numerical simulations of air–sea interaction under high...

2190 VOLUME 128M O N T H L Y W E A T H E R R E V I E W

q 2000 American Meteorological Society

Numerical Simulations of Air–Sea Interaction under High Wind Conditions Using aCoupled Model: A Study of Hurricane Development

J.-W. BAO

Cooperative Institute for Research in Environmental Sciences, University of Colorado, andNOAA/Environmental Technology Laboratory, Boulder, Colorado

J. M. WILCZAK

NOAA/Environmental Technology Laboratory, Boulder, Colorado

J.-K. CHOI AND L. H. KANTHA

Department of Aerospace Engineering Sciences, Colorado Center for Astrodynamics Research,University of Colorado, Boulder, Colorado

(Manuscript received 30 March 1999, in final form 18 August 1999)

ABSTRACT

In this study, a coupled atmosphere–ocean wave modeling system is used to simulate air–sea interaction underhigh wind conditions. This coupled modeling system is made of three well-tested model components: The Penn-sylvania State University–National Center for Atmospheric Research regional atmospheric Mesoscale Model, theUniversity of Colorado version of the Princeton Ocean Model, and the ocean surface gravity wave model developedby the Wave Model Development and Implementation Group. The ocean model is initialized using a 9-monthspinup simulation forced by 6-hourly wind stresses and with assimilation of satellite sea surface temperature (SST)and altimetric data into the model. The wave model is initialized using a zero wave state. The scenario in whichthe study is carried out is the intensification of a simulated hurricane passing over the Gulf of Mexico. The focusof the study is to evaluate the impact of sea spray, mixing in the upper ocean, warm-core oceanic eddies shed bythe Gulf Loop Current, and the sea surface wave field on hurricane development, especially the intensity.

The results from the experiments with and without sea spray show that the inclusion of sea spray evaporationcan significantly increase hurricane intensity in a coupled air–sea model when the part of the spray that evaporatesis only a small fraction of the total spray mass. In this case the heat required for spray evaporation comes fromthe ocean. When the fraction of sea spray that evaporates increases, so that the evaporation extracts heat fromthe atmosphere and cools the lower atmospheric boundary layer, the impact of sea spray evaporation on increasinghurricane intensity diminishes.

It is shown that the development of the simulated hurricane is dependent on the location and size of a warm-coreanticyclonic eddy shed by the Loop Current. The eddy affects the timing, rate, and duration of hurricane intensification.This dependence occurs in part due to changes in the translation speed of the hurricane, with a slower-moving hurricanebeing more sensitive to a warm-core eddy. The feedback from the SST change in the wake of the simulated hurricaneis negative so that a reduction of SST results in a weaker-simulated hurricane than that produced when SST is heldunchanged during the simulation. The degree of surface cooling is strongly dependent on the initial oceanic mixedlayer (OML) depth. It is also found in this study that in order to obtain a realistic thermodynamic state of the upperocean and not distort the evolution of the OML structure during data assimilation, care must be taken in the dataassimilation procedure so as not to interfere with the turbulent dynamics of the OML.

Compared with the sensitivity to the initial OML depth and the location and intensity of the warm eddy associatedwith the loop current, the model is found to be less sensitive to the wave-age-dependent roughness length.

1. Introduction

The atmosphere and the ocean are coupled dynami-cally and thermodynamically by momentum and en-

Corresponding author address: Dr. Jian-Wen Bao, NOAA/ETL,Mail Stop ET7, 325 Broadway, Boulder, CO 80303-3328.E-mail: [email protected]

thalpy exchanges at the air–sea interface. The interac-tion of the atmosphere and the ocean has been longrecognized as an important element of atmospheric andoceanic circulation on a wide range of scales. Althoughnumerical modeling of the atmosphere and the ocean asseparate geophysical fluid systems has made tremendousprogress over the past four decades, significant uncer-tainties remain in how these two systems influence oneanother. These uncertainties concern the physical pro-

JULY 2000 2191B A O E T A L .

cesses that are important for coupling the atmospherethrough the transfer of momentum, heat, and moistureacross the air–sea interface.

One manifestation of the interaction between the at-mosphere and the ocean is ocean surface gravity waves,which can have a significant impact on the transfer ofmomentum and enthalpy across the air–sea interface(see, e.g., Geernaert 1990; Kraus and Businger 1994).Conventionally, in atmospheric modeling the effect ofocean waves on flux transfer at the air–sea interface istaken into account by using an average roughness lengththat is linked to the surface stress through the Charnockrelationship (see, e.g., Garratt 1992; Kraus and Businger1994). The surface stress is taken to be a function ofonly wind speed, the roughness length, and the stabilityof the surface layer above the air–sea interface. Re-cently, both observations and numerical modeling stud-ies indicate that the surface stress is also a function ofsea state; in other words, it is dependent on the windwave spectrum (see, e.g., Komen et al. 1994). Part ofthe momentum imparted by the wind stress is propa-gated away by surface gravity waves instead of drivinglocal currents. Ocean waves consist of a distribution ofmoving elements that are related to the wind stress,which together determine the rate of input of energyfrom wind to waves. The nonlinear, resonant, wave–wave interaction mechanism redistributes energy in thewave spectrum. Despite the complexity, advances havebeen made over the past two decades in understandingand modeling these surface wave processes (Komen etal. 1994).

Another manifestation of air–sea interaction is thechange of sea surface temperature (SST) due to wind-driven mixing in the upper ocean, and to the heat, mois-ture, and radiative fluxes at the air–sea interface. Thedynamical response of atmospheric models can be verysensitive to temporal changes in the thermodynamicfluxes at the air–sea interface, which in turn can besensitive to SST changes. For example, idealized sim-ulations of tropical cyclone–ocean interaction within acoupled atmosphere–ocean model (Bender et al. 1993)indicate that the cooling of the sea surface produced bythe tropical cyclone results in a significant reduction ofthe hurricane intensity. At the other extreme, air–seafluxes under low wind conditions are sensitive to var-iations of SST induced by the cool skin and the dy-namics of the diurnal warm layer at the air–sea interface(Fairall et al. 1996).

SST changes are strongly dependent on turbulentmixing in the upper ocean. Both the surface momentumflux and an upward enthalpy flux across the interfacewill produce turbulent mixing in the upper ocean, re-sulting in an ocean mixed layer (OML) within whichhorizontal velocity, temperature, and salinity are nearlyconstant with depth. The OML can have large variabilityon a wide range of temporal and spatial scales resultingeither from changes in atmospheric forcing or fromchanges in the ocean circulation. Because all oceanic

changes are communicated to the atmosphere throughthe OML, any numerical model intended to simulateair–sea interaction must include an accurate descriptionof ocean mixed layer dynamics.

Flux transfer processes over the ocean are commonlyparameterized in atmospheric models using Monin–Ob-hukov similarity theory and a specification of the sur-face characteristics (e.g., surface roughness length). Re-cent observations and modeling studies indicate that thesea spray generated by ejection of droplets from break-ing waves should be taken into account in the air–seaflux parameterization used in atmospheric models, es-pecially under high wind conditions (see Andreas et al.1995; Kepert et al. 1999). High winds produce sea spraydroplets that modify the mean thermodynamic state ofthe air surrounding them. As a result, the physics in-volved in enthalpy transfer across the air–sea interfaceis different from that in situations where the sea sprayis absent. If the lowest model level is well above thedroplet evaporation zone, the effects of the sea spraymay be included as a modification of the surface fluxesthat can be applied within the Monin–Obhukov simi-larity framework. If, however, the lowest model levelis within the droplet evaporation zone, a modificationof Monin–Obhukov similarity theory may be necessary.

Although it is believed that the surface fluxes can bestrongly altered by intensive mixing within the OML,by sea spray, or by sea surface waves, the collectiveimpact of these processes on air–sea interaction has notbeen assessed in field programs to the same degree ashas each of these processes individually. This is due inpart to the difficulty of making simultaneous observa-tions of the momentum, and sensible and latent heatfluxes across the air–sea interface along with measure-ments of all the atmospheric and oceanic parametersaffecting the fluxes. Therefore it is appealing to use anumerical model to evaluate the combined impact ofOML dynamics, sea spray, and sea surface waves onthe surface fluxes. Obviously it is a basic requirementthat in the model, air–sea interaction be treated in a two-way fashion, with mutual feedback from the ocean andthe atmosphere. Numerical evaluations such as this, al-though they cannot replace observational studies of air–sea interaction, can indicate the potential importance ofthe parameterized physical processes as well as high-light processes for which additional observational fieldstudies would be useful.

This study describes numerical simulations in whicha limited-area, coupled air–sea modeling system is usedto evaluate the impact of air–sea interaction on the de-velopment of a hurricane. The modeling system consistsof a regional atmospheric model, an ocean surface grav-ity wave model, and an ocean circulation model that aredirectly coupled at each integration time step. The pur-pose of these numerical experiments is to assess theimpact of mixing in the OML, sea spray, and sea surfacewaves on air–sea interaction under high wind condi-tions.


