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Tropical cyclone induced asymmetry of sea level surge andfall and its presentation in a storm surge model with

parametric wind fields

Machuan Peng a,*, Lian Xie a, Leonard J. Pietrafesa b

a Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Box 8202,

Raleigh, NC 27695-8208, United Statesb

College of Physical & Mathematical Sciences, Box 8201, North Carolina State University, Raleigh, NC, United States

Received 22 July 2005; received in revised form 14 March 2006; accepted 15 March 2006Available online 11 May 2006

Abstract

The asymmetry of tropical cyclone induced maximum coastal sea level rise (positive surge) and fall (negative surge) isstudied using a three-dimensional storm surge model. It is found that the negative surge induced by offshore winds is moresensitive to wind speed and direction changes than the positive surge by onshore winds. As a result, negative surge isinherently more difficult to forecast than positive surge since there is uncertainty in tropical storm wind forecasts. Theasymmetry of negative and positive surge under parametric wind forcing is more apparent in shallow water regions.For tropical cyclones with fixed central pressure, the surge asymmetry increases with decreasing storm translation speed.For those with the same translation speed, a weaker tropical cyclone is expected to gain a higher AI (asymmetry index)value though its induced maximum surge and fall are smaller. With fixed RMW (radius of maximum wind), the relation-ship between central pressure and AI is heterogeneous and depends on the value of RMW. Tropical cyclones wind inflowangle can also affect surge asymmetry. A set of idealized cases as well as two historic tropical cyclones are used to illustratethe surge asymmetry. 2006 Elsevier Ltd. All rights reserved.

Keywords: Asymmetry; Storm surge; Tropical cyclone; Parametric wind

1. Introduction

Tropical cyclone (TC) induced storm surge is a major threat to coastal residents. Measures of the impacts ofthese storms on coastal communities are in the loss of human lives and property destruction. Fortunately, the

1463-5003/$ - see front matter 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ocemod.2006.03.004

* Corresponding author. Tel.: +1 919 515 1436; fax: +1 919 515 7802.E-mail address: [email protected] (M. Peng).

Ocean Modelling 14 (2006) 81101

www.elsevier.com/locate/ocemod
mailto:[email protected]:[email protected]



In fact, the asymmetric sea level response to symmetric wind forcing can be explained in a simple 1-D case.As the pressure gradient force required to balance a given wind is proportional to ( h + n)dn/dx (where h, n andx are respectively the undisturbed water depth, sea surface elevation, and distant away from the coast), a lar-ger sea level drop is required during fall (when n is negative) than the corresponding surge (when n is positive),provided that the model cross-shore domain is larger than the barotropic radius. Of course, Coriolis force,bottom friction and the other nonlinear features are not considered in the above assumption.

In this study, the Holland parametric wind model is employed for all hypothetical TCs. It is also used,based on observed data, for the historic TCs to assess the errors in negative surge due to misspecificationof the wind model. This explains why more accurate HRD (Hurricane Research Division) Realtime HurricaneWinds, or H*winds, should be used in real TC cases.

This paper contains five sections. In Section 2, the three-dimensional surge model is briefly described. Theasymmetry of sea level rise and fall under steady onshore and offshore-wind forcing is examined in Section 3.Section 4 discusses how TC parameters, such as translation speed, RMW and inflow angles, affect the waterlevel risefall asymmetry. Two historic TCs are presented in Section 5 to further demonstrate that accurateparameterization of wind model may greatly lessen the deficiencies in storm surge results. Finally, discussion

and conclusion are presented in Section 6.

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S1

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Hurricane Isabel

2003

Fig. 1. The track of Hurricane Isabel and the locations of eight water level stations. Sl-8 are Beaufort, Cape Hatteras, Duck Pier,Chesapeake Bridge, Windmill Point, Solomons Island, Baltimore, and Chesapeake City, respectively. The box shows the inner domain ofthe nesting system in the model.

M. Peng et al. / Ocean Modelling 14 (2006) 81101 83



2. The storm surge model

The storm surge model employed in this study is described in detail in Xie et al. (2004) and Peng et al.(2004). The hydrodynamic component of the modeling system is based on the POM Model ( Mellor, 1996),which uses a terrain-following sigma (r) coordinate in the vertical and a staggered Arakawa C grid in thehorizontal plane. An embedded second moment turbulence closure scheme is used to compute the vertical

mixing coefficients. The model uses a free surface, and thus allows explicit prediction of sea level change.In POM, the horizontal finite differencing is explicit, whereas the vertical differencing is implicit. The lattereliminates time-step constraints on the vertical resolution and permits the use of fine vertical resolution nearthe surface and in shallow water regions. A three-time level leapfrog scheme is used for temporal integration.

