41

Journal of Oceanography, Vol. 61, pp. 41 to 57, 2005

Keywords:⋅⋅⋅⋅⋅ Mixed layer model,⋅⋅⋅⋅⋅ typhoon,⋅⋅⋅⋅⋅ sea surfacecooling,

⋅⋅⋅⋅⋅ entrainmentscheme,

⋅⋅⋅⋅⋅ upwelling,⋅⋅⋅⋅⋅ atmosphericforcing.

* E-mail address: awada@mri-jma.go.jp

Copyright © The Oceanographic Society of Japan.

Numerical Simulations of Sea Surface Cooling by aMixed Layer Model during the Passage of Typhoon Rex

AKIYOSHI WADA*

Meteorological Research Institute, Japan Meteorological Agency,Tsukuba, Ibaraki 305-0035, Japan

(Received 20 January 2003; in revised form 15 April 2004; accepted 23 April 2004)

In order to investigate the formation mechanism of rapid decrease of maritime seasurface temperature (SST) observed by R/V Keifu Maru, the ocean response to Ty-phoon Rex is simulated using a mixed layer model. The rapid decrease of the mari-time SST is successfully simulated with realistic atmospheric forcing and an entrain-ment scheme of which sources of turbulent kinetic energy (TKE) are production dueto wind stress, generation during free convection, and production due to current shear.The rapid decrease at the observed station by R/V Keifu Maru is not produced byinstant atmospheric forcing but is mainly produced by entrainment on the right sideof the running typhoon as a part of cooling area during its passage, and remainedduring a few days. The sea surface cooling (SSC) is evident along the track and on theright side of the running typhoon, which is similar to the SSC of satellite observationby TRMM/TMI. The conspicuous SSC produced by both entrainment and upwellingis situated just under the track of typhoon when the typhoon moves slower.Intercomparison of entrainment schemes of the mixed layer model is implemented.Frictional velocity and buoyancy effects are effective for a gradual SSC covering thewide region. In contrast, the effect of current shear at the mixed layer base is relatedto the amount of SSC and the sharp horizontal gradient of SSC. The entrainmentscheme including all three TKE sources has the best performance for SSC simula-tion.

(2003) investigated effects of an entrainment scheme onthe ocean mixed layer response during the passage ofHurricane Gilbert in 1988 using four kinds of entrain-ment schemes. According to Jacob and Shay (2003),mixed layer temperatures simulated by the scheme usingthe bulk Richardson number shows the best performancefor the observed temperatures of four kinds of entrain-ment schemes, although the overall pattern remainedqualitatively similar.

Intercomparison of mixed layer models with differ-ent entrainment schemes has been performed for cases ofdiurnal cycle or seasonal cycle of SST (e.g. Kantha andClayson, 1994; Large et al., 1994; Anderson and Weller,1996). Ginis (1995) conducted intercomparison of threedifferent entrainment schemes of a moving idealizedstorm, which translation speed was 5 m/s. However, real-case simulation during the passage of a tropical stormwas very few in number. Besides, it is difficult to vali-date the result of a mixed-layer model due to poor obser-vation during and even after the passage of a tropical cy-clone. The numerical simulation of the upper ocean re-

1. IntroductionGenesis and development of a tropical cyclone are

sensitive to upper ocean heat potential where sea surfacetemperature (SST) is over 26–27°C (Palmén, 1948). Atropical cyclone produces local cooling of the sea sur-face (SSC) after its passage. The ocean response of a tropi-cal cyclone has been investigated through observationalapproaches (e.g. Leipper, 1967; Black, 1983; Jacob et al.,2000) and numerical approaches (e.g. Elsberry et al.,1976; Chang and Anthes, 1978; Price, 1981; Greatbatch,1983; Ginis, 1995; Wada, 2002a; Jacob and Shay, 2003).A numerical approach by a mixed layer model is one ofthe effective ways to understand the upper ocean responseduring the passage of a tropical cyclone.

One of the oceanic variations after the passage of atropical cyclone is caused by turbulent mixing in the en-trainment zone. Jacob et al. (2002) and Jacob and Shay

42 A. Wada

sponse to a tropical cyclone with real-case forcing fieldhas hardly ever been performed. Even in the numericalexperiment of Jacob et al. (2002) and Jacob and Shay(2003), constant air temperature and humidity were as-sumed to estimate the surface heat fluxes. The role of thesurface heat fluxes was in fact small for local SSC duringthe passage of a tropical cyclone (Price, 1981; Bender etal., 1993). After the passage of the tropical cyclone, how-ever, surface heat fluxes might play an important role tosimulate an increase of SST.

A mixed-layer model has been often used to investi-gate local SSC during the passage of a tropical cyclone(Elsberry et al., 1976; Chang and Anthes, 1978; Price,1981; Greatbatch, 1983; Ginis, 1995; Wada, 2002a). Themixed-layer model is still available in view of computa-tional efficiency or saving memory and storage area. Inaddition, it is easy to understand the physics of the mixedlayer. However, it was difficult to simulate a diurnal cy-cle of SST and a variation of mixed layer depth becausethe mixed-layer model simply consists of a mixed layer,a thermocline and undisturbed layers. As a consequencedetailed of the inside of the mixed layer could not be simu-lated. In fact, observation by air-deployed deep floatssuggested that the seawater could be cooled at the sur-face, at the bottom of the trajectories by entrainment, andin occasional mid-depth events by horizontal mixing be-neath a hurricane (D’Asaro, 2003). For the purpose ofsimulating the detail of the mixed layer, K-Profile (Largeet al., 1994), the level 2.5 turbulent closure scheme(Mellor and Yamada, 1982; Kantha and Clayson, 1994),or the bulk Richardson number closure (Price et al., 1986)have been often applied in an ocean general circulationmodel.