The methodology used for carrying out the numericalexperiments is similar to that of Bender et al. (1993).All the experiments use the same atmospheric boundaryconditions and hurricane vortex initialization so that theatmospheric environmental conditions that predomi-nantly control the hurricane track remain constant. Theinitial and boundary conditions are prescribed by ana-lyzed fields for Hurricane Opal (1995). The model do-main contains realistic geographic features such ascoastlines, the bathymetry of the Gulf of Mexico, andland topography.

Observations suggest that hurricane developmentmay be strongly affected by warm oceanic eddies shedby the Loop Current in the Gulf, which possesses arelatively deep and warm OML (Shay et al. 1998). Inthis study, a realistic oceanic warm eddy is introducedinto the numerical experiments through assimilation ofsatellite data in order to evaluate how the existence ofthe warm eddy affects the intensification of the hurri-cane.

It should be noted that it is not the purpose of thisstudy to explore the details of the internal dynamics ofthe hurricane or to investigate the interaction of thelarge-scale atmospheric environment with the hurricane.Because the purpose of this study is to evaluate theimpact of mixing in the OML, sea spray, and sea surfacewaves in numerical simulations of storm evolution, ide-alized experiments are used. Liu et al. (1997) haveshown that in order to simulate reasonably well the in-tensity and inner-core structures of hurricanes, not onlyis it required that the atmospheric model have high res-olution (;6 km) and realistic cloud physics, but it isalso necessary that the hurricane vortex (depth, size,and intensity) be properly initialized in relation to large-scale atmospheric conditions. Their results also indicatethat an apparently realistic simulation of hurricane evo-lution can be obtained even if the model does not havea physically faithful description of fluxes at the air–seainterface, so long as the amount of momentum and en-thalpy fluxes from the model’s lower boundary fortu-itously is sufficient to sustain the simulated hurricaneevolution.

The paper is organized as follows. Brief descriptionsof individual model components in the coupled mod-eling system are presented in section 2. Parameteriza-tions used for the surface roughness lengths and tur-bulent fluxes are described in section 3. A parameteri-zation scheme is then introduced in section 4 that takesinto account sensible and latent heat fluxes contributedfrom sea spray droplets. This is followed in section 5with a discussion of the coupling procedure for all themodel components. The assimilation procedure for thesatellite data and the numerical experiments are pre-sented in section 6, followed by a discussion and sum-mary in section 7.

2. Model descriptionThe Pennsylvania State University–National Center

for Atmospheric Research (Penn State–NCAR) Meso-

scale Model version 5 (MM5) (Grell et al. 1994) is aregional, hydrostatic or nonhydrostatic, sigma-coordi-nate model designed to simulate or predict mesoscaleand regional-scale atmospheric circulation. It has beendeveloped at Penn State and NCAR as a communitymesoscale model and is continuously being improvedby contributions from users at numerous universities andgovernment laboratories. The model has a variety ofresolvable-scale microphysics and subgrid-scale cu-mulus parameterization schemes for precipitation phys-ics, along with several options for the parameterizationof planetary boundary layer and surface-layer processes.The model also includes three well-tested atmosphericradiation schemes.

The ocean wave model (WAM) is a third-generationwave model (WAMDI Group 1988) which solves thewave transport equation explicitly without any prior as-sumptions about the shape of the spectrum. It representsthe physics of the wave evolution in accordance withtoday’s knowledge for the full set of degrees of freedomof a 2D wave spectrum. WAM describes the evolutionof the directional wave spectrum by solving the waveenergy equation. The forcing in the wave energy equa-tion includes the wind input and dissipation terms fromthe quasi-linear wind-wave generation theory (Janssen1991; Komen et al. 1994), in which the wind input termincludes the square of the inverse of the wave age (de-fined as c/u*, c being the wave phase speed and u* thefriction velocity), and the dissipation term is propor-tional to the fourth power of the frequency. The non-linear wave–wave interaction term in the forcing isbased on the theory of Hasselmann et al. (1985). Themodel was developed at the Max Planck Institute forMeteorology in Hamburg, Germany, has been installedat many institutions worldwide, and is used for bothresearch and operational applications. It is also beingapplied for interpretation and assimilation of satellitewave data. So far, four cycles of the wave model havebeen issued. It is the last cycle, cycle 4 (see Gunther etal. 1992; Komen et al. 1994), that is coupled to MM5.

The Princeton Ocean Model (POM) is used in thecoupled modeling system to simulate the OML pro-cesses and oceanic circulation. POM is a sigma-coor-dinate, free-surface, primitive equation ocean model,which includes a turbulence submodel. POM uses thefollowing three assumptions: 1) the flow is incompress-ible; 2) the vertical accelerations are negligible com-pared to gravity, thus, the vertical pressure distributionsatisfies the hydrostatic approximation; and 3) densityis approximated by its mean value except when mul-tiplied by gravity, that is, when the Boussinesq approx-imation is used. POM was developed in the late 1970sby G. Mellor’s group (Blumberg and Mellor 1987; Kan-tha and Piacsek 1996) at Princeton University, with sub-sequent contributions from many other institutions. Themodel has been applied to modeling of estuaries, coastalregions, and open oceans, and is being used routinelyby many worldwide institutes for both research and op-

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erational forecasting. The version of POM used in thismodeling system is the University of Colorado versiondeveloped by L. Kantha (hereafter referred as CUPOM),which incorporates an improved turbulence submodel(Kantha and Clayson 1994) to solve explicitly for tur-bulent mixing in the water column. CUPOM also has adata assimilation module using in situ temperature andsalinity observation data, satellite altimetric data, andsea surface temperatures inferred from satellite multi-channel infrared imagery (MCSST). This assimilativemodel has been used in simulations of regional seassuch as the Red Sea, Mediterranean Sea, the Sea ofJapan, and the Gulf of Mexico (Choi et al. 1995; Banget al. 1996; Clifford et al. 1997; Horton et al. 1997).

3. Sea surface roughness and turbulent fluxparameterization

The transfer of momentum flux across the so-calledwave boundary layer is described by the bulk param-eterization based on the Monin–Obukhov similarity the-ory, in which the stress, t , is related to the resolvablewind via the drag coefficient, Cd. By definition, the dragcoefficient is fully determined by the roughness lengthof the ocean surface. Data from field and laboratoryexperiments indicate that the roughness length of theocean surface depends upon the stage of wind–wavedevelopment. In the coupled modeling system, the fol-lowing parameterization is used to describe the depen-dence of the drag coefficient on the wave state.

Assume that the total stress close to the surface canbe expressed as the sum of contributions from surfacewave and turbulence: t 5 t w 1 t t, where t , t w, andt t are the total stress, wave-induced stress, and atmo-spheric turbulence–induced stress, respectively. Themean wind profile above the wave surface is assumedto be logarithmic. Following Janssen (1991), we assumethat the effective roughness length of gravity–capillarywaves can be modeled by means of the Charnock re-lation

tz 5 a , (1)0 r ga

where a is a constant, g the acceleration of gravity, andra the air density. The effective wave-induced roughnesslength of the developing gravity waves is modeled bya parametric height, z1, so that the mean wind profileunder neutral stratification is given by

Ït /r z 1 za 1U(z) 5 ln , (2)k z 1 z0 1

where k is the von Karman constant. Consider thesteady-state stress balance of airflow over sea waves.Following Janssen (1991), the atmospheric turbulence-induced stress at z 5 z0 is given by

2z0t (z ) 5 t , (3)t 0 1 2z 1 z0 1

in which it is assumed that t t is modeled by

]U(z) ]U(z)2t (z) 5 l , (4)t ) )]z ]z

where U(z) is the wind profile given by (2) and l is themixing length (given by kz for neutral stratification).Substituting (3) into the expression of the total stressand using (1) then gives

t 1z 5 a 2 1 . (5)1 1 2gr Ï1 2 t /ta w

With the above parameterization of the sea-state-de-pendent roughness length, the coupling of MM5 andWAM takes place in the following sequence. First, thetotal stress, t 5 , is calculated in MM5 using a2ru*stability-dependent scheme based on the Monin–Obu-khov similarity theory,

kUu* 5 , (6)

ln(z /z ) 2 c0 m

where cm is a nondimensional stability correction factor.The total stress is then entered into WAM to obtain t w.Then both t w and t are used to compute the new sea-state-dependent z1; the sum of z0 and z1 is then used atthe next time step in MM5 as the new roughness lengthto obtain the new total stress t .

In recent experiments of ocean wave models that arecoupled to atmospheric models (e.g., Doyle 1995), thewave model uses the wind at the lowest level of theatmospheric model to approximate the 10-m wind. Thewave model then makes a stability-independent estimateof the effective roughness length z1, total stress, andwave-induced stress (which drives the wave field). Onlythe effective roughness length is then used by the at-mospheric model, which calculates its own stability-dependent stress for use in the atmospheric model. Thisresults in a total stress that is not continuous across theair–sea interface. This approach to coupling is improvedwith the aforementioned approach based on (1)–(5),which for nonneutral stratification will now produce thesame total stress in the atmospheric and ocean models.Although this parameterization is derived for neutralstratification, it is easy to show that the equation for z1

holds under nonneutral stratification if the wind profilefollows Monin–Obukhov similarity and can still be ex-pressed as

k(z 1 z ) ]U(z) kz1 5 5 w(z /L), (7)]z lÏt /ra

where w is the well-known Monin–Obukhov similarityfunction and L is the Monin–Obukhov length.