The surface kinematic wind stress is applied at the sea surface through the following boundary condition:

KM

H

o~W

or

! s at r 0 1

where H, KM, ~W and s are respectively the water depth, vertical eddy viscosity, horizontal velocity and thesurface kinematic wind stress, which is computed by using the conventional bulk formula s qCdj~VwjVw,where Vw is wind speed at height of 10 m, q is air density and the drag coefficient, Cd, is assumed to vary with

wind speed.

S1 S2 S3 S4 S5* S6* S7 S80

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1

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2.5

3

Max

imum

Storm

Tide

(Metera

bove

N.G.V.D.)

a

Observed

Simulation

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0

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2

Storm

Tide

(m)

b

Chesapeake Bridge (S4)ObservedSimulation

17th00Z 12Z 18th00Z 12Z 19th00Z 12Z

1

0

1

2

c

Duck Pier (S3)

Storm

Tide

(m) Observed

Simulation

Fig. 2. (a) The observed and simulated overall maximum storm tide at eight stations. Time series of storm tide at (b) Chesapeake Bridgeand (c) Duck Pier.

84 M. Peng et al. / Ocean Modelling 14 (2006) 81101



103Cd

2:16 j~VwjP 26 m s10:49 0:065j~Vwj 10 m s1 6 j~Vwj < 26 m s11:14 3 6 j~Vwj < 10 m s10:62 1:56=j~Vwj 1 6 j~Vwj < 3 m s12:18 j~Vwj < 1 m s1

8>>>>>>>>>>>>>:2

This Cd formula follows Large and Pond (1981) when the wind speed is less than 26 m s1, otherwise, it is

assumed as a constant as indicated in Powell et al. (2003).At the sea bed, vertical velocity is assumed to be zero, and bottom stress is determined by the horizontal

current velocity (U, V) at the lowest vertical layer through

KM

H

oU

or;oV

or

CzU2 V21=2U; V at r 1 3

where the bottom drag coefficient, Cz, is determined by

Cz MAX k2

lnf1 rkb1H=z0g2 ; 0:0025" # 4

where k (= 0.4) is the Von Karman constant, kb, the number of vertical layers and z0 is the roughness length.Zero mass and momentum fluxes are the solid boundary conditions. Passive open boundary conditions

(OBCs) are employed in the study, which means the dynamics of the flow at the open boundary are determinedby the interior circulation. Storm surge results are sensitive to the OBCs used in the model. The details of thesensitivity study can be found in Palma and Matano (1998, 2000). The OBCs employed in our model followstheir works. For external mode, Flather radiation condition is used to determine normal flows along the openboundary. This OBC has good behavior in storm surge simulation. It not only allows conservation of mass inthe interior domain, but also handles well the passage of dispersive waves. It can be written as

U U0t CH

g g0t 5

where Uand g are respectively the velocity normal to the open boundary, and sea surface elevation, U0 and g0are prescribed values, C ffiffiffiffiffiffiffigHp is the phase speed of the incoming wave. Since in the case of passive OBCsthe exact values ofU0 and g0 are unknown, they are assumed to be zero at the boundary. The OBC of internalmode has not so much influence on model results as of external mode. The conventional radiation OBC forinternal flows in Mellor (1996) is employed in this study.

For the two historic TCs (Hurricane Isabel and Charley), the domain of interest is oneway nested within alarger domain to improve the inner horizontal resolution, and to lessen the spurious effects of the outer openboundaries. On the land side, runoffs from major rivers can be prescribed, but are not used in this study. Asmentioned before, the flooding module of the model is purposely shut off while the drying module is kept on.

3. The asymmetry of surge and fall with steady wind forcings

It is indicated in Section 1 that symmetric TC wind forcing may produce an asymmetry sea level surge andfall. This section is to investigate the extent of such asymmetry with different symmetric wind forcings andvarious bathymetry conditions. Steady onshore and offshore winds with the same magnitude of speed offerideal symmetric wind forcings, and will be employed in this section.

A square region (100 100 grid points) with grid size of 5 km in both directions, as shown in Fig. 3, is cho-sen as the study domain. The water depth contours in the figure show the original bathymetry configuration,which linearly increases from zero at the shoreline to the ocean at a slope of 1/10,000. Such a slope is muchsmaller than on typical continental shelf. It is used to emphasize the shallow water effects, and to make storm

surge more striking. Location A in Fig. 3 is where the model results are given. In the experiments, 10, 20, 30




and 50 m are arbitrarily chosen as the minimum water depth to readjust the original bathymetry. These fourcases are respectively named Case 1, Case 2, Case 3 and Case 4. In Case 1, the water depth is assumed to be10 m at the location where the original value is less than it. Similar are the other cases. A steady onshore/offshore wind with speed of 30 m s1 is the driving force. An asymmetry index is introduced as: AI =(jfallmaxj surgemax)/surgemax 100%, where fallmax and surgemax are respectively the maximum sea level fallunder the offshore-wind forcing, and the maximum surge under the onshore-wind forcing.