In the present study, numerical simulations were car-ried out to investigate the ocean response to Typhoon Rexof 1998, using a mixed-layer model with a realistic forc-ing field based on global analysis data, best track data ofTyphoon Rex, and ship observation. The relationship be-tween stages of the typhoon and the ocean response tothe typhoon (SSC and deepening of the mixed layer depth)was examined in this paper.

This paper is organized as follow: An outline of themixed layer model and the way of estimation of sea sur-face fluxes are reported in Section 2. Section 3 describesresults of SSC observations during the passage of TyphoonRex by R/V Keifu Maru and TRMM/TMI. Section 4presents an outline of a numerical experiment concern-ing with the ocean response to the passage of TyphoonRex. In section 4, the formation mechanism of rapid de-crease of the SST is discussed using nondimensional num-bers. Section 5 describes results of intercomparison offour entrainment schemes of which sources of turbulentkinetic energy (TKE) are respectively different. Section6 is devoted to summary and discussion.

2. Numerical Model and Sea Surface Fluxes

2.1 Basic equationsA mixed layer model, which is an updated version

of Wada (2002a), is based on a slab model used for a hur-ricane-ocean coupled model developed by Bender et al.(1993). Prognostic variables of the model are horizontalcurrent velocity in longitude and latitude, layer thicknessof all layers plus sea temperature and salinity in a mixedlayer and a thermocline. The model is formulated withhydrostatic and Boussinesq assumption, a reduced grav-ity approximation, and a flat bottom in the ocean of whichdepth is 1,500 m. The model consists of equations ofmotion, thermodynamic, salinity, and continuity equa-tions. Unlike the equations of motion described by Benderet al. (1993), calculation of horizontal viscosity bySmagorinsky (1963) from deformation fields is added tothe equations of motion. In addition, the friction termsexpressed as a function of an entrainment rate are modi-fied to those of Ginis (1995). A horizontal grid resolutionis 0.25° by 0.25° with a longitude-latitude coordinatedsystem. The model has eight vertical layers, including amixed layer (30 m), a thermocline (170 m), and undis-turbed layers (100 m, 100 m, 100 m, 200 m, 300 m, and500 m), which the last layers are controlled only by thepressure gradient term. The number of the layers is thesame as those reported by Bender et al. (1993).

2.2 Sea surface processesIn the present study, we estimated solar and longwave

radiations and turbulent fluxes by empirical formulas. Themomentum, sensible and latent heat fluxes are calculatedaccording to Kondo (1975). The downward solar radia-tion is defined by Reed (1977) and its coefficients arereferred to the results of Schiano (1996). Because Reed’sformula does not include the cloud cover, the formula withthe cloud cover is used for estimation of the downwardsolar radiation. The upward solar radiation is determinedas a function of downward solar radiation and albedo ofthe surface. The downward longwave radiation for thetemperature range between 275 K and 302 K under theclear sky is specified as described by Swinbank (1963).Using the longwave radiation under the clear sky, thelongwave radiation under the cloudy sky is derived fromBignami et al. (1995). The upward longwave radiationwas a summation of radiation with a black body tempera-ture and the reflectance of downward longwave radiation.

The longwave radiation, which penetration depth isabout 10 µm (Fairall et al., 1996), is presumed to leavedirectly from the sea surface. The physical property ofsensible and latent heat fluxes is similar to that oflongwave radiation (Price et al., 1986). On the other hand,solar radiation is absorbed within the water column withdouble exponential depth dependence (Kraus, 1972; Price

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 43

et al., 1986). In this study, formulation used in Price etal. (1986) is applied to the oceanic water type “Type IA”defined by Paulson and Simpson (1977).

In order to reflect the effect of solar absorption tosea temperature at any depths near the surface, a prelimi-nary level model with a vertical resolution of 1 m isconfigured within the mixed layer. This enables to ex-press the vertical gradient of sea temperature caused bysolar absorption that declines exponentially near the sur-face. In contrast, the longwave radiation, sensible andlatent heat fluxes are released directly on the surface.Therefore, a vertical profile of sea temperature may beunstable in the case that seawater at the surface becomescool during the night. Otherwise, seawater near the sur-face is also stirred by wind. In the present study, stabilitycriteria for static stability and mixed layer stability in thevertical profile of level model are taken into accountwithin the mixed layer. The following criterion by Priceet al. (1986) is used to comprise static and mixed layerstability,

∂∂

≥ ( )ρz

0 1

for convective and stabilizing the buoyancy flux, and

Rg h

Vb =

( )≥ ( )∆

∆ρ

ρ02 0 65 2.

for mixed layer stability, where ρ is the density ofseawater, z is the vertical coordinate, ρ0 is the referencedensity (1024 kg/m3), V is the horizontal current veloc-ity, h is the thickness in the mixed layer, g is the accel-eration of gravity, and ∆( ) indicates the difference be-tween the mixed layer and the level just beneath. Because∆V is determined by wind stresses, this process is called“wind-induced” vertical mixing in the present paper.

After the determination of sea surface temperature,the mixed layer thickness is also modified due to conser-vation of ocean heat content in the mixed layer. Subse-quently, the temperature at the mixed layer base and thick-ness in the thermocline are modified in a similar way dueto the conservation of the ocean heat content above thethermocline base.