It has been recognized that the roughness length usedfor the surface momentum flux calculation need not be


the same as that used for the surface enthalpy flux.Strictly speaking, the roughness length obtained by us-ing the parameterization obtained as the sum of (1) and(5) is only applicable to the momentum flux. Surfaceroughness lengths for heat and moisture could be ob-tained using a surface renewal model (e.g., Liu et al.1979; Fairall et al. 1996), or using aerodynamicallysmooth scaling laws (Beljaars 1995), although for hur-ricane force winds there is little heat flux data to validateany parameterization choice. Recognizing that consid-erable uncertainty exists for the scalar roughnesslengths, in the present simulations we simply use thesame roughness length in the calculation of the surfacethermal and momentum fluxes. The surface sensible andlatent heat fluxes are then given by

H 5 2rC ku*T* and (8)s p

H 5 2rL ku*q*, (9)l e

where

DTT* 5 and (10)

ln(z /z ) 2 c0 h

Dqq* 5 , (11)

ln(ku*z /K 1 z /z ) 2 ca 0 h

where DT and Dq are the air–sea temperature and mois-ture differences, ch is a stability correction factor forthermal fluxes, and Ka is a background diffusivity (seeGrell et al. 1994).

4. The spray contribution to sensible and latentheat fluxes from the ocean

When the wind speed is in excess of approximately15 m s21, a substantial amount of sea spray is producedby breaking waves, bursting bubbles, and wind gusts(e.g., Kraus and Businger 1994; Andreas et al. 1995).This results in the development of a near-surface layerthat can be characterized as a droplet evaporation zone.Both theory and observations suggest that, at high windspeeds, evaporation from sea spray is significant. Abovethe droplet evaporation zone, the droplet contributionto the flux takes the form of an enhanced turbulent fluxof water vapor, and a corresponding change in the tur-bulent flux of sensible heat that is dependent on theenhanced water vapor flux. Simple scaling models toparameterize the spray effect on sensible and latent heatfluxes have been developed based on recent observa-tions (see, e.g., Andreas 1992, 1998; Fairall et al. 1994).The thermodynamic effect of sea spray in these modelsis characterized as a competition between their evapo-ration rate and their lifetime in the air. Two factors de-termine the lifetime of sea spray in the air: the fallvelocity of the droplets and their vertical transport byturbulence. The evaporation rate of sea spray is con-trolled by the amount of heat available for evaporationand interactions between droplets of different sizes. The

heat for the spray evaporation comes from two sources:1) upward transfer of heat from the ocean by turbulenceand the spray droplets, and 2) downward heat transferfrom the atmosphere by MBL turbulence and, whencumulus convection exists, convective downdrafts.These heat sources adjust internally until some equilib-rium is reached, with the spray evaporation acting as amoisture source and as a heat source or sink to the MBL.As a result, the MBL structure is adjusted accordinglyand this adjustment feeds back on the dynamic processesabove the MBL. Obviously, a coupled air–sea modelwith an accurate, well-verified MBL parameterizationis ideal for investigation of the net effect of sea sprayon air–sea interaction.

A bulk parameterization of the sea-spray-mediatedsensible and latent heat fluxes based on Fairall et al.(1994) is used in the coupled modeling system. Thisparameterization includes three physical processes: 1)the cooling of spray droplets from sea surface temper-ature (Ts) to air temperature (Ta) that occurs by con-duction of heat to the atmosphere, producing spray-sen-sible heat flux Qs; 2) the cooling of spray droplets fromTa to the wet-bulb temperature Tw (corrected for salinityand droplet curvature effects) that occurs by evapora-tion, producing latent heat flux Ql1; 3) additional evap-oration of the spray droplets that occurs at the expenseof cooling the atmosphere, producing additional latentheat fluxes Ql2. The first two processes occur rapidly(tenths of a second), while the timescale for the thirdprocess can be much longer.

From Fairall et al. (1994), droplet-mediated evapo-ration and sensible fluxes, Ql and Qs, are described by

26 4.4Q 5 3.0 3 10 u B(T )H [q (T ) 2 q]l a l s a

4 [q (T ) 2 q] and (12)s s

25 2.4Q 5 2.7 3 10 u H , (13)s s

where u is the 10-m wind speed (approximated by thewind speed at the lowest level of MM5), B is a parameterthat is related to the fact that the sea spray droplets areat the wet-bulb temperature (B varies from 0.59 at 273K to 0.21 at 303 K), q the specific humidity, qs thesaturation specific humidity, Hl the turbulent latent heatflux, Hs the turbulent sensible heat flux, and Ql 5 Ql1

1 Ql2 is the total latent heat flux generated by dropletevaporation. We note that Qs and Ql are the droplet-mediated fluxes that would occur if the sea spray doesnot alter the normal logarithmic profile of mean q andT in the droplet evaporation zone. Fairall et al. (1994)argue that (12) and (13) represent upper limits, and thatthe actual spray-dependent fluxes will be reduced by afactor a due to the fact that mean profiles of q and Tin the droplet zone do not remain logarithmic, but aremodified by the presence of the spray. Based on Andreas(1998) reanalysis of his 1992 results, the actual spray-dependent fluxes can be a factor of 2 smaller than as

JULY 2000 2195B A O E T A L .

FIG. 1. Schematic diagram of parameter exchanges between MM5,WAM, and CUPOM when the coupling takes place.

given by Fairall et al. (1994) (C. W. Fairall 1999, per-sonal communication).

Since sea spray droplets evaporate at the expense ofthe sensible heat that they carry, and the sensible heatavailable in the surrounding air, the flux boundary con-ditions at the air–sea interface become

total sensible heat flux 5 H 1 aQ 2 abQ (14)s s l

and

total latent heat flux 5 H 1 aQ , (15)l l

where a is the profile-change feedback parameter andb is the evaporation partitioning parameter. Equations(14) and (15) are the same as given by Fairall et al.(1994), except for the inclusion of b, which is describedbelow. Because the sea spray parameterization is de-rived from data with wind speed less than 30 m s21,Fairall et al. (1994) suggest that an upper bound of 30m s21 should be used in numerical model simulationsof weather and climate. This upper bound is used in thisstudy.

In this study, a simple ad hoc parameterization for a(see Kepert et al. 1999) is used,

Htota 5 , (16)H 1 Qtot tot

where Htot 5 Hs 1 Hl and Qtot 5 Qs 1 Ql. The profile-change feedback parameter thus defined varies from 0to 1. It limits the total production of water vapor fromsea spray, reflecting the feedback effect of sea spray toreduce the evaporation.

The evaporation partitioning parameter b is definedas the ratio

Ql2b 5 . (17)Q 1 Ql1 l2

For the range of wind speeds and droplet sizes consid-ered by Fairall et al. (1994), it was assumed that Ql2 kQl1, and b 5 1. However, for extremely high windspeeds, the droplet size may be so large that they fallback to the ocean before further evaporation can extractheat from the atmosphere, in which case Ql2 and b ap-proach zero.

Andreas and Emanuel (1999) consider the case b 50 by assuming that only a very small fraction (#1%)of the spray mass evaporates, just sufficient to bring thespray droplets to a new temperature, Teq, that is closeto the wet-bulb temperature. In this case, the enthalpyof the air is increased in part by conduction of sensibleheat from the spray droplets to the air when they un-dergo a temperature change from their initial tempera-ture to the air temperature, together with the transfer oflatent heat from the droplets to the atmosphere as thedroplets temperature continues to fall to Teq. Using anidealized hurricane model, Andreas and Emanuel (1999)show that in this case sea spray evaporation can sig-nificantly increase hurricane intensity.

Although it has long been postulated that the evap-oration of spray droplets influences the energy budgetat the air–sea interface, the process of heat transfer me-diated by spray droplets is still poorly understood dueto the complex nature of the interactions between thedroplets and the air–sea system. Numerical experimentscarried out in this study indicate that different valuesof b lead to different impacts of sea spray on the en-thalpy flux from the ocean to the atmosphere, and thuson the simulated hurricane development.

5. Coupling the atmospheric model with the oceancirculation model and the ocean wave model

Figure 1 shows schematically how MM5 is coupledwith WAM and CUPOM at the time step when the cou-pling takes place. Each model computes its prognosticvariables using its own prognostic equations and inte-gration time steps. Because the computational stabilityconditions of the three models are different, the inte-gration time steps used in both WAM and CUPOM arelarger than that used in MM5 for the same horizontalresolution. In all the numerical experiments presentedhere, the horizontal resolutions of both WAM and CU-POM are no finer than that of MM5. Each time step ofeither WAM or CUPOM contains a few time steps ofMM5. Therefore, variable passing required for the cou-pling takes place only when either WAM or CUPOMadvances one time step in the integration. Because allthree models have their own horizontal grids, linear in-terpolation is applied to those variables that are passedbetween the models. WAM takes the surface stress com-puted in MM5 as input at the most recent time step. Ituses the diagnosed wave-induced stress and the diag-nostic relation from (5) to compute the wave-inducedroughness length. The roughness length then feeds backto MM5 for the computation of the surface fluxes at thenext MM5 time step, while the wave-induced stress istaken by CUPOM along with the total stress from MM5.After CUPOM is integrated for one time step, the mostrecent SST is passed into MM5. During the MM5 in-


tegration, both the SST and the wave-induced roughnesslength are kept constant until WAM or CUPOM pro-vides a new value. Salinity fluxes associated with evap-oration (including sea spray evaporation) and freshwaterinflux by precipitation at the air–sea interface, and en-thalpy flux modulation by sea spray are taken into ac-count in the surface flux calculation.