As shown in Fig. 4, there is no apparent asymmetry of sea level surge and fall in Case 3 and Case 4 (AI isless than 10%). The spin-up (or spin-down) time for these two deep water cases is around 10 h, after which thesteady state is reached due to the balance of the wind stress and the horizontal pressure gradient in the vicinityof the location A. But for the shallow water cases, the offshore wind induces more negative surge than theonshore wind induces positive surge. This is especially true in Case 1, where the maximum surge is less than3.5 m, but the maximum fall is more than 5 m. AI is as large as 56% in this case. This indicates the asymmetryof the maximum surge and fall is pronounced in shallow water regions.

The balance between the wind stress and the horizontal pressure gradient is also reflected in the kinks on thecurves. In Fig. 4, the sudden sea level drop/rise at kinks indicates the horizontal pressure gradient is greater/smaller than the wind stress at the time. If there is a kink and how pronounced it is depend on the sea surfacedistribution near the concerned location, which, at any time, is a function of wind stress force, domain con-figuration and bathymetry. This explains why the kinks in Fig. 5 (as will be shown later) are not so noticeable,when the bathymetry and wind force are changed.

To further investigate the asymmetry of sea level surge and fall with different wind forcings, wind speeds of20, 25, 30 and 35 m s1 are respectively used in 4 model runs. The minimum water depth is set to 10 m in allcases. The asymmetry of surge and fall, as illustrated in Fig. 5, is not evident when the wind speed is 20 or

25 m s

1, and AI in both cases is less than 30%. When the wind speed increases to 30 m s

1, AI increases

10 20 30 40 50 60 70 80 90 100

10

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30

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100

1

0

20

30

40

A

Land

Land

Fig. 3. The bathymetry contours (in meter) of the ideal square domain, and A is the location where model output is given.




accordingly to 56%. Under 35 m s1 wind forcing, the difference of the maximum fall and surge increases to4.1 m, with AI as large as 98%. The extent of the asymmetry, therefore, increases with wind forcing. However,as will be shown in the next section, stronger TC does not necessarily induce larger AI since wind duration of aTC may be not long enough to reach the steady state for sea surface elevation.

As indicated in Fig. 5, spin-up time increases moderately with wind forcing. A balance is nearly reachedbetween the wind forcing and the horizontal pressure gradient less than 10 h with 20 or 25 m s1 steady wind.Even for a higher speed wind (e.g. 30 or 35 m s1), the contribution of sea level increase after 10 h is less than15% of the total surge. The spin-down time is different, though the difference is not evident when the windspeed is small. Sea surface elevation is far from steady state after 10 h of 30 or 35 m s1 wind forcing. Thecontribution of sea level fall after 10 h is about 1.5 m for 30 m s1 wind, or 29% of its total fall. For35 m s1 offshore wind, the steady state is not reached after the first 50 h wind forcing as illustrated in Fig. 5.

The above experiments imply the difficulties to achieve sound sea level simulation in a TCs offshore-windquadrant, where wind speed or duration mistake is prone to lead to more sea surface elevation errors. As thewind speed, duration, and fetch of a TC are the functions of RMW, translation speed, and wind inflow angle,

accurate specification of the parametric wind model is the key to achieve good storm surge results.

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a

Sea

Leve

l(m)

10 hour 20 hour 30 hour 40 hour 50 hour7

6

5

4

3

2

1

0

b

Sea

Leve

l(m)

Case 1Case 2Case 3Case 4

Fig. 4. Spin-up/spin-down experiments with different bathymetry. Case 14 respectively takes 10, 15, 30 and 50 m as the minimum waterdepth: (a) spin-up with 30 m s1 onshore wind and (b) spin-down with 30 m s1 offshore wind.




4. The asymmetry of surge and fall with parametric wind forcings

4.1. Parametric wind models

Many parametric models have been developed in TC wind studies (Holland, 1980; Harper and Holland,

1999; Vickery et al., 2000). In this study, as in Xie et al. (2004) and Peng et al. (2004), the Holland (1980) para-metric wind model is employed to generate symmetrical, 0th order (circular) wind fields:

P Pc Pn Pc expA=rB 6V0w ABPn Pc expA=rB=qrB1=2 7A RBmax 8B eqV0wmax=Pn Pc 9

where q is the air density, P, the atmospheric pressure at radius r, Pc and Pn are respectively central and ambi-ent pressures, A and B are scaling parameters, Rmax is RMW, V

0w is the pressure gradient induced wind velo-

city and V0wmax is its maximum value at Rmax, and e is the base of natural logarithms. For the hypothetical TCsin Sections 4.24.4, the above parameters are set as: Pn = 1010 mb, q = 1.2 kg m

3, and B= 1.9, an arbitrary

value from its typical range (1.52.5) in Holland (1980), and Rmax is specified in the experiments. For the two