2.3 Entrainment rate In an integral sense, the sources of turbulent kinetic

energy in the mixed layer are: 1) production due to windstress, which is proportional to the frictional velocity tothe third power; 2) generation during free convection,which is proportional to the net heat flux on the surface;3) production due to current shear, which is proportionalto the current shear square at the mixed-layer base (Niller

and Kraus, 1977; Price et al., 1978). The entrainmentscheme used in this study is the entrainmentparameterization by Deardorff (1983). This scheme wasalso used in Bender et al. (1993) although salinity wasassumed to be constant in their numerical experiment.Here, not only prognostic sea temperature but also prog-nostic salinity is used to determine sea water density,which is used to define a velocity scale in the entrain-ment zone just below the mixed layer. The other refine-ment is the way of estimation of current shear. Becausethis model has been developed as a part of the atmos-phere-ocean coupled model for a tropical cyclone pre-diction, computational time of spin-up procedure shouldbe shortened as completely as possible to save computa-tional time. That is the reason why geostrophic current atthe initial field is calculated in advance. Current shear isestimated as the summation of diagnostic current(geostrophic current) shear and prognostic current shear.This ingenuity should be abolished if sufficient spin-upprocedure is feasible.

Performance of a mixed layer model depends on theway of entrainment scheme. As for the ocean response totropical cyclones, many schemes of entrainment rate havebeen proposed. Chang and Anthes (1978) included thesource 1) described above, which was a modifiedparameterization of the Kraus and Turner (1967) formu-lation (hereafter CA). Elsberry et al. (1976) assumed thatmixed layer turbulence was generated only by frictionalvelocity and negative heat flux at the surface (hereafterEL). The parameterization took account of the source 1)and 2). In contrast, estimating the entrainment rate Price(1981) (hereafter PR) assumed that only velocity shearmechanism corresponded to source 3).The concept of thisPrice’s scheme was similar to Pollard et al. (1973).

The entrainment scheme by Deardorff (1983) (here-after DF) took account of sources 1), 2), and 3) describedabove. This entrainment parameterization is equivalentto that described by Chen et al. (1994), based jointly onthe Kraus-Turner type mixed layer (Kraus and Turner,1967) and Price’s dynamical instability model (Price etal., 1986). A brief description how to estimate the en-trainment rate by DF is as follows: Assuming horizon-tally uniform, the second-moment turbulent equations fordensity flux and density variation are integrated through-out the mixed layer; Each term of integrated equationssuch as TKE variation, buoyancy flux, velocity jump atthe mixed layer base, turbulent transport, and dissipation,is respectively parameterized and then a parameterizedequation is formulated; The entrainment rate is repeat-edly solved from the parameterized equation; After theconvergence, the entrainment rate is determined.

3. ObservationA tropical depression was generated in the south of

44 A. Wada

Okinawa Island on August 24, 1998 and developed toTyphoon Rex on August 25. The trajectory of TyphoonRex was like a trochoid (Fig. 1). Typhoon Rex had beendeveloping to 960 hPa on August 26 and then had sus-tained its intensity till August 31 (Fig. 2). The minimumsea level pressure (MSLP) was 955 hPa when the transla-tion speed of Typhoon Rex at that time was nearly 1m/s and the slowest from August 29 to August 30 (Fig.2). From August 23 to 27, maritime and hydrographic ob-servations at the regular station were implemented around130°E and 20°N. The hydrographic observation was con-ducted by conductivity-temperature-depth (CTD) meas-

urement round noon from day to day. The vertical profileof sea temperature in the upper ocean indicates that amixed layer had been around 30 m in depth (Fig. 3). Agradual decrease of mixed layer temperature shown inFig. 3 corresponds to that of the SST shown in Fig. 4.Figure 3 also reveals that a variation in the mixed layertemperature is smaller than that in a thermocline, whichis defined as a steep gradient of sea temperature belowthe mixed layer. Occurrence of slight upwelling, prob-ably caused by Typhoon Rex, is observed on August 25.

Maritime conditions at the fixed observation hadbeen already reported in figures 21(a) and (b) of Wada(2002a) of which horizontal axis was not UTC but JST.According to Wada (2002a), air-temperature suddenlydecreased and the deviation between air-temperature anddew-point temperature became small on August 24. Atthe same period, wind velocity temporarily reached 18m/s. These observational results suggest that precipita-tion, caused by the passage of rainbands of Typhoon Rex,should have occurred in this region. In fact, light waterspread over near the surface was observed at the station(not shown). Except this light layer, however, heavy andvertically homogeneous water lay at around 30 m in depth.Therefore, the mixed layer thickness of the mixed layermodel is determined to be 30 m in the later numericalsimulation.

After the fixed observation was completed, R/VKeifu Maru got on the trail of Typhoon Rex from August27 to 29. Then, R/V Keifu Maru logged across the trackof Typhoon Rex from August 29 to 30. Figure 4 indicatesthat a sudden decrease of maritime SST occurred whereR/V Keifu Maru logs across the track of Typhoon Rex.The SST decreased from 30°C to 27.2°C during severalhours. The amount of SSC, nearly 3°C, is in the range ofprevious observation of Black (1983). However, it shouldbe noticed that a sudden decrease of maritime SST was

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Fig. 1. Map of observed locations by R/V Keifu Maru and cen-tral position Typhoon Rex every 6 hours (open) and every24 hours (shaded). Triangle marks indicate observationalstations by R/V Keifu Maru and the circle marks the trackof Typhoon Rex.

Fig. 2. Time series of minimum sea level pressure and translation speed of Typhoon Rex. Closed circles indicate minimum sealevel pressure of Typhoon Rex every 6 hours. Cross marks show translation speed of Typhoon REX every 6 hours.

development sustenance slow

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 45

observed when three days had passed after the passage ofTyphoon Rex.