The momentum transfer from the atmosphere to theocean is complicated by the presence of waves. Withoutwaves, all momentum from the atmosphere is trans-ferred directly into the ocean current. When waves arepresent, some of the momentum is transferred to thewaves. The wave momentum is partly dissipated to thesurface ocean current and partly radiated away from thearea of wave generation. For a steady wind, after thewave field has reached equilibrium all of the momentumtransferred to the waves immediately is transferred tothe currents through wave breaking, as the waves areno longer growing. As this limit is approached, it canbe assumed that all of the surface stress goes into drivingthe surface current (Lionello et al. 1993, 1998). How-ever, for waves that are far from equillibrium, as are thewaves that grow and radiate out from the center of ahurricane, an appreciable fraction of the momentum im-parted to the waves remains in the growing wave field.This fraction will vary spatially, decreasing with dis-tance from the center of the hurricane. In theory, withan accurate description of the wave dissipation at thesurface as a function of frequency and wavenumberfrom a wave model, one could determine the amount ofwave momentum lost to the current. However, for sim-plicity, in the present coupled model hurricane simu-lation we assume that only the part of the total stressleft by subtracting the wave-induced stress (i.e., t 2 t w

5 t t) directly drives the ocean circulation in CUPOM.The three models are initialized independently.

MM5V2 is initialized by performing a successive-scanCressman objective analysis on conventional surfaceand rawinsonde observations (including available shipreports), together with the first-guess fields from thegridded global analyses of wind, temperature, geopo-tential, and relative humidity at the mandatory levelsfrom the National Centers for Environmental Prediction(NCEP). CUPOM is initialized using results from a mul-timonth spinup simulation forced by 6-hourly windstresses from the U.S. Navy Fleet Numerical Meteo-rology and Oceanography Center (FNMOC). During thesimulation, CUPOM assimilates Ocean Topography Ex-periment (TOPEX) and European Remote Sensing Sat-ellite (ERS) altimetric data and the SST of the modelis nudged to weekly composite MCSSTs derived fromthe National Oceanic and Atmospheric Administration’s(NOAA) Advanced Very High Resolution Radiometer(AVHRR) data to provide a realistic state of the oceanat the start of the coupled model simulation. The ini-tialization of WAM can be carried out either by as-signing a known spectrum at all grid points, or by com-puting a spectrum at each grid point from the MM5

initial wind fields according to fetch laws with a cos2

directional distribution (see Komen et al. 1994). In ap-plications when reliable observations of waves are notavailable, WAM is initialized by simply assigning a zerostate at each grid point. This is what is used in this study(with high winds it usually takes a few hours for thewaves to become fully developed).

6. Numerical experiments

Numerical experiments in this study are designed toexamine the sensitivities of the atmospheric circulationsystem to physical processes at the air–sea interface.Because it is well known that the intensity of a hurricaneis controlled by the enthalpy flux across the air–seainterface for a given large-scale environment, we choosethe scenario of a hurricane passing over an initiallywarm water surface to be used for the sensitivity ex-periments. Specifically, atmospheric analyses fromNCEP for the period surrounding the intensification andlandfall of Hurricane Opal (1995) beginning at 1200UTC 2 October 1995 are used to provide boundary con-ditions for MM5. The initial conditions are constructedby incorporating a Rankine vortex into the analysis at1200 UTC 2 October 1995, with the center of the vortexat the center of Hurricane Opal (based on the NCEPbest track information). All model simulations are car-ried out for 72 h.

In this study, MM5 uses a nested grid system of twomeshes, with grid resolutions of 45 km and 15 km. Thefiner mesh covers the entire Gulf of Mexico. Both mesh-es contain 25 sigma levels with the lowest level 15 mabove the surface. The model physics includes theBetts–Miller parameterization scheme (Betts and Miller1986) for subgrid water condensation, an explicitscheme (Reisner et al. 1998) for grid-resolvable watervapor condensation (taking into account cloud water,rainwater, and ice), and a Monin–Obukhov scheme forthe surface flux [including the parameterized sea sprayeffect by Fairall et al. (1994) as an option]. The Black-adar scheme (Blackadar 1979; Grell et al. 1994) is usedfor the PBL mixing processes and for vertical diffusion.

a. Initialization of CUPOM

The grid of CUPOM used in this study has a hori-zontal resolution of 1⁄58 in longitude (about 20 km) and1⁄258–1⁄58 in latitude (about 4–20 km with the higher res-olution occurring near the coastline) and consists of 863 87 grid points (see Fig. 2). A total of 21 verticalsigma levels is used with corresponding physical depthsof 0, 1, 2, 5, 10, 20, 40, 70, 100, 150, 250, 400, 600,850, 1150, 1500, 2000, 2500, 3000, 3500, 4000 m in4000-m water.

CUPOM is initialized with the output of a 9-monthspinup run (ending 0000 UTC 1 October 1995) in whichCUPOM is forced by 6-hourly wind stresses from theU.S. Navy FNMOC. The spinup run is initialized using

JULY 2000 2197B A O E T A L .

FIG. 2. Grid distribution of the ocean model (CUPOM).

temperature and salinity profiles indicative of the Gulfwater masses. During the spinup run, TOPEX- andERS-2-derived altimetric sea surface height (SSH)anomaly data, as well as weekly composite MCSSTsderived from NOAA AVHRR satellite data, are assim-ilated into the model. Time-independent temperatureand salinity profiles are prescribed at the basin inflow–outflow boundaries and the inflow–outflow are assumedto be geostrophic. The average inflow at the YucatanChannel is constrained to be 28 Sv (1 Sv 5 106 m3 s21)and the inflow rate at the Yucatan Channel is variedmonthly during the spinup run based on historical hy-drographic data.

The MCSSTs used in this study are a 7-day compositewith a horizontal resolution of about 14 km. Assimi-lation of MCSSTs is carried out by nudging the modelSST to the observed value (Clifford et al. 1997; Hortonet al. 1997). Altimetric SSH anomalies are assimilatedtrack by track into the model by using the followingapproach. First, the altimetric SSH anomalies are con-verted into temperature profile anomalies using a sta-tistical relationship between the dynamic height andtemperature profile anomalies at each model grid point.This relationship is derived by carrying out empiricalorthogonal function analysis (see, e.g., Carnes et al.1990) using the SSH anomalies and temperature profileanomalies from a 10-yr model run. Second, the tem-perature profile anomalies are interpolated to the modelgrids using a statistical interpolation scheme (Horton et

al. 1997). Third, the interpolated temperature profileanomalies are assimilated into the model in the upper1000 m of the ocean using the nudging method (Choiet al. 1995; Bang et al. 1996).

A major feature of the large-scale Gulf circulation isthe shedding of large clockwise-rotating warm-core ed-dies (often referred as Loop Current eddies, or LCEs).These are shed periodically by the Loop Current, whichenters the Gulf from the Caribbean and exits throughthe Florida Straits to eventually become the GulfStream. It has been observed that the Loop Current inthe Gulf of Mexico sheds roughly one to three warm-core eddies a year with a diameter of 100–400 km anda depth of about 1000 m (see, e.g., Elliott 1982; Kirwanet al. 1988). A number of numerical simulations of eddyshedding have appeared in the literature (see, e.g., Hurl-burt and Thompson 1980; Arango and Reid 1991; Die-trich and Lin 1994).

Physical and dynamical characteristics of LCEs havebeen studied through hydrographic surveys (Merrell andMorrison 1981; Elliott 1982; Lewis and Kirwan 1987;Cooper et al. 1990), drifting buoys (Kirwan et al. 1988;Lewis and Kirwan 1987), and satellite infrared images(e.g., Vukovich and Crissman 1986). By the time theLoop Current passes through the Yucatan Channel, thisflow achieves characteristics of a western boundary cur-rent. Because of its high momentum, it may penetrateseveral degrees northward into the Gulf of Mexico(about 268N) before looping around anticyclonically to


FIG. 3. The ocean model temperatures at 200-m depth at the endof the spinup from three 9-month spinup runs ending at 1200 UTC2 Oct 1995: (a) eddy 1, (b) eddy 2, and (c) eddy 3.

TABLE 1. Summary of CUPOM spinup runs.