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1

2

3

4

5

a

Sea

Leve

l(m)


9

8

7

6

5

4

3

2

1

0

b

Sea

Leve

l(m)

wind speed=35m/swind speed=30m/s

wind speed=25m/swind speed=20m/s

Fig. 5. Spin-up/spin-down experiments with different wind forcings: (a) spin-up with onshore winds and (b) spin-down with offshorewinds.




historic TCs in Section 5, P and q are the same as for the hypothetical TCs, B is determined by (9), whereV0wmax is the maximum symmetric wind speed, which is achieved from the difference of the observed maximumwind speed and the translation speed, and Rmax is deduced from observations. The way to choose these param-eters in historic TCs is due to the fact that V0wmax is generally easier to obtain from the observations.

The wind fields used in the storm surge model are the combination of (7) and the TCs translation speed VH

as in (10). For symmetry purpose,VH is set to zero for the hypothetical TCs, but it takes the observed value forthe two historic TCs.

~Vw ~V0w ~VH 10The parametric wind model, assuming to the lowest order, gives a circular wind flow pattern around its

center. This does not adequately reflect the actual surface wind directions, and wind inflow angles shouldbe considered in real cases (Huston et al., 1999). However, as one major purpose of Sections 4.2 and 4.3 ison the asymmetry of sea level surge and fall with symmetric wind forcing, asymmetric factors, such as inflowangle and VH, are not considered in these two subsections.

4.2. Translation speed

To assess the asymmetry of the TC induced sea level surge and fall, the idealized square domain ( Fig. 3),again, is employed with the hypothetical track running along the shoreline from south to north with land onthe left. The minimum water depth is set to 20 m in this and the next two subsections to avoid potential drying

8

6

4

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0

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4

6

StormSu

rge(m)

a

25km/h

970mb960mb950mb940mb930mb920mb b

20km/h

970mb960mb950mb940mb930mb920mb


6

4

2

0

2

4

6

StormS

urge(m)

c

15km/h


20 hour 40 hour 60 hour 80 hour 100 hour

d

10km/h


Fig. 6. The effect of tropical cyclones translation speed on the asymmetry of the maximum surge and fall in various central pressure

conditions: (a) 25 km h1, (b) 20 km h1, (c) 15 km h1 and (d) l0 km h1.

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http:///reader/full/tropical-cyclone-induced-asymmetry-of-sea-level-surge-and-fall-and-its-presentation-in-a-storm 10/21

that makes it difficult to evaluate the maximum sea level fall. Central pressure varies from 970 to 920 mb.RMW remains at 50 km though, statistically, RMW varies from 46 to 51 km according to Hsu and Yan(1998) for TCs with the specified intensity. The hypothetical TC starts 300 km away from the southern borderof the domain, and the translation speed is specified to 25, 20, 15 or 10 km h1 respectively.

Time series of sea surface elevation at location A are shown in Fig. 6. One has to bear in mind that a slower

translation speed implies more wind duration for both onshore and offshore winds, though such winds are notalways perpendicular to the coast as in the previous section. For TCs with fixed central pressure, the slower thetranslation speed, the greater the asymmetry of the maximum surge and fall. For instance, AI for a 950 mb TCtraveling at 25 km h1 is only 32%, but when its speed decreases to 10 km h1 the value of AI will increase to71%. This is because the maximum fall, as presented in the previous section, is more slowly achieved, and itsmagnitude is larger than the maximum surge.

Translation speed has almost no influence on the maximum surge, but has significant effect on the maxi-mum fall (Fig. 6). This indicates that a steady state for positive surge has been reached at some time for everycase. A steady state for negative surge, however, has never been reached. When a 920 mb TC slows down from15 to 10 km h1, for example, the maximum surge is not changed, while the maximum fall (its absolute value)increases from 5.51 to 6.02 m. A stead state of fall, therefore, is not obtained. As a result, AI is increased. Thedetails on how AI changes with translation speed are shown in Fig. 9a.

For those with the same translation speed, a weaker TC is expected to gain a higher AI value though itsinduced maximum surge and fall are relatively smaller. Of the group with translation speed of 20 km h1,for instance, the maximum surge and fall for a 970 mb TC are only 1.55 m and 2.46 m respectively (see

12

8

4

0

4

8

StormSu

rge(m)

a

RMW=30km


RMW=50km



8

4

0

4

8

StormS

urge(m)

RMW=70km

c



d

RMW=90km


Fig. 7. The effect of tropical cyclones RMW on the asymmetry of the maximum surge and fall in various central pressure conditions:

(a) 30 km, (b) 50 km, (c) 70 km and (d) 90 km.