In order to investigate how to produce the suddendecrease of SST, a three-day average SST by TRMM/TMI,which can be obtained via a ftp site ftp://ftp.ssmi.com, isused for analysis. Not daily SST but three-day averageSST is used because TRMM/TMI can not observe SSTdirectly under cloudy conditions and as a consequencethe null region is conspicuous in the case of using dailySST. Horizontal resolution of SST by TRMM/TMI is0.25° by 0.25°, which is covered with a region from 40°Sto 40°N. The deviation of TRMM/TMI SST from August24 is respectively shown in Fig. 5. The day on August 27corresponds to the stage of Typhoon Rex when the ty-phoon changed its stage from intensification to suste-nance. SSC occurred behind and on the right side of therunning typhoon (Fig. 5(a)). The appearance of SSC onthe right side of the running typhoon is similar to previ-

ous observations (e.g. Black, 1983) and numerical stud-ies (e.g. Price, 1981). However, SSC around the typhooncenter can not be observed due to thick clouds of thestrong typhoon. The day on August 29 corresponds to thestage of the typhoon when the translation of the typhoonis the slowest. The region of SSC is extended along thetrack of Typhoon Rex (Fig. 5(b)). In addition, a coolingregion at the intersection between the track of TyphoonRex and the course of R/V Keifu Maru is still remaining.Maximum SSC in Fig. 5(b) is over 6.9°C. The translationspeed of Typhoon Rex on August 31 is again faster thanthat under the slowest translation on August 29. Maxi-mum SSC in Fig. 5(c) is over 7.8°C which appeared atthe place where the translation speed is the slowest. Inconclusion, SSC under the slowest translation stage is thegreatest through the generation, development, and suste-nance stages of Typhoon Rex. In contrast, the SST devia-tion at the intersection becomes smaller after the typhoonpassage. This shows that the SST increased in five daysafter the passage of Typhoon Rex.

4. Numerical Simulation during the Passage of Ty-phoon Rex

4.1 Initial conditionsTRMM/TMI 3-days average SST data on August 24

are used as an initial SST field at 09 JST on August 24.An initial sea temperature and salinity except for the SSTare created by linear interpolation from Levitus’ clima-tology data (Levitus, 1982). Geostrophic currents are pri-mary calculated as the initial ocean currents as describedin Subsection 2.1.

As for atmospheric initial conditions, global analy-sis (GANAL) data provided by the Japan MeteorologicalAgency (JMA), which horizontal resolution is 1.25° by1.25°, are used by linear interpolation. Atmosphericboundary conditions on the surface are updated every 6hours during the numerical experiment. Atmospheric in-

Fig. 3. Time series of vertical profiles of sea temperature byCTD measurement at the fixed observed station (130°E,20°N) during the period from August 23 to August 26, 1998.Shaded area represents over 29°C. Contour interval is 0.5°C.

Fig. 4. Time series of maritime SST observed by R/V Keifu Maru during the period from August 24 to August 31.

46 A. Wada

gredients using as initial and boundary conditions are airtemperature, sea level pressure, and wind velocity innorth-south and east-west components, which north andeast components are positive. In fact, GANAL data cannot reproduce realistic MSLP of Typhoon Rex due to thecoarse resolution, which is the reason why we mergedthe typhoon-like vortex into the GANAL field (Wada,2002a). In a practical sense, the typhoon-like vortex iscreated using a Rankin vortex introduced by Chang andAnthes (1978). Horizontal distribution of surface wind isprimarily determined based on the maximum wind ve-locity of Typhoon Rex recorded by JMA best track data.Cloud cover, which is observed by R/V Keifu Maru every3 hours, is used in the numerical experiment, assuminghorizontally uniformly. Precipitation occurring concur-rently with Typhoon Rex is neglected in this numericalexperiment because rainfall around the eyewall andrainband of the typhoon is presumed to be rather heavyin comparison to the rainfall observed by R/V Keifu Maru.In addition, presumption of horizontal distribution of pre-cipitation is difficult even in the atmospheric model. Infact, no precipitation data is supported by the GANALdataset.

4.2 Numerical simulationA numerical experiment, which target is simulation

of SSC during and subsequent to the passage of TyphoonRex is performed using a mixed layer model. Detailedtargets of the numerical simulation are the following:

1) To investigate a gradual decrease of maritimeSST at the fixed station observed from August 24 to 27.

2) To investigate a rapid decrease of maritime SSTobserved at the intersection between the track of TyphoonRex and the course of R/V Keifu Maru.

3) To reproduce a horizontal distribution of thecooling region on the sea surface along the track of Ty-phoon Rex.

Time variations of observed and simulated SSTs atobservational stations of R/V Keifu Maru are representedin Fig. 6. As for the target 1), a gradual decrease of SSTobserved from August 24 to 27 can not be simulated bythe model of Wada (2002a) and the model in the presentstudy compared to the observed SST. However, thegradual decrease of observed SST can be successfullysimulated by the 1-dimensional mixed layer model byWada (2002b) with observed atmospheric forcing at a 10-minute interval. Therefore, the unsuccessful simulationfor the gradual decrease of SST is considered to be causedby the difference between GANAL wind velocities andobserved ones. It is noted that wind-induced mixing hardlyworks well in the numerical experiment during the pe-riod of the target 1). As for the target 2), on the otherhand, a rapid decrease of SST observed at the intersec-tion between the track of Typhoon Rex and the course of

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Fig. 5. Horizontal distribution of SST deviation from the ini-tial time, August 24 by TRMM/TMI. (a): SST deviation onAugust 27, (b): August 29, and (c): August 31. Open andshaded, circle and triangle marks are the same as Fig. 1.

(a)

(b)

(c)

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 47

(b)

Fig. 6. Time series of maritime SST observed by R/V Keifu Maru (open circle), simulated SST by a mixed layer model (closecircle), and simulated SST by Wada (2002a) (open triangle). Time unit is JST.