Name FNMOC wind stress Assimilation of MCSST Assimilation of altimetry data

Eddy 1Eddy 2Eddy 3

YesYesYes

YesYesYes

NoYes, but only for the layer of 100–1000 mYes, for the entire upper 1000 m

the east and then south, and then bending eastward andexiting through the Straits of Florida. Occasionally aninstability develops and an LCE is generated. As theanticyclonic LCE propagates to the west, it slowlyweakens before dissipating at the western Gulf shelf.Elliott (1982) calculated a mean radius of 183 km andtranslation speed of 2.1 km day21 for LCE’s using hy-drographic data during 1965–72.

An LCE named Aggie was present in the Gulf ofMexico during and prior to the development of Hurri-cane Opal. This eddy, which AVHRR data indicate wasapproximately 250 km in diameter, has been presumedto have had a considerable influence on the evolutionof Hurricane Opal over the Gulf (see Shay et al. 1998;Black and Shay 1998). In the CUPOM spinup run, thepurpose of assimilating both altimetry and MCSST datais to ensure that the ocean model state, including theLCE location and size, is close to that observed. Thealtimetry and SST data assimilation are found to benecessary to obtain a realistic representation of EddyAggie in the model state at the end of the spinup run.Results from several test spinup runs indicate that theshedding time and the size of an LCE are strongly de-pendent on how the altimetry and SST data assimilationis carried out. As shown later, when the data assimilationprocedure is not performed properly, it is difficult toobtain a simulated Eddy Aggie that is in good agreementwith its observed location and size.

Figure 3 shows the ocean model temperatures at200-m depth at the end of the spinup from three CUPOMspinup runs (see Table 1 for a summary). SST dataassimilation is performed in all three runs. In the firstrun (denoted as eddy 1), there is no assimilation ofaltimetry-derived temperature anomalies during the en-tire spinup period. In the other two runs (denoted aseddy 2 and eddy 3), assimilation of altimetry-derivedtemperature anomalies is carried out, respectively, forthe layer between 100 and 1000 m, and for the entireupper 1000 m of the ocean. It can be seen that withoutassimilation of altimetry-derived temperature anoma-lies, the model produces an LCE at the end of the run(Fig. 3a), but the LCE is located to the south of theobserved Eddy Aggie that was centered at about 268Nand 898W (see Black and Shay 1998; Shay et al. 1998;Shay et al. 2000 hereafter SGMCB). When the assim-ilation takes place within the layer between 100 and1000 m, or within the entire upper 1000 m, the resultingLCE is at the observed location of Eddy Aggie (Figs.3b,c). However, when the assimilation is carried outwithin the entire 1000-m layer, the size of the LCE is

JULY 2000 2199B A O E T A L .

FIG. 4. The upper-100-m mean temperature profiles for the three9-month spinup runs: eddy 1 (long dash), eddy 2 (solid), and eddy3 (short dash).

TABLE 2. Summary of numerical experiments using the coupledmodeling system.

Experimentno. Experiment description

1 Fully coupled with sea spray; CUPOM was initializedwith eddy 2

2 Fully coupled without sea spray; CUPOM was intiali-zed with eddy 2

3 Fully coupled with sea spray; CUPOM was initializedwith eddy 3 and with prescribed 10-m OML



6 Fully coupled with sea spray; CUPOM was initializedwith eddy 1

7 Fully coupled with sea spray; CUPOM was intializedwith eddy 3

8 Fully coupled with sea spray; CUPOM was initializedwith eddy 2 but with modification of the water col-umn of the warm eddy enclosed by the 15-Kcalcontour of upper ocean heat content

9 MM5 and CUPOM coupled; CUPOM was initializedwith eddy 2

10 MM5 alone

noticeably reduced and the temperature anomaly de-creases by about 38C. These results indicate that al-though the assimilation of the altimetry-derived tem-perature anomalies is needed to obtain the right locationof the LCE in the ocean model initialization, whetheror not the assimilation is carried out within the OMLleads to different model initialization states. The im-plication of these results will be discussed later in thesection on discussion and summary.

The upper-100-m mean temperature profiles averagedover the Gulf for the above three CUPOM spinup runsare presented in Fig. 4. It is seen that the mean tem-perature of the upper-100-m layer in eddy 3 is coolerthan those in the other two (with the difference beinga little less than 18C at the surface and the 100-m depth,and more in between). The difference between eddy 1and eddy 2 is much smaller than that between either ofthem and eddy 3. Note that the mean OML in eddy 3barely exists, while in both eddy 1 and eddy 2 it is about20 m, which is consistent with the shallow late summerseasonal thermocline in the Gulf (Monterey and Levitus1997). Further examination of the results indicates thatthe failure in the OML development in eddy 3 is causedby the fact that the forcing introduced by the altimetrydata assimilation interferes with the intrinsic mixing dy-namics in the OML. In eddy 1, assimilation of altimetrydata is not carried out; in eddy 2, it is applied onlybelow the 100-m depth. Therefore, the OML is welldeveloped in these two runs and the altimetry assimi-lation in eddy 2 generates an LCE with the correct lo-cation and size without interfering with the OML de-velopment. The impact on air–sea interaction of the dif-

ferences in the upper-100-m mean temperature profilesfor these three CUPOM spinup runs will be discussedlater.

b. Initialization of WAM

The horizontal resolution of WAM is 0.48 (;40 km).The wave spectrum is discretized into 25 frequencybands and 24 directional bands. The frequency bandsare logarithmically spaced from 0.042 Hz to 0.41 Hz atintervals of D f/ f 5 0.1, while the directional bans arespaced evenly by 158. WAM is initialized from a zerowave state. Under high wind conditions, the wave statedescribed by WAM adjusts rapidly to the input windforcing. Except for nowcasting applications, an elabo-rate initialization of WAM seems unnecessary for sim-ulations in which the time integration of the model iscarried for more than 1 day. Furthermore, because ob-servational data are not routinely available, such an ini-tialization is usually not possible.

c. Experiment design

Table 2 summarizes the numerical experiments car-ried out in this study. The purpose of these experimentsis to examine the sensitivity of the simulated hurricaneto the physical processes associated with air–sea inter-action under high wind conditions.

1) SENSITIVITY TO SEA SPRAY EFFECT

Experiments with and without the sea spray param-eterization (expt 1 and expt 2) are carried out to evaluatehow sensitive the air–sea coupled modeling system is


to the enthalpy flux contributed by sea spray. Threedifferent values of b (1, 0.5, and 0) are used in exper-iment 1 to reveal the sensitivity of the simulated hur-ricane to the uncertainty in the sea spray evaporationpartitioning parameter. However, b is set to be 0 in allthe other experiments. The initial state of the oceanmodel resulting from the spinup run eddy 2 is used inexperiments 1 and 2. The LCE in eddy 2 is located atthe observed location of Eddy Aggie and has the ap-proximately correct size and location. Although recentstudies using idealized models (e.g., Fairall et al. 1994;Andreas and Emanuel 1999) have shown that sea spraydescribed by existing parameterizations can have sub-stantial effects on the evolution of tropical cyclones andthe atmospheric boundary layer under high winds, it isstill uncertain whether the inclusion of sea spray willhave a significant impact on hurricane development ina realistic coupled air–sea model. Because the presentcoupled modeling system realistically takes into accountatmosphere–ocean feedbacks (including atmosphericconvection), it is a promising tool to assess the impor-tance of sea spray evaporation.

2) SENSITIVITY TO OML

Three experiments (expts 3, 4, and 5) are carried outto examine the sensitivity of the coupled model simu-lation to different prescribed horizontally uniformdepths of the OML (i.e., 10, 30, and 50 m). The initialstates of the ocean model used in these three experi-ments are specified by modifying the output of the spi-nup run eddy 3, such that the model state within theOML of a prescribed depth is equal to that in the topmodel layer. The LCE in eddy 3 is located at the ob-served location of Eddy Aggie, but it is smaller andcooler than that in eddy 2. The reason for modifyingthe initial state from eddy 3 is that the mean OML depthin it barely exists (Fig. 4). These experiments are mo-tivated by the following considerations. The first is thatan important aspect of air–sea interaction under highwind conditions is SST changes resulting from windstirring and its feedback to the atmospheric circulation.The SST changes simulated by the coupled modelingsystem are strongly dependent on the distribution of theOML depth at the initial time of the coupled modeling.For the same wind condition, in areas where the OMLis shallow, the SST change will take place more rapidlythan in areas where the OML is deep.

The second consideration is that there are significantuncertainties in the initialization of the distribution ofthe OML depth. Presumably the spinup of CUPOMwould produce a realistic distribution of the OML depthat the end of the spinup (i.e., the initial time of thecoupled simulation) if the imposed forcing at the surfaceis realistic. However, due to the lack of wind obser-vations over the Gulf, the forcing imposed during thespinup run comes from analyses that are strongly modeldependent. Even if the surface forcing is realistic, it may

not make up for a poor assimilation system that distortsthe OML dynamics. Furthermore, the resulting OMLdepth of the spinup run is very much dependent uponthe data assimilation procedure and the present algo-rithm has been calibrated mainly with deep sea obser-vations of LCEs. Unfortunately, there have been no ob-servations of the OML depth during and prior to Opaland, in general, expendable bathythermograph or con-ductivity–temperature–depth soundings in the Gulf ofMexico are sparse. Therefore, it is important to evaluatethe sensitivity of the coupled model simulations to theinitial OML depth.

