv en in T able 2{3 The ner resolution w a v e eld is the w a v e region. The resolution for the w a v e region is 0.1 degree. The resolution for the w a v e basin and wind and pressure elds is 0.2 degree. W a v e data is pro vided as w a v e heigh t, p eak p erio d, and mean direction on the Cartesian grid. The gradien ts of the radiation stresses are calculated using 2 nd order cen tral dierences ev erywhere except at the b oundaries where a rst order forw ard dierence is implemen ted. The forcing is then calculated from the gradien ts using Eqs. 2{12 2{13 F x = 1 @ S xx @ x + @ S y x @ y (2{12) F y = 1 @ S y y @ y + @ S xy @ x (2{13) whereS xx = E 2 (2 ncos 2 + (2 n 1)) S xy = S y x = E ncos sin S y y = E 2 (2 nsin 2 + (2 n 1)) n = C g C The momen tum forcing is then in terp olated to the nite elemen t grid, Figure 2{5 The ner domain data is nested in the coarser set during the in terp olation pro cess. This data set is output to the w a v e forcing le, fort.23, to b e read b y the ADCIR C mo del. 2.3.3 Implemen tation Due to the larger grid resolution used for the h urricane predictions, the Couran t n um b er stabilit y do es not pla y suc h a restrictiv e role as in the idealized

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23 b eac h exp erimen ts. F or the h urricane Georges hindcast, w e use a time step of 30.0 seconds. Our friction co ecien t is set to a more realistic v alue of 0.006, as is the GW CE w eigh ting factor, o = 0 : 006. The time w eigh ting factors for the GW CE are 0.35, 0.30 and 0.35. W e run the mo del for 6 da ys, ramping the forcings up o v er 0.5 da y The input data is pro vided at 30 min ute in terv als, and the initial conditions are u = v = = 0. Additional details and sample ADCIR C input les (fort.15) for the h urricane Georges exp erimen ts are giv en in App endix B. This denes our problem and our metho d for dev eloping a solution. W e run the mo dels for the t w o geometries and eac h input parameter that w e ha v e set. W e rep ort on the results of our n umerical exp erimen ts b elo w.

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CHAPTER 3 RESUL TS 3.1 Wind Stress The rst test w e p erform using the Adv anced Circulation Mo del for Coasts, Shelv es, and Estuaries (ADCIR C), is a test of the drag co ecien t and wind stress form ulation. W e test sev en drag co ecien t form ulations, the six giv en in T able 2{1 and the constan t v alue, C d = 0 : 003. Figure 3{1 sho ws ho w eac h of the drag co ecien t form ulations resp onds to wind sp eed. The Miller co ecien t, 4 : 0 10 3 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10 WIND SPEED (m/s)DRAG COEFFICIENT Large & Pond(1981)KlapstovGarratt(1977)Geernaert(1987)Smith (1980)Miller(1964)3.0 max Figure 3{1: The sev en drag co ecien t form ulations plotted vs. wind sp eed. w as dev elop ed for wind sp eeds o v er 50 m/sec. The plot of 3 : 0 10 3 represen ts the maxim um v alue for C d that is usually allo w ed in ADCIR C. Other form ulas are tted to data sets for whic h wind sp eeds v ary from 2 to 26 m/sec. Garratt's form ula ts the middle of the spread of the remaining form ulas. The resulting wind stress magnitudes are plotted in Figure 3{2 Notice that at high wind sp eeds eac h of the form ulas k eeps increasing, passing the, C d = 0 : 003 cuto. Geernaert's form ula increases more rapidly than the others, reac hing the cuto v alue so oner. Garratt's, the standard form ulation in ADCIR C, and 24

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25 0 10 20 30 40 50 60 0 0.5 1 1.5 2 2.5 3 x 10 4 WIND SPEED (m/s)WIND STRESS (N/m2) Large & Pond(1981)KlapstovGarratt(1977)Geernaert(1987)Smith (1980)Miller(1964)3.0 max. Figure 3{2: Wind stress calculated using the dieren t drag form ulas and the cuto v alue, plotted vs. wind sp eed. Klapsto v's form ulas pro duce results that lie in the middle of the other plots. A t lo w er wind sp eeds all the form ulations, except the t w o constan ts, b eha v e similarly The wind stress v alues are calculated for h urricane Georges. These stress v alues are used as inputs to force the ADCIR C mo del. The results of maxim um set-up and set-do wn during the storm from the sev en tests are sho wn in Figure 3{3 Early in the sim ulation, as the storm en ters the domain and mak es its w a y across deep er w aters, all but the t w o constan t form ulations are in close agreemen t. W e w ould exp ect Miller's appro ximation to b e greater than the others throughout the domain. During the time asso ciated with the sim ulation, h urricane Georges w as a Category 2 storm with winds less than 50 m/sec. W e also see that the surge lev el asso ciated with the cuto v alue for C d is greater than the results asso ciated with the other form ulations. The surge driv en b y Geernaert's form ula comes close to that forced b y the cuto v alue, but only for a short p erio d of time. The w ater elev ation predicted using the wind stresses generated b y Garratt's simple form ula and Klapsto v's more complicated form ula, lie in the middle of the other predictions. Our purp ose of conducting these tests w as to quan tify the sensitivit y of the surge resp onse to the wind stress parameterization, and to estimate error bars asso ciated with this uncertain t y Without further insigh t in to the optimal

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26 T i m e ( h o u r s ) S u r f a c e E l e v a t i o n ( m e t e r s ) 5 0 1 0 0 2 1 5 1 0 5 0 0 5 1 1 5 2 2 5 3M i l l e r m i n m a x 0 0 0 3 c u t o f f m i n m a x G e e r n a e r t m i n m a x G a r r a t t m i n m a x K l a p s t o v m i n m a x L a r g e & P o n d m i n m a x S m i t h m i n m a x Figure 3{3: Maxim um and minim um surge generated for eac h of the wind stress form ulations using the sev en dieren t drag co ecien ts. drag co ecien t resp onse to high winds, w e accept the Garratt form ulation; as it is simple and seems to capture the middle of the road solution. W e recognize that the resulting surge prediction can v ary as m uc h as 0 : 5 meter dep ending on the c hoice of drag co ecien t form ulation. Similar sensitivit y tests w ere conducted for the co ecien t of b ottom friction, and a mo derate v alue of 0.006 w as selected. 3.2 Bath ymetric Sensitivit y No w w e examine the results of the bath ymetric sensitivit y tests with v aried forcings. The w a v e heigh ts and forcing comp onen ts output b y SW AN are sho wn in Figure 2{3 and Figure 2{4 resp ectiv ely for eac h bath ymetric prole and forcing pair. F rom these results w e calculate the in tegral F = R of f shor e 0 F x dx for F x > 0. The magnitude of F will giv e us an idea of what to exp ect for the surge. Figure 3{4 sho ws the magnitude of the in tegrals for eac h forcing lev el o v er

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27 10 30 56 0 10 20 30 40 50 60 Forcing Level (wind speed in m/sec)Integral of Fx (N/m) SteepMildShallow Figure 3{4: The in tegral sum of F output b y SW AN for the three dieren t forcings o v er the three bath ymetric proles. The v alue of the forcing is giv en b y equation 2{9 eac h prole. W e see a trend of decreased F as the proles get shallo w er. This dierence in F b ecomes more pronounced as the forcing lev el increases. The larger w a v es asso ciated with the stronger forcing, will ha v e a greater in teraction with the b ottom b oundary Dissipativ e eects of b ottom friction will pla y a larger role for these cases. Across the shallo w er domains, the w a v es will break farther from shore. The wind stress imparted on the w ater column prior to breaking will therefore b e smaller than o v er a steep er prole. It follo ws that the w a v e heigh t at breaking will b e smaller, as sho wn in Figure 2{3 Breaking farther oshore also allo ws more dissipation in a wider surf zone than the steep domain. Ha ving obtained our w a v e forcing comp onen ts with SW AN, w e use ADCIR C to test the c hange in sea lev el for eac h set of forcings : wind, w a v e, wind and w a v e. The results are summarized in T able 3{1 and Figure 3{5

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28 T able 3{1: Maxim um calculated surge for forcing comp onen ts o v er eac h bath ymetric prole Bath y Strength W a v e(m) Wind(m) Wind&W a v e(m) Linear Com bination(m) Shallo w W eak 0.079 0.02 0.10 0.10 Shallo w Medium 0.27 0.30 0.53 0.56 Shallo w Strong 0.40 1.00 1.33 1.40 Mild W eak 0.085 0.01 0.09 0.09 Mild Medium 0.31 0.16 0.45 0.47 Mild Strong 0.51 0.56 1.00 1.07 Steep W eak 0.032 0.005 0.037 0.037 Steep Medium 0.50 0.08 0.56 0.58 Steep Strong 1.29 0.30 1.48 1.59 10 30 56 0 0.5 1 1.5 2 A ) Forcing Level (by Wind Speed in m/s)Surge (meters) wavewindwind wavelinear comb 10 30 56 0 0.5 1 1.5 2 B ) Forcing Level (by Wind Speed in m/s)Surge (meters) wavewindwind wavelinear comb 10 30 56 0 0.5 1 1.5 2 C ) Forcing Level (by Wind Speed in m/s)Surge (meters) wavewindwind wavelinear comb Figure 3{5: The surge lev els for eac h forcing group o v er eac h b ottom top ograph y (data from T able 3{1 ) A) Steep slop e. B) Mild slop e. C) Shallo w slop e. The wind-w a v e en try represen ts the com bined forcing for the mo del run. The linear com bination en try represen ts the sum of the surge predicted from the wind forcing, and that predicted using only the w a v e forcing. The lev el of wind set-up v aried dep ending on the steepness of the bath ymetric prole. F or eac h lev el of input forcing, the wind set-up w as greatest o v er the

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29 shallo w bath ymetry and the set-up decreased as the prole b ecame steep er (Figure 3{5 ). This is in agreemen t with the go v erning equation, Eq. 1{4 for the steady state solution for wind set-up. The equilibrium state for the w ater surface elev ation, calculated for the dieren t w a v e stresses alone, also v aried o v er the dieren t bath ymetric proles. The steady state solution for w a v e set-up o v er a mildly sloping b ottom is giv en b y Eq. 3{1 ( Dean & Dalrymple 1991 ). d dx = 1 g ( h + ) dS xx dx (3{1) where | mean surface displacemen t After some simplications it can b e sho wn that at the shore, the equation for the surface displacemen t can b e appro ximated b y equation 3{2 (0) = b + 3 2 8 1 + 3 2 8 h b (3{2) where b | mean surface displacemen t at breaking h b | depth at breaking | breaking constan t Th us, b y this appro ximation, the w a v e-induced set-up of iden tical w a v e elds at the shore is indep enden t of the prole. The appro ximation also assumes that the breaking constan t (and break er t yp e) is the same for eac h prole and eac h forcing strength, for our tests = 0 : 73. W e ha v e just sho wn that our results predict a decrease in w a v e set-up for the same forcing strength (output b y SW AN) as the proles b ecome more shallo w. In part this can b e attributed to dieren t steady w a v e elds dev eloping o v er dieren t bath ymetries for the same wind eld conditions. T o b etter understand the results w e compare the ADCIR C results with the analytic solution, Eq. 3{1 This comparison, presen ted in Figure 3{6

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30 sho ws that the mo del results are in close agreemen t with the analytic steady state solution for the mild and strong forcing cases. C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 0 0 5 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 0 4 5 0 5 e t a ( a n a l y t i c ) a d c i r c t r a n s e c t w a v e C ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 1 0 0 0 2 0 0 0 3 0 0 0 0 5 0 2 5 0 0 2 5 0 5 0 7 5 1 1 2 5 1 5 I ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 0 1 0 0 1 0 2 0 3 0 4 0 5 0 6 F ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 0 0 5 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 0 4 E ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 0 0 0 5 0 1 0 1 5 0 2 D ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 B ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 2 5 0 5 0 0 7 5 0 1 0 0 0 0 0 5 0 0 0 5 0 1 0 1 5 0 2 0 2 5 0 3 0 3 5 G ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 0 0 5 1 H ) C r o s s s h o r e D i s t a n c e ( m e t e r s ) S u r f a c e E l e v a t i o n ( e t a i n m e t e r s ) 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 0 0 0 5 0 1 0 1 5 0 2 A ) Figure 3{6: Comparison of Mo del results for w a v e forcing with the analytic solution for steady state w a v e set-up. Sho wn are all nine prole and forcing com binations: A) Shallo w prole, w eak forcing. B) Shallo w prole, medium forcing. C) Shallo w prole, strong forcing. D) Mild prole, w eak forcing. E) Mild prole, medium forcing. F) Mild prole, strong forcing. G) Steep prole, w eak forcing. H) Steep prole, medium forcing. I) Steep prole, strong forcing. W e see that the cases of the w eak w a v e forcing o v er the mild and steep bath ymetry are not sucien tly resolv ed on the 20 meter ADCIR C grid to capture the full set-up at the shoreline. Though the nite elemen t mo del and theory agree outside of the breaking region, the mo del output under predicts the surge lev el. Grid spacing at the shoreline for the circulation mo del is to o coarse to reasonably resolv e the spatial gradien ts of breaking. F or more in tense forcing comp onen ts, the 20 meter spacing adequately resolv es the system. In these cases the ADCIR C results agree with the results predicted b y Eq. 3{1 when calculated with the SW AN

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31 output. It is the v ariation in w a v e forcing elds calculated b y SW AN that pro duces dieren t w a v e-induced set-up for similar wind forcing conditions. This v ariation is caused b y altered breaking w a v e conditions that dev elop due to the length dierences of the wind fetc h prior to breaking. The predicted v ariation in the lev el of w a v e set-up o v er the dieren t bath ymetries is dep enden t on the strength of the forcing. T otal dissipativ e eects are increased for increased w a v e heigh ts. Large w a v es feel the b ottom more strongly than smaller w a v es, and the eect of b ottom friction in SW AN pla ys a greater role in the case of larger w a v e heigh ts. These eects are rerected in the output from SW AN and translated to the results of the circulation mo del. Figure 3{5 sho ws that the surge from the com bined forcing is smallest o v er the mild prole. P eak wind set-up o ccurs o v er the shallo w prole, and the p eak w a v e set-up o ccurs o v er the steep prole. The lev el of wind set-up is fetc h limited. Our domain is only 20 km in the cross-shore. W e w ould exp ect that o v er a larger cross-shore domain, the winds w ould b egin to dominate the storm surge. In summary the results sho w that the imp ortance of the w a v es increases as the prole b ecomes steep er. Set-up due to w a v es do es v ary o v er the dieren t proles, and the steep er prole allo ws for a greater w a v e-induced set-up than the shallo w er prole. In addition, the wind has less of an eect on the steep er proles, and th us the w a v es dominate the set-up. Winds pla y a larger role when the domain has a wide shallo w shelf. On the shallo w prole, the wind induces the ma jorit y of the set-up. In b oth cases, our test results indicate that w a v es mak e a signican t con tribution to the resulting surge lev els. These results, ho w ev er, are sp ecic to the presen t, fetc h limited, idealized domains. The next step is to examine what happ ens when w e use realistic temp orally and spatially dep enden t wind elds, include a v ariable pressure eld, compute the asso ciated w a v e elds, and run the mo dels o v er a real domain with complex coastal bath ymetry

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32 3.3 Hurricane Georges W e p erform a hindcast of h urricane Georges. Elev ation output from ADCIR C is con v erted in to a time series of con tour plots sho wing the w ater lev el as h urricane Georges mak es its w a y from the Straits of Florida to the Gulf Coast. A series of these plots is sho wn in Figure 3{7 Time is measured from t=0 on Septem b er 25 at 00:00 hour. The ey e of the storm en ters the Gulf, t = 30.00 h, and mo v es north w est. The mo del captures the in v erted barometer eect under the ey e, and the set-up and blo w-do wn as the ey e passes and winds shift direction. Set-up is pro duced on the windw ard side of barrier islands and in the ba ys. L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 8 2 2 4 2 6 2 8 3 0 3 2e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 B ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 8 2 2 4 2 6 2 8 3 0 3 2e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 A ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 8 2 2 4 2 6 2 8 3 0 3 2e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 C ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 8 2 2 4 2 6 2 8 3 0 3 2e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 F ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 8 2 2 4 2 6 2 8 3 0 3 2e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 E ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 8 2 2 4 2 6 2 8 3 0 3 2e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 D ) Figure 3{7: A series of surface con tour plots sho ws the surge as h urricane Georges mak es its w a y across the Gulf of Mexico and mak es landfall (prediction w as made with the com bined forcings). A) t = 10 hours in to the sim ulation. B) t = 30 hours. C) t = 50 hours. D) t = 70 hours. E) t = 90 hours. F) t = 110 hours. W e compare con tour plots at the same time from three dieren t forcing predictions. The dierence b et w een wind and pressure only w a v e only and

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33 com bined wind, pressure and w a v e forced sim ulations are eviden t in Figure 3{8 The dierence in surface elev ation in the bac k of ba ys is greatest. The h urricane L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 2 8 4 2 8 6 2 8 8 2 9 2 9 2 2 9 4 2 9 6 2 9 8 3 0 3 0 2 3 0 4 3 0 6 3 0 8 3 1 e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 A ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 2 8 5 2 9 2 9 5 3 0 3 0 5 3 1 e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 C ) L o n g i t u d e L a t i t u d e 9 0 8 8 8 6 8 4 2 8 5 2 9 2 9 5 3 0 3 0 5 3 1 e l e v 2 5 0 0 2 2 6 7 2 0 3 3 1 8 0 0 1 5 6 7 1 3 3 3 1 1 0 0 0 8 6 7 0 6 3 3 0 4 0 0 0 1 6 7 0 0 6 7 0 3 0 0 0 5 3 3 0 7 6 7 1 0 0 0 B ) Figure 3{8: A series of surface con tour plots sho ws the surge as h urricane Georges mak e landfall, t=82 h. A) Surface elev ation generated from the meteorological forcing. B) Surge created b y w a v e forcing. C) Surge generated from the com bined forcing.winds are blo wing in a cyclonic (coun ter-clo c kwise) pattern. Dep ending on the orien tation of the shore to wind direction, w e observ e either set-up or set-do wn at the land b oundary In the case of w a v es only the mo del predicts an initial set-do wn just oshore of the barrier islands. The w ater lev el then rises closer to the land b oundaries. F or the com bined forcing prediction the eects of w a v e set-up reduce the net set-do wn at the land b oundary caused b y the wind and pressure only Oshore, in the region of w a v e set-do wn, the blo w-up from the wind is reduced. The con tour plots giv e us a general indication of the spatial distribution

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34 of the w ater surface. F or a more quan titativ e represen tation, w e plot the time series of the w ater elev ation at dieren t lo cations. A time series of the maxim um surge predicted o v er the whole domain is giv en b y Figure 3{9 The com bined, wind, pressure, and w a v e forced prediction is T i m e ( h o u r s ) E l e v a t i o n ( m e t e r s ) 5 0 1 0 0 0 0 5 1 1 5 2 2 5 3 m a x W i n d & P r e s s u r e m a x W a v e m a x C o m b i n e d Figure 3{9: F or eac h set of mo del prediction forcings, the maxim um w ater surface elev ation is plotted at ev ery time step. greater than the predictions for separate forcings for nearly the whole time series. There is a p oin t, ab out 25 hours in to the prediction, when the results forced only b y the w a v es exceed the com bined results. F rom appro ximately t=25 hours to t=35 hours the maxim um elev ation from com bined forcing decreases rapidly and the w a v e forced results can b e the largest of the three predictions. This surge is not asso ciated with the h urricane making landfall, but with w a v es reac hing the shore while the ey e is still in op en w ater. Wind and w a v es can w ork with eac h other forcing in the same direction, and pro duce a large set-up. The t w o can also opp ose