Fig. 7. Time series of atmospheric forcing at the observed station of R/V Keifu Maru. (a): Wind stresses in north-south (opencircle) and ease-west (shaded circle) directions of which unit is N/m2, (b): Solar insolation (shaded circle) in the right verticalaxis, longwave radiation (open circle), sensible heat (square), and latent heat (cross) fluxes in the left vertical axis of whichunit are all W/m2. Downward radiation and fluxes show heating in the ocean.

48 A. Wada

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Fig. 8. Contribution of the terms in the thermodynamic equation in the mixed layer to a SST variation at the observed station byR/V Keifu Maru. Open circles indicate an SST variation per hour caused by the sea surface flux. Cross marks indicate an SSTvariation caused by the divergent term. Shaded triangles indicate an SST variation caused by entrainment. The unit of thevertical axis is expressed as °C per hour.

Fig. 9. Results of numerical simulation at 08 JST on August 31 during the passage of Typhoon Rex. (a) Horizontal distribution ofSSC (°C) from the initial time, August 24. (b) Horizontal distribution of SSC (°C), (c) horizontal distribution of the depth ofa mixed layer (m), and (d) horizontal distribution of depth at the base of a thermocline (m).

(a) (c)

(b) (d)

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 49

R/V Keifu Maru is successfully simulated in comparisonto the result of Wada (2002a). However, both computedSSTs under-evaluate compared to the observation becausethe location of Typhoon Rex in the GANAL data on Au-gust 24 is erroneous.

Atmospheric forcing at the observed stations of R/VKeifu Maru is shown in Fig. 7. Wind stresses were com-parably stronger on August 24, which were caused bygeneration of Typhoon Rex. However, wind stresses wereless than 0.1 N/m2 from August 26 to 31 (Fig. 7(a)). So-lar radiation varied with diurnal cycle, while longwaveradiation and latent heat fluxes were less than 200 W/m2

and sensible heat fluxes were much less than latent heatfluxes (Fig. 7(b)). As for the net heat flux, solar radiationis more dominant during the day than any other fluxes onthe surface. In order to check each contribution of physi-cal processes, the amount of SST variations per hour atthe observed station by entrainment, heat flux and diver-gence terms is investigated in Fig. 8. The SST rose dur-ing the day with the diurnal cycle of solar radiation. Incontrast, the entrainment works well during the night andprobably deepen the mixed layer. The net heat flux with-out solar radiation works as an enhanced SSC. This im-plies that the unstable vertical profile by buoyancy fluxinside the mixed layer is responsible for enhancing anentrainment process. Heat loss on the sea surface drivespenetrative convection that deepens the mixed layer thick-ness, while mixing depth is progressively inhibited bysolar heating during the day (Denman and Gargett, 1995).The rest of the physical processes expressed as the diver-gence term is called “advection” in this study. This is toosmall compared to that of the net heat flux and entrain-ment, which is consistent with the result of idealized nu-merical experiments by Wada (2002a).

To sum up the results at the observed station of R/VKeifu Maru, nevertheless, it is found that the rapid de-crease of SST at the intersection between the track ofTyphoon Rex and the course of R/V Keifu Maru can notbe produced by instant atmospheric forcing. As for target2), therefore, it was considered that the rapid decrease ofSST was already been produced before R/V Keifu Maruarrived at the place.

For the purpose of verifying target 3), horizontal dis-tributions on August 31 of the SST deviation from theinitial time (Fig. 9(a)), the SST itself (Fig. 9(b)), the mixedlayer depth (Fig. 9(c)), and the depth at the base of athermocline (Fig. 9(d)) are represented. The maximumnegative deviation of simulated SST from the initial timewas nearly 6°C around 141.5°E and 28.25°N, which wassmaller than that of the observed SST by TRMM/TMI(Fig. 5(c)). Characteristic of the distribution of SST de-viation shown in Fig. 5(c), namely appearance of a re-gion where salient SSC occurred, is similar to Fig. 9(a).Figures 9(a) and (b) indicate that SST anomalies are lo-

cated on and around the track of Typhoon Rex, in par-ticular on the right side of the running typhoon. At thesame time, a mixed layer on and around the track of Ty-phoon Rex deepened, in particular on the right side ofthe running typhoon (Fig. 9(c)). It is considered that avariation of mixed layer thickness corresponds to that ofthe SST under an enhanced entrainment process. Not onlythe entrainment process but also an upwelling process isimportant for producing SSC (Chang and Anthes, 1978;Price, 1981; Wada, 2002a). The elevation at the base ofthe thermocline shown in Fig. 9(d) reveals the upwellingregion where maximum SSC occurred. This upwellingregion is related to the slow translation stage of TyphoonRex.

How salient SSC observed by R/V Keifu Maru andby TRMM/TMI was produced? Figure 10 represents thepositions where the maximum SSC occurred in the nu-merical simulation. In the early integration, when the stageof Typhoon Rex is a tropical depression, the positions ofmaximum SSC is far from the track of Typhoon Rex be-cause wind velocity of GANAL is greater than that ofRankin vortex. As the integration goes on, the positionsof maximum SSC are situated just under the track. Then,the positions are shifted on the right side of the runningtyphoon. As the typhoon moves slower, the position againturns to be situated just under the track. Finally, the posi-tion hardly changes although the typhoon moves with afaster translation. At the position of maximum SSC, acontribution of the entrainment term is dominant for SSC,in particular on August 26 and 27, which is in agreementwith the place where the positions of maximum SSC aresituated on the right side of the typhoon (Fig. 11). Theplace is also including the intersection between the track

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Fig. 10. Map of locations where the maximum SSC occurred.Shaded circle indicates the place where the maximum SSCoccurred in the mixed layer model with Deardorff scheme.Open circles are positions of Typhoon Rex every 24 hours.Open triangles indicate the observed station by R/V KeifuMaru.