Fig. 6), or AI = 59%. A 920 mb strong TC generates 3.87 m surge and 5.03 m fall. The corresponding AI,however, is only 30%. This is different from the case when both onshore and offshore steady winds are longenough to reach the steady states. For most TCs, considering their typical RMW and translation speed, off-shore wind is not long enough to reach the steady state for negative surge. For those with fixed translationspeed, a weaker TC (whose spin-up/spin-down time is shorter) is closer to reach the steady state, so the asym-

metry feature is well revealed.

4.3. RMW

RWM is another important parameter in the wind model that can influence TC induced storm surge (Penget al., 2004). The RMW of an individual TC may be much different from its intensity-based statistic value ( Hsuand Yan, 1998). Larger RMW not only increases wind duration for both onshore and offshore winds, but alsoincreases wind fetch. The effect of the latter is important and makes peculiar the relationship between RMWand AI as will be discussed later. In our experiments, the TCs translation speed is set to 15 km h1, and RMWare respectively 30, 50, 70 and 90 km.

As expected, the extent of both surge and fall increases as RMW is enlarged ( Fig. 7). For a 940 mb TC,when RMW is 30 km, the maximum surge and fall are 1.55 and

2.49 m respectively. As RMW increases

to 90 km, the maximum surge and fall increases to 4.66 and 7.49 m. This is different from when the relation-ship between translation speed and the maximum surge and fall was addressed in the previous subsection. In

6

4

2

0

2

4

6

StormSu

rge(m)

a

10 degree


20 degree



4

2

0

2

4

6

StormS

urge(m)

c

30 degree



d

40 degree


Fig. 8. The effect of tropical cyclones wind inflow angle on the asymmetry of the maximum surge and fall in various central pressure

conditions: (a) 10, (b) 20, (c) 30 and (d) 40.




the former case, only the maximum fall changes with translation speed. The correlation between RMW andthe maximum surge in Fig. 7 is due largely to wind fetch variation as RMW changes.

For those with fixed RMW, the relationship between central pressure and AI depends on the value ofRMW. If RMW is small, AI decreases as the central pressure decreases. This is true when RMW is 30 or50 km as illustrated in Fig. 9b. However, for TCs with large RMW, there is no clear correlation between

central pressure and AI. As RMW increases to 90 km, there is almost no AI change as central pressure varies.This reflects that RMW affects AI in a way that is different from translation speed. Again, the difference maybe due to the variation of wind fetch. The results in Fig. 9b imply a balance between wind duration (whoseincrease may increase AI) and TCs intensity and wind fetch (whose increase may decrease AI).

4.4. Tropical cyclones inflow angle

Another parameter that can change the maximum surge and fall and the consequent AI is the TCs inflowangle, which is the angle between the wind direction and the tangent to a circle concentric with the TC center.Unlike translation speed (without considering VH in the wind fields as in the two former subsections) andRMW, which influence the maximum surge and fall by varying wind duration or fetch, inflow angle affectsthe surge and fall by changing the symmetric nature of the lowest-order wind fields. No matter how much

is changed of the wind duration or fetch owing to the change of translation speed or RMW, the variationitself, in terms of the accumulation of wind force on spin-up and spin-down, is symmetric. Holland (1980)model generates symmetric wind fields, so the asymmetry of the maximum surge and fall, as previouslyaddressed, is the shallow waters intrinsic feature of responding to symmetric wind forcing asymmetrically.

The consideration of inflow angle fundamentally changes the symmetry of wind fields, and provides thesurge model with an asymmetrical (with respect to its center) exterior forcing as in real TCs. If inflow angle

930 940 950 9600.5

0

0.5

1.0

Asymme

try

Index

a

25km/h20km/h15km/h10km/h

930 940 950 960

Central Pressure (mb)

b

30km50km70km90km

930 940 950 960

c

10 degree20 degree30 degree

40 degree

Fig. 9. The relationship of AI with central pressure and (a) translation speed, (b) RMW, and (c) inflow angle.




is considered in the model, a TC moving northward with land on its left in the Northern Hemisphere, as will beshown, is expected to generate larger surge and smaller fall. As a result, the overestimation of the asymmetryof surge and fall as discussed in the Introduction may be moderated.

Fig. 8 shows how inflow angles affect the maximum surge and fall. In our experiments, the RMW and trans-lation speed are respectively fixed to 50 km and 15 km h1 for comparison with the former cases. When no

inflow angles were considered (Fig. 7b), the asymmetry of the maximum surge and fall was evident. For exam-ple, the maximum surge, fall and AI for the 970 mb case are respectively 1.51 m, 2.57 m and 70.3%. If 10 isconsidered as the inflow angle homogeneously across the field (Fig. 8a), the maximum surge, fall and AI turnto 1.78 m, 2.23 m and 25.5%. The asymmetry of the maximum surge and fall is significantly reduced. As theinflow angle increase continues, the asymmetry of surge and fall is further reduced. In fact, as the angleincreases to 20 and above, AI becomes negative for all central pressures (Fig. 9c), which indicates themaximum surge surpasses the maximum fall.