3) SENSITIVITY TO LCE: LOCATION AND INTENSITY

The energy to sustain a hurricane comes from theenthalpy input from the sea surface (Emanuel 1986;Rotunno and Emanuel 1987; Holland 1997), which isstrongly dependent on the SST distribution along thepassage of the hurricane. Numerical simulations (see,e.g., Bender et al. 1993; Ginis et al. 1997) have dem-onstrated that the cooling of the sea surface can have aprofound influence on the intensity of hurricanes. It hasalso been observed that the decrease in SST in the wakesof hurricanes ranges from 1.58 to 98C, depending on thetranslation speed of the hurricane, the intensity of thehurricane, and the underlying OML structure (Anthes1982; Hodur 1996; Emanuel 1998; Sakaida et al. 1998).The decrease of SST is caused by extraction of enthalpyat the sea surface by the hurricane, and entrainment ofthe colder water below in the OML forced by strongwind. Previous studies (e.g., Anthes 1982) indicate thatthe effect of entrainment mixing is much larger than theeffect of enthalpy extraction at the sea surface. The roleof warm LCEs on hurricane intensification over the Gulfof Mexico has recently been examined by Shay et al.(1998) using satellite-derived altimetry and SST data.Within warm LCEs such as Eddy Aggie, the OML iswarm and deep compared with the surrounding watermass; the decrease of SST caused by the wind-drivenmixing is slower; thus, the enthalpy flux to the air canbe larger. The results from Shay et al. (1998) suggestthat the enthalpy flux into Hurricane Opal from the seawas enhanced when the hurricane passed over EddyAggie. To examine the impact of oceanic warm eddieson the evolution of hurricanes, two experiments (expts6 and 7) are conducted with different ocean model initialstates, respectively, from the spinup runs (eddy 1 andeddy 3), in which the location and intensity/size of theLCE are different. To further examine the impact of theLCE itself on the simulated hurricane development, athird numerical experiment (expt 8) is carried out inwhich the water column in and near the warm eddy ismodified by linearly interpolating the physical charac-teristics of the water neighboring the LCE. Comparisonof this experiment with experiment 1 will be discussedin section 6d.

JULY 2000 2201B A O E T A L .

FIG. 5. Time series of (a) minimum sea level pressure (in hPa) and (b) maximum surface wind speed (in m s21) sampled every 6 h forthe numerical experiments with (dot for b 5 0, diamond for b 5 0.5, and cross for b 5 1) and without (triangle) sea spray effect; (c)shows the track of the simulated hurricane along with sea level pressure at 51 h into the simulation for the experiment with sea spray effectand b 5 0.

4) SENSITIVITY TO WAVES

The existence of sea surface waves alters the mo-mentum and thermal fluxes at the air–sea interface.Since the development of hurricanes depends upon theenergy fluxes across the air–sea interface, it is of interestto determine the importance of sea surface waves onhurricane development when air–sea interaction is sim-ulated by existing model components. For this purpose,one experiment without WAM (expt 9) is carried out tocompare with experiment 1 in order to evaluate howsensitive the coupled model simulation is to the wave-

age-dependent roughness length. In this experiment, theocean model is initialized with the spinup run eddy 2.

d. Results

Figure 5a shows the time series of minimum sea levelpressure (hPa) sampled every 6 h for the numericalexperiments with and without the sea spray parameter-ization. When the effect of sea spray is included, dif-ferent b (1, 0.5 and 0) values are used. The time seriesof surface maximum wind speed (also sampled every 6


FIG. 6. Time series of surface stress at the grid point where thesimulated hurricane passed by at about 51 h into the simulation forthe numerical experiments with (dot for b 5 0, diamond for b 50.5, and cross for b 5 1) and without (triangle) sea spray effect.

FIG. 7. Time series of thermodynamic fluxes at the grid point wherethe simulated hurricane passed by at about 51 h into the simulationfor the numerical experiments with (dot for b 5 0, diamond for b5 0.5, and cross for b 5 1) and without (triangle) sea spray effect:(a) latent heat flux, and (b) sensible heat flux.

h) is shown in Fig. 5b for different b values to comparewith the simulation without sea spray. For b 5 0, thetrack of the simulated hurricane with the inclusion ofsea spray effect is shown in Fig. 5c, together with thesea level pressure at 51 h into the simulation. Note thatfor the first two days the simulated hurricane movesslowly in the southern half of the Gulf (i.e., south of258N) with translation speeds as small as 1.5 m s21,while it moves as rapidly as 11 m s21 as it crosses thenorthern half of the Gulf during the third day, reachingthe coast at about 0009 UTC 5 October 1995. It can beseen from Figs. 5a and 5b that the inclusion of sea sprayincreases the intensity of the simulated hurricane sig-nificantly when b 5 0.

Figures 6 and 7 depict the time series of surface stressand thermodynamic fluxes for the experiments with andwithout sea spray at the fixed location of the minimumsea level pressure (hereafter referred to as point C)shown in Fig. 5c. The maximum wind speed at thelowest model level at the same point is about 30 m s21

in the simulation without sea spray (not shown). Whensea spray is included, for b 5 0 the maximum surfacestress increases by about 57% and 227% at the peakwinds on either side of the hurricane eye (Fig. 6), whilethe maximum latent heat flux increases by about 68%and 160% (Fig. 7a), and the sensible heat flux by about23% and 229% (Fig. 7b). When b increases to 0.5, themaximum surface stress increases by about 50% and70% at the peak winds, while the latent heat flux in-creases by about 58% and 78%, and the sensible heatflux decreases to small values that are slightly abovezero. When b 5 1, the maximum surface stress at point

C increases by about 22% and 27% at the peak winds,while latent heat flux increases by about 31% and 42%.In this situation, however, the sensible heat flux de-creases and becomes negative at the peak winds, forspray evaporation consumes more sensible heat in theair than both turbulence and sea spray can supply. It isinteresting to note that when b 5 1, the intensity of thesimulated hurricane is not significantly affected by seaspray in comparison with the experiment without seaspray. This apparently is the result of the feedback ofthe spray evaporation that readjusts the sensible heatflux so that the lower atmospheric boundary layer be-

JULY 2000 2203B A O E T A L .

FIG. 8. Time series of minimum sea level pressure (in hPa) sampledevery 6 h from the simulations in which the ocean mode was ini-tialized with different, prescribed, horizontally uniform depths of theOML: 10 m (dot), 30 m (square), and 50 m (cross). The result fromthe uncoupled simulation (triangle) is included for comparison.

comes cooler and more stably stratified. This reducesthe turbulent enthalpy flux from the ocean to the air,which is compensated by the additional spray-mediatedflux so that the total enthalpy flux from the ocean tothe air remains nearly the same as when sea spray isneglected. Finally, we note that the change in hurricanetrack among these different simulations is negligible andthat the region of high velocity winds at this modelresolution is quite broad. Therefore the differencesshown in Figs. 6 and 7 are in fact due to differences inb, and not to changes in hurricane position relative tothe sampled grid point.

Sensitivity of the coupled simulation to differentdepths of the OML is illustrated by the time series ofminimum sea level pressure (hPa) sampled every 6 h(Fig. 8). It can be seen that deeper OMLs lead to asignificantly more intense hurricane, at least for the oneshown in this study, which has a slow translation speedin its early stages. This is consistent with the resultsfrom earlier idealized numerical studies (see, e.g.,Chang and Anthes 1978; Sutyrin and Khain 1984; Khainand Ginis 1991). We note that sensitivity of the hurri-cane to OML depth is very large, with a change of 35mb in minimum sea level pressure for a 50% variationin OML depth about a nominal value of 20 m that issimilar to that expected in the Gulf at the start of thehurricane season. For comparison, the result from thesimulation in which MM5 is run alone without couplingto either CUPOM or WAM (expt 10) is also includedin Fig. 8. In this simulation, the SST is held constantand prescribed with the distribution obtained in the spi-

nup run eddy 2, and the sea spray effect is turned off.A temporally constant SST is equivalent to an infinitelydeep OML. In this case, the minimum sea level pressurereaches 910 mb.

In contrast to intensity, for the simulation shown inFig. 8 it is found that the depth of the OML does nothave significant impact on the hurricane track, with thehurricane’s position at landfall changing by no morethan one to two grid points (not shown). However, thetiming of landfall does change by as much as 6 h, withthe most intense hurricane moving the most rapidly.

Figure 9 shows the simulated SST reduction at 72 hinto the simulation for three different initial OMLdepths. Under hurricane conditions, SST changes arecaused mainly by cold water entrainment across the ther-mocline (see, e.g., Anthes 1982, section 6.3). As theinitial OML depth increases from 10 to 50 m, the areaof SST cooling decreases substantially. However, themaximum change of SST decreases only slightly, re-maining at approximately 48–58C. SSTs at earlier timesin the simulations (not shown) also indicate that the areaof SST decrease in the wake of the hurricane is morespatially confined and that the change in SST is onlyslightly smaller for a greater initial OML depth. Themagnitude of SST cooling is in agreement with resultsfrom the numerical study of Price (1981) for a slowlymoving hurricane, but somewhat larger than that foundby Elsberry et al. (1976) in a similar numerical study.