50 A. Wada

of Typhoon Rex and the course of R/V Keifu Maru takenas target 2). In contrast, contributions of the net heat fluxterm and the advection term are smaller than that of theentrainment term. In contrast, even under conditions ofstrong intensity of Typhoon Rex and enhanced SSC, acontribution of the entrainment term at the slower trans-lation stage is comparably smaller than that on August 26and 27. We must emphasize the contribution of upwellingat this stage for producing salient SSC shown in Fig. 9(d).The upwelling is also related to the position of the maxi-mum SSC. Leipper (1967) reported that SSC by Hurri-cane Hilda appeared on the left side of the moving direc-tion. However, in general, it is confirmed by observations(e.g. Black, 1983) and numerical experiments (e.g. Price,1981) that SSC appeared on the right of the moving di-rection. In the present paper, the position of the maxi-mum SSC caused by Typhoon Rex depends on its stages.In each stage of the typhoon, the contribution of entrain-ment and upwelling for SSC is different.

4.3 Nondimensional analysisAs described earlier, physical processes of SSC dur-

ing the passage of a tropical cyclone are caused by en-trainment and upwelling (Price, 1981; Wada, 2002a). Inthis section, the relationship between the ocean responseduring the passage of the typhoon and internal (oceanic)or external (atmospheric) factors is investigated usingthree nondimensional variables: a nondimensional stormspeed, a Burger number, and a Rossby number, which areall introduced by Price et al. (1994). Price et al. (1994)suggested a representative value for each hurricane. How-ever, the nondimensional variables should be changed inresponse to the stage of a tropical cyclone because a tropi-cal cyclone has various stages of genesis, development,sustenance, and lysis (change to extratropical cyclone).

The nondimensional storm speed (S) is

SU

fRH= ( )π

43

max

,

where UH is a translation speed, f is the Colioris param-eter, and Rmax is a radius of maximum wind velocity. Forexample, typical values of UH = 5 m/s and Rmax = 50 kmimply that S is O(1). This variable represents a ratio of alocal inertial period to a tropical cyclone residence time.Wind stresses observed from the ocean change on a timescale comparable to the local inertial period (Price et al.,1994). The lower S implies that the size of a tropical cy-clone is larger or the translation is slower. In the case of alarger and slower tropical cyclone, we expect that theocean response will be stronger. On the other hand, a tropi-cal cyclone with a smaller size or a faster translation speedhas a larger S, which characterizes strong inertial andasymmetric motions across the track (Wada, 2002a).

In the case of Typhoon Rex, S has the maximum valueon August 28 of which maximum value is 1.9. It is lowerthan 2.4 in Hurricane Norbert and is higher than 0.8 and1.1 in Hurricane Josephine and Hurricane Gloria, whichwere all investigated by Price et al. (1994) (Fig. 12(a)).Roughly the value S is lower from August 29 to August30 when the translation of Typhoon Rex becomes slowerand its intensity becomes stronger. During the time, theadditional SSC of nearly 1°C is simulated (Fig. 12(a)).On the other hand, Fig. 12(a) implies that the value S isirrelevant to the rapid decrease of the SST that occurredfrom August 26 to 28. Therefore, the additional SSC ofnearly 1°C from August 29 to August 30 can be explainedby the effect of the typhoon translation although we cannot explain the salient SSC from August 26 to 28 usingthe nondimensional storm speed S. In order to resolvethe mechanism of the salient SSC, another factor is re-quired.

Fig. 11. Same as Fig. 8 except for the location where the maximum SSC occurred in the results of the simulation during thepassage of Typhoon Rex by the mixed layer model.

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 51

The Burger number (B) is

Bg h

f R= ( )′ 1

2 244

max

,

where g′ is the reduced gravity and h1 is a mixed layerthickness where the maximum SSC occurred. The Burgernumber B represents a direct measure of the pressure cou-pling between currents in the mixed layer and those inthe thermocline. The large number of B is an evidence ofenhanced pressure coupling connected with the dynam-

ics at the relaxation stage. Stronger wind stresses are re-quired for a mixed layer to become deepening. There-fore, the Burger number B is considered to represent ascale of turbulent mixing due to entrainment.

In the case of Typhoon Rex, the Burger number in-creases from August 25 till August 27, which agrees tothe period when SST suddenly decreases from August 26to 28 (Fig. 12(b)). The maximum Burger number of Ty-phoon Rex is nearly 0.12, which is higher than that inHurricane Josephine (0.04) and Hurricane Gloria (0.02),and is lower than that in Hurricane Norbert (0.37) (Price

Fig. 12. Time series of (a) the nondimensional storm speed S, (b) the Berger number B, and (c) the Rossby number Q. The crossindicates the amount of maximum SST cooling. The left axis indicates the scale of S, B, and Q while right axis indicatesdeviation of SST from the initial condition for the comparison.

(a)

(b)

(c)

52 A. Wada

et al., 1994). The Burger number is maintained from 0.06to 0.12 from August 28 to 30. Note that the Burger numberdecreases after 18 JST on August 28. It is because Ty-phoon Rex moves far away that the region of SSC is ir-relevant to in-situ atmospheric forcing.

The Rossby number (Q) is

Qh U fH

= ( )τρ0 1

5,

where τ is magnitude of the wind stress. Q represents aratio of horizontal momentum wind forcing to the Coriolisforce. The higher Rossby number represents the oceanresponse of a tropical cyclone under a slower translation,a thinner mixed layer thickness, and a stronger wind stress.According to Wada (2002a), this condition is related tothat of enhancing upwelling.