The reason why inflow angle can change the maximum surge and fall and the consequent AI is due to theasymmetry of wind fields and the orientation of the TC track. When inflow angles are considered, the TCsmoving in the Northern Hemisphere with land on the left may cause larger surge and smaller fall. HurricaneIsabel and Charley that will be addressed in the next section are this kind of TC. Reverse conclusions may holdfor a TC with land on its right, or the same orientation in the Southern Hemisphere.

In some sense, inflow angle is more meaningful on AI adjustment than translation speed and centralpressure. This is because inflow angle is more elusive to TC forecasters than the other two parameters. Moreimportant, it exists in all TCs. In real case, inflow angle may vary spatially at a time. Generally, its value nearthe eye is smaller than around its periphery. Although the upper limit of the inflow angle is 25 as suggested in

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37.0N

Sunset BeachSpringmaid Pier

Charleston

Fort Pulaski

Hurricane Charley

(2004)

Fig. 10a. The track of Hurricane Charley and the locations of water level stations. The box shows the inner domain of the nesting system.




some models (Phadke et al., 2003), it may be far out of the range in real cases. Accurate estimate of the inflowangle can greatly improve the storm surge model output in real cases as will be illustrated in the next section.

5. Historic tropical cyclones

Any mistakes in wind model specification may lead to errors in surge simulation. The errors, as indicated inthe previous section, are more evident in the negative surge phase. As inflow angles are not systematically mea-sured and documented as the other parameters, it is singled out in the following hindcast studies to assess itseffects on the asymmetry of the surge and fall. Hurricane Charley (2004) and Isabel (2003) are the two historicTCs to be studied, and their track, RMW, and central pressure are obtained from the interpolation of theobserved data.

5.1. Hurricane Charley

Hurricane Charley passed over the mid-eastern coast of the US on August 14, 2004, as shown in Fig. 10a.This Category One hurricane was not a severe case in this region. However, before landfall at Sunset Beach,North Carolina its track was almost parallel to the coast. So, it was similar to the hypothetical TCs in the

previous section. Furthermore, this hurricanes surface wind fields at every 3 h were digitally archived byNOAA/HRD. So, not only its track, central pressure, and RMW, but also inflow angles were systematicallydocumented.

For instance, at 08/14/1330Z the Hurricanes maximum wind speed, as indicated in Fig. 10b, is about35 m s1 northeast of its eye. Its RMW is also suggested in the figure. More directly, Fig. 10c provides theobserved wind fields by which the wind inflow angles may be inferred. Based on the observation, 40 wasfound to be the best wind inflow angle (least square fitting for the two components of wind vectors) for the

Fig. 10b. NOAA/HRD H*Wind surface wind analysis of Hurricane Charley on August 14, 2004 1330 UTZ. The contours show windspeed (kt) and the position of the maximum surface wind is indicated by the arrow. The radii of 34, 50, and 64 kt winds for each stormquadrant are shown in the upper left corner of the figure. Winds are maximum 1-min sustained at 10 m and valid for marine and open

terrain exposures.




parametric wind fields (Fig. 10d). Consideration of this inflow angle greatly improves the reliability of the sim-ulated wind fields. Land friction has been considered for mapping of Fig. 10d, though wind stress over landhas no influence on coastal surge calculation, and this was accomplished by giving a specified friction factor in(10) when wind speed over land was calculated. The same will be performed in Fig. 11c when Hurricane Isabelis addressed in the next subsection.

As mentioned before, only wind inflow angle is considered as a variable in the experiments while others,such as track, central pressure, translation speed, and RMW, take their interpolated values at each time.Sea level data are available at four stations whose locations are illustrated in Fig. 10a. In the experiments,the inflow angles vary from 0 to 50, but for clarity, only the results of 0, 20 and 40 are mapped inFig. 10e in comparison with the observations.

Hurricane Charley induced sea level disturbance was evident at Sunset Beach, Springmaid Pier, andCharleston, but there was almost no perturbation at Fort Pulaski, which is about 300 km south of the landfalllocation. For the 0 case, in which no wind inflow angle is considered, the maximum difference of the simu-lated and observed sea level is near 2.0 m at the three northern stations. Severe discrepancy of sea level occursafter the surge maxima. As wind inflow angle increases, the difference is getting smaller. The maximum dis-crepancy dwindles to about 1.0 m for these stations when the inflow angle is 40. As shown in Fig. 10e, wheninflow angle is considered in the parametric wind model, the maximum negative surge is significantly reduced,but the maximum positive surge is not significantly changed. As a result, the asymmetry of the maximum surgeand fall is moderated.