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35 eac h other and reduce the maxim um surge, when the wind is blo wing do wn the area where the w a v es are setting-up, as is seen in these time series. These scenarios illustrate the complex nature of the system. W e also note that for the com bined forcing prediction, the maxim um surge in the domain is alw a ys greater than or equal to the wind only prediction. The addition of w a v e forcing to the mo del pro duces an increase in the maxim um w ater elev ation, o v er the whole domain, on the order of 0.4 meter o v er the meteorologic forcing alone (during the p eak hours). In the analysis ab o v e w e compared the maxim um surges pro duced in the mo del domain. These maxim um elev ations, ho w ev er, do not necessarily corresp ond to the same lo cations. A t sp ecic lo cations w e ma y observ e a greater dierence b et w een the meteorological and com bined forcing predictions. Therefore, it is of in terest to examine the b eha vior of the sea surface at sp ecic lo cations. W e c ho ose lo cations where historical w ater lev el data is a v ailable and asso ciate these with nearest no des on our grid. In addition to selecting station lo cations, w e also retriev e data at three prescrib ed lo cations: Mobile Ba y AL, P erdido Ba y FL, and Lak e Borgne, LA. T able 3{2: Lo cations of selected tidal stations No de Latitude Longitude Lo cation 4138 29.2915 -89.9288 Grande Isle, LA 5313 29.3551 -89.3419 Grande P ass, LA 9552 30.2546 -88.1925 Dauphin Island, AL 9965 30.3807 -87.2435 P ensacola, FL 9990 30.2086 -89.3807 W a v eland, MS 9991 30.2452 -89.4003 W a v eland, MS 10290 30.3888 -87.2261 P ensacola, FL 11020 30.6678 -87.9489 Mobile Ba y AL 11043 29.9664 -89.7226 Lak e Borgne, LA 13266 30.4823 -87.4180 P erdido Ba y FL The maxim um elev ation o v er the en tire duration of the sim ulation for eac h forcing com bination is plotted, for selected lo cations giv en b y T able 3{2 in Figure 3{10 Also plotted is the maxim um dierence in w ater lev el b et w een the

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36 4138 5313 9552 9965 9990 9991 10290 11020 13266 0 0.5 1 1.5 2 2.5 3 node #meters of water maximum elevation at node (combined forcing)maximum wind setupmaximum wave setupmaximum difference between max. elev and max. wind setup Figure 3{10: F or the sp ecied no des giv en in T able 3{2 w e plot the maxim um surge o v er the duration of the sim ulation for com bination of eac h forcing. Also plotted is the maxim um dierence b et w een the com bined forcing and wind only forced elev ation. exp erimen t with meteorological forcing and that with com bined forcing ac hiev ed at an y time during the sim ulation. F rom this plot w e can infer that the dierence b et w een the total w ater elev ation and the wind forced set-up comes from the addition of w a v e forcing. The maxim um dierence is less than the surge predicted b y the w a v e only forced run in all cases sho wn. This indicates that the eect of com bining the forcings in the mo del run in not simply a linear sup erp osition of the separate surge lev els. So far w e ha v e lo ok ed at spatial maxima and temp oral maxima. These ha v e giv en us an indication of the maxim um observ ed eects of adding w a v e forcing to wind and pressure and ho w the sea surface resp onds. Next w e lo ok at the time history of w ater lev el at individual lo cations. The b eha vior of the sea surface is

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37 particularly in teresting at the t w o follo wing lo cations ev en though there w as no station data a v ailable there. 0 50 100 150 0.5 0 0.5 1 1.5 2 2.5 Elevation (meters)Time (hours) wind wavelinear combinationwindwave Figure 3{11: The w ater lev el at No de{13266:P erdido Ba y FL. W e sho w the surge as predicted b y the meteorological forcing, the w a v e forcing, and the com bined forcing. Also plotted is the linear com bination of the t w o individually forced mo del results. W e start with the lo cation at P erdido Ba y FL, Figure 3{11 since it had the greatest lev el of w a v e set-up. The maxim um surge due to the w a v es has a sligh tly greater magnitude than the surge from the meteorologic forcing. The wind forced case ac hiev es its maxima ab out 6 hours after the w a v e forced sim ulation, consisten t with the observ ation that storm w a v es often reac h the shore b efore the storm's strongest winds. The com bined forcing run is less than the linear com bination of the wind and w a v es separately y et is appro ximately 1 meter higher than the wind and pressure forced prediction. A second notew orth y lo cation is Lak e Borgne, LA, sho wn in Figure 3{12 A t

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38 0 50 100 150 3 2 1 0 1 2 3 Elevation (meters)Time (hours) wind wavelinear combinationwindwave Figure 3{12: The w ater lev el at No de{11043:Lak e Borgne, LA. W e sho w the surge as predicted b y the meteorological forcing, the w a v e forcing, and the com bined forcing. Also plotted is the linear com bination of the t w o individually forced mo del results.this lo cation w e can see the dramatic eect of the ey e passing. The drop in w ater elev ation tak es place o v er a 30 hour p erio d, appro ximately t = 80 h to t = 110 h. During this time the w ater lev el go es from b eing pushed up ab out 2.4 meters, to b eing blo wn do wn ab out 2.4 meters. The no de at that lo cation is considered 'dry' (Elev ation = 0), and oscillates with w etting and drying b et w een appro ximately t = 135 h and t = 145 h. The p eak surge calculated with com bined forcing is ab out 40 cen timeters greater than that computed using just the meteorologic forcing. The output from the n umerical mo del is compared to historical data obtained from the NO AA National Oceanographic Data Cen ter, (NODC) W e fo cus on t w o stations where the surge is greatest. In order to pro vide the b est estimate, w e add in the astronomical tides. Our NOPP partner, Scott Hagen, at the Univ ersit y of

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39 Cen tral Florida has pro vided us with a tidal prediction at eac h of the lo cations of in terest, using ADCIR C on a ner resolution grid o v er a longer duration sim ulation. These mo deled tides matc h the observ ed phase at the stations. With the tides added, w e ha v e a comprehensiv e prediction of the w ater lev el. W e also rectify the denition of mean sea lev el b et w een our plots and the station data. ADCIR C denes the mean w ater lev el as zero. The station data is referenced to the mean lo w er lo w w ater con v en tion, MLL W (Figures 3{13 and 3{15 ). Figure 3{13 sho ws the predicted w ater lev el at P ensacola Ba y starting four Figure 3{13: The NO AA station data for P ensacola Ba y FL. W ater elev ation is referenced to MLL W. da ys b efore our sim ulation p erio d. F rom this w e estimate the predicted mean w ater lev el for the time of our sim ulation as +0.3 meter. When w e add this oset to our prediction the results can b e compared. Figure 3{14 sho ws that w e impro v e our prediction of the p eak elev ations at P ensacola, Florida b y 60% with the addition of w a v e forcing to the wind stress

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40 0 50 100 150 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time (hours)Elevation (meters)station datawind wavewind Figure 3{14: F orced b y the com bination of w a v e and meteorological inputs, the output from the ADCIR C mo del at P ensacola Ba y is plotted with the historical data recorded b y the station at the same corresp onding time p erio d. Our prediction is translated in order to more closely matc h the start time mean w ater lev el at the station. and atmospheric pressure. On either side of the p eak, the mo del under-predicts the w ater elev ations. The prediction is o b y as m uc h as 0.44 meter, with the greatest dierences o ccurring 10 to 20 hours on either side of the p eak. These coincide with the lo w tide cycles. The mean dierence b et w een the station data and the com bined forcing prediction is 0.11 meter. This is 50% less than the mean dierence b et w een the station data and the meteorological forcing (0.20 meter). W e quan tify the error in our prediction b y computing the mean square error, (MSE), and the ro ot mean square error, (RMSE), normalized b y the maxim um elev ation recorded b y the station using Eqs. 3{3 and 3{4 MSE (WL1 ; WL2 ) = 1 N N X i =1 (WL1(i) WL2(i)) 2 (3{3)

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41 RMSE(WL1 ; WL2 ) = 1 N N X i =1 (WL1(i) WL2(i)) 2 1 2 MAX(WL1) (3{4) whereN { n um b er of data records WL1 { station w ater lev el record WL2 { mo del prediction The MSE for the com bined forcing is 0.03 m 2 F or the wind and pressure prediction the MSE is 0.09 m 2 In this case, the normalized RMSE impro v es from 20% to 10% b y including the w a v es in the mo del prediction, a 50% reduction in error. A t the W a v eland lo cation, Figure 3{15 sho ws the predicted w ater lev el four da ys prior to and during our sim ulation. F rom this plot w e estimate a mean w ater Figure 3{15: The NO AA station data for W a v eland, MS (w ater elev ation is referenced to MLL W).

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42 lev el of +0.35 meters. Using this mean w ater lev el, w e translate the mo del results. Figure 3{16 sho ws go o d agreemen t b efore and during the storm. 0 20 40 60 80 100 120 140 0.5 0 0.5 1 1.5 2 2.5 Time (hours)Elevation (meters)station datawind wavewind Figure 3{16: F orced b y the com bination of w a v e and meteorological inputs, the output from the ADCIR C mo del at W a v eland is plotted with the historical data recorded b y the station at the same corresp onding time p erio d. Our prediction is translated in order to more closely matc h the start time mean w ater lev el at the station. With only the meteorologic forcing, the mo del under-predicts the w ater lev el at t=79 hours b y appro ximately 0.4 meter, in W a v eland, MS (Figure 3{16 ). When the w a v es are added, the prediction ac hiev es the p eak w ater lev el at t=79 hours to within 0.005 meter. The p eak w ater elev ation for our predictions, ho w ev er, do es not o ccur at t=79 hours. The predicted p eak w ater lev el of 1.98 meters, for the com bined forcing case, o ccurs at t=80 hours. The dierence b et w een the station data p eak and the com bined forcing p eak is 0.05 meter. The mean dierence b et w een the prediction and the station w ater lev el is 0.1 meter. W e compute the MSE to b e 0.08 m 2 with the w a v es added. This impro v ed from the MSE of the

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43 wind and pressure forced run of 0.11 m 2 The normalized RMSE, computed with Eq. 3{4 for the com bined forcing case is impro v ed from 17% to 14% b y adding the w a v es. A ma jor source for error at this lo cation o ccurs after the storm has passed, t > 120 h. Our mo del o v er-predicts the amoun t of set-do wn b y as m uc h as 0.75 meter. The second largest source for error is just b efore the p eak of the surge, when the tidal cycle is lo w. W e p erform the same error analysis for the time p erio d of t = 40 h to t = 110 h. During this p erio d, w e nd that the MSE impro v es from 0.15 m 2 to 0.06 m 2 with the addition of the w a v e forcing. The normalized RMSE impro v es from 20% to 13%, almost cut in half, b y including the w a v es. T i m e H o u r s S u r f a c e E l e v a t i o n 0 5 0 1 0 0 0 5 0 0 5 1 1 5 2 2 5W a v e l a n d r e s o l v e d w i n d w a v e P e n s a c o l a r e s o l v e d w i n d w a v e m a x r e s o l v e d w i n d w a v e W a v e l a n d r e s o l v e d w a v e P e n s a c o l a r e s o l v e d w a v e m a x r e s o l v e d w a v e W a v e l a n d w i n d w a v e P e n s a c o l a w i n d w a v e m a x w i n d w a v e W a v e l a n d w a v e P e n s a c o l a w a v e m a x w a v e Figure 3{17: W e compare the surface resp onse to com bined forcing and w a v e only forcing at the P ensacola lo cation and the W a v eland lo cation. Also plotted is the maxim um surface elev ation o v er the whole domain for the t w o forcing com binations. F or the resolv ed case, the nite elemen t grid has 121296 no des, compared to the 31435 no des of the curren t grid.

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44 Ab o v e, our bath ymetric sensitivit y tests ha v e sho wn that grid resolution can pla y a role. In order to b e sure that w e ha v e resolv ed the system adequately w e rene the nite elemen t grid, Figure 2{5 b y splitting eac h elemen t in to four. In doing so w e increase the n um b er of no des from 31435 to 121296. The surface resp onse from com bined forcing and w a v e only forcing is compared at the P ensacola lo cation and the W a v eland lo cation. W e also compare the maxim um surface elev ation resp onse to the t w o forcing cases. These comparisons are sho wn in, Figure 3{17 W e can see from the plot, that the t w o are in close agreemen t; ho w ev er, the computational time for the higher resolution grid is on the order of 5 times longer. W e determine that our system is adequately resolv ed and the mo del runs in an ecien t time frame with the curren t grid. The results sho w that the eect of including w a v es in the mo del forcing dep ends on the lo cation. The w a v es can ha v e a large eect as in the case of P erdido Ba y FL. In the comparisons of our results with historical data, w e nd that b y adding the w a v e forcing w e are b etter able to predict the p eak w ater lev el. Alternately at some lo cations the addition of w a v e forcing ma y not pro vide a signican t impro v emen t to the predictiv e p o w er of the mo del. Predictions made b y forcing the mo del with only the meteorologic constituen ts w ould suce at those lo cations; ho w ev er, w e cannot kno w whic h lo cations those are without the com bined forcing prediction results. The implications of the results are discussed Chapter 4.

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CHAPTER 4 CONCLUSIONS The ADCIR C tests demonstrate that the addition of w a v e forces can result in a 30% to 50% increase in sea surface elev ation. The results are sensitiv e to the station lo cation with resp ect to the storm, coastal features suc h as ba ys and islands and grid resolution in the near-shore region. The mo del captures the set-up and set-do wn for idealized bath ymetries in close agreemen t with analytical solutions for steady state conditions. Mo del sensitivit y to the drag co ecien t, C d form ulation has b een sho wn to eect the results b y as m uc h as 0.5 meter. W e selected the Garratt ( 1977 ) form ula 1{1 b ecause it pro duced results that w ere close to the mean of the v arious form ulations. Ho w ev er, further researc h to w ard the parameterizations of air-sea in teraction at high winds is needed. 4.1 Bath ymetry W e observ e from the bath ymetric tests that the depth proles ha v e an eect on the w a v e-induced set-up. The w a v e eld is sucien tly altered b y dissipativ e forces to eect a c hange in the on-shore momen tum transfer. Wind duration and fetc h will also eect the breaking w a v e heigh t. Wind has a c hance to impart more of its energy in to the w ater column b efore the w a v es break o v er the steep er prole, resulting in a larger breaking w a v e heigh t. W e conducted 27 tests for the nine com binations of wind sp eed and bath ymetry with wind, w a v e and com bined forcing. The output from the w a v e mo del, SW AN, w as con v erted to input for the circulation mo del, ADCIR C. W e also used the SW AN output in computing the steady state analytical solution. Our ADCIR C domain grid w as to o coarse to fully resolv e near-shore w a v e breaking in the case of the 1 meter w a v es; ho w ev er, w e w ere able to resolv e the stronger w a v e forcing o v er eac h of the bath ymetries. 45

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46 Up on comparing the ADCIR C results with the analytical solution, w e nd that with adequate resolution the t w o are in close agreemen t. Grid resolution at the shoreline is imp ortan t. In the cases where the breaking is resolv ed, the mo del only sligh tly under-predicts the analytical solution. The fact that w e obtain suc h close agreemen t with theory reinforces our condence in the output of the circulation mo del. Our results indicate that a reduction in the w a v e-induced set-up o ccurs when the w a v es propagate o v er a wide shallo w shelf. As the prole steep ens, the w a v e set-up will increase. Wind induced set-up is also a function of the bath ymetry Shallo w proles allo w for a larger set-up for the same wind strength compared to steep er proles. The lev el of surge from winds is also inruenced b y the fetc h. In our case w e ha v e a relativ ely short fetc h, th us reducing the lev el of wind set-up. W ere w e to increase the cross-shore domain of our sim ulation, w e w ould exp ect to see the wind set-up increase and dominate the system. F or the strongest forcing runs, the com bined wind and w a v e forcing runs for our domain are largest o v er the steep domain, where the w a v es dominate. The winds dominate o v er the shallo w prole, and there w e ha v e the second highest surge. Ov er the mild domain, b oth con tribute appro ximately equally and w e see the smallest total set-up. These results suggest that the individual con tribution from wind or w a v e forcing alone could b e greater than the com bined con tributions for b ed proles with extreme slop es. The v ariabilit y of w a v e set-up and the sensitivit y of wind-induced set-up to bath ymetry leads us to the conclusion that the relativ e imp ortance of the w a v e forcing increases o v er steep er coastal proles. 4.2 Hindcast The addition of w a v e forcing impro v es our o v erall predictiv e capabilities and can reduce the RMS error b y 20% to 50% dep ending on lo cation. F rom the con tour plots w e see that the w a v e set-up acts to oset the blo w-do wn and amplify the

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47 set-up generated b y the wind and pressure. The eect of w a v es on surge is also eviden t b efore the storm mak es landfall since the w a v es reac h the shore sev eral hours b efore the p eak winds. Set-up is most prominen t in the ba ys and coastal lak es. The mo del predicts that w a v es alone can accoun t for more than 1 meter of surge, as is the case in P erdido Ba y where the w a v e set-up w as more than half the total surge predicted with the com bined forcing. Ov er the whole domain the maxim um surge from the w a v es amoun ted to more than 30% of the maxim um w ater lev el predicted in the domain. During the p eak of the storm ev en t, the prediction and the recorded w ater lev els are in close agreemen t when w e include the wind, pressure and w a v e forcing. The addition of w a v es can allo w for as m uc h as a 60% increase in predictiv e p o w er, as sho wn b y the analysis at P ensacola Ba y 4.3 Signicance of W a v e Set-Up W a v es and w a v e momen tum rux are an imp ortan t part of the natural system resp onsible for storm surge. The signicance of the w a v e set-up, and therefore the inclusion of w a v e forcing in mo del predictions, is dep enden t on the bath ymetric prole in the path of the storm. If there is a wide, shallo w shelf, there will b e greater wind set-up at the shoreline. When wind-induced set-up dominates, the w a v es are not as signican t. Ho w ev er, the w a v e forces remain an activ e participan t in generating storm surge at dieren t phases of storm passage and in regions farther a w a y from the lo cation of the ey e of the storm, and should b e k ept in the computational mo dels for completeness. Our future plan of researc h includes griding up the lo wland coastal regions, allo wing for in undation, and mo deling the resp onse. W a v es can accoun t for more than 1 meter of set-up for our predictions of h urricane Georges. In general w e ha v e found that w a v es pro vide on the order of one-third of the set-up along the coast during h urricane Georges. The w a v e forcing is an imp ortan t factor in our case for represen ting h urricane storm surge.

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APPENDIX A BA THYMETR Y TEST:INPUT FILES A.1 W a v e Mo del Inputs The follo wing les are samples of the input les used to implemen t SW AN. W e sho w one le for eac h forcing strength. There will also b e separate les for eac h b ottom prole. The only c hanges in those other cases are the names of the input and output les. The follo wing le is the input used for the strongest of the forcings. $PROJ 'strongmedium' '0102' TEST 30 0 POOL$$ PURPOSE OF TEST: to calculate a wave climate on a simple $ bathymetry to input into ADCIRC $$ --|--------------------------------------------------------------|$ | This SWAN input file is template for all input in future for | $ | SWAN. | $ --|--------------------------------------------------------------|$$***********MODEL INPUT********************************** *** $CGRID REG 0. 0. 0. 50000. 10200. 25 2040 CIRCLE 90 0.05 0.25 40 $INPGRID BOTTOM 0. 0. 0. 2 510 25000. 20. READINP BOTTOM 1. 'mild.bot' 1 0 FREE $BOUN SHAPE JONSWAP 2. PEAK DSPR DEGREES BOUN SIDE S CCW CON PAR 7.0 15.0 90. 5. $SETUPWIND 56.0 90.0 $NUMERIC SETUP -3. 0.0001 2 30 $$************ OUTPUT REQUESTS ************************* $ 48

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49 CURVE 'CTA11' 25000. 0. 2040 25000. 10200. TABLE 'CTA11' XP YP DEPTH HS HSWELL DIR PDIR TDIR TABLE 'CTA11' HEAD 'o_strong_mild1.tab' XP YP DEPTH HS DIR PDIR TDIR $CURVE 'CTA12' 25000. 0. 2040 25000. 10200. TABLE 'CTA12' XP YP RTP FORCE TRANSP VEL DEPTH TABLE 'CTA12' HEAD 'o_strong_mild2.tab' RTP FORCE TRANSP $POOLCOMPUTESTOP$ The medium strength forcing in SW AN w as input using the next le. $PROJ 'thesis_01_01' 'test' TEST 30 0 POOL$$ PURPOSE OF TEST: to calculate a wave climate on a simple $ bathymetry to input into ADCIRC $$ --|--------------------------------------------------------------|$ | This SWAN input file is template for all input in future for | $ | SWAN. | $ --|--------------------------------------------------------------|$$***********MODEL INPUT********************************** *** $CGRID REG 0. 0. 0. 50000. 10200. 50 510 CIRCLE 90 0.05 0.25 40 $INPGRID BOTTOM 0. 0. 0. 2 510 25000. 20. READINP BOTTOM 1. 'shallow.bot' 1 0 FREE $BOUN SHAPE JONSWAP 2. PEAK DSPR DEGREES BOUN SIDE S CCW CON PAR 5.0 10. 90. 5. $SETUPWIND 30.0 90.0 $NUMERIC SETUP -3. 0.0001 2 30 $$************ OUTPUT REQUESTS ************************* $CURVE 'CTA11' 25000. 0. 510 25000. 10200. TABLE 'CTA11' XP YP DEPTH HS HSWELL DIR PDIR TDIR TABLE 'CTA11' HEAD 'o_mild_shallow102.tab' XP YP DEPTH HS DIR PDIR TDIR $