Figure 12(c) shows that the Rossby number has amaximum value of 1.2 on August 30, which is higher thana value of 0.7 in Hurricane Norbert and 0.2 in HurricaneJosephine and Hurricane Gloria (Price et al., 1994). Themaximum value of Rossby number occurred during theperiod when SST suddenly decreases again. Therefore,this sudden decrease of SST from August 29 to 30 iscaused by upwelling, while the upwelling does not play asignificant role in the sudden decrease of SST from Au-gust 26 to 28.

The nondimensional storm speed S, the Burgernumber B, and the Rossby number Q all depend on bothstages of Typhoon Rex. In the case of Typhoon Rex, thereare two stages when the ocean response during and sub-sequent to the typhoon is enhanced. One stage is linked

to intensification of Typhoon Rex. The other stage is re-lated to the slowest translation of Typhoon Rex. In thestage when Typhoon Rex becomes stronger, a contribu-tion by entrainment for SSC is dominant. However, thearea where maximum SSC occurred shifts to the runningdirection as Typhoon Rex is moving.

On the other hand, the Burger number and the Rossbynumber keep high values under the low nondimensionalstorm speed S under the slowest translation of TyphoonRex. Under the slow translation, the depth in the mixedlayer deepens nearly at the same place. At that time,upwelling is enhanced just behind Typhoon Rex in spiteof simultaneously occurrence of the entrainment process.Once SSC is enhanced by upwelling, a cooling area isstill remaining, even when Typhoon Rex moves far awaywith a low Berger number.

5. Intercomparison of Entrainment SchemesIn this section, intercomparison of entrainment

schemes introduced in Subsection 2.3 is implementedapplying the mixed layer model to the case of TyphoonRex under the same atmospheric and oceanic conditions.Actually, the entrainment rate plays an important role inthe ocean response to a typhoon. Figure 13 shows devia-tions of SSTs simulated by the mixed layer model withdifferent entrainment schemes from the maritime SST byR/V Keifu Maru at the equivalent time. All entrainmentschemes used in this study tend to numerically evaluatethe SSTs higher till August 27, and lower from August 29than the maritime SSTs. The former corresponds to theperiod of target 1) described in the previous section. Inthe latter period, R/V Keifu Maru went back to Japanacross the Kuroshio region. The deviation in Fig. 13 var-

Fig. 13. Time series of SST deviations from the observation by R/V Keifu Maru. The shaded circle indicates SST deviationsderived from the computed SST by Deardorff (1983) (DF). The open triangle indicates those by Chang and Anthes (1978)(CA). The shaded square indicates those by Price (1981) (PR). The open diamond indicates those by Elsberry et al. (1978)(EL).

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 53

Fig. 15. Same as Fig. 9(c) except for (a) entrainmentparameterization by Chang and Anthes (1978) (CA), (b) byElsberry et al. (1978) (EL), and (c) by Price (1981) (PR).

(a)

(b)

(c)

128° 132° 136° 140° 144°

16°

20°

24°

28°

32°

-6

-5

-4

-3

-2

-1

CA

128° 132° 136° 140° 144°

16°

20°

24°

28°

32°

-6

-5

-4

-3

-2

-1

EL

128° 132° 136° 140° 144°

16°

20°

24°

28°

32°

-6

-5

-4

-3

-2

-1

PR

(a)

(b)

(c)

128° 132° 136° 140° 144°

16°

20°

24°

28°

32°

30

40

50

60

70

80

90

100

CA

128° 132° 136° 140° 144°16°

20°

24°

28°

32°

30

40

50

60

70

80

90

100

EL

128° 132° 136° 140° 144°

16°

20°

24°

28°

32°

30

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PR

Fig. 14. Same as Fig. 9(a) except for (a) entrainmentparameterization by Chang and Anthes (1978) (CA), (b) byElsberry et al. (1978) (EL), and (c) by Price (1981) (PR).

54 A. Wada

ies from August 28 to 29 when Typhoon Rex has gone onthe left side of the ship track of R/V Keifu Maru (Fig. 1).During this period, two peaks of the minimum SST de-viation are easily recognized. One peak implies thatthe model with EL entrainment scheme can not simulatesudden cooling of the sea surface at around 00 JST onAugust 29. The other peak means that the computed SSTby PR scheme is recovered to warmer water earlier thanthe maritime SST. As for target 1) and target 2), the modelwith DF entrainment scheme has the best performance,although the model with CA entrainment scheme providescomparative results.

As for target 3), Fig. 14 indicates respectively hori-zontal distributions of SST deviation on August 31 fromAugust 24 by CA, EL, and PR schemes. The distributionby CA (Fig. 14(a)) is the most similar to that by DF (Fig.9(a)), which is similar to that by TRMM/TMI (Fig. 5(c))from the viewpoint of magnitude of maximum SSC andthe area where SSC is produced. In the case of the ELscheme (Fig. 14(b)), the cooling area is comparable tothat by DF, CA, and TRMM/TMI. Nevertheless, the mag-nitude of maximum SSC is too small against that by DF,CA, and TRMM/TMI. As for the small evaluation of SSCin the EL entrainment scheme, the mixing factor of CA isapproximately double compared to that of EL accordingto Chang and Anthes (1978). In other words, SSC by ELis under-evaluated compared to that by CA. In the caseof PR scheme (Fig. 14(c)), the magnitude of maximumSSC is plausible, while the cooling area is too narrowand the horizontal gradient of SST deviation is sharp,which is similar to that by TRMM/TMI (Fig. 5(c)).