5.2. Hurricane Isabel

The track of Hurricane Isabel has been shown in Fig. 1. As mentioned previously, the parametric

wind fields with no inflow angle correction lead to an apparent mistake of negative surge, though the overall

82.0W 81.0W 80.0W 79.0W 78.0W

32.0N

33.0N

34.0N 30m/s

Fig. 10c. Charleys gridded H*Wind analysis wind fields for both marine and open terrain at 08/14/1330Z.




maximum positive surge at most stations agreed well with the observations. In this subsection, different inflowangles will be fed into the model to see how much difference they can make with regard to sea level surge andfall and their asymmetry.

Before landfall, the asymmetry of Hurricane Isabels wind fields was not as noticeable as of HurricaneCharley. This is shown in Fig. 11a and Fig. 11b, which respectively depict the wind structure and field at09/18/1330Z. The maximum wind speed is about 44 m s1 in the NE quadrant. In this case, 25 was foundto be the best inflow angle to match the observation, and the corresponding model wind field is shown inFig. 11c. Again, the sea level results at Chesapeake Bridge and Duck Pier of taking 0, 20 and 40 as the windinflow angles are mapped in Fig. 11d to compare with the observations.

For the overall maximum sea level surge, the results are the best when the inflow angle is 30 (not shown).Taking 20 and 40 as the inflow angle respectively underestimates and overestimates the maximum surge. Fornegative surge, the error is largely reduced as inflow angle increases. This is true at least within the selectedrange of inflow angles. Although Fig. 11d illustrates that increasing inflow angles moderate the asymmetryof the surge and fall and hence improve the simulation results, it does not indicate that the inflow angle of40 is closer to the truth than 20. In fact, as mentioned before, 25 is the best inflow angle to match theobservation. It is apparent that the maximum negative surge is still overestimated even with considerationof inflow angles.

As Hurricane Isabels track, central pressure, and translation speed were accurately measured andemployed in the model, the possible mistakes may come from the input of RMW which can only be inferredfrom observations. Furthermore, Hurricane Charley is not a perfect circle (see Fig. 11a), and its RMW shouldtake its own value in each quadrant at any time.

One has to keep in mind that other factors which may also contribute to storm surge, such as precipitationand runoffs, are not considered in this study. The freshwater contribution may be important in the inner

domain of Fig. 1. This is especially true at Chesapeake Bridge which is at the mouth of Chesapeake Bay,

82.0W 81.0W 80.0W 79.0W 78.0W

32.0N

33.0N

34.0N 30m/s

Fig. 10d. Charleys simulated wind fields at 08/14/1330Z with wind inflow angle of 40 as a correction of Holland wind fields, and landfriction has been considered for the mapping.




the largest estuary system in the US. Even at Duck, 100 km south of the estuary mouth, sea level is still, tosome extent, under the influence of the inland runoff. This is because freshwater in an estuary in the NorthernHemisphere generally moves to its right after jetting out from its mouth due to the earths rotation (Zhanget al., 1987; Pietrafesa and Janowitz, 1988). This may be another reason why, as shown in Fig. 11d, the max-imum sea level fall is overestimated even with consideration of inflow angles. The freshwater contribution, ofcourse, may be far less than RMW.

6. Conclusion and discussion

TC induced asymmetry of the maximum surge and fall is studied in this paper. It is found that offshorewinds are more effective in inducing sea level fall than the corresponding onshore winds in inducing positivesurge. As a result, the response of sea level in the TCs offshore-wind quadrant is more sensitive to wind forc-ing than in the onshore wind quadrant. Any misspecification of wind parameters, such as translation speed,RMW, and inflow angle may lead to inaccurate sea level simulation.

The study finds that the asymmetry of the maximum surge and fall is evident in shallow water regions. Ittakes more time for an offshore wind to reach the steady state. Or, the spin-down time is longer than spin-uptime. In deep water, the huge original undisturbed water depth subdues the asymmetry of sea level surge andfall. For steady onshore and offshore winds with long duration, the asymmetry increases with wind forcing.

Any change of parameters in the TC parametric wind model may lead to changes in sea level surge and fall

and the consequent asymmetry. Generally, the parameters fall into two major categories as to how to affect

1

0

1

2

Sunset Beach, NC

Observed0 degree20 degree

40 degree

1

0

1

2

Springmaid Pier, SC

Observed0 degree20 degree40 degree

1

0

1

2

Charleston, SC


14/0000Z 14/0600Z 14/1200Z 14/1800Z

1

0

1

2

Fort Pulaski, GA


Sea

leve

lun

dert

he

influenceo

fHurr

icane

Charley

(m)

Fig. 10e. The results of sea surface elevation time series taking 0, 20 and 40 as the wind inflow angle are compared with the observationat four stations for Hurricane Charley.