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50 CURVE 'CTA12' 25000. 0. 510 25000. 10200. TABLE 'CTA12' XP YP RTP FORCE TRANSP VEL DEPTH TABLE 'CTA12' HEAD 'o_mild_shallow202.tab' RTP FORCE TRANSP $POOLCOMPUTESTOP Third is the w eak est forcing input le. $PROJ 'thesis_01_01' 'test' TEST 30 0 POOL$$ PURPOSE OF TEST: to calculate a wave climate on a simple $ bathymetry to input into ADCIRC $$ --|--------------------------------------------------------------|$ | This SWAN input file is template for all input in future for | $ | SWAN. | $ --|--------------------------------------------------------------|$$***********MODEL INPUT********************************** *** $CGRID REG 0. 0. 0. 50000. 10200. 25 2040 CIRCLE 90 0.05 0.25 40 $INPGRID BOTTOM 0. 0. 0. 2 510 25000. 20. READINP BOTTOM 1. 'shallow.bot' 1 0 FREE $BOUN SHAPE JONSWAP 2. PEAK DSPR DEGREES BOUN SIDE S CCW CON PAR 1.0 10. 90. 5. $SETUPWIND 10.0 90.0 $NUMERIC SETUP -3. 0.0001 2 30 $$************ OUTPUT REQUESTS ************************* $CURVE 'CTA11' 25000. 0. 2040 25000. 10200. TABLE 'CTA11' XP YP DEPTH HS HSWELL DIR PDIR TDIR TABLE 'CTA11' HEAD 'o_weak_shallow102.tab' XP YP DEPTH HS DIR PDIR TDIR $CURVE 'CTA12' 25000. 0. 2040 25000. 10200. TABLE 'CTA12' XP YP RTP FORCE TRANSP VEL DEPTH TABLE 'CTA12' HEAD 'o_weak_shallow202.tab' RTP FORCE TRANSP $POOL

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51 COMPUTESTOP A.2 Circulation Mo del Inputs ADCIR C is run using an input le, fort.15. As men tioned b efore, con trol v ariables are dened in this le. The t w o tests, v aried forcings o v er bath ymetries and the h urricane Georges hindcast, will ha v e dieren t fort.15 les. These tests ha v e dieren t temp oral and spacial scales. These scales determine suc h v ariables as time step and duration. The time step should not exceed a v alue suc h that the Couran t n um b er is greater than 1.5. The Couran t n um b er is giv en as C # = ( g h ) 1 2 t x (A{1) The fort.15 les will b e sligh tly dieren t for eac h run of eac h test. Most of the parameters will b e the same for eac h run. W e rename our meteorological, wind stress and pressure, forcing le to the ADCIR C con v en tion of fort.22. W e also create a fort.22 le with ev ery v alue at all no des for eac h time step set to zero. This zero forcing is used when the w a v e forced mo del prediction is run. The w a v e forcing le is renamed to fort.23. This le is only read when the NWS rag is set to 102 in the fort.15 le. The NWS v ariable indicates whic h forcings are to b e read and the format of those forcings. The NWS rag is set to matc h the format of the meteorological forcing le and the w a v e forcing le. W e set NWS = 2 or 102. NWS = 2, corresp onds to a mo del run with meteorological forcing only NWS = 102, corresp onds to a run with meteorological forcing and w a v e stress forcing. The NWS parameter and the RSTIMINC are the only input v ariables that c hange b et w een the separate runs. RSTIMINC is the v ariable whic h tells the mo del the time incremen t at whic h the w a v e forcing, fort.23, input le is to b e read, if w a v e forces are used. Both runs that in v olv e w a v e radiation stress forcing ha v e NWS set to 102 and the RSTIMINC v ariable is set to

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52 1800, the same as the wtiminc v ariable. All other input v ariables in the fort.15 le are set to recommended v alues, as found in the ADCIR C man ual. The output consists of a le with the elev ation at ev ery no de at selected time step in terv als. W e c ho ose to not output the curren t or the wind and pressure as a time and space sa ving measure. As discussed ab o v e the in terv als w ere decided on after initial runs w ere completed. These les are then read to extract the maxim um surface elev ation time history The follo wing les are input les, fort.15, for ADCIR C. This le is used when the only input to the mo del is meteorologic forcing, (ie. wind and pressure). Thesis_01_01.wind 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION 01_01_01 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION 1 NFOVER NONFATAL ERROR OVERRIDE OPTION 0 NABOUT ABREVIATED OUTPUT OPTION PARAMETER 1 NSCREEN UNIT 6 OUTPUT OPTION PARAMETER 0 IHOT HOT START PARAMETER 1 ICS COORDINATE SYSTEM SELECTION PARAMETER 0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL) 1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER 2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER 1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER 0 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER 0 NTIP TIDAL POTENTIAL OPTION PARAMETER 2 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER 1 NRAMP RAMP FUNCTION OPTION 9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS 0.06 TAU0 WEIGHTING FACTOR IN GWCE 0.10 DT TIME STEP (IN SECONDS) 0.0 STATIM STARTING TIME (IN DAYS) 0.0 REFTIM REFERENCE TIME (IN DAYS) 1800. WTIMINC-RSTIMINC TIME INTERVAL-WIND & RAD.STRESS VALUES (seconds) 1.00 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS) 0.25 DRAMP DURATION OF RAMP FUNCTION (IN DAYS) 0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION 0.1 10 10 0.1 H0 MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin 265.5 29.0 SLAM0,SFEA0 CENTER OF CPP PROJECTION (NOT USED IF ICS=1) 0.06 FFACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFFICIENT 0.0 EVM LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1 0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1

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53 0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED 0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES 45.0 ANGINN INNER ANGLE THRESHOLD 0 0.0 .75 10000 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61) 16 !# of recording stations 100.0 5000.0 120.0 5000.0 140.0 5000.0 160.0 5000.0 180.0 5000.0 200.0 5000.0 220.0 5000.0 240.0 5000.0 260.0 5000.0 280.0 5000.0 300.0 5000.0 320.0 5000.0 340.0 5000.0 360.0 5000.0 380.0 5000.0 400.0 5000.0 0 0.0 .75 10000 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL STATION OUTPUT INFO(UNIT 62) 16 !#of recording stations 100.0 5000.0 120.0 5000.0 140.0 5000.0 160.0 5000.0 180.0 5000.0 200.0 5000.0 220.0 5000.0 240.0 5000.0 260.0 5000.0 280.0 5000.0 300.0 5000.0 320.0 5000.0 340.0 5000.0 360.0 5000.0 380.0 5000.0 400.0 5000.0 0 0.0 .750 10000 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STAT OUTPUT INFO(UNIT 71&72) 16 !#of recording stations 100.0 5000.0 120.0 5000.0 140.0 5000.0 160.0 5000.0 180.0 5000.0 200.0 5000.0

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54 220.0 5000.0 240.0 5000.0 260.0 5000.0 280.0 5000.0 300.0 5000.0 320.0 5000.0 340.0 5000.0 360.0 5000.0 380.0 5000.0 400.0 5000.0 1 0.0 1.00 1000 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELV OUT INFO(UNIT 63) 1 0.0 1.00 1000 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL OUT INFO(UNIT 64) 1 0.0 1.00 1000 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBALVEL OUTINFO(UNIT73&74) 0 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS 0.50 .75 10000 0. THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS 0 0 0 0 NHASE,NHASV,NHAGE,NHAGVHARMONIC ANALY & OUTPUT TO UNITS 51,52,53,54 1 10000 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS 1 2 0.000015 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS This input le is used to include the w a v es in the mo del prediction. Thesis_01_01.wave.wind 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION 01_01_01 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION 1 NFOVER NONFATAL ERROR OVERRIDE OPTION 0 NABOUT ABREVIATED OUTPUT OPTION PARAMETER 1 NSCREEN UNIT 6 OUTPUT OPTION PARAMETER 0 IHOT HOT START PARAMETER 1 ICS COORDINATE SYSTEM SELECTION PARAMETER 0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL) 1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER 2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER 1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER 0 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER 0 NTIP TIDAL POTENTIAL OPTION PARAMETER 102 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER 1 NRAMP RAMP FUNCTION OPTION 9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS 0.06 TAU0 WEIGHTING FACTOR IN GWCE 0.10 DT TIME STEP (IN SECONDS) 0.0 STATIM STARTING TIME (IN DAYS) 0.0 REFTIM REFERENCE TIME (IN DAYS) 1800. 1800. WTIMINC-RSTIMINC TIME INTERVAL-WIND & RAD.STRESS VALUES (seconds) 1.00 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS) 0.25 DRAMP DURATION OF RAMP FUNCTION (IN DAYS) 0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION 0.1 10 10 0.1 H0 MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin 265.5 29.0 SLAM0,SFEA0 CENTER OF CPP PROJECTION (NOT USED IF ICS=1)

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55 0.06 FFACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFFICIENT 0.0 EVM LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1 0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1 0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED 0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES 45.0 ANGINN INNER ANGLE THRESHOLD 0 0.0 .75 10000 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61) 16 !# of recording stations 100.0 5000.0 120.0 5000.0 140.0 5000.0 160.0 5000.0 180.0 5000.0 200.0 5000.0 220.0 5000.0 240.0 5000.0 260.0 5000.0 280.0 5000.0 300.0 5000.0 320.0 5000.0 340.0 5000.0 360.0 5000.0 380.0 5000.0 400.0 5000.0 0 0.0 .75 10000 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL STATION OUTPUT INFO(UNIT 62) 16 !#of recording stations 100.0 5000.0 120.0 5000.0 140.0 5000.0 160.0 5000.0 180.0 5000.0 200.0 5000.0 220.0 5000.0 240.0 5000.0 260.0 5000.0 280.0 5000.0 300.0 5000.0 320.0 5000.0 340.0 5000.0 360.0 5000.0 380.0 5000.0 400.0 5000.0 0 0.0 .750 10000 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STAT OUT INFO(UNIT 71&72) 16 !#of recording stations 100.0 5000.0 120.0 5000.0 140.0 5000.0

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56 160.0 5000.0 180.0 5000.0 200.0 5000.0 220.0 5000.0 240.0 5000.0 260.0 5000.0 280.0 5000.0 300.0 5000.0 320.0 5000.0 340.0 5000.0 360.0 5000.0 380.0 5000.0 400.0 5000.0 1 0.0 1.00 1000 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELE OUT INFO(UNIT 63) 1 0.0 1.00 1000 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL OUT INFO(UNIT 64) 1 0.0 1.00 1000 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBALVEL OUTINFO(UNIT73&74) 0 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS 0.50 .75 10000 0. THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS 0 0 0 0 NHASE,NHASV,NHAGE,NHAGVHARMONIC ANALY&OUTPUT TO UNITS 51,52,53,54 1 10000 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS 1 2 0.000015 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS

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APPENDIX B HINDCAST TEST:CIR CULA TION MODEL INPUT FILES As in the Bath ymetry tests the NWS rag is set dep ending on whic h forcings are to b e read in to the mo del. F or the meteorological forced run, NWS is set to 2 and there is no RSTIMINC v ariable. Both runs that in v olv e w a v e radiation stress forcing ha v e NWS set to 102 and the RSTIMINC v ariable is set to 1800.0, the same as the wtiminc v ariable. Again, a fort.22 le consisting of all zero v alues for the wind stress and the pressure has b een generated to b e used in the w a v e only forcing prediction. Output is written to the resp ectiv e les ev ery hour. Using this le, w e can generate a time series of the w ater lev el during the storm at an y lo cation in the domain. Again, the NWS parameter and the RSTIMINC are the only input v ariables that c hange b et w een the separate runs. The follo wing les are input les, fort.15, for ADCIR C. This le is used when the only input to the mo del is meteorologic forcing (i.e., wind and pressure). Georges_OFCL 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION all_runs 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION 1 NFOVER NONFATAL ERROR OVERRIDE OPTION 0 NABOUT ABREVIATED OUTPUT OPTION PARAMETER 1 NSCREEN UNIT 6 OUTPUT OPTION PARAMETER 0 IHOT HOT START PARAMETER 2 ICS COORDINATE SYSTEM SELECTION PARAMETER 0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL) 1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER 2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER 1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER 1 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER 0 NTIP TIDAL POTENTIAL OPTION PARAMETER 102 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER 1 NRAMP RAMP FUNCTION OPTION 57

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58 9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS 0.006 TAU0 WEIGHTING FACTOR IN GWCE 30.0 DT TIME STEP (IN SECONDS) 0.0 STATIM STARTING TIME (IN DAYS) 0.0 REFTIM REFERENCE TIME (IN DAYS) 1800.0 1800.0 wtiminc rtiminc seconds 30min 6.0000 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS) 0.5 DRAMP DURATION OF RAMP FUNCTION (IN DAYS) 0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION 0.1 10 10 0.1 H0 MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin 265.5 29.0 SLAM0,SFEA0-CENTER OF CPP PROJ(NOT USED IF ICS=1,NTIP=0,NCOR=0) 0.006 FFACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFF 0.0 ESL LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1 0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1 0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED 0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES 45.0 ANGINN INNER ANGLE THRESHOLD 1 0.0 6.0 120 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61) 5 TOTAL NUMBER OF ELEVATION RECORDING STATIONS -8.9366667e+01 3.0281700e+01 waveland ms -8.9140000e+01 2.8999000e+01 South Pass LA -8.9418330e+01 2.8925000e+01 SW pass LA -8.7211667e+01 3.0405300e+01 pensacola FL -8.9956667e+01 2.9263333e+01 Grand Isle LA 1 0.0 6.0 120 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL. STATION OUTPUT INFO(UNIT 62) 5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS -8.9366667e+01 3.0281700e+01 waveland ms -8.9140000e+01 2.8999000e+01 South Pass LA -8.9418330e+01 2.8925000e+01 SW pass LA -8.7211667e+01 3.0405300e+01 pensacola FL -8.9956667e+01 2.9263333e+01 Grand Isle LA 1 0.0 6.0 120 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STATION OUT INFO(UNIT 71&72) 5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS -8.9366667e+01 3.0281700e+01 waveland ms -8.9140000e+01 2.8999000e+01 South Pass LA -8.9418330e+01 2.8925000e+01 SW pass LA -8.7211667e+01 3.0405300e+01 pensacola FL -8.9956667e+01 2.9263333e+01 Grand Isle LA 1 0.0 6.0 120 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELEV OUT INFOUNIT 63) 1 0.0 6.0 120 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL OUT INFO(UNIT 64) 1 0.0 6.0 120 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBAL VEL OUT INFO(UNIT 73&74) 8 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS STEADY HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=1 0.00000000000000 1.0 0.0 HAFREQ(I=1),HAFF(I=1),HAFACE(I=1) K1 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=3 0.000072921165921 0.903 4.685423643 HAFREQ(I=3),HAFF(I=3),HAFACE(I=3) O1 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=4

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59 0.000067597751162 0.841 6.254177935 HAFREQ(I=4),HAFF(I=4),HAFACE(I=4) M2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=8 0.000140518917083 1.033 0.607861211 HAFREQ(I=8),HAFF(I=8),HAFACE(I=8) S2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=9 0.000145444119418 1.0 0.0 HAFREQ(I=9),HAFF(I=9),HAFACE(I=9) M4 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=16 0.000281037834166 1.066 2.932537116 HAFREQ(I=16),HAFF(I=16),HAFACE(I=16) M6 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18 0.000421556751249 1.101 1.25721302 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18) N2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18 0.000138000000000 1.033 1.128599708 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18) 0.00 6.00 120 1.0 THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS 1 1 1 1 NHASE,NHASV,NHAGE,NHAGV-HARMONIC ANALY & OUTPUT TO UNITS 51,52,53,54 1 200 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS 1 0 1.E-5 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS This input le is used to include the w a v es in the mo del prediction. Georges_OFCL 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION all_runs 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION 1 NFOVER NONFATAL ERROR OVERRIDE OPTION 0 NABOUT ABREVIATED OUTPUT OPTION PARAMETER 1 NSCREEN UNIT 6 OUTPUT OPTION PARAMETER 0 IHOT HOT START PARAMETER 2 ICS COORDINATE SYSTEM SELECTION PARAMETER 0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL) 1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER 2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER 1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER 0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER 1 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER 0 NTIP TIDAL POTENTIAL OPTION PARAMETER 102 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER 1 NRAMP RAMP FUNCTION OPTION 9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS 0.006 TAU0 WEIGHTING FACTOR IN GWCE 30.0 DT TIME STEP (IN SECONDS) 0.0 STATIM STARTING TIME (IN DAYS) 0.0 REFTIM REFERENCE TIME (IN DAYS) 1800.0 1800.0 wtiminc rtiminc seconds 30min 6.0000 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS) 0.5 DRAMP DURATION OF RAMP FUNCTION (IN DAYS) 0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION 0.1 10 10 0.1 H0 MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin 265.5 29.0 SLAM0,SFEA0-CENTER OF CPP PROJEC(NOT USED IF ICS=1,NTIP=0,NCOR=0) 0.006 FFACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFF 0.0 ESL LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1 0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1

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60 0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED 0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES 45.0 ANGINN INNER ANGLE THRESHOLD 1 0.0 6.0 120 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61) 5 TOTAL NUMBER OF ELEVATION RECORDING STATIONS -8.9366667e+01 3.0281700e+01 waveland ms -8.9140000e+01 2.8999000e+01 South Pass LA -8.9418330e+01 2.8925000e+01 SW pass LA -8.7211667e+01 3.0405300e+01 pensacola FL -8.9956667e+01 2.9263333e+01 Grand Isle LA 1 0.0 6.0 120 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL. STATION OUTPUT INFO(UNIT 62) 5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS -8.9366667e+01 3.0281700e+01 waveland ms -8.9140000e+01 2.8999000e+01 South Pass LA -8.9418330e+01 2.8925000e+01 SW pass LA -8.7211667e+01 3.0405300e+01 pensacola FL -8.9956667e+01 2.9263333e+01 Grand Isle LA 1 0.0 6.0 120 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STATION OUT INFO(UNIT 71&72) 5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS -8.9366667e+01 3.0281700e+01 waveland ms -8.9140000e+01 2.8999000e+01 South Pass LA -8.9418330e+01 2.8925000e+01 SW pass LA -8.7211667e+01 3.0405300e+01 pensacola FL -8.9956667e+01 2.9263333e+01 Grand Isle LA 1 0.0 6.0 120 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELEOUTPUT INFO(UNIT 63) 1 0.0 6.0 120 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VELOUTPUT INFO(UNIT 64) 1 0.0 6.0 120 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBAL VELOUT INFO(UNIT 71&74) 8 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS STEADY HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=1 0.00000000000000 1.0 0.0 HAFREQ(I=1),HAFF(I=1),HAFACE(I=1) K1 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=3 0.000072921165921 0.903 4.685423643 HAFREQ(I=3),HAFF(I=3),HAFACE(I=3) O1 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=4 0.000067597751162 0.841 6.254177935 HAFREQ(I=4),HAFF(I=4),HAFACE(I=4) M2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=8 0.000140518917083 1.033 0.607861211 HAFREQ(I=8),HAFF(I=8),HAFACE(I=8) S2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=9 0.000145444119418 1.0 0.0 HAFREQ(I=9),HAFF(I=9),HAFACE(I=9) M4 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=16 0.000281037834166 1.066 2.932537116 HAFREQ(I=16),HAFF(I=16),HAFACE(I=16) M6 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18 0.000421556751249 1.101 1.25721302 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18) N2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18 0.000138000000000 1.033 1.128599708 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18) 0.00 6.00 120 1.0 THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS

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61 1 1 1 1 NHASE,NHASV,NHAGE,NHAGVHARMONIC ANALY&OUT TO UNITS 51,52,53,54 1 200 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS 1 0 1.E-5 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS

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REFERENCES Anthes, R. A. 1982 T r opic al Cyclones, Their Evolution Structur e and Ee cts American Meterological So ciet y Boston, Mass. 1.3 Blain, C. A. 1997 Mo deling metho dologies for the prediction of h urricane storm surge. R e c ent A dvanc es In Marine Scienc e and T e chnolo gy 96 177{189. 1.1 Blain, C. A., Westerink, J. J. & Luettich, R. A. 1994 The inruence of domain size on the resp onse c haracteristics of a h urricane storm surge mo del. Journal of Ge ophysic al R ese ar ch 99 18,467{18,479. 1.1 Blain, C. A., Westerink, J. J. & Luettich, R. A. 1998 Grid con v ergence studies for the prediction of h urricane storm surge. International Journal for Numeric al Metho ds in Fluids 26 369{401. 1.1 2.3.1 Brebbia, C. A., Tra versoni, L. & Wr obel, L. C. ed. 1995 Application of a Domain Size and Gridding Strategy for the Prediction of Hurricane Storm Surge. In: Computer Mo del ling of Se as and Co astal R e gions II pp. 301{308. Computational Mec hanics Publications, Southampton, UK. 1.1 Dean, R. G. & D alr ymple, R. A. 1991 Water Wave Me chanic e for Engine ers and Scientists W orld Scien tic Press, Riv er Edge, New Jersey 1 1.4 1.4 3.2 Dean, R. G. & D alr ymple, R. A. 2002 Co astal Pr o c esses with Engine ering Applic ations Cam bridge Univ ersit y Press, Cam bridge, UK. 1.4 2.2.1 Donelan, M. A. 1998 Air-w ater exc hange pro cesses. Co astal and Estuarine Studies 54 19{36. 1.2 Donelan, M. A., Dobson, F. W., Smith, S. D. & Anderson, R. J. 1993 On the dep endence of sea surface roughness on w a v e dev elopmen t. Journal of Physic al Oc e ano gr aphy 23 2143{2149. 1.2 Garra tt, J. R. 1977 Review of drag co ecien ts o v er o ceans and con tinen ts. Monthly We ather R eview 105 915{929. 1.2 4 Geernaer t, G. L. & Plant, W. J. ed. 1990 Bulk P arameterizations for the Wind Stress and Heat Fluxes. In: Surfac e Waves and Fluxes I c hap. 5, pp. 91{172. Klu w er Academic Publishers, Netherlands. 1.2 2.1 Guiney, J. L. 1999 Pr eliminary R ep ort, Hurric ane Ge or ges, 15 Septemb er 01 Octob er 1998 T e ch. R ep. NO AA, National Hurricane Cen ter, Miami, Florida. URL http://www.nhc.noaa.gov/1998georges.html 08/2002. 1.5 62

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63 Ha gen, S. C., Westerink, J. J. & K olar, R. L. 2000 One-dimensional nite elemen t grids on a lo calized truncation error analysis. International Journal for Numeric al Metho ds in Fluids 32 241{261. 1.1 Ha gen, S. C., Westerink, J. J., K olar, R. L. & Horstmann, O. 2001 Tw o-dimensional, unstructured mesh generation for tidal mo dels. International Journal for Numeric al Metho ds in Fluids 35 669{686. 1.1 Hol thuijsen, L. H. 2000 SW AN Cycle III version 40.11 User Manual (Not the Short V ersion) Delft Univ ersit y NL. 2.2.2 2.2.3 James, I. D. 1974 Non-linear w a v es in the nearshore region: Shoaling and set-up. Estuarine and Co astal Marine Scienc e 2 207{234. 1.4 K omar, P. D. 1998 Be ach Pr o c esses and Se dimentation 2nd edn. Pren tice-Hall, Upp er Saddle Riv er, New Jersey 1.4 K omen, G. J., Ca v aleri, L., Donelan, M., Hasselmann, K., Hasselmann, S. & Janssen, P. 1996 Dynamics and Mo del ling of Oc e an Waves Cam bridge Univ ersit y Press, Cam bridge, UK. 2.3.2 Longuett-Higgins, M. S. 1983 W a v e set-up, p ercolation and underto w in the surf zone. Pr o c e e dings of the R oyal Sc o ciety of L ondon, Series A, Mathematic al and Physic al Scienc es 390 283{291. 1.4 Longuett-Higgins, M. S. & Stew ar t, R. W. 1964 Radiation stresses in w ater w a v es; a ph ysical discussion with applications. De ep-Se a R ese ar ch 11 529{562. 1 Luettich, R. A., Westerink, J. J. & Sheffner, N. W. 1992 ADCIR C: A n A dvanc e d Thr e e-Dimensional Cir culation Mo del for Shelves, Co asts and Estuaries. R ep ort 1: The ory and Metho dolo gy of ADCIR C-2DDI and ADCIR C-3DL with Applic ations T e ch. R ep. DRP-92-6. Departmen t of the Arm y W ashington, DC. 1.1 2.1 2.1 2.1 McDougal, W. G. & Hudspeth, R. T. 1981 Non-Planar Be aches: Wave Induc e d Setup/Setdown and L ongshor e Curr ent T e ch. R ep. ORESU-R-81-016. Oregon State Univ ersit y Sea Gran t College Program, Corv alis, Oregon. 1.4 Sa ville, T. 1961 Exp erimen tal determination of w a v e set-up. National Hurric ane R ese ar ch Pr oje ct R ep ort 50 242{252. 1.4 Stive, M. J. F. & Wind, H. G. 1982 A study of radiation stress and set-up in the nearshore region. Co astal Engine ering 6 1{25. 1.4 Turner, P. J. & Baptist a, A. M. 1999 A CE/gr e dit Online Do cumentation Oregon Health & Science Univ ersit y Cen ter for Coastal and Land-Margin Researc h (CCALMR), Bea v erton, Oregon. URL http://www.ccalmr.ogi.edu/software/xmgredit5/ 11/2002. 2.2.1

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BIOGRAPHICAL SKETCH Born in Oklahoma during the y ear 1973, I w as raised in North Carolina. Gro wing up, m y paren ts w ould tak e m y brother and sister and m yself on all kinds of tra v els. I recall visiting man y of the National P arks and camping out of our 1971 Do dge v an. These exp eriences culminated in a mon th-long trip around the United States when I w as 10 y ears old, whic h included hiking the Grand Can y on. Through these exp eriences I gained resp ect for nature and an abilit y to cop e, adapt and accomplish what I put m y mind to nishing. I b ecame certied in SCUBA diving at the age of 16 while carving m y path through high sc ho ol. I sp en t m y 18th birthda y in England, tra v eling outside the USA for the rst time. The exp erience w as ey e-op ening. In 1992, I found m y w a y to college at the Univ ersit y of North Carolina at Greensb oro. As an undergrad, I serv ed as presiden t of the So ciet y of Ph ysics Studen ts (SPS), and w as inducted to and ME (the ph ysics and mathematics honor so cieties). I sp en t 2 w eeks during the summer of 1997 in Ha w aii as a researc h div er for the P acic Whale F oundation, cataloging sh and coral life at 4 reef sites around Maui. My last semester w as sp en t abroad, studying at the Univ ersit y of Stuttgart in German y and learning the German language and culture. While in Europ e, I w as able to tra v el and exp erience dieren t cultures, and broaden m y w orld view. I graduated from UNC-G in Decem b er 1999, cum laude, with a Bac helor of Science degree in mathematics and a minor in ph ysics. After graduation I sp en t 2 y ears in Connecticut, w orking at a lo cal newspap er and teac hing at a lo cal high sc ho ol. Though I enjo y ed teac hing, I felt that I w as not reac hing m y full p oten tial. Lo oking for a w a y to bring together m y lo v e of the sea and m y educational bac kground, I decided it w as time to go bac k to sc ho ol. 64

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65 I applied to graduate sc ho ol at the Univ ersit y of Florida departmen t of Coastal Engineering. In addition to the past 2.5 y ears of researc h and graduate course w ork, I ha v e also b een certied as a NA UI Div emaster and cleared as a Science Div er for the Univ ersit y of Florida. My lo v e of the o cean, nature and science brough t me to this p oin t in m y life, and will con tin ue to driv e the decisions I mak e. F or no w, I ha v e tak en steps to w ard a Ph.D.,with ten tativ e plans onpursuing a career in the storm prediction / damage mitigation / comm unit y organization. In the future I could see m yself at some p oin t teac hing again. Where there are go o d teac hers there is hop e for so ciet y


Permanent Link: http://ufdc.ufl.edu/UFE0003304/00001

Material Information

Title: Effect of Wave Forces on Storm Surge
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
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Material Information

Title: Effect of Wave Forces on Storm Surge
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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EFFECT OF WAVE FORCES ON STORM SURGE


By

ROBERT J. WEAVER
















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004


































Copyright 2004

by

Robert J. Weaver















I dedicate this to Jacqueline, Moose and Chaos.














ACKNOWLEDGMENTS

I would like to thank my parents for encouraging me to pursue my goals,

giving their support, and being there when I needed an ear to bend. Thanks

to Jacqueline for keeping me on track, and tolerating me when I would go off

on a tangent. I would like to acknowledge my adviser, Donald Slinn, and my

committee members Robert Dean and Max Sheppard for their support and advice.

I would like to thank the National Oceanographic Partnership Program, NOPP,

partners for their help and contributions. Special acknowledgments to Robert

Jensen at Engineer Research and Development Center, ERDC, for his help with

the wave fields, Scott Hagen at the University of Central Florida, UCF, for his

help in understanding the Advanced Circulation Model for Coasts, Shelves, and

Estuaries (ADCIRC) and grid generation, as well as providing the tides for our

use in the prediction. I would also like to credit Vince Cardone and Andrew Cox

at OceanWeather, Inc. for providing the wind and pressure fields for our model

prediction.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... .......... iv

LIST OF TABLES ................... .............. vii

LIST OF FIGURES ................... ............. viii

ABSTRACT ........................................ x

1 INTRODUCTION .................. ... 1

1.1 Surge Model ................... .......... 2
1.2 Air-Sea Coupling ................... ....... 3
1.3 Atmospheric Pressure ...... ........... .. ..... 4
1.4 Coastal Bathymetry ...... ........... ........ 5
1.5 Hurricane Simulation ...... ........... .. ..... 7

2 METHODOLOGY ....... ......... ........ 9

2.1 Numerical Model ................... ........ 9
2.2 Bathymetric Tests ............... ........ 13
2.2.1 Domain ................ ......... 13
2.2.2 Forcings ................... ......... 14
2.2.3 Implementation . . . 17
2.3 Hurricane Georges Hindcast .. . ... 18
2.3.1 Dom ain . . . 19
2.3.2 Forcing . . . 20
2.3.3 Implementation . . . 22

3 RESULTS ..... . ... ............... 24

3.1 Wind Stress . ... .......... 24
3.2 Bathymetric Sensitivity .. . .. 26
3.3 Hurricane Georges . . . 32

4 CONCLUSIONS . . .. .......... 45

4.1 Bathymetry . ... .......... 45
4.2 Hindcast ...... . ...... 46
4.3 Significance of Wave Set-Up . . ..... 47









APPENDIX

A BATHYMETRY TEST-INPUT FILES .. ........... 48

A.1 Wave Model Inputs ................... ....... 48
A.2 Circulation Model Inputs ..... ............ .... 51

B HINDCAST TEST CIRCULATION MODEL INPUT FILES ..... 57

REFERENCES ......................................... 62

BIOGRAPHICAL SKETCH ................... ......... 64















LIST OF TABLES
Table page

2-1 Drag coefficient formulations to test model sensitivity . 10

2-2 Wind strength and wave height for bathymetric sensitivity tests 15

2-3 Model input domains .. . ... ...... 22

3-1 Surge generated by forcing components over each bottom profile 28

3-2 Coordinates of selected locations . ....... 35















LIST OF FIGURES
Figure

2-1 Profiles created for bathymetric sensitivity tests . .

2-2 Finite Element Grid created for bathymetric sensitivity tests .

2-3 Wave fields from SWAN . . .

2-4 F, from SW AN . . .... .

2-5 North-West Atlantic Domain . . .

2-6 Gulf Coast region of model domain . . .

2-7 Nested domains for wave field data . . .

3-1 Drag coefficients plotted vs. wind speed . .

3-2 Wind stress plotted vs. wind speed . . .

3-3 Surge profiles for wind stress formulations . .

3-4 F output from SWAN . . .

3-5 Surge levels for each forcing group over each bathymetry .


Comparison of Model results with analytic solution .

Surface contour plots as Georges crosses Gulf .

Surface contour plots for each forcing combination at t-

Time series of maximum surface elevation .

Maximum surge predicted at selected locations .

Surge at Node-13266:Perdido Bay, FL . .

Surge at Node-11043:Lake Borgne, LA . .

NOAA station data for Pensacola Bay, FL .

Model results at Pensacola Bay, FL . .

NOAA station data for Waveland, MS . .


hours


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3-16 Model results at Waveland, MS . . ... 42

3-17 Grid resolution comparison . . ... .. 43















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

EFFECT OF WAVE FORCES ON STORM SURGE

By

Robert J. Weaver

M\.v 2004

Chair: Donald N. Slinn
Major Department: Civil and Coastal Engineering

The disastrous effects of hurricanes on coastal communities are well known,

and there is a need to better understand the causes of storm surge to prepare for

future events. To better understand the mechanisms, we examine the influence of

individual factors that produce surge. The total surge depends on wind surface

stress, inverted barometer effects, and wave forcing, as well as tidal stage and

bathymetry in the path of the storm. We are particularly interested in the effect

of wave stresses on overall surge. In the past, many models have neglected the

influence of wave induced set-up. Wave stresses could be left out of numerical

models for computational efficiency, when they are not a significant player. On

the other hand, for conditions when wave stresses are significant, it is of interest to

know if the total surge is a linear superposition of the wind and wave set-up, or if

there is a more complicated relationship. Our work is a component of a real-time

wind, wave, and surge forecasting system for tropical cyclones being developed

under the National Oceanographic Partnership Program.

To test the rise in surface elevation, we use the Advanced Circulation Model

for Coasts, Shelves, and Estuaries in two-dimensional depth-integrated mode









(ADCIRC 2DDI). We conduct a suite of model studies including tests of wind

stress formulation, grid resolution, and bottom friction.

To test sensitivity to coastal bathymetry, we generate three simple finite

element grids on idealized coastal topographies. We use these to test three different

strengths of storms. The storms range in intensity from a strong gust (10 m/s), to

a medium strength tropical storm (30 m/s), to a Category 3 hurricane (56 m/s).

Here, steady winds are applied on our coastal domain, and the associated wave

fields are predicted using SWAN (Simulating Waves X. -lIre). We examine

relationships between bathymetry and set-up due to wind and waves. These tests

aid us in interpreting more complicated results from historical storm events over

real bathymetry. Our results indicate that for the same wind forcing and offshore

wave conditions, wave generated surge can vary for different coastal bathymetries.

The shallower bathymetric profile yields the greater level of wind-induced surge,

and the steeper profile allows for a greater surge from wave set-up for the same

forcing levels. We also note that the linear combination of wind and wave forced

set-up is slightly larger than the model prediction with combined forcing.

The final application of our model system is a hindcast of hurricane Georges

(1998). When Georges made landfall in the Biloxi, Mississippi area, it was a

strong category 2 hurricane on the Saffir-Simpson scale. We use the North West

Atlantic basin for the model domain. We run the model three times, first with

wind and atmospheric pressure forcing. The second time we force the model

with wave radiation stresses from the predicted wave fields. The final model run

combines wind and pressure fields with wave forcing. The resulting changes in

surface elevation are compared with each other and with NOAA station data. We

demonstrate that, in this case, to more accurately predict the surge it is necessary

to include the wave forcing. Here, the wave forcing contributes approximately 25%

to 33% of the total rise in water level.















CHAPTER 1
INTRODUCTION

Tropical cyclones are low-pressure systems that form in the tropics. In the

northern hemisphere the wind will rotate around the low-pressure center in a

cyclonic pattern, counter-clockwise. As this low-pressure system moves over warmer

waters, it can intensify. A hurricane is a strong tropical cyclone. By the time the

system is classified as a hurricane, there are maximum sustained winds of 74 mph

(33 m/s). The surface of the ocean under the storm will react to the pressure and

wind. The threat to coastal communities from a hurricane includes high winds

causing damage, as well as coastal flooding caused by the storm tide. Storm surge

is the rise in water level due to hurricanes. There are three main causes of storm

surge: wind set-up, wave set-up, and the inverse barometric effect of the low central

pressure of the storm. The tides will also play a role in the effect of the hurricane

on the coast. Storm tide is the combination of the surge with the tide. If the storm

makes landfall during high tide, the effect is a higher water level than if the surge

hits the shore during low tide. The wind set-up is caused by the wind blowing

across the surface of the water over hundreds of square kilometers. Wave set-up is

caused by the generation and then release of wave momentum (or radiation stress)

in the water column as waves are formed, shoal, and then break.

Radiation stress is the flux of momentum due to waves (Longuett-Hi:'iii-' & Stewart,

1964). It is the transfer of wave momentum to the water column that forces a

change in the mean water level. Near the coast, wave momentum flux is balanced

by a pressure gradient associated with a change in the local water depth. As

wave momentum increases in the presence of nonbreaking waves, the mean water

level lowers. As breaking commences, the wave energy and momentum decrease,









resulting in a reduction of the radiation stress carried by the waves. These stresses

(force per unit area) are imparted into the water column. The rapid reduction of

wave radiation stress near the coast forces a rise in mean sea level. The discharged

momentum from the waves pushes against the water column, and produces an

opposing hydrostatic pressure gradient. During storm events, the resulting rise in

water level can play a major role in storm surge.

According to linear theory, the effective change in water level from a steady

train of linear waves approaching normal to the shore on a gently sloping bottom

is about 19% of the breaking wave height (Dean & Dalrymple, 1991). This may

increase or decrease as we take into account nonlinear effects, dissipative forces, and

wave obliquity. The amount of wave set-up is also affected by the bottom contour

of the near-shore and beach face. We examine the effect of wave radiation stress

on sea surface elevation for complex forcing conditions. Our goal is to increase

understanding of the role that waves play in storm surge.

Our work is a component of a real-time wind, wave, and surge forecasting

system for tropical cyclones being developed under the National Oceanographic

Partnership Program (NOPP). This partnership involves four academic institutions

and six government agencies, sharing data, models, and resources.

1.1 Surge Model

The hydrodynamic model we use to predict the sea surface elevation is the

Advanced Circulation Model for Coasts, Shelves, and Estuaries in two-dimensional

depth-integrated mode (ADCIRC 2DDI) (Luettich et al., 1992). It is a finite

element model that solves the conservation laws for mass and momentum through a

Generalized Wave Continuity Equation in nonconservative form. We predict water

level changes by driving the hydrodynamics with
Wind stress and atmospheric pressure only
Wave radiation stress only
A combination of wind and wave stresses and atmospheric pressure fields.









From this series of predictions we determine the significance of including wave

stresses in our model system. As a test case, we perform hindcasts of hurricane

Georges (1998) with each of the forcing options. We compare the results with

water-level data for that time period, and evaluate the predictive value of including

the wave forces in the model inputs.

Domain sensitivity studies have been performed using the ADCIRC model

(Blain, 1997; Blain et al., 1994; Brebbia et al., 1995; Blain et al., 1998). It was

found that selecting an appropriate sized domain was an important factor in the

development of an accurate prediction. With a large enough domain, the key

features of resonance and circulation are captured (in our case, the domain includes

the Northwest Atlantic Basin with the Caribbean and the Gulf of Mexico). A

benefit to such a large domain is the simplicity of the boundary conditions. The

open boundaries are primarily located in the deep ocean, minimizing boundary

effects on the coastal region of interest. Hagen et al. (2000, 2001) showed that

sufficient grid resolution over regions of varying bathymetry is important. In these

regions, a finer mesh is required to capture the evolution of the water elevation.

1.2 Air-Sea Coupling

Storm surge is dependent on wind surface stress, inverted barometer effects,

tidal stage, bathymetry, and changes in wave radiation stresses. Momentum

transfer at the air-sea interface produces wind-generated waves and has been

studied extensively (Geernaert & Plant, 1990; Donelan et al., 1993; Donelan,

1998). The wind stress is usually approximated as T = pCd|UIU where p is the

density of air, U is the mean wind speed taken at 10 meters above the surface, and

Cd is the drag coefficient. The drag coefficient depends on sea surface roughness

and atmospheric stratification, and has a magnitude on the order of 10-3. There

are many different recommended forms for the drag coefficient, Cd. The range

of validity of the different formulas for Cd depend on wind conditions, and other









factors. There has been relatively little research, however, into what formulation

would best suit hurricane wind and sea conditions. It is difficult to make open

ocean measurements during hurricane conditions. Most equations produce (by

extrapolating from data) an increasing drag coefficient with increasing wind

speed. This formulation fits data sets at lower wind speeds. But, when the

strength of the winds becomes large, the tops of the waves can be sheared and

the relative wave surface roughness changes. This is analogous to a slip boundary

condition. One possibility, currently being debated, is that at higher wind speeds

the drag coefficient may level off as the waves are sheared off at the crests, and

the net momentum imparted to the water column begins to level off. With such

complicated possible scenarios, one must be aware of the sensitivity of the surge

predictions to the choice of the coefficient of drag in the wind stress formulation.

We pursue such sensitivity tests below and then proceed with our hindcasts

using one of the standard ADCIRC formulas (Garratt, 1977) for drag coefficient

(Eq. 1-1), with a maximum allowable drag coefficient of 0.003. The corresponding

formulas for wind stress are given by Eqs. 1-2, 1-3.