The small variation in maximum SST change shownin Fig. 9 can be explained by the fact that a deeper OMLgenerates a stronger hurricane and greater ocean mixing,which tends to counter the effect of the greater thermalinertia of the deeper OML. Although the ocean mixingwill not lead to a SST change for an infinite OML depth,it obviously can cause a significant SST response evenfor the 50-m OML depth. This illustrates how the oceanmixing works as an effective regulator to constrain hur-ricanes from reaching their maximum potential inten-sity.

For comparison, the SST reduction in experiment 1(initialized with eddy 2) is included in Fig. 9d. It is seenthat the deep OML depth within the warm eddy resultsin less SST cooling than the area outside of the warmeddy even though the hurricane passes right over theLCE. The magnitude of the SST cooling in Fig. 9d isclose to that observed for Opal from AVHRR imagery(Black and Shay 1998), although the area of cooling islarger than observed.

Figure 10 depicts the sensitivity of the intensity ofthe simulated hurricane to the location and size of theLCE (i.e., eddy 1–expt 6, eddy 2–expt 1, and eddy 3–expt 7 in Table 2) in terms of the time series of minimumsea level pressure (hPa) sampled every 6 h. Because theOML depth within the LCE is deeper than outside theLCE, the spatial distributions of the OML depth in thesesimulations are different. Also, since the Gulf-averagedmean temperature profiles are nearly the same for eddy1 and eddy 2 (Fig. 4), the difference between these two


FIG. 9. Simulated SST reduction in the wake of hurricane with different prescribed horizontally uniform depths of the OML at 72 h intothe simulation: (a) 10, (b) 30, and (c) 50 m. The contour interval is 18C. The SST reduction in expt 1 (initialized with eddy 2) is shown in(d) for comparison.

runs shown in Fig. 10 reflects the effects of the spatiallyvarying deviation of OML depth. It is interesting to notethat when CUPOM is initialized with the output of eddy1 (in which the LCE is located to the south of the ob-served location of Eddy Aggie), the simulated hurricaneintensifies at a different rate than when CUPOM is ini-tialized with the output of eddy 2 (in which the LCE isat the observed location). With the more southerly po-sitioned LCE (eddy 1–expt 6), the rate of intensificationis almost linear before 0000 UTC 5 October 1995, whilewith the LCE at the location of Eddy Aggie (eddy 2–expt 1) there is a rapid intensification that apparentlyaccompanies the passage of the hurricane over the LCE

(which started at about 1000 UTC 4 October 1995).Because the size and temperature excess of the LCEsin runs eddy 1 and eddy 2 are similar, the major dif-ference in the time series of minimum sea level pressurebetween these two runs can be attributed to the differ-ence in position of the LCE and the difference in trans-lation speed of the hurricane. The more southerly po-sition of the LCE in the run eddy 1 allows for the hur-ricane to intensify at an earlier time when the hurricaneis moving slowly. It is also interesting to note that whenCUPOM is initialized with the spinup run eddy 3, thesimulated hurricane fails to intensify because in thisspinup run the upper-ocean temperature is cooler and

JULY 2000 2205B A O E T A L .

FIG. 10. Time series of minimum sea level pressure (in hPa) sam-pled every 6 h for the numerical experiments in which the oceanmodel was initialized using three spinup runs: eddy 1 (cross), eddy2 (diamond), and eddy 3 (dot).

more stably stratified than the other two runs (see Fig.4). Despite this result, it is not yet clear that the LCEin the simulation initialized with eddy 2 is responsiblefor the rapid intensification of the simulated hurricane.This will be further investigated below with the resultsfrom experiment 8.

Figure 11 shows the initial bulk heat content of theupper ocean relative to the depth of the 268C isothermas defined in SGMCB by modifying the original defi-nition in Leipper and Volgenau (1972). The magnitudeof the heat content along the simulated hurricane trackfor eddy 2 is qualitatively consistent with the altimeter-derived values presented by SGMCB, although the peakvalue within the LCE is somewhat less (;25 vs ;30Kcal cm2). For eddy 3 the heat content is significantlylower. With hurricane forcing, the upper ocean loses heatto the atmosphere through the enthalphy flux across theair–sea interface, and to the deeper ocean beneath thethermocline through entrainment. The latter, based onSGMCB and references cited therein, accounts for 75%–90% of the upper ocean cooling. The cooling of theupper ocean leads to the reduction of enthalpy flux fromthe ocean to the atmosphere. For the same wind con-dition, the greater initial heat content the upper oceanhas, the slower it cools, and the more enthalpy flux itcan provide to the atmosphere. Therefore, the resultsshown in Fig. 11 provides a further explanation whythe simulated hurricane initialized with the output ofeddy 3 does not intensify: the upper ocean heat contentis insufficient to fuel the storm.

Figure 12 shows the time series of minimum sea levelpressure for the numerical experiment in which the wa-

ter column within the 15-Kcal heat content contour linefor the LCE has been modified to be a constant 15 Kcal.It can be seen that the impact on the simulated hurricaneof the warm water with heat content greater than 15Kcal is rather small, causing a difference of less than 3mb in minimum sea level pressure. It is interesting tonote that in this experiment the simulated hurricane stilltends to intensify rapidly when it starts to acceleratenorthward (at about 1000 UTC 4 October 1995). Thisindicates that the rapid intensification that occurs as thesimulated hurricane moves into the northern half of theGulf is due at least in part to the hurricane’s faster trans-lation speed over water that has not yet been cooled dueto the hurricane-forced oceanic mixing.

It is worth mentioning that the heat content to thenorth of the LCE in the eddy 2 spinup run is less thanthat within the LCE (Fig. 11b) due to a shallower andcooler OML. However, the potential negative feedbackof this lower heat content water has little effect on thesimulated hurricane, with the hurricane continuing tointensify until it reaches the coast (Fig. 5). This can beexplained by the fact that the simulated hurricane movesrapidly through the northern half of the Gulf so that itis not able to react as effectively to the SST cooling inits wake.

The impact of the wave-age-dependent roughness onthe intensity of the simulated hurricane is shown in Fig.13 in terms of the time series of minimum sea levelpressure (hPa) sampled every 6 h. It is seen that thedifference made by the wave-age-dependent roughnessis not very dramatic, with an approximately 6-mb sealevel pressure minimum difference. This is can be ex-plained by examining the nondimensional wave-age-de-pendent roughness, z, found by substituting the totalroughness z0 1 z1 into the Charnock relation (1). Phys-ically, the values of z for young waves are larger thanthose for old waves. Figure 14 presents a map of z andsignificant wave height along with the dominant prop-agation direction of waves at 51 h into the simulationfor experiment 1. One can see that for most of the do-main the values of z lie between 0.01 and 0.025; theexception is a small area of very young waves wherethe maximum value of z is 0.045. Further examinationin the temporal variation of the horizontal distributionof z indicates that young waves do not last long and thedominant value of z is between 0.015 and 0.025, whilein the atmospheric model (MM5) the Charnock param-eter has been set to its default value of 0.032. BecauseWAM produces overall smaller values of the Charnockparameter than the MM5 default value, one would ex-pect a smaller surface stress and more intense hurricanewith WAM, as is found. However, if instead of 0.032a more conventional Charnock value of z 5 0.018 isused in MM5 (not shown) very little difference in thehurricane’s intensity is found, and WAM still results ina lower minimum sea level pressure. This is the oppositeeffect found by Doyle (1995), and by Lionello et al.(1998) in the majority of their simulations of idealized


FIG. 11. Upper ocean heat content (in Kcal cm22) relative to the depth of the 268C isotherm at the initial time of the coupled simulations:(a) eddy 1, (b) eddy 2, and (c) eddy 3.

extratropical cyclones. This result suggests that althoughreduced surface roughness does reduce the surface fric-tion, it does not necessarily lead to the intensificationof a hurricane because of either the spatially variabledistribution of roughness produced by WAM, or becausethe enthalpy flux is reduced as well. This result alsosuggests that the interaction of a changing sea state witha hurricane is dynamically complicated; simply chang-ing the Charnock parameter may not be sufficient todescribe the dynamics involved in wave–air interaction.

7. Discussion and summary

In this study, a coupled air–sea modeling system isused to simulate air–sea interaction under high windconditions. This coupled modeling system consists ofthree well-tested model components: the Penn State–NCAR Mesoscale Model, the University of Coloradoversion of the Princeton Ocean Model, and the WAMDIwave model. The scenario in which the study is carriedout is the intensification of a simulated hurricane passingover the Gulf of Mexico. The focus of this study is to

evaluate the impact of air–sea interaction on hurricaneintensification and evolution.