Fig. 11a. NOAA/HRD H*Wind surface wind analysis of Hurricane Isabel on September 18, 2003 1330 UTZ. The contours show windspeed (kt) and the position of the maximum surface wind is indicated by the arrow. The radii of 34, 50 and 64 kt winds for each stormquadrant are shown in the upper left corner of the figure. Winds are maximum 1-min sustained at 10 m and valid for marine and openterrain exposures.

78.0W 77.0W 76.0W 75.0W 74.0W 73.0W 72.0W

32.0N

33.0N

34.0N

35.0N

36.0N

37.0N 30m/s

Fig. 11b. Isabels gridded H*Wind analysis wind fields for both marine and open terrain at 09/18/1330Z.




1

0

1

2

Max

imum

Storm

Tide

(m)

Chesapeake Bridge (S4)Observed0 degree20 degree40 degree

17th00Z 12Z 18th00Z 12Z 19th00Z 12Z

1

0

1

2Duck Pier (S3)

Max

imum

Storm

Tide

(m)

Observed

0 degree20 degree40 degree

Fig. 11d. The results of sea surface elevation time series taking 0, 20 and 40 as the wind inflow angle are compared with the observation

at two stations for Hurricane Isabel.

78.0W 77.0W 76.0W 75.0W 74.0W 73.0W 72.0W

32.0N

33.0N

34.0N

35.0N

36.0N

37.0N 30m/s

Fig. 11c. Isabels simulated wind fields at 09/18/1330Z with wind inflow angle of 25 as a correction of Holland wind fields, and landfriction has been considered for the mapping.




surge and fall. Varying wind duration and fetch is one and varying the symmetry of wind field is the other.Translation speed and RMW are the parameters of the first category while the inflow angle is of the second.In the first category, translation speed only changes wind duration for a location, but RMW changes bothwind duration and fetch.

For TCs with fixed intensity, the slower the translation speed, the greater the asymmetry of the surge and

fall. This is because in most TC cases the steady state for onshore wind is reached. However, the steady statefor offshore wind is not. It is closer to be reached as translation speed decreases. The asymmetry of the max-imum surge and fall, therefore, becomes more evident as the translation speed decreases. For TCs with thesame translation speed, a weaker one is more likely to gain a higher AI value though its induced maximumsurge and fall are relatively smaller. This is different from the long steady wind forcing case.

It should be noticed that the wind used to drive the storm surge model for the hypothetical TCs is not thecombination of the circularly parametric wind and translation speed VH. The latter is ignored for the purposeof obtaining a symmetric wind field and emphasizing the variation of wind duration due to translation speedchange. In the two historic TCs, however, the translation speed is combined with the circular wind as thedriving force.

If translation speed is fixed, a larger RMW offers longer wind duration and larger wind fetch. As a result,the extent of both surge and fall increases with RMW. The relationship between central pressure and AI, how-

ever, depends on the value of RMW. If RMW is small, AI decreases with increasing TC intensity. However,for large RMW, there is no distinct correlation between central pressure and AI. These conclusions may beonly correct within the specified parameter ranges in the experiments. The results indicate that RMW affectsAI in a way that is different from translation speed, and it is the changing fetch that makes the difference. Infact, the relationship among RMW, central pressure, and AI, implies a balance of wind duration, fetch andTCs intensity.

Another parameter that can change the asymmetry index is the TCs inflow angle, which is the only param-eter in the study that changes the circular feature of the parametric wind fields. This is different from the othertwo parameters in the way to induce asymmetry of surge and fall.

No matter how much wind duration or fetch is changed owing to the change of a TCs translation speed orRMW, the variation itself is symmetric. The asymmetry of surge and fall reflects the shallow waters intrinsic

feature ofasymmetricalresponse to symmetric wind forcing. The consideration of TCs inflow angle, however,fundamentally changes the symmetry of parametric wind field and offers an asymmetrical wind forcing. Add-ing inflow angles to symmetric wind as a correction may increase the maximum surge and, simultaneously,decrease its maximum fall. The asymmetry index, as a result, is reduced. This may be only the case forTCs moving northward with land on the left in the Northern Hemisphere. As inflow angle is more elusiveto TC forecasters than the other two parameters in real cases, its misspecification may lead to large errorsin storm surge forecast.

The importance of considering a reasonable TC inflow angle is illustrated in the hindcast of HurricaneCharley and Hurricane Isabel. In both cases, adding inflow angles greatly improves sea level simulationresults. The consideration of inflow angle for these two TCs results in AI decrease at all coastal stationsdue to the moderation of the maximum sea level fall. This greatly improves storm surge results.

Acknowledgements

This study is supported by the Carolina Coastal Ocean Observation and Prediction System (Caro-COOPS)project under NOAA Grant No. NA16RP2543. Caro-COOPS is a partnership between the University ofSouth Carolina and North Carolina State University. We thank Madilyn Fletcher and Earle Buckley forconstructive comments and project coordination, Shaowu Bao for helpful discussions on the tropical cyclonewind model.

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