Cd = 0.001 (0.75 + 0.067 U) (1-1)


,-. = Cd 0.001293 v,(n) *U (1-2)

,- =Cd 0.001293 vy(n) U (1-3)

where
U = [v,(n)2 + Vy(n)'2- wind speed
., horizontal wind stress in x-direction
horizontal wind stress in y-direction
v1(n) horizontal wind velocity in x-direction
vy(n) horizontal wind velocity in y-direction
1.3 Atmospheric Pressure

Ambient atmospheric pressures are around 1012 mb. The low-pressure center

of a tropical storm causes a local rise in the sea surface. This inverted barometer







5

effect is important when attempting to predict water levels. One can expect around

1 cm of water rise for each millibar of pressure drop in deep water (Anthes, 1982).

Though this effect may seem small, hurricane Georges had a minimum recorded

central pressure of 938 mb while in the Atlantic, corresponding to a 0.75 m rise in

sea surface elevation. Georges weakened by the time it made landfall on the Gulf

Coast. The central pressure increased to 964 mb, corresponding to an approximate

0.5 m rise in sea level in deep water. As a storm approaches land, the height of

the sea level rise associated with the inverse barometer effect can increase due to

the horizontal convergence of the water. The convergence and reflection against

the coastline can increase the surge level. If the barometric effect is neglected, the

prediction of surge would be less than the actual rise in elevation measured at the

coast.

1.4 Coastal Bathymetry

The bathymetry of the shelf and near-shore region will also play a role in

the level of storm surge measured at the coastline. The magnitude of the wind

blow-up is dependent on the depth and width of the continental shelf. Wind stress

over a shallow wide shelf will produce a larger set-up than the same wind stress

over a narrower or deeper shelf. The steady state, one-dimensional solution for

wind-induced sea level rise (Dean & Dalrymple, 1991) is shown in Eq. 1-4.


a9 nw ) (14)
ax pg(h + r)

where
h mean water depth
q displacement free surface about the mean
x cross-shore location
n = I x(-h) and n is greater than 1
Tx(') wind surface stress in x-direction
Tx(-h) bottom shear stress in x-direction
p reference density of water
g gravity









As seen in Eq. 1-4, in the deeper waters when h > 7, the set-up goes to zero.

In the depth-averaged approximation, near a coast in steady state, the horizontal

velocity is zero and the bottom shear stress vanishes and n = 1.

We present results below of experiments concerning wave set-up on a variety

of profiles. The simplest beach model is a planar beach. Many planar beach

models were used to derive the approximate formulas for wave set-up (Saville, 1961;

Longuett-Hii->in-. 1983; Stive & Wind, 1982; James, 1974; Dean & Dalrymple,

1991). For a planar beach, the mean water surface displacement from small

amplitude normally incident waves is about 0.19Hb (Dean & Dalrymple, 1991).

Komar (1998) empirically fits a more complex relationship between the slope of the

foreshore and the maximum set-up elevation at the shoreline, Eq. 1-5, based on the

Irribaren number, Eq. 1-6 (ratio of beach face slope to wave steepness).


77m =. 0.18g'SH T (1-5)


Coo (16)

Where S is the slope of the bottom, Ho and L, are the significant wave height

and wavelength of the incident waves in deep water, and T is the wave period.

Additional studies have been performed on beaches with a concave-up

Equilibrium Beach Profile, (EBP) (Dean & Dalrymple, 2002).


h = AX3 (1-7)


The results of these tests are compared to the case of a planar beach, and it was

found that the set-up on a concave-up beach will mirror the bottom curvature

(\I. I)ougal & Hudspeth, 1981). Smaller waves will break closer to the shoreline

and the overall breaking pattern is inversely proportional to the water depth. To

a first approximation, the maximum surge level will be the same at the shoreline

as for a plane beach. Farther offshore, however, the planar beach will allow for a









greater increase in elevation, as the mean water level mimics the bottom contour.

The EBP allows waves to propagate closer to the shoreline before breaking,

imparting their momentum to the water column closer to shore than on a planar

beach. The first set of tests described below were performed using the Equilibrium

Beach Profile as the bathymetric contour.

Guza and Thornton (1981) developed a relation based on measurements of

irregular wave set-up on beaches in Southern California, Eq. 1-8. The study was

performed on a beach with a mild slope (0.02), where the waves break across a

wide surf zone. This would be classified as a dissipative beach (Komar, 1998). The

incident wave heights ranged from 0.6 m to 1.6 m.


maO = 0.17H, (1-8)

This relation yields a result approximately 10% less than the linear solution. Our

research focuses on much more powerful wave events, with time varying wave fields

and complex shorelines. Our domain is the Gulf of Mexico shelf. This region has

a much milder sloping beach and near-shore region than that of California. We

expect more dissipation from nonlinear effects and bottom friction in our test due

to this bathymetric difference.

1.5 Hurricane Simulation

For our most comprehensive numerical experiment, we perform a hindcast

of hurricane Georges. Hurricane Georges made landfall in the Biloxi, Mississippi

area on September 28, 1998 (Guiney, 1999). At the time of landfall the storm was

rated a strong Category 2 hurricane on the Saffir-Simpson scale, with estimated

maximum sustained one minute winds of 90 knots (103.6 mph, 46.3 m/s). During

previous days, as the storm made its way across the Caribbean, Georges peaked as

a Category 4 hurricane with estimated top wind speeds of 135 knots (155.4 mph,

69.5 m/s). The storm caused extensive damage and loss of life. The relief effort is









estimated to have cost $2.5 Billion and 602 lives were lost, predominantly in Puerto

Rico, Cuba, and the Caribbean islands. We model the last 6 days of the storm,

from the 25th September, 1998 until the 1st of October, 1998. After this time, the

storm is well over land. The domain of our model predictions encompasses the

North West Atlantic Basin. The finite element grid was provided by Dr. Rick

Luettich, of the University of North Carolina. Wind, wave, and barometric pressure

data was provided within the domain by our NOPP partners, including NOAA, the

National Hurricane Center, the National Weather Service, and OceanWeather Inc.

Our results will be compared to tidal station data at different locations on the Gulf

Coast.














CHAPTER 2
METHODOLOGY

2.1 Numerical Model

To predict the rise in surface elevation, we use the Advanced Circulation

Model for Coasts, Shelves, and Estuaries in two-dimensional depth-integrated

mode (ADCIRC 2DDI). ADCIRC was developed by the Army Corps of Engineers

Dredging Research Program (DRP). The principal developers were J.J. Westerink

and Rick Luettich (Luettich et al., 1992). One of the purposes of the research

was to develop a model that could compute storm surge hydrographs and provide

surface elevation data. There are four main inputs for the ADCIRC model. These

include the finite element grid and bathymetry file, the numerical parameter

set, the meteorological forcing and the wave forcing files. The grid is defined by

node numbers and locations, element neighbors and boundary information. The

input parameters include the time step, duration of the model run, coordinate

system definitions, friction coefficient, horizontal eddy viscosity, output parameters,

input file parameters, etc. (Luettich et al., 1992). Two other main input fields are

necessary to force the model run, the meteorologic (wind stress and atmospheric

pressure) and the wave stress forcing files.

The meteorological forcing file contains the wind stress and pressure data

at specified time intervals. Wind stress is computed from the wind speed and

direction using Eqs. 1-2 and 1-3. In order to make this conversion, we must

decide on the formula to use for drag coefficient. There are numerous relationships

that attempt to parameterize the drag coefficient, Cd. We tested seven different

formulations, six given in Table 2-1 (Geernaert & Plant, 1990) and a constant

value of Cd = 0.003. Garratt's (1977) formula represents a compilation of results









Table 2-1: Drag coefficient formulations used to test model sensitivity

Authors Cd 103
Garratt (1977) 0.75 + 0.067|UI
Miller (1964) 4.0
Klapstov (1983) 0.49 + 0.07U + 58 1.06Wi -T
Geernaert (1987) 0.58 + 0.085|UI
Smith (1980) 0.61 + 0.063|UI
Large & Pond (1981) 0.44 + 0.063| U


calibrated for wind speeds between 4 and 21 m/sec. The ADCIRC model uses

Garratt's formula; however, the model puts a cap on the maximum value at

Cd = 0.003. We remove this maximum requirement for the sensitivity tests. Miller

(1964) proposed a maximum drag coefficient of 4.0 10-3, for wind speeds of 52

m/sec. The value was inferred using the ageostrophic technique. This method

assumes a transfer of angular momentum in a cyclonic system which results in

a cross-isobaric flow. Klapstov (1983) provides a comprehensive formulation

determined from 214 records of data for wind speeds ranging from 2 to 21 m/sec.

Geernaert's (1987) formula, for wind speeds of 5 to 25 m/sec, was fit to 116 data

points. The Large & Pond (1981) formula is a fit to 1001 data points, for wind

speeds of 10 to 26 m/sec. Smith (1980) fit 120 points for wind speeds ranging

from 6 to 22 m/sec. There have been no direct measurements of drag formula for

wind speeds over 26 m/sec. When Georges made landfall the estimated one minute

winds were 90 knots (46.3 m/sec). Holding all other variables constant, we ran the

ADCIRC model for each of the drag coefficient formulations, and determined the

sensitivity of the model. Once we have decided on a satisfactory formulation, we

generate the wind and pressure input file, fort.22.

The wave forcing fields specify the x and y directed wave stresses. These

are also provided for every node at predetermined time intervals. We will discuss

the generation of the wave fields in more detail for each test case below. Once

calculated, we generate the wave forcing input file, fort.23.









The ADCIRC model output includes surface elevation and depth averaged

current velocities for every node at user specified time intervals. One can also

prescribe recording stations for time series of velocity and sea level at predefined

time intervals for any location in the domain. The model also has the ability to

perform harmonic analysis of the surface elevation.

This finite element model solves the conservation laws for mass and momentum.

Conservation of mass is implemented by way of the Generalized Wave Continuity

Equation (GWCE) (Luettich et al., 1992) derived from Eq. 2-1. The momentum

equations in nonconservative form are derived from the turbulent incompressible

Navier-Stokes (Reynolds averaged) equations. First the three dimensional equations

are simplified using the Boussinesq approximation and the hydrostatic pressure

approximation, yielding Eqs. 2-2-2-4.

Ou Ov Ow
+5 + o 0 (2-1)
ox oy oz

9u 9u 9u 9u 9 p 1 87,x 87,x 87z
S+ u + v +w- fv= -- [ F + -+ ] (2-2)
ot ox ay oz ox po po ox ay oz
Ov ov Ov Ov O p 1r Owxv __ 8zv
S+ t + v +w + fu = + [x + + (2-3)
ot ox oy oz oy po po x oy oz

S-pg (2-4)

where
f = 2Qsinr = Coriolis parameter
g = acceleration due to gravity
F = tide generating parameter
v = molecular viscosity
p(x, y, z, t) = time-averaged pressure
p(x, y, z, t) = density of water
po = reference density of water
t = time
T = integration time scale for separating turbulent and time-averaged quantities
Tx,(x, y, z, t) v= [2 ] f u'u'dt combined viscous and turbulent Reynolds
stress
,y(x, y, z, t) = v[4 + ] { oT u'v'dt combined viscous and turbulent Reynolds
stress









T,,(x, y, z, t) = v[V + 2] foT u'w'dt combined viscous and turbulent Reynolds
stress
,xy(x, y, z, t) = v[j + ] { oT v'u'dt combined viscous and turbulent Reynolds
stress
Tyy(x, y, z, t) = v[2#] 4 o v'v'dt combined viscous and turbulent Reynolds
stress
rzy (xy, Z, zt) = v[ + ] oT v'w'dt combined viscous and turbulent Reynolds
stress
9 = degrees latitude
u(x, y, z, t), v(x y, y, z, t), w(x, y, z, t) = time-averaged velocities in the x, y and z
directions
u'(x, y, z, t), v'(x y, y, z, t), w'(x, y, z, t) = departures of the instantaneous turbulent
velocities from the time-averaged velocities
x, y = horizontal coordinate direction
z = vertical coordinate direction
S=- angular speed of the Earth (7.29212x10-5 rad/s)

After eliminating pressure as a dependent variable using 2-4 and defining

the top and bottom boundary conditions, Eqs. 2-1, 2-2 and 2-3 are vertically

integrated to yield two-dimensional equations for free surface displacement and

depth-averaged velocity. The depth-integrated form of the continuity equation is

given by Eq. 2-5. The vertically integrated momentum conservation equations are

given by Eq. 2-6 and 2-7.


a( OUH aVH
ot Ox ay


(2-5)


OU OU OU ap 1 TsI Tb
+ U + V fu V [+ g((- a)]+ [M+ D, +1] (2-6)
at Ox ay Ox po H po po
aV aV V P s 1 Ts Tb
+- U +V + fU = + ((- aq)] + .+D,+ -] (27)
at ax ay fy po H po po
where
a = effective Earth elasticity factor (a = 0.69)
Dx D- -- momentum dispersion
D O -D momentum dispersion
Duu ft uudz, Duu, f vuDdz, Duu _fh v dz
rq(x, y, z) Newtonian equilibrium tidal potential
Sdz + -L (-dz depth-integrated, horizontal momentum
diffusion









, f_ dz + -b 7J dz depth-integrated, horizontal momentum
diffusion
U(x, y, t) k j, udz depth-averaged horizontal velocity
V(x, y, t) f_ vdz depth-averaged horizontal velocity
ui(x, y, z,t) 1u U departure of horizontal velocity from depth-averaged
velocity
v(x, y, z, t) v -V departure of horizontal velocity from depth-averaged velocity
H(x, y, t) (+ h total water depth to free surface
( free surface
h(x, y) bathymetric depth relative to geoid
Tsx Ty applied free surface stresses
Tbx, Tby applied bottom stresses

The bottom stresses are replaced by a quadratic friction term. The equations

are differentiated and combined to get the GWCE. DSRP-92-6, Report 1: Theory

and Methodology (Luettich et al., 1992) gives a complete derivation.

2.2 Bathymetric Tests

The first set of tests we perform are a series of experiments examining set-up

over idealized bathymetric conditions for different wind and wave conditions. Our

purpose is to determine the model response to separate and combined influences of

variations in wind speed, wave height, and water depth.

2.2.1 Domain

We generate wind and wave fields over three bathymetries. Contours are

created, Figure 2-1, using the equilibrium beach profile method (Dean & Dalrymple,

2002):

h = Ax A = 0.2, 0.1, 0.05 (2-8)

Where A is a parameter based on the average grain size of the near-shore

sediment, x is the cross-shore distance and h is water depth. We define the

average near-shore slope as the slope from the shore, x = 0, to the water depth at

x = 1 km. The beach profiles have average near-shore slopes of 0.017, 0.0091 and

0.004, from steepest to mildest. Farther offshore, in the region 2 km to 20 km, the

average slopes are 0.0065, 0.0028 and 0.0017, respectively. The profile is uniform













20

0

-20

S-40

-60

I -80-

-100-

-120 h=0.20*x"'
Sh = 0.10 x"'
h = 0.05*x"'
MWL
-140
0 5000 10000 15000 20000
Crossshore Distance (meters)



Figure 2-1: Bathymetric contours created to test the wave and wind set-up


in the alongshore. We generate a finite element grid, Figure 2-2, for the model

domains using ACE/gredit (Turner & Baptista, 1999). Resolution at the shoreline

is on the order of 20 meters, and decreases as the depth increases.

2.2.2 Forcings

Three different strength shore normal winds are chosen. The weakest wind

forcing is a 10 m/s wind that corresponds to a strong gust. The intermediate

case is a 30 m/s wind, corresponding to a medium strength tropical storm. The

strongest wind used corresponds to a Category 3 hurricane on the Saffir-Simpson

scale, with a 56 m/s wind speed. The associated wave forces were generated using

SWAN (Simulating Waves Near-shore) (Holthuijsen, 2000). The offshore wave

heights specified are 1.0 m, 5.0 m, and 7.0 m, corresponding to the wind speeds

of 10, 30 and 56 m/s respectively (Table 2-2). These offshore wave heights were

selected after a series of iterations with SWAN, keeping the wind speed constant.














10000


S8000


6000


4000


2000

2500 5000 7500 10000
Cross-shore (meters)


Figure 2-2: Finite Element Grid created with ACE/gredit (resolution at the
shoreline is 20 m)

Table 2-2: Wind intensity and off-shore wave height used to force the circulation
model for the bathymetry tests

Strength Wind(m/s) Wave(m)
Weak 10 1.0
Medium 30 5.0
Strong 56 7.0


Our applied winds are uniform in time and space. The domain SWAN uses to

compute the wave fields is 20 km cross-shore and 50 km along-shore. We make sure

that the along-shore direction is large enough that the center line of the domain

will be unaffected by boundary effects. SWAN uses a Cartesian computational grid

with 5 m spacing. The wave fields generated in SWAN are based on a JONSWAP

distribution with directional spreading of 5 degrees. Bottom friction is turned

on, as is white-capping. The SET-UP function is also turned on. SWAN outputs

the momentum transfer from the wave field to the depth averaged currents by











integrating the radiation stresses over the wave direction and frequency spectrum.

The x and y components of the momentum transfer are



F = s[- as (2
p Ox ay


asyx
drJ


where
S,, = pg f [ncos20 +n ]EdadO
S, = Sy = p9 f [nsinOcoso] EdadO
Syy pg f [nsin20 +n ]EdadO

C

The wave heights and forcing output by SWAN are shown in Figure 2-3 and

Figure 2-4, respectively, for the three bathymetric contours and three specified

wind fields. The wind speed is converted into a wind stress for ADCIRC as





8-


2 Steep Slope
-Mild Slope
Shallow Slope
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Crossshore Distance (meters)

10 Steep Slope
Mild Slope
Shallow Slope

4-



0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Crossshore Distance (meters)

Steep Slope
Mild Slope
1:! Shallow Slopej
s \


Figure 2-3: The wave fields output by SWAN over the three bathymetric contours.
A) Strong forcing. B) Medium forcing. C) Weak forcing.


9)


(2-10)


1 OS
F,= [-
p By




















0
0
O
B )
1


0





0
0



-"-0

0
;O









0
0-




0-




0-


-0


S Strong Forcing
1 Medium Forcing
Weak Forcing
,8 -
6-
4-



1000 2000 3000 4000 5000 6000 7000 8000 9000 1 OOOC
Crossshore Distance (meters)

S Strong Forcing
04 Medium Forcing
S Weak Forcing
03 -



Oil -d

1000 2000 3000 4000 5000 6000 7000 8000 9000 10 OOOC
Crossshore Distance (meters)

Strong Forcing
04 Medium Forcing
S Weak Forcing
03 -
02 -
01 -


01


500 600 7000 800 9000 10 00
Crossshore Distance (meters)


Figure 2-4: The F, output field from SWAN for each of the three forcing strengths

(the value of the forcing is given by Equation 2-9). A) Steep slope. B) Mild slope.

C) Shallow slope.




described previously and then interpolated to the finite element grid, Figure 2-2.


Using ADCIRC, we test the change in sea level for three scenarios

atmosphere forcing only

wave forcing only

combined wind and wave forcing.


2.2.3 Implementation


The time step for ADCIRC is determined by the Courant number and is set


such that C# < 1.5. The Courant number is given as


C# (gh)1At
CW =


(2-11)


On the finely resolved grid, a time step of 0.10 sec is necessary to ensure reliable,


stable results. With such a small time step, the total run length needs to be as


short as possible, but long enough for the system to reach equilibrium. We use


1000


2000 3000 400









time weighting factors for the free surface terms in the GWCE of 0.35, 0.30 and

0.35. The free surface terms at the Kth time level are weighted by g (0.35 + 0.30).

These terms at the K 1 time level are weighted by g 0.35. These factors are

chosen such that the sum is 1.0. The initial conditions are u = v = 0q = 0. In

order to damp out the wave created by the initial overshoot of the equilibrium

position, the model is ramped up by gradually introducing the forcing over 6 hours

and the bottom friction is increased to 0.06. This is acceptable because we are

interested in obtaining a steady state solution in which the depth averaged currents

and associated bottom stresses are zero. In SWAN, for the wave fields, we used the

more realistic default bottom friction, the semi-empirical formula derived from the

JONSWAP results (Holthuijsen, 2000).

The factor that weights the wave and primitive continuity contributions to the

GWCE is set to match the value of the friction coefficient as recommended in the

ADCIRC manual, To = 0.06. Without these steps an overshoot wave will seiche

through the basin, potentially introducing a numerical instability or requiring

a smaller time step and take much longer to achieve steady state conditions.

Taking the ramp-up time into consideration, we obtain a steady state set-up by

running the model for a period of 1 day. For this grid resolution, a model run

takes approximately 2 days of CPU time on a 3.0 GHz Pentium processor. After

inspecting the output, we notice that the system equilibrates after approximately

0.75 day. Appendix A gives sample ADCIRC input files for the bathymetric test.