The results from the experiments with and withoutsea spray effects show that in a coupled air–sea modelthe impact of sea spray evaporation on the simulatedhurricane development depends on the evaporation ef-ficiency of sea spray. When only a small amount of seaspray evaporates at the expense of cooling the remainingspray, the increase of enthalpy flux due to the evapo-ration produces stronger surface winds, which in turnincreases the surface enthalpy flux. This positive feed-back results in a significantly more intense hurricane.The model results, however, show that sea spray evap-oration does not affect the hurricane intensity signifi-cantly when the evaporation efficiency is so high thatthe spray droplets evaporate at the expense of sensibleheat from the ambient air. This is because the dropletevaporation cools the lower atmospheric boundary layer,and produces stable stratification so that the turbulententhalpy flux within it decreases, which compensatesthe spray-mediated enthalpy flux. As indicated by Ke-pert et al. (1999), the effect of sea spray in this situation

JULY 2000 2207B A O E T A L .

FIG. 12. Time series of minimum sea level pressure (in hPa) sam-pled every 6 h for the numerical experiments initialized with eddy2 and modified eddy 2. Eddy 2 (dot). The water column of the warmeddy enclosed by the 15-Kcal contour of upper ocean heat contentis modified (diamond).

FIG. 13. Time series of minimum sea level pressure (in hPa) sam-pled every 6 h for the numerical experiments with and without thecoupling of WAM.

will not directly change the total sea–air enthalpy fluxto any great degree for a fixed wind speed; it will alterthe partitioning of this flux into latent and sensible com-ponents.

For the atmospheric model’s horizontal resolutionused in these experiments (15 km), the enthalpy flux atthe air–sea interface calculated using the traditionalMonin–Obukhov theory alone (i.e., without sea sprayparameterization) appears to be insufficient to sustainan intense simulated hurricane when the negative feed-back of ocean SST cooling is present. Sea spray mayplay an important role in the enthalpy transfer from theocean to the atmosphere under extreme wind conditions.However, while the significant increase in intensificationrate found when the sea spray parameterization is in-troduced is interesting, we caution that our conclusionshere are based on a somewhat idealized study of a singlecase, with one parameterization scheme of the sea sprayeffect. Because systematic observations are not avail-able to verify our results, uncertainties still remain, es-pecially with respect to the source of sensible heat con-sumed by spray evaporation. Additional observationsand modeling studies are necessary to fully elucidatethe role of sea spray in tropical cyclone dynamics.

Proper initialization of the coupled modeling systemis crucial to air–sea interaction studies. Although it iswell known that successful simulations and forecasts ofthe structure and movement of hurricanes using an at-mospheric model alone are strongly dependent on goodinitialization (see, e.g., Kurihara et al. 1995; Liu et al.1997), it is one of the findings in this study that thedevelopment of hurricanes simulated by a coupled air–

sea modeling system is quite sensitive to the initial meanOML depth. This senstivity seems large compared toprevious coupled model simulations (e.g., Hodur 1996),in which a larger OML depth of 50 m was used. How-ever, the sensitivity found in the present simulations issimilar to that found by Bender and Ginis (2000) incoupled model simulations of Hurricane Opal using re-alistic, climatological values of OML depth for the Gulfof Mexico. Results of the sensitivity experiments carriedout in this study also demonstrate that the impact of thewarm eddy shed from the Loop Current in the Gulf ofMexico on the development of the simulated hurricaneis dependent on the location of the eddy relative to thehurricane path, and the structure of the eddy. The warmeddy changes the timing, rate, and duration of hurricaneintensification.

It is shown in this study that the size, intensity, andposition of the warm eddy associated with the LoopCurrent in the Gulf of Mexico are sensitive to the meth-od of assimilating satellite altimetry data during theocean model spinup run. Results of the ocean modelspinup runs using different ways of assimilating altim-etry data also suggest that in order not to distort theevolution of the OML structure during data assimilation,care must be taken during the procedure to preserve thephysics in the OML. That is, the forcing introduced bydata assimilation should not interfere with the intrinsicdynamics of the OML. In this study, when the satellitealtimetry data were not assimilated into the top 100 mof the ocean, the OML depth and the characteristics ofthe warm eddy shed from the loop current appear to bereproduced more accurately.

In agreement with previous studies, the present results


FIG. 14. Output from WAM at 51 h into the simulations: (a) nondimensional wave-age-dependent roughness length 3 102 (contourinterval is 0.5) and (b) significant wave height along with dominant wave propagation direction (contour interval is 1 m).

indicate that the intensification of the model-simulatedhurricane depends on the SST cooling due to the windforcing associated with the hurricane. In contrast withthe positive feedback from sea spray, the feedback fromthe SST change is negative in the sense that the reduc-tion of SST results in a weaker simulated hurricane thanwhen the SST is held constant during the simulation.The spatial extent of surface cooling is found to bestrongly dependent on the initial OML depth, while themagnitude of the SST cooling is more weakly dependenton initial OML depth. Results from this study demon-strate that any numerical model intended to simulateair–sea interaction with physical soundness must in-clude an accurate depiction of the oceanic mixed layer,including variations in the OML due to oceanic dynamicprocesses. However, again due to the scarcity of obser-vations at high wind speeds, considerable uncertaintyexists on the accuracy of presently available ocean mix-ing parameterizations in hurricane conditions. Our re-sults also suggest that assimilation of both MCSST andsatellite altimetry data is necessary to accurately de-scribe the initial upper ocean structure in a region oflarge mesoscale variability.

The degree to which the hurricane is modified by SSTcooling is dependent on the hurricane’s movement. Hod-ur (1996) discussed the relationship between the move-ment of a hurricane and the SST change caused by thehurricane in a coupled modeling study: the SST changehas less effect on a faster moving hurricane than thaton a slower moving one (see, also, Chang and Anthes1978; Sutyrin and Khain 1984; Khain and Ginis 1991).Because Hurricane Opal exhibited a wide range of trans-lation speeds as it traveresed the Gulf, the importance

of SST feedback also varied significantly. The largesensitivity to mean OML depth found in our experimentsis due in part to the exceptionally slow (1.5 m s21)translation speed of Opal in its early stages.

It has been demonstrated in the numerical experi-ments that the development of the simulated hurricaneis dependent on the location and size of the warm eddyshed from the loop current and that this sensitivity de-pends on the translation speed of the simulated hurri-cane. Since the hurricane is moving rapidly as it passesover the LCE and approaches the coast in the eddy 2simulation, it is affected little by the potential positivefeedback of the LCE and by the potential negative feed-back of the lower heat content water to the north of theLCE. This suggests that the existence of the warm LCEwas not a primary contributing factor in the suddenintensification and weakening of Hurricane Opal. Wenote, however, that heat content estimated from satellitealtimeter data using statistical regression has a consid-erable uncertainty, as seen in the 5 Kcal cm2 differencebetween our assimilation result and the analysis ofSGMCB for the core of the LCE. The larger heat contentfound by SGMCB would have produced a somewhatlarger hurricane response to the LCE. Given that theobserved sudden intensification of Opal cannot be at-tributed solely to the effect of the LCE, it appears thatatmospheric forcing or hurricane eyewall contractiondynamics must have played an important role. Bosartet al. (1998) provide evidence that an upper-level at-mospheric trough helped intensify Opal. Our results alsosuggest that the sudden weakening of Hurricane Opalbefore it made landfall (shown by the NCEP best trackinformation) may have been caused by atmospheric

JULY 2000 2209B A O E T A L .

forcing or by internal hurricane dynamics rather thanair–sea interaction. Further research effort is requiredto understand what are primary factors to cause Opal’ssudden intensification and weakening

Compared with the sensitivity to the initial OMLdepth and the location and intensity of the warm eddyassociated with the Loop Current, the model is less sen-sitive to the wave-age-dependent roughness length.However, although the results from this study suggestthat the Charnock parameter used in MM5 for obtainingthe roughness length over the open sea may be too largeunder high wind conditions, it appears that the inter-action of changing sea state with hurricane is dynami-cally complicated. Simply changing the Charnock pa-rameter with different values may not be sufficient todescribe the dynamics involved in wave–air interaction.The best way to evaluate the roughness length over theopen sea is through use of a good ocean surface wavemodel.

Finally, it should be pointed out that this study ad-dresses only one of several important factors contrib-uting to hurricane intensity change: air–sea interaction.Hurricane development is a synergistic process that in-volves not only air–sea interaction but also the inter-action of the hurricane with its atmospheric environ-ment. In addition, the small-scale internal dynamics ofspiral rainbands and eyewall contraction plays a vitalrole in hurricane intensity change. Even within the re-stricted scope of an air–sea interaction study, we cautionthat the results obtained in this are derived from a singleevent that is simulated only by using one model reso-lution configuration and a limited set of model physics.Uncertainties still remain with respect to the parame-terization of sea spray effect, the initialization of theocean model using altimetry data, and the degree towhich one model component responds and feeds backto the other two components in the coupled modelingsystem. For example, whether the sensitivity of the sim-ulated hurricane intensity change to the OML depth isrealistic is a question that needs to be answered withfurther observations and modeling studies of high windspeed events.

Acknowledgments. We are grateful to several review-ers for their careful reading of this paper and their help-ful comments. We also wish to acknowledge helpfuldiscussions with C. Fairall and P. Lionello.

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