2.3 Hurricane Georges Hindcast

We conducted a hindcast of a historical storm event. The landfall of hurricane

Georges on the Mississippi coast was chosen as the subject storm. In order to

accomplish this we needed to decide on the proper model domain and forcing to

be used. We also obtained historical data to compare to our surge predictions from










the NOAA National Ocean Service Center for Operational Oceanographic Products

and Services, (NOAA NOS CO-OPS) web site.

2.3.1 Domain

It is important to ensure that the domain is large enough to capture the true

resonant characteristics of a basin (Blain et al., 1998). We also want to formulate

our modeling system to accommodate the majority of tropical cyclones so we can

have a general use domain for future model forecasts. The model domain is the

North West Atlantic Basin, including the Caribbean Sea and the Gulf of Mexico,

Figure 2-5. This grid was provided by Rick Leuttich. With such a large domain,


S25
-J
20

15

10


-90 -80 -70 -60
Longitude


Figure 2-5: Finite Element Grid of the Northwest Atlantic Domain consisting ov
31435 Nodes and 58369 Elemants. The nodal spacing is 0.03 to 0.06 degree at the
coast, 0.016 degree in the inlets, and about 0.5 deg maximum spacing in the Gulf of
Mexico.


we have the ability to model any storm that enters the western Atlantic, not just

the Gulf of Mexico. In addition, the only open boundary is at the easternmost










wall. This is far enough from the coastlines of interest that boundary effects will

be minimized. In the case of hurricane Georges, our simulation starts as the storm

enters the Gulf of Mexico between Florida and Cuba, and lasts until after landfall.

The region of landfall is shown in Figure 2-6. From this perspective we are

able to see the relatively high resolution in the coastal region.





30.5 -

30 -

29.5

29











.2.3.2 Forcin5
-J
28

27.5

27

26.5

Longitude


Figure 2-6: The Gulf Coast region of our model domain (Louisiana to Florida).
This is where hurricane Georges made landfall in the Continental U.S.


2.3.2 Forcing

Our forcing for hurricane Georges are provided by the NOPP partners.

The wind and pressure inputs are a product of satellite, aircraft flight level, and

buoy data from the National Hurricane Center, assimilated by OceanWeather

Inc. (Cardone and Cox). The data are given over the whole domain, 5N-53N and

99W-50W, in 30 minute intervals, on a 0.20 degree Cartesian grid. The wind and

pressure fields are then interpolated onto the finite element grid, Figure 2-5. The









wind speed is converted into a wind stress as described previously. The wind stress

and pressure are then written out to the meteorological forcing file, fort.22, to be

read by ADCIRC.

Wave fields were generated by Robert Jensen at the US Army Corps of

Engineers, Engineer Research and Development Center (ERDC). The assimilated

wind and pressure data are used to force WAM-3G (Wave Action Model, Third

Generation) (Komen et al., 1996). Wave fields are calculated at two resolutions

over the portion of the domain shown in Figure 2-7 The coarser resolution data set,


30






" 25






20
20


Longitude


Figure 2-7: The wave fields are provided at two levels of resolution. Near the
region of landfall the waves are given at every 0.1 degree. In the Gulf of Mexico
basin the waves are given at every 0.2 degree.


0.2 degree, is given over a basin domain consisting of the Gulf of Mexico, portions

of the Caribbean and Northwest Atlantic. A finer resolution grid, 0.1 degree, is

provided for the region of interest near landfall along the Gulf Coast, including

the coastal regions of Louisiana, Mississippi, Alabama, and Florida. The domains









Table 2-3: Model and forcing domains

Domain S-N W-E
NW Atlantic FE Grid 8N-46N 98W-60W
Wind and Pressure 5N-53N 99W-50W
Wave Basin 18N-31N 98W-75W
Wave Region 28N-30.4N 97W-82W


for the inputs are given in Table 2-3. The finer resolution wave field is the wave

region. The resolution for the wave region is 0.1 degree. The resolution for the

wave basin and wind and pressure fields is 0.2 degree.

Wave data is provided as wave height, peak period, and mean direction on

the Cartesian grid. The gradients of the radiation stresses are calculated using

2"d order central differences everywhere except at the boundaries where a first

order forward difference is implemented. The forcing is then calculated from the

gradients using Eqs. 2-12,2-13.


F, + sY] (2-12)


F 1[ SYY + ] (2-13)
p 9y Ox
where
S, = -(2n2 (2nc 1))
Sxy = Sy = EncosOsinO
S,, Y (2nsin2 (2n ))
C
The momentum forcing is then interpolated to the finite element grid, Figure 2-5.

The finer domain data is nested in the coarser set during the interpolation process.

This data set is output to the wave forcing file, fort.23, to be read by the ADCIRC

model.

2.3.3 Implementation

Due to the larger grid resolution used for the hurricane predictions, the

Courant number stability does not play such a restrictive role as in the idealized









beach experiments. For the hurricane Georges hindcast, we use a time step of

30.0 seconds. Our friction coefficient is set to a more realistic value of 0.006, as

is the GWCE weighting factor, To = 0.006. The time weighting factors for the

GWCE are 0.35, 0.30 and 0.35. We run the model for 6 days, ramping the forcing

up over 0.5 day. The input data is provided at 30 minute intervals, and the initial

conditions are u = v = 0r = 0. Additional details and sample ADCIRC input files

(fort.15) for the hurricane Georges experiments are given in Appendix B.

This defines our problem and our method for developing a solution. We run

the models for the two geometries and each input parameter that we have set. We

report on the results of our numerical experiments below.
















CHAPTER 3
RESULTS

3.1 Wind Stress

The first test we perform using the Advanced Circulation Model for Coasts,

Shelves, and Estuaries (ADCIRC), is a test of the drag coefficient and wind stress

formulation. We test seven drag coefficient formulations, the six given in Table 2-1,

and the constant value, Cd = 0.003. Figure 3-1 shows how each of the drag

coefficient formulations responds to wind speed. The Miller coefficient, 4.0 10-3,




7- -----


0 IIo I(1 0354)




S WIND SP ED (m/s)


Figure 3-1: The seven drag coefficient formulations plotted vs. wind speed.


was developed for wind speeds over 50 m/sec. The plot of 3.0 10-3 represents

the maximum value for Cd that is usually allowed in ADCIRC. Other formulas

are fitted to data sets for which wind speeds vary from 2 to 26 m/sec. Garratt's

formula fits the middle of the spread of the remaining formulas.

The resulting wind stress magnitudes are plotted in Figure 3-2. Notice that

at high wind speeds each of the formulas keeps incre.'-iin. passing the, Cd = 0.003

cutoff. Geernaert's formula increases more rapidly than the others, reaching

the cutoff value sooner. Garratt's, the standard formulation in ADCIRC, and











IVIIi(1 9S40)



o -







Figure 3-2: Wind stress calculated using the different drag formulas and the cutoff
value, plotted vs. wind speed.


Klapstov's formulas produce results that lie in the middle of the other plots. At

lower wind speeds all the formulations, except the two constants, behave similarly.

The wind stress values are calculated for hurricane Georges. These stress

values are used as inputs to force the ADCIRC model. The results of maximum

set-up and set-down during the storm from the seven tests are shown in Figure 3-3.

Early in the simulation, as the storm enters the domain and makes its way across

deeper waters, all but the two constant formulations are in close agreement. We

would expect Miller's approximation to be greater than the others throughout the

domain. During the time associated with the simulation, hurricane Georges was

a Category 2 storm with winds less than 50 m/sec. We also see that the surge

level associated with the cutoff value for Cd is greater than the results associated

with the other formulations. The surge driven by Geernaert's formula comes

close to that forced by the cutoff value, but only for a short period of time. The

water elevation predicted using the wind stresses generated by Garratt's simple

formula and Klapstov's more complicated formula, lie in the middle of the other

predictions. Our purpose of conducting these tests was to quantify the sensitivity

of the surge response to the wind stress parameterization, and to estimate error

bars associated with this uncert.iiil1 v. Without further insight into the optimal













3 ----- Milermin
-- max
0.003 cutoff min
2.5 max I
Geernaert min *
max
2 ^ Garratt min
max
Klapstov min
Large & Pond min /
max
1 Smith min
max
Co
0.5
> Time (hours)








-2






Figure 3-3: Maximum and minimum surge generated for each of the wind stress
formulations using the seven different drag coefficients.


drag coefficient response to high winds, we accept the Garratt formulation; as it

is simple and seems to capture the middle of the road solution. We recognize that

the resulting surge prediction can vary as much as 0.5 meter depending on the

choice of drag coefficient formulation. Similar sensitivity tests were conducted for

the coefficient of bottom friction, and a moderate value of 0.006 was selected.

3.2 Bathymetric Sensitivity

Now we examine the results of the bathymetric sensitivity tests with varied

forcing. The wave heights and forcing components output by SWAN are shown

in Figure 2-3 and Figure 2-4, respectively, for each bathymetric profile and

forcing pair. From these results we calculate the integral F = foshore Fxdx,

for Fx > 0. The magnitude of F will give us an idea of what to expect for the

surge. Figure 3-4 shows the magnitude of the integrals for each forcing level over












60
SSteep
m Mild
Shallow
50-



40-


LL-
b 30



20-



10-



10 30 56
Forcing Level (wind speed in m/sec)



Figure 3-4: The integral sum of F output by SWAN for the three different
forcing over the three bathymetric profiles. The value of the forcing is given by
equation 2-9


each profile. We see a trend of decreased F as the profiles get shallower. This

difference in F becomes more pronounced as the forcing level increases. The larger

waves associated with the stronger forcing, will have a greater interaction with the

bottom boundary. Dissipative effects of bottom friction will play a larger role for

these cases. Across the shallower domains, the waves will break farther from shore.

The wind stress imparted on the water column prior to breaking will therefore

be smaller than over a steeper profile. It follows that the wave height at breaking

will be smaller, as shown in Figure 2-3. Breaking farther offshore also allows more

dissipation in a wider surf zone than the steep domain.

Having obtained our wave forcing components with SWAN, we use ADCIRC

to test the change in sea level for each set of forcing : wind, wave, wind and wave.

The results are summarized in Table 3-1 and Figure 3-5.









Table 3-1: Maximum calculated
bathymetric profile


surge for forcing components over each


Bathy Strength Wave(m) Wind(m) Wind&Wave(m) Linear Combination(m)
Shallow Weak 0.079 0.02 0.10 0.10
Shallow Medium 0.27 0.30 0.53 0.56
Shallow Strong 0.40 1.00 1.33 1.40
Mild Weak 0.085 0.01 0.09 0.09
Mild Medium 0.31 0.16 0.45 0.47
Mild Strong 0.51 0.56 1.00 1.07
Steep Weak 0.032 0.005 0.037 0.037
Steep Medium 0.50 0.08 0.56 0.58
Steep Strong 1.29 0.30 1.48 1.59


-E1-
o wave
mwnd
1 5 linear comb
2


*_ni


B)


7II


I wave
O wind
O wind wave
W linear comb


i=nmlE


Orni


Forcing Level (by Wind Speed in m/s)


Figure 3-5: The surge levels for each forcing group over each bottom topography
(data from Table 3-1) A) Steep slope. B) Mild slope. C) Shallow slope. The
wind-wave entry represents the combined forcing for the model run. The linear
combination entry represents the sum of the surge predicted from the wind forcing,
and that predicted using only the wave forcing.


The level of wind set-up varied depending on the steepness of the bathymetric

profile. For each level of input for' in-r. the wind set-up was greatest over the


10 30 56(by nd Spd n s)
Forcing Level (by Wind Speed in m.s>


10 30 56
Forcing Level (by Wind Speed in m/s)


1 -
E









shallow bathymetry, and the set-up decreased as the profile became steeper (Figure 3-5).

This is in agreement with the governing equation, Eq. 1-4, for the steady state

solution for wind set-up.

The equilibrium state for the water surface elevation, calculated for the

different wave stresses alone, also varied over the different bathymetric profiles.

The steady state solution for wave set-up over a mildly sloping bottom is given by

Eq. 3-1 (Dean & Dalrymple, 1991).

dj 1 dS,
A 1 dS (31)
dx pg(h +-r) dx

where
7 mean surface displacement

After some simplifications it can be shown that at the shore, the equation for

the surface displacement can be approximated by equation 3-2.

3V2
71(0) = + 32 b (3-2)


where
Tb mean surface displacement at breaking
hb depth at breaking
K breaking constant

Thus, by this approximation, the wave-induced set-up of identical wave fields

at the shore is independent of the profile. The approximation also assumes that

the breaking constant (and breaker type) is the same for each profile and each

forcing strength, for our tests c = 0.73. We have just shown that our results

predict a decrease in wave set-up for the same forcing strength (output by SWAN)

as the profiles become more shallow. In part this can be attributed to different

steady wave fields developing over different bathymetries for the same wind field

conditions. To better understand the results we compare the ADCIRC results

with the analytic solution, Eq. 3-1. This comparison, presented in Figure 3-6,









shows that the model results are in close agreement with

solution for the mild and strong forcing cases.

A) B).




K I .


the analytic steady state



C) eta (analytic)
adcirc transect wave















I) i


Figure 3-6: Comparison of Model results for wave forcing with the analytic
solution for steady state wave set-up. Shown are all nine profile and forcing
combinations: A) Shallow profile, weak forcing. B) Shallow profile, medium forcing.
C) Shallow profile, strong forcing. D) Mild profile, weak forcing. E) Mild profile,
medium forcing. F) Mild profile, strong forcing. G) Steep profile, weak forcing. H)
Steep profile, medium forcing. I) Steep profile, strong forcing.


We see that the cases of the weak wave forcing over the mild and steep

bathymetry are not sufficiently resolved on the 20 meter ADCIRC grid to capture

the full set-up at the shoreline. Though the finite element model and theory agree

outside of the breaking region, the model output under predicts the surge level.

Grid spacing at the shoreline for the circulation model is too coarse to reasonably

resolve the spatial gradients of breaking. For more intense forcing components,

the 20 meter spacing adequately resolves the system. In these cases the ADCIRC

results agree with the results predicted by Eq. 3-1 when calculated with the SWAN









output. It is the variation in wave forcing fields calculated by SWAN that produces

different wave-induced set-up for similar wind forcing conditions. This variation

is caused by altered breaking wave conditions that develop due to the length

differences of the wind fetch prior to breaking.

The predicted variation in the level of wave set-up over the different

bathymetries is dependent on the strength of the forcing. Total dissipative

effects are increased for increased wave heights. Large waves feel the bottom

more strongly than smaller waves, and the effect of bottom friction in SWAN plays

a greater role in the case of larger wave heights. These effects are reflected in the

output from SWAN and translated to the results of the circulation model.

Figure 3-5 shows that the surge from the combined forcing is smallest over

the mild profile. Peak wind set-up occurs over the shallow profile, and the peak

wave set-up occurs over the steep profile. The level of wind set-up is fetch limited.

Our domain is only 20 km in the cross-shore. We would expect that over a larger

cross-shore domain, the winds would begin to dominate the storm surge.

In summary, the results show that the importance of the waves increases as the

profile becomes steeper. Set-up due to waves does vary over the different profiles,

and the steeper profile allows for a greater wave-induced set-up than the shallower

profile. In addition, the wind has less of an effect on the steeper profiles, and thus

the waves dominate the set-up. Winds play a larger role when the domain has

a wide shallow shelf. On the shallow profile, the wind induces the majority of

the set-up. In both cases, our test results indicate that waves make a significant

contribution to the resulting surge levels. These results, however, are specific to

the present, fetch limited, idealized domains. The next step is to examine what

happens when we use realistic temporally and spatially dependent wind fields,

include a variable pressure field, compute the associated wave fields, and run the

models over a real domain with complex coastal bathymetry.











3.3 Hurricane Georges

We perform a hindcast of hurricane Georges. Elevation output from ADCIRC

is converted into a time series of contour plots showing the water level as hurricane

Georges makes its way from the Straits of Florida to the Gulf Coast. A series

of these plots is shown in Figure 3-7. Time is measured from t=0 on September

25 at 00:00 hour. The eye of the storm enters the Gulf, t = 30.00 h, and moves

northwest. The model captures the inverted barometer effect under the eye, and

the set-up and blow-down as the eye passes and winds shift direction. Set-up is

produced on the windward side of barrier islands and in the bays.


A) B) C)

32 32 32

30 30 30

28 c 28- o 28-

26 26 26

24 24 24

90 -88 -86 -84 -82 -90 -88 -86 -84 -82 90 -88 -86 84 -82
Longitude Longitude Longitude

D) E) F)
32 :b 32 | 32

30 IH 30

I28 I28 !28

26 26 26

24 24 24

90 88 86 84 82 90 88 86 84 82 90 88 86 84 82
Longitude Longitude Longitude


Figure 3-7: A series of surface contour plots shows the surge as hurricane Georges
makes its way across the Gulf of Mexico and makes landfall (prediction was made
with the combined forcings. A) t = 10 hours into the simulation. B) t = 30 hours.
C) t = 50 hours. D) t = 70 hours. E) t = 90 hours. F) t = 110 hours.



We compare contour plots at the same time from three different forcing


predictions. The difference between wind and pressure only, wave only, and










combined wind, pressure and wave forced simulations are evident in Figure 3-8.

The difference in surface elevation in the back of bays is greatest. The hurricane


Longitude
B)






Longitude
C)






Longitude

Figure 3-8: A series of surface contour plots shows the surge as hurricane Georges
make landfall, t=82 h. A) Surface elevation generated from the meteorological
forcing. B) Surge created by wave forcing. C) Surge generated from the combined
forcing.


winds are blowing in a cyclonic (counter-clockwise) pattern. Depending on the

orientation of the shore to wind direction, we observe either set-up or set-down

at the land boundary. In the case of waves only, the model predicts an initial

set-down just offshore of the barrier islands. The water level then rises closer to

the land boundaries. For the combined forcing prediction the effects of wave set-up

reduce the net set-down at the land boundary caused by the wind and pressure

only. Offshore, in the region of wave set-down, the blow-up from the wind is

reduced. The contour plots give us a general indication of the spatial distribution










of the water surface. For a more quantitative representation, we plot the time series

of the water elevation at different locations.

A time series of the maximum surge predicted over the whole domain is

given by Figure 3-9. The combined, wind, pressure, and wave forced prediction is


3


2.5




E
1.5


LU 1


0.5


0


max Wind & Pressure
max Wave
max Combined

















50 100
Time (hours)


Figure 3-9: For each set of model prediction forcing, the maximum water surface
elevation is plotted at every time step.


greater than the predictions for separate forcing for nearly the whole time series.

There is a point, about 25 hours into the prediction, when the results forced only

by the waves exceed the combined results. From approximately t=25 hours to

t=35 hours the maximum elevation from combined forcing decreases rapidly, and

the wave forced results can be the largest of the three predictions. This surge is not

associated with the hurricane making landfall, but with waves reaching the shore

while the eye is still in open water. Wind and waves can work with each other

forcing in the same direction, and produce a large set-up. The two can also oppose









each other and reduce the maximum surge, when the wind is blowing down the

area where the waves are setting-up, as is seen in these time series. These scenarios

illustrate the complex nature of the system. We also note that for the combined

forcing prediction, the maximum surge in the domain is always greater than or

equal to the wind only prediction. The addition of wave forcing to the model

produces an increase in the maximum water elevation, over the whole domain, on

the order of 0.4 meter over the meteorologic forcing alone (during the peak hours).

In the analysis above we compared the maximum surges produced in the

model domain. These maximum elevations, however, do not necessarily correspond

to the same locations. At specific locations we may observe a greater difference

between the meteorological and combined forcing predictions. Therefore, it is

of interest to examine the behavior of the sea surface at specific locations. We

choose locations where historical water level data is available and associate these

with nearest nodes on our grid. In addition to selecting station locations, we also

retrieve data at three prescribed locations: Mobile Bay, AL, Perdido Bay, FL, and

Lake Borgne, LA.

Table 3-2: Locations of selected tidal stations
Node Latitude Longitude Location
4138 29.2915 -89.'L2 Grande Isle, LA
5313 29.3551 -89.3419 Grande Pass, LA
9552 30.2546 -88.1925 Dauphin Island, AL
9965 30.3807 -87.2435 Pensacola, FL
9990 30.21'", -89.3807 Waveland, MS
9991 30.2452 -89.4003 Waveland, MS
10290 30.3888 -87.2261 Pensacola, FL
11020 30.6678 -87.9489 Mobile Bay, AL
11043 29.9664 -89.7226 Lake Borgne, LA
13266 30.4823 -87.4180 Perdido Bay, FL


The maximum elevation over the entire duration of the simulation for each

forcing combination is plotted, for selected locations given by Table 3-2, in

Figure 3-10. Also plotted is the maximum difference in water level between the




























05



4138 5313 9552 9965 9990 9991 10290 11020 13266
node #


Figure 3-10: For the specified nodes given in Table 3-2, we plot the maximum
surge over the duration of the simulation for combination of each forcing. Also
plotted is the maximum difference between the combined forcing and wind only
forced elevation.


experiment with meteorological forcing and that with combined forcing achieved

at any time during the simulation. From this plot we can infer that the difference

between the total water elevation and the wind forced set-up comes from the

addition of wave forcing. The maximum difference is less than the surge predicted

by the wave only forced run in all cases shown. This indicates that the effect of

combining the forcing in the model run in not simply a linear superposition of the

separate surge levels.

So far we have looked at spatial maxima and temporal maxima. These have

given us an indication of the maximum observed effects of adding wave forcing to

wind and pressure and how the sea surface responds. Next we look at the time

history of water level at individual locations. The behavior of the sea surface is











particularly interesting at the two following locations even though there was no

station data available there.



2.5
wind wave
linear combination
wind
wave
2-



1.5



L 1



0.5



0.5




0 50 100 150
Time (hours)



Figure 3-11: The water level at Node-13266:Perdido Bay, FL. We show the surge
as predicted by the meteorological forcing, the wave forcing, and the combined
forcing. Also plotted is the linear combination of the two individually forced model
results.



We start with the location at Perdido Bay, FL, Figure 3-11, since it had the

greatest level of wave set-up. The maximum surge due to the waves has a slightly

greater magnitude than the surge from the meteorologic forcing. The wind forced

case achieves its maxima about 6 hours after the wave forced simulation, consistent

with the observation that storm waves often reach the shore before the storm's

strongest winds. The combined forcing run is less than the linear combination of

the wind and waves separately, yet is approximately 1 meter higher than the wind

and pressure forced prediction.

A second noteworthy location is Lake Borgne, LA, shown in Figure 3-12. At






















0-






-2 -



0 50 100 150
Time (hours)


Figure 3-12: The water level at Node-11043:Lake Borgne, LA. We show the surge
as predicted by the meteorological forcing, the wave forcing, and the combined
forcing. Also plotted is the linear combination of the two individually forced model
results.


this location we can see the dramatic effect of the eye passing. The drop in water

elevation takes place over a 30 hour period, approximately t = 80 h to t = 110 h.

During this time the water level goes from being pushed up about 2.4 meters, to

being blown down about 2.4 meters. The node at that location is considered 'dry'

(Elevation = 0), and oscillates with wetting and drying between approximately t

= 135 h and t = 145 h. The peak surge calculated with combined forcing is about

40 centimeters greater than that computed using just the meteorologic forcing.

The output from the numerical model is compared to historical data obtained

from the NOAA National Oceanographic Data Center, (NODC). We focus on two

stations where the surge is greatest. In order to provide the best estimate, we add

in the astronomical tides. Our NOPP partner, Scott Hagen, at the University of










Central Florida has provided us with a tidal prediction at each of the locations

of interest, using ADCIRC on a finer resolution grid over a longer duration

simulation. These modeled tides match the observed phase at the stations. With

the tides added, we have a comprehensive prediction of the water level.

We also rectify the definition of mean sea level between our plots and the

station data. ADCIRC defines the mean water level as zero. The station data

is referenced to the mean lower low water convention, MLLW (Figures 3-13 and

3-15). Figure 3-13 shows the predicted water level at Pensacola Bay starting four


1.600

1.400 -------------- --------------




0.000........ .............................
(1U
IS1 0 0 --- -- -I-- ------------- -.- -- -- .......... ..... L .















Oate/Time (UTC (GMT))

Figure 3-13: The NOAA station data for Pensacola Bay, FL.
referenced to MLLW.


09/30 10/02
00:00 00:00


Water elevation is


days before our simulation period. From this we estimate the predicted mean water

level for the time of our simulation as +0.3 meter. When we add this offset to our

prediction the results can be compared.

Figure 3-14 shows that we improve our prediction of the peak elevations at

Pensacola, Florida by 60% with the addition of wave forcing to the wind stress






















0
0.8
LI


Time (hours)


Figure 3-14: Forced by the combination of wave and meteorological inputs, the
output from the ADCIRC model at Pensacola Bay is plotted with the historical
data recorded by the station at the same corresponding time period. Our
prediction is translated in order to more closely match the start time mean water
level at the station.


and atmospheric pressure. On either side of the peak, the model under-predicts

the water elevations. The prediction is off by as much as 0.44 meter, with the

greatest differences occurring 10 to 20 hours on either side of the peak. These

coincide with the low tide cycles. The mean difference between the station data

and the combined forcing prediction is 0.11 meter. This is 50% less than the mean

difference between the station data and the meteorological forcing (0.20 meter). We

quantify the error in our prediction by computing the mean square error, (\!SK),

and the root mean square error, (RMSE), normalized by the maximum elevation

recorded by the station using Eqs. 3-3, and 3-4.

SN
MSE(WL1, WL2) (WL1(i) W2 (i))2 (3-3)
i=1












RMSE(WL1, WL2)


Y[ (WL1(i) WL2(i))2

MAX(WL1)


where
N number of data records
WL1 station water level record
WL2 model prediction

The MSE for the combined forcing is 0.03 m2. For the wind and pressure

prediction the MSE is 0.09 m2. In this case, the normalized RMSE improves

from 20% to 10% by including the waves in the model prediction, a 50% reduction

in error.

At the Waveland location, Figure 3-15 shows the predicted water level four

days prior to and during our simulation. From this plot we estimate a mean water

2.000 1 I I I I I I I


1.500



1.000



0.500


Figure 3-15: The NOAA station
referenced to MLLW).


09/24 09/26 09/28 09/30
00:00 00:00 00:00 00:00
Date/Time (UTC (GMT))

data for Waveland, MS (water elevation is


(3-4)











level of +0.35 meters. Using this mean water level, we translate the model results.

Figure 3-16 shows good agreement before and during the storm.



2.5
station data
wind wave
wind
2



1.5


E
C 1



0.5







0.5
0 20 40 60 80 100 120 140
Time (hours)



Figure 3-16: Forced by the combination of wave and meteorological inputs, the
output from the ADCIRC model at Waveland is plotted with the historical data
recorded by the station at the same corresponding time period. Our prediction is
translated in order to more closely match the start time mean water level at the
station.


With only the meteorologic forcing, the model under-predicts the water level

at t=79 hours by approximately 0.4 meter, in Waveland, MS (Figure 3-16). When

the waves are added, the prediction achieves the peak water level at t=79 hours to

within 0.005 meter. The peak water elevation for our predictions, however, does

not occur at t=79 hours. The predicted peak water level of 1.98 meters, for the

combined forcing case, occurs at t=80 hours. The difference between the station

data peak and the combined forcing peak is 0.05 meter. The mean difference

between the prediction and the station water level is 0.1 meter. We compute the

MSE to be 0.08 m2 with the waves added. This improved from the MSE of the








43


wind and pressure forced run of 0.11 m2. The normalized RMSE, computed with

Eq. 3-4, for the combined forcing case is improved from 17% to 14% by adding

the waves. A major source for error at this location occurs after the storm has

passed, t > 120 h. Our model over-predicts the amount of set-down by as much as

0.75 meter. The second largest source for error is just before the peak of the surge,

when the tidal cycle is low.

We perform the same error analysis for the time period of t = 40 h to t =

110 h. During this period, we find that the MSE improves from 0.15 m2 to 0.06 m2

with the addition of the wave forcing. The normalized RMSE improves from 20%

to 1;;' .; almost cut in half, by including the waves.


Waveland resolved windwave
Pensacola resolved windwave
max resolved windwave
Waveland resolved wave
Pensacola resolved wave
max resolved wave
2.5 Waveland windwave
S Pensacola windwave
max windwave
-. Waveland wave
Pensacola wave
2 max wave


1.5
Co

SIt



U) 0.5 /'N






-0.5
0 50 100
Time Hours



Figure 3-17: We compare the surface response to combined forcing and wave
only forcing at the Pensacola location and the Waveland location. Also plotted
is the maximum surface elevation over the whole domain for the two forcing
combinations. For the resolved case, the finite element grid has 121296 nodes,
compared to the 31435 nodes of the current grid.









Above, our bathymetric sensitivity tests have shown that grid resolution can

play a role. In order to be sure that we have resolved the system adequately, we

refine the finite element grid, Figure 2-5, by splitting each element into four. In

doing so we increase the number of nodes from 31435 to 121296. The surface

response from combined forcing and wave only forcing is compared at the Pensacola

location and the Waveland location. We also compare the maximum surface

elevation response to the two forcing cases. These comparisons are shown in,

Figure 3-17. We can see from the plot, that the two are in close agreement;

however, the computational time for the higher resolution grid is on the order of 5

times longer. We determine that our system is adequately resolved and the model

runs in an efficient time frame with the current grid.

The results show that the effect of including waves in the model forcing

depends on the location. The waves can have a large effect as in the case of

Perdido Bay, FL. In the comparisons of our results with historical data, we find

that by adding the wave forcing we are better able to predict the peak water level.

Alternately, at some locations the addition of wave forcing may not provide a

significant improvement to the predictive power of the model. Predictions made

by forcing the model with only the meteorologic constituents would suffice at

those locations; however, we cannot know which locations those are without the

combined forcing prediction results. The implications of the results are discussed

Chapter 4.















CHAPTER 4
CONCLUSIONS

The ADCIRC tests demonstrate that the addition of wave forces can result

in a 30% to 50% increase in sea surface elevation. The results are sensitive to

the station location with respect to the storm, coastal features such as bays and

islands and grid resolution in the near-shore region. The model captures the

set-up and set-down for idealized bathymetries in close agreement with analytical

solutions for steady state conditions. Model sensitivity to the drag coefficient,

Cd, formulation has been shown to effect the results by as much as 0.5 meter. We

selected the Garratt (1977) formula 1-1 because it produced results that were close

to the mean of the various formulations. However, further research toward the

parameterizations of air-sea interaction at high winds is needed.

4.1 Bathymetry

We observe from the bathymetric tests that the depth profiles have an effect

on the wave-induced set-up. The wave field is sufficiently altered by dissipative

forces to effect a change in the on-shore momentum transfer. Wind duration

and fetch will also effect the breaking wave height. Wind has a chance to impart

more of its energy into the water column before the waves break over the steeper

profile, resulting in a larger breaking wave height. We conducted 27 tests for the

nine combinations of wind speed and bathymetry with wind, wave and combined

forcing. The output from the wave model, SWAN, was converted to input for the

circulation model, ADCIRC. We also used the SWAN output in computing the

steady state analytical solution. Our ADCIRC domain grid was too coarse to

fully resolve near-shore wave breaking in the case of the 1 meter waves; however,

we were able to resolve the stronger wave forcing over each of the bathymetries.









Upon comparing the ADCIRC results with the analytical solution, we find that

with adequate resolution the two are in close agreement. Grid resolution at the

shoreline is important. In the cases where the breaking is resolved, the model only

slightly under-predicts the analytical solution. The fact that we obtain such close

agreement with theory reinforces our confidence in the output of the circulation

model. Our results indicate that a reduction in the wave-induced set-up occurs

when the waves propagate over a wide shallow shelf. As the profile steepens, the

wave set-up will increase.

Wind induced set-up is also a function of the bathymetry. Shallow profiles

allow for a larger set-up for the same wind strength compared to steeper profiles.

The level of surge from winds is also influenced by the fetch. In our case we have a

relatively short fetch, thus reducing the level of wind set-up. Were we to increase

the cross-shore domain of our simulation, we would expect to see the wind set-up

increase and dominate the system.

For the strongest forcing runs, the combined wind and wave forcing runs for

our domain are largest over the steep domain, where the waves dominate. The

winds dominate over the shallow profile, and there we have the second highest

surge. Over the mild domain, both contribute approximately equally and we see

the smallest total set-up. These results -II.'. -1 that the individual contribution

from wind or wave forcing alone could be greater than the combined contributions

for bed profiles with extreme slopes. The variability of wave set-up and the

sensitivity of wind-induced set-up to bathymetry leads us to the conclusion that the

relative importance of the wave forcing increases over steeper coastal profiles.

4.2 Hindcast

The addition of wave forcing improves our overall predictive capabilities and

can reduce the RMS error by 20% to 50% depending on location. From the contour

plots we see that the wave set-up acts to offset the blow-down and amplify the









set-up generated by the wind and pressure. The effect of waves on surge is also

evident before the storm makes landfall since the waves reach the shore several

hours before the peak winds. Set-up is most prominent in the bays and coastal

lakes. The model predicts that waves alone can account for more than 1 meter

of surge, as is the case in Perdido Bay where the wave set-up was more than half

the total surge predicted with the combined forcing. Over the whole domain the

maximum surge from the waves amounted to more than 30% of the maximum

water level predicted in the domain. During the peak of the storm event, the

prediction and the recorded water levels are in close agreement when we include the

wind, pressure and wave forcing. The addition of waves can allow for as much as a

60% increase in predictive power, as shown by the analysis at Pensacola Bay.

4.3 Significance of Wave Set-Up

Waves and wave momentum flux are an important part of the natural system

responsible for storm surge. The significance of the wave set-up, and therefore the

inclusion of wave forcing in model predictions, is dependent on the bathymetric

profile in the path of the storm. If there is a wide, shallow shelf, there will be

greater wind set-up at the shoreline. When wind-induced set-up dominates, the

waves are not as significant. However, the wave forces remain an active participant

in generating storm surge at different phases of storm passage and in regions

farther away from the location of the eye of the storm, and should be kept in

the computational models for completeness. Our future plan of research includes

griding up the lowland coastal regions, allowing for inundation, and modeling the

response.

Waves can account for more than 1 meter of set-up for our predictions of

hurricane Georges. In general we have found that waves provide on the order of

one-third of the set-up along the coast during hurricane Georges. The wave forcing

is an important factor in our case for representing hurricane storm surge.
















APPENDIX A
BATHYMETRY TEST:INPUT FILES

A.1 Wave Model Inputs

The following files are samples of the input files used to implement SWAN. We

show one file for each forcing strength. There will also be separate files for each

bottom profile. The only changes in those other cases are the names of the input

and output files.

The following file is the input used for the strongest of the forcing.
$
PROJ 'strongmedium' '0102'
TEST 30 0
POOL
$
$ PURPOSE OF TEST: to calculate a wave climate on a simple
$ bathymetry to input into ADCIRC
$
$ -- -----------------|---------------------------------------
$ | This SWAN input file is template for all input in future for I
$ | SWAN.
$ -- -----------------|---------------------------------------
$
$***********MODEL INPUT********************************** ***
$
CGRID REG 0. 0. 0. 50000. 10200. 25 2040 CIRCLE 90 0.05 0.25 40
$
INPGRID BOTTOM 0. 0. 0. 2 510 25000. 20.
READINP BOTTOM 1. 'mild.bot' 1 0 FREE
$
BOUN SHAPE JONSWAP 2. PEAK DSPR DEGREES
BOUN SIDE S CCW CON PAR 7.0 15.0 90. 5.
$
SETUP
WIND 56.0 90.0
$
NUMERIC SETUP -3. 0.0001 2 30
$
$************ OUTPUT REQUESTS *************************
$










CURVE
TABLE
TABLE
$
CURVE
TABLE
TABLE


'CTA11'
'CTA11'
'CTA11'

'CTA12'
'CTA12'
'CTA12'


25000. 0. 2040 25000. 10200.
XP YP DEPTH HS HSWELL DIR PDIR TDIR
HEAD 'o_strong_mildl.tab' XP YP DEPTH HS DIR PDIR TDIR

25000. 0. 2040 25000. 10200.
XP YP RTP FORCE TRANSP VEL DEPTH
HEAD 'o_strong_mild2.tab' RTP FORCE TRANSP


POOL
COMPUTE
STOP
$


The medium strength forcing in SWAN was input using the next file.
$
PROJ 'thesis_01 01' 'test'
TEST 30 0
POOL
$
$ PURPOSE OF TEST: to calculate a wave climate on a simple
$ bathymetry to input into ADCIRC
$
$ ---------------------------------------------------------
$ | This SWAN input file is template for all input in future for I
$ | SWAN.
$ ---------------------------------------------------------
$
$***********MODEL INPUT********************************** ***
$
CGRID REG 0. 0. 0. 50000. 10200. 50 510 CIRCLE 90 0.05 0.25 40
$
INPGRID BOTTOM 0. 0. 0. 2 510 25000. 20.
READINP BOTTOM 1. 'shallow.bot' 1 0 FREE
$
BOUN SHAPE JONSWAP 2. PEAK DSPR DEGREES
BOUN SIDE S CCW CON PAR 5.0 10. 90. 5.
$
SETUP
WIND 30.0 90.0
$
NUMERIC SETUP -3. 0.0001 2 30
$
$************ OUTPUT REQUESTS *************************


CURVE 'CTA11'
TABLE 'CTA11'
TABLE 'CTA11'
$


25000. 0. 510 25000. 10200.
XP YP DEPTH HS HSWELL DIR PDIR TDIR
HEAD 'omildshallowl02.tab' XP YP DEPTH HS DIR PDIR TDIR










CURVE 'CTA12'
TABLE 'CTA12'
TABLE 'CTA12'
$
POOL
COMPUTE
STOP


25000. 0. 510 25000. 10200.
XP YP RTP FORCE TRANSP VEL DEPTH
HEAD 'omildshallow202.tab' RTP FORCE TRANSP


Third is the weakest forcing input file.


PROJ 'thesis_01 01' 'test'
TEST 30 0
POOL
$
$ PURPOSE OF TEST: to calculate a wave climate on a simple
$ bathymetry to input into ADCIRC
$
$ ---------------------------------------------------------
$ | This SWAN input file is template for all input in future for I
$ | SWAN.
$ ---------------------------------------------------------
$
$***********MODEL INPUT********************************** ***
$
CGRID REG 0. 0. 0. 50000. 10200. 25 2040 CIRCLE 90 0.05 0.25 40
$
INPGRID BOTTOM 0. 0. 0. 2 510 25000. 20.
READINP BOTTOM 1. 'shallow.bot' 1 0 FREE
$
BOUN SHAPE JONSWAP 2. PEAK DSPR DEGREES
BOUN SIDE S CCW CON PAR 1.0 10. 90. 5.
$
SETUP
WIND 10.0 90.0
$
NUMERIC SETUP -3. 0.0001 2 30
$
$************ OUTPUT REQUESTS *************************
$


25000. 0. 2040 25000. 10200.
XP YP DEPTH HS HSWELL DIR PDIR TDIR
HEAD 'o weak shallowl02.tab' XP YP DEPTH


HS DIR PDIR TDIR


25000. 0. 2040 25000. 10200.
XP YP RTP FORCE TRANSP VEL DEPTH
HEAD 'oweakshallow202.tab' RTP FORCE TRANSP


'CTA11'
'CTA11'
'CTA11'

'CTA12'
'CTA12'
'CTA12'


CURVE
TABLE
TABLE
$
CURVE
TABLE
TABLE
$
POOL









COMPUTE
STOP

A.2 Circulation Model Inputs

ADCIRC is run using an input file, fort.15. As mentioned before, control

variables are defined in this file. The two tests, varied forcing over bathymetries

and the hurricane Georges hindcast, will have different fort.15 files. These tests

have different temporal and spacial scales. These scales determine such variables

as time step and duration. The time step should not exceed a value such that the

Courant number is greater than 1.5. The Courant number is given as

(gh)2At A
c, = (A-1)

The fort.15 files will be slightly different for each run of each test. Most of the

parameters will be the same for each run.

We rename our meteorological, wind stress and pressure, forcing file to the

ADCIRC convention of fort.22. We also create a fort.22 file with every value at all

nodes for each time step set to zero. This zero forcing is used when the wave forced

model prediction is run. The wave forcing file is renamed to fort.23. This file is

only read when the NWS flag is set to 102 in the fort.15 file. The NWS variable

indicates which forcing are to be read and the format of those forcing. The NWS

flag is set to match the format of the meteorological forcing file and the wave

forcing file. We set NWS = 2 or 102. NWS = 2, corresponds to a model run with

meteorological forcing only. NWS = 102, corresponds to a run with meteorological

forcing and wave stress forcing. The NWS parameter and the RSTIMINC are

the only input variables that change between the separate runs. RSTIMINC is

the variable which tells the model the time increment at which the wave forcing,

fort.23, input file is to be read, if wave forces are used. Both runs that involve wave

radiation stress forcing have NWS set to 102 and the RSTIMINC variable is set to










1800, the same as the wtiminc variable. All other input variables in the fort.15 file

are set to recommended values, as found in the ADCIRC manual.

The output consists of a file with the elevation at every node at selected time

step intervals. We choose to not output the current or the wind and pressure as

a time and space saving measure. As discussed above the intervals were decided

on after initial runs were completed. These files are then read to extract the

maximum surface elevation time history. The following files are input files, fort.15,

for ADCIRC.

This file is used when the only input to the model is meteorologic forcing, (ie.

wind and pressure).
Thesis_01_01.wind 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION
01 01 01 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION
1 NFOVER NONFATAL ERROR OVERRIDE OPTION
0 ABOUT ABREVIATED OUTPUT OPTION PARAMETER
1 SCREEN UNIT 6 OUTPUT OPTION PARAMETER
0 IHOT HOT START PARAMETER
1 ICS COORDINATE SYSTEM SELECTION PARAMETER
0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL)
1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER
2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER
1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER
0 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER
0 NTIP TIDAL POTENTIAL OPTION PARAMETER
2 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER
1 NRAMP RAMP FUNCTION OPTION
9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS
0.06 TAUO WEIGHTING FACTOR IN GWCE
0.10 DT TIME STEP (IN SECONDS)
0.0 STATIM STARTING TIME (IN DAYS)
0.0 REFTIM REFERENCE TIME (IN DAYS)
1800. WTIMINC-RSTIMINC TIME INTERVAL-WIND & RAD.STRESS VALUES (seconds)
1.00 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS)
0.25 DRAMP DURATION OF RAMP FUNCTION (IN DAYS)
0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION
0.1 10 10 0.1 HO MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin
265.5 29.0 SLAMO,SFEAO CENTER OF CPP PROJECTION (NOT USED IF ICS=1)
0.06 FACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFFICIENT
0.0 EVM LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1
0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1










0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED
0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES
45.0 ANGINN INNER ANGLE THRESHOLD
0 0.0 .75 10000 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61)
16 !# of recording stations
100.0 5000.0
120.0 5000.0
140.0 5000.0
160.0 5000.0
180.0 5000.0
200.0 5000.0
220.0 5000.0
240.0 5000.0
260.0 5000.0
280.0 5000.0
300.0 5000.0
320.0 5000.0
340.0 5000.0
360.0 5000.0
380.0 5000.0
400.0 5000.0
0 0.0 .75 10000 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL STATION OUTPUT INFO(UNIT 62)
16 !#of recording stations
100.0 5000.0
120.0 5000.0
140.0 5000.0
160.0 5000.0
180.0 5000.0
200.0 5000.0
220.0 5000.0
240.0 5000.0
260.0 5000.0
280.0 5000.0
300.0 5000.0
320.0 5000.0
340.0 5000.0
360.0 5000.0
380.0 5000.0
400.0 5000.0
0 0.0 .750 10000 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STAT OUTPUT INFO(UNIT 71&72)
16 !#of recording stations
100.0 5000.0
120.0 5000.0
140.0 5000.0
160.0 5000.0
180.0 5000.0
200.0 5000.0










220.0 5000.0
240.0 5000.0
260.0 5000.0
280.0 5000.0
300.0 5000.0
320.0 5000.0
340.0 5000.0
360.0 5000.0
380.0 5000.0
400.0 5000.0
1 0.0 1.00 1000 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELV OUT INFO(UNIT 63)
1 0.0 1.00 1000 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL OUT INFO(UNIT 64)
1 0.0 1.00 1000 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBALVEL OUTINFO(UNIT73&74)
0 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS
0.50 .75 10000 0. THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS
0 0 0 0 NHASE,NHASV,NHAGE,NHAGV- HARMONIC ANALY & OUTPUT TO UNITS 51,52,53,54
1 10000 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS
1 2 0.000015 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS

This input file is used to include the waves in the model prediction.
Thesis_01_01.wave.wind 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION
01 01 01 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION
1 NFOVER NONFATAL ERROR OVERRIDE OPTION
0 ABOUT ABREVIATED OUTPUT OPTION PARAMETER
1 SCREEN UNIT 6 OUTPUT OPTION PARAMETER
0 IHOT HOT START PARAMETER
1 ICS COORDINATE SYSTEM SELECTION PARAMETER
0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL)
1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER
2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER
1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER
0 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER
0 NTIP TIDAL POTENTIAL OPTION PARAMETER
102 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER
1 NRAMP RAMP FUNCTION OPTION
9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS
0.06 TAUO WEIGHTING FACTOR IN GWCE
0.10 DT TIME STEP (IN SECONDS)
0.0 STATIM STARTING TIME (IN DAYS)
0.0 REFTIM REFERENCE TIME (IN DAYS)
1800. 1800. WTIMINC-RSTIMINC TIME INTERVAL-WIND & RAD.STRESS VALUES (seconds)
1.00 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS)
0.25 DRAMP DURATION OF RAMP FUNCTION (IN DAYS)
0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION
0.1 10 10 0.1 HO MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin
265.5 29.0 SLAMO,SFEAO CENTER OF CPP PROJECTION (NOT USED IF ICS=1)











0.06 FACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION
0.0 EVM LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP
0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1
0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED
0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES
45.0 ANGINN INNER ANGLE THRESHOLD
0 0.0 .75 10000 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT
16 !# of recording stations
100.0 5000.0
120.0 5000.0
140.0 5000.0
160.0 5000.0
180.0 5000.0
200.0 5000.0
220.0 5000.0
240.0 5000.0
260.0 5000.0
280.0 5000.0
300.0 5000.0
320.0 5000.0
340.0 5000.0
360.0 5000.0
380.0 5000.0
400.0 5000.0
0 0.0 .75 10000 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL STATION OUTPUT
16 !#of recording stations
100.0 5000.0
120.0 5000.0
140.0 5000.0
160.0 5000.0
180.0 5000.0
200.0 5000.0
220.0 5000.0
240.0 5000.0
260.0 5000.0
280.0 5000.0
300.0 5000.0
320.0 5000.0
340.0 5000.0
360.0 5000.0
380.0 5000.0
400.0 5000.0
0 0.0 .750 10000 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STAT OUT INFO(1
16 !#of recording stations
100.0 5000.0
120.0 5000.0
140.0 5000.0


COEFFICIENT
=1






INFO(UNIT 61)


INFO(UNIT 62)























UNIT 71&72)










160.0 5000.0
180.0 5000.0
200.0 5000.0
220.0 5000.0
240.0 5000.0
260.0 5000.0
280.0 5000.0
300.0 5000.0
320.0 5000.0
340.0 5000.0
360.0 5000.0
380.0 5000.0
400.0 5000.0
1 0.0 1.00 1000 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELE OUT INFO(UNIT 63)
1 0.0 1.00 1000 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL OUT INFO(UNIT 64)
1 0.0 1.00 1000 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBALVEL OUTINFO(UNIT73&74)
0 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS
0.50 .75 10000 0. THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS
0 0 0 0 NHASE,NHASV,NHAGE,NHAGV- HARMONIC ANALY&OUTPUT TO UNITS 51,52,53,54
1 10000 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS
1 2 0.000015 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS
















APPENDIX B
HINDCAST TEST:CIRCULATION MODEL INPUT FILES

As in the Bathymetry tests the NWS flag is set depending on which forcing

are to be read into the model. For the meteorological forced run, NWS is set to 2

and there is no RSTIMINC variable. Both runs that involve wave radiation stress

forcing have NWS set to 102 and the RSTIMINC variable is set to 1800.0, the same

as the wtiminc variable. Again, a fort.22 file consisting of all zero values for the

wind stress and the pressure has been generated to be used in the wave only forcing

prediction. Output is written to the respective files every hour. Using this file, we

can generate a time series of the water level during the storm at any location in

the domain. Again, the NWS parameter and the RSTIMINC are the only input

variables that change between the separate runs. The following files are input files,

fort.15, for ADCIRC.

This file is used when the only input to the model is meteorologic forcing (i.e.,

wind and pressure).
Georges_OFCL 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION
allruns 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION
1 NFOVER NONFATAL ERROR OVERRIDE OPTION
0 ABOUT ABREVIATED OUTPUT OPTION PARAMETER
1 SCREEN UNIT 6 OUTPUT OPTION PARAMETER
0 IHOT HOT START PARAMETER
2 ICS COORDINATE SYSTEM SELECTION PARAMETER
0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL)
1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER
2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER
1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER
1 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER
0 NTIP TIDAL POTENTIAL OPTION PARAMETER
102 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER
1 NRAMP RAMP FUNCTION OPTION










9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS
0.006 TAUO WEIGHTING FACTOR IN GWCE
30.0 DT TIME STEP (IN SECONDS)
0.0 STATIM STARTING TIME (IN DAYS)
0.0 REFTIM REFERENCE TIME (IN DAYS)
1800.0 1800.0 wtiminc rtiminc seconds 30min
6.0000 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS)
0.5 DRAMP DURATION OF RAMP FUNCTION (IN DAYS)
0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION
0.1 10 10 0.1 HO MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin
265.5 29.0 SLAMO,SFEAO-CENTER OF CPP PROJ(NOT USED IF ICS=1,NTIP=0,NCOR=0)
0.006 FACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFF
0.0 ESL LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1
0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1
0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED
0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES
45.0 ANGINN INNER ANGLE THRESHOLD
1 0.0 6.0 120 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61)
5 TOTAL NUMBER OF ELEVATION RECORDING STATIONS
-8.9366667e+01 3.0281700e+01 waveland ms
-8.9140000e+01 2.8999000e+01 South Pass LA
-8.9418330e+01 2.8925000e+01 SW pass LA
-8.7211667e+01 3.0405300e+01 pensacola FL
-8.9956667e+01 2.9263333e+01 Grand Isle LA
1 0.0 6.0 120 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL. STATION OUTPUT INFO(UNIT 62)
5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS
-8.9366667e+01 3.0281700e+01 waveland ms
-8.9140000e+01 2.8999000e+01 South Pass LA
-8.9418330e+01 2.8925000e+01 SW pass LA
-8.7211667e+01 3.0405300e+01 pensacola FL
-8.9956667e+01 2.9263333e+01 Grand Isle LA
1 0.0 6.0 120 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STATION OUT INFO(UNIT 71&72)
5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS
-8.9366667e+01 3.0281700e+01 waveland ms
-8.9140000e+01 2.8999000e+01 South Pass LA
-8.9418330e+01 2.8925000e+01 SW pass LA
-8.7211667e+01 3.0405300e+01 pensacola FL
-8.9956667e+01 2.9263333e+01 Grand Isle LA
1 0.0 6.0 120 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELEV OUT INFOUNIT 63)
1 0.0 6.0 120 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VEL OUT INFO(UNIT 64)
1 0.0 6.0 120 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBAL VEL OUT INFO(UNIT 73&74)
8 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS
STEADY HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=1
0.00000000000000 1.0 0.0 HAFREQ(I=1),HAFF(I=1),HAFACE(I=1)
K1 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=3
0.000072921165921 0.903 4.685423643 HAFREQ(I=3),HAFF(I=3),HAFACE(I=3)
01 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT 1=4










0.000067597751162 0.841 6.254177935 HAFREQ(I=4),HAFF(I=4),HAFACE(I=4)
M2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=8
0.000140518917083 1.033 0.607861211 HAFREQ(I=8),HAFF(I=8),HAFACE(I=8)
S2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT 1=9
0.000145444119418 1.0 0.0 HAFREQ(I=9),HAFF(I=9),HAFACE(I=9)
M4 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT 1=16
0.000281037834166 1.066 2.932537116 HAFREQ(I=16),HAFF(I=16),HAFACE(I=16)
M6 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18
0.000421556751249 1.101 1.25721302 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18)
N2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18
0.000138000000000 1.033 1.128599708 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18)
0.00 6.00 120 1.0 THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS
1 1 1 1 NHASE,NHASV,NHAGE,NHAGV-HARMONIC ANALY & OUTPUT TO UNITS 51,52,53,54
1 200 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS
1 0 1.E-5 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS

This input file is used to include the waves in the model prediction.
Georges_OFCL 32 CHARACTER ALPHANUMERIC RUN DESCRIPTION
allruns 24 CHARACTER ALPHANUMERIC RUN IDENTIFICATION
1 NFOVER NONFATAL ERROR OVERRIDE OPTION
0 ABOUT ABREVIATED OUTPUT OPTION PARAMETER
1 SCREEN UNIT 6 OUTPUT OPTION PARAMETER
0 IHOT HOT START PARAMETER
2 ICS COORDINATE SYSTEM SELECTION PARAMETER
0 IM MODEL TYPE (0 INDICATES STANDARD 2DDI MODEL)
1 NOLIBF BOTTOM FRICTION TERM SELECTION PARAMETER
2 NOLIFA FINITE AMPLITUDE TERM SELECTION PARAMETER
1 NOLICA SPATIAL DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
1 NOLICAT -TIME DERIVATIVE CONVECTIVE TERM SELECTION PARAMETER
0 NWP VARIABLE BOTTOM FRICTION AND LATERAL VISCOSITY OPTION PARAMETER
1 NCOR VARIABLE CORIOLIS IN SPACE OPTION PARAMETER
0 NTIP TIDAL POTENTIAL OPTION PARAMETER
102 NWS WIND STRESS AND BAROMETRIC PRESSURE OPTION PARAMETER
1 NRAMP RAMP FUNCTION OPTION
9.81 G ACCELERATION DUE TO GRAVITY DETERMINES UNITS
0.006 TAUO WEIGHTING FACTOR IN GWCE
30.0 DT TIME STEP (IN SECONDS)
0.0 STATIM STARTING TIME (IN DAYS)
0.0 REFTIM REFERENCE TIME (IN DAYS)
1800.0 1800.0 wtiminc rtiminc seconds 30min
6.0000 RNDAY TOTAL LENGTH OF SIMULATION (IN DAYS)
0.5 DRAMP DURATION OF RAMP FUNCTION (IN DAYS)
0.35 0.30 0.35 TIME WEIGHTING FACTORS FOR THE GWCE EQUATION
0.1 10 10 0.1 HO MINIMUM CUTOFF DEPTH nodedrymin nodewetmin velmin
265.5 29.0 SLAMO,SFEAO-CENTER OF CPP PROJEC(NOT USED IF ICS=1,NTIP=0,NCOR=0)
0.006 FACTOR HOMOGENEOUS LINEAR OR NONLINEAR BOTTOM FRICTION COEFF
0.0 ESL LATERAL EDDY VISCOSITY COEFFICIENT; IGNORED IF NWP =1
0.0 CORI CORIOLIS PARAMETER IGNORED IF NCOR = 1










0 NTIF NUMBER OF TIDAL POTENTIAL CONSTITUENTS BEING FORCED
0 NBFR TOTAL NUMBER OF FORCING FREQUENCIES ON OPEN BOUNDARIES
45.0 ANGINN INNER ANGLE THRESHOLD
1 0.0 6.0 120 NOUTE,TOUTSE,TOUTFE,NSPOOLE:ELEV STATION OUTPUT INFO(UNIT 61)
5 TOTAL NUMBER OF ELEVATION RECORDING STATIONS
-8.9366667e+01 3.0281700e+01 waveland ms
-8.9140000e+01 2.8999000e+01 South Pass LA
-8.9418330e+01 2.8925000e+01 SW pass LA
-8.7211667e+01 3.0405300e+01 pensacola FL
-8.9956667e+01 2.9263333e+01 Grand Isle LA
1 0.0 6.0 120 NOUTV,TOUTSV,TOUTFV,NSPOOLV:VEL. STATION OUTPUT INFO(UNIT 62)
5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS
-8.9366667e+01 3.0281700e+01 waveland ms
-8.9140000e+01 2.8999000e+01 South Pass LA
-8.9418330e+01 2.8925000e+01 SW pass LA
-8.7211667e+01 3.0405300e+01 pensacola FL
-8.9956667e+01 2.9263333e+01 Grand Isle LA
1 0.0 6.0 120 NOUTM,TOUTSM,TOUTFM,NSPOOLM:VEL STATION OUT INFO(UNIT 71&72)
5 TOTAL NUMBER OF VELOCITY RECORDING STATIONS
-8.9366667e+01 3.0281700e+01 waveland ms
-8.9140000e+01 2.8999000e+01 South Pass LA
-8.9418330e+01 2.8925000e+01 SW pass LA
-8.7211667e+01 3.0405300e+01 pensacola FL
-8.9956667e+01 2.9263333e+01 Grand Isle LA
1 0.0 6.0 120 NOUTGE,TOUTSGE,TOUTFGE,NSPOOLGE:GLOBAL ELEOUTPUT INFO(UNIT 63)
1 0.0 6.0 120 NOUTGV,TOUTSGV,TOUTFGV,NSPOOLGV:GLOBAL VELOUTPUT INFO(UNIT 64)
1 0.0 6.0 120 NOUTGM,TOUTSGM,TOUTFGM,NSPOOLGM:GLOBAL VELOUT INFO(UNIT 71&74)
8 NHARFR NUMBER OF CONSTITUENTS TO BE INCLUDED IN THE HARMONIC ANALYSIS
STEADY HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=1
0.00000000000000 1.0 0.0 HAFREQ(I=1),HAFF(I=1),HAFACE(I=1)
K1 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=3
0.000072921165921 0.903 4.685423643 HAFREQ(I=3),HAFF(I=3),HAFACE(I=3)
01 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT 1=4
0.000067597751162 0.841 6.254177935 HAFREQ(I=4),HAFF(I=4),HAFACE(I=4)
M2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=8
0.000140518917083 1.033 0.607861211 HAFREQ(I=8),HAFF(I=8),HAFACE(I=8)
S2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT 1=9
0.000145444119418 1.0 0.0 HAFREQ(I=9),HAFF(I=9),HAFACE(I=9)
M4 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT 1=16
0.000281037834166 1.066 2.932537116 HAFREQ(I=16),HAFF(I=16),HAFACE(I=16)
M6 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18
0.000421556751249 1.101 1.25721302 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18)
N2 HAFNAM(I) ALHPANUMERIC DESCRIPTION OF HARMONIC CONSTITUENT I=18
0.000138000000000 1.033 1.128599708 HAFREQ(I=18),HAFF(I=18),HAFACE(I=18)
0.00 6.00 120 1.0 THAS,THAF,NHAINC,FMV HARMONIC ANALYSIS PARAMETERS







61

1 1 1 1 NHASE,NHASV,NHAGE,NHAGV- HARMONIC ANALY&OUT TO UNITS 51,52,53,54
1 200 NHSTAR,NHSINC HOT START FILE GENERATION PARAMETERS
1 0 1.E-5 25 ITITER, ISLDIA, CONVCR, ITMAX-ALGEBRAIC SOLUTION PARAMETERS















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BIOGRAPHICAL SKETCH

Born in Oklahoma during the year 1973, I was raised in North Carolina.

Growing up, my parents would take my brother and sister and myself on all kinds

of travels. I recall visiting many of the National Parks and camping out of our

1971 Dodge van. These experiences culminated in a month-long trip around the

United States when I was 10 years old, which included hiking the Grand C.iir. 11-

Through these experiences I gained respect for nature and an ability to cope, adapt

and accomplish what I put my mind to finishing. I became certified in SCUBA

diving at the age of 16 while carving my path through high school. I spent my 18th

birtlil.1v in England, traveling outside the USA for the first time. The experience

was eye-opening. In 1992, I found my way to college at the University of North

Carolina at Greensboro. As an undergrad, I served as president of the Society of

Physics Students (SPS), and was inducted to HUE and HME (the 1.1ir, -i. and

mathematics honor societies). I spent 2 weeks during the summer of 1997 in Hawaii

as a research diver for the Pacific Whale Foundation, cataloging fish and coral

life at 4 reef sites around Maui. My last semester was spent abroad, studying at

the University of Stuttgart in Germany and learning the German language and

culture. While in Europe, I was able to travel and experience different cultures,

and broaden my world view. I graduated from UNC-G in December 1999, cum

laude, with a Bachelor of Science degree in mathematics and a minor in ]'li- -i. -

After graduation I spent 2 years in Connecticut, working at a local newspaper

and teaching at a local high school. Though I enjoyed t.' liiir-. I felt that I was

not reaching my full potential. Looking for a way to bring together my love of the

sea and my educational background, I decided it was time to go back to school.







65

I applied to graduate school at the University of Florida department of Coastal

Engineering. In addition to the past 2.5 years of research and graduate course

work, I have also been certified as a NAUI Divemaster and cleared as a Science

Diver for the University of Florida. My love of the ocean, nature and science

brought me to this point in my life, and will continue to drive the decisions I make.

For now, I have taken steps toward a Ph.D.,with tentative plans onpursuing a

career in the storm prediction / damage mitigation / community organization. In

the future I could see myself at some point teaching again. Where there are good

teachers there is hope for society.