Not only SSC but also mixed layer depth is an im-portant factor to evaluate the performance of the entrain-ment scheme because the mixed layer deepens due toentrainment. Figure 15 indicates horizontal distributionsof simulated mixed layer depth on August 31 by CA, EL,and PR schemes respectively. The distribution by CA (Fig.15(a)) is the most similar to that by DF (Fig. 9(c)), butthe magnitude of mixed layer thickness by CA is deeperthan that by DF. As for the mixed layer depth, no ob-served data can verify the validity of the entrainmentscheme in the present study. In the case of the EL scheme(Fig. 15(b)), not only magnitude of the mixed layer thick-ness is smaller but also the horizontal distribution of thedepth in the mixed layer is different from the typical pat-tern introduced by Ginis (1995). In the case of PRschemes, the deepest area in the mixed layer is concen-trated along the track of Typhoon Rex so that this is dif-ferent from the typical pattern by Ginis (1995), too. Thelatter result suggests that the PR scheme can not simulatethe salient rightward bias of the mixed layer depth. How-ever, Price (1981) suggested that a PR scheme somewhatenhanced the asymmetry in the SST response, while aCA scheme yielded a symmetric SST response to a sym-

metric storm. This implies that the ocean response to atyphoon depends not only on its stages but also on thehorizontal structure of wind velocity including the sizeof the eye and the distance of maximum wind velocity,which is related to the distribution of current shears. Thesefactors can also influence the estimation ofnondimensional numbers shown in the previous section.

The above examination shows that the DF scheme isthe best performance of four schemes in target 3) intro-duced in the previous section. As for target 1), frictionalvelocity and buoyancy effects included in the CA, EL,and DF schemes are significant to evaluate not only thegradual SST variation, but also the SST deviation widelyrecognized around the Typhoon Rex. The wide area ofSSC, which is similar to the area shown in Fig. 5(c) orFig. 9(a) can be simulated in the cases of CA and ELschemes. However, the rapid SST decrease on August 29(Fig. 13) can not be quantitatively simulated due to over-deepening of the mixed layer in the case of the CA scheme.On the other hand, as for target 2), the effect of currentshear included in PR and DF contributes to the suddenSSC and horizontal sharp gradient of SSC. In fact, themagnitude of SSC by PR scheme is the greatest of fourschemes. In addition, a cooling region by the passage ofTyphoon Rex is too narrow in comparison to the regionby TRMM/TMI. However, the wide area and asymmetricdistribution of SSC shown in Fig. 5(c) can not be simu-lated in a PR entrainment scheme. As for target 3), bothfactors of target 1) and target 2) are required so that theDF scheme has the best performance for the SSC simula-tion by the passage of Typhoon Rex.

These results are in agreement with those describedby Jacob and Shay (2003), i.e., the DF scheme predictedintense entrainment due to enhanced shears; whereas theresponse is broader and weaker in a CA-like scheme.However, the effect of radiation fluxes on the sea surfaceis not included in the result of Jacob and Shay (2003). Inaddition, the priority of this study for Jacob and Shay(2003) is reliable evaluation of contribution of the sourcesof turbulent kinetic energy to each entrainment schemefor the SSC, using not only the computed SSTs but alsoship and TRMM/TMI SST data.

Note that no salient difference of elevation at the baseof the thermocline is detected by four schemes (notshown). This reveals that the vertical velocity of fourschemes at the base of the thermocline is all almost alikein Fig. 9(d). This result is in agreement with that ofO’Brien and Reed (1967). The strong upwelling causedby wind stresses is irrelevant to the entrainment process.

6. Summary and DiscussionNumerical simulations during the passage of Ty-

phoon Rex by a mixed layer model were carried out toinvestigate the ocean response to Typhoon Rex using the

Numerical Simulations of Sea Surface Cooling of Typhoon Rex 55

realistic forcing field based on global analysis data, besttrack data of Typhoon Rex, and ship observation. Theformation mechanism of cooling of the sea surface (SSC)during and subsequent to the typhoon was examined.

A mixed layer model outlined by Wada (2002a),which is based on Bender et al. (1993), is used in thisstudy. Applying the mixed layer model with a realisticatmospheric forcing field in the case of Typhoon Rex,two types of SST decreases observed by R/V Keifu Maru,one is gradual cooling and the other is rapid cooling, canbe much improved compared to results by Wada (2002a).The horizontal distribution of SSC by the mixed layermodel is similar to the distribution of SST observed byTRMM/TMI. Local SSC along the track of Typhoon Rexis quite evident in the simulated and observed distribu-tion of SST deviations.

A rapid decrease of maritime SST by R/V Keifu Maruat the intersection between the track of Typhoon Rex andthe course of R/V Keifu Maru is not produced by instantatmospheric forcing at the observational station but isproduced by strong wind during the passage of TyphoonRex and remaining at that place after its passage. Theplace of the maximum SSC varied from just under thetyphoon to the right side of the typhoon in accordancewith the stage of Typhoon Rex, i.e., intensification ormaintenance stages. From the analyses of three kinds ofnondimensional number, formation mechanism of SSCin the case of Typhoon Rex is proposed. A rapid SST de-crease observed by R/V Keifu Maru is caused by enhancedentrainment, while SSC under the slow translation is in-duced not only by entrainment but also by upwelling. Inthe area where upwelling is greatly enhanced, maximumSSC is remaining in a sustainable way. In contrast, thearea of maximum SSC moved to the right side of the ty-phoon when entrainment is greatly enhanced. Under anon-stormy condition, solar radiation dominates a varia-tion of SST directly. However, the contribution of heatfluxes for SSC is comparably small under a stormy con-dition. The results are consistent with the idealized nu-merical experiment (Price, 1981; Wada, 2002a) and theobservation (D’Asaro, 2003). The transition of physicalprocesses from only entrainment to both entrainment andupwelling is determined by the stage of a typhoon, inten-sification or maintenance stages. Not only the amount ofSSC but also the place of the maximum SSC is related tothe stage of a typhoon. Intensification and translation ofa typhoon play an important role for the ocean responseto the typhoon.

Intercomparison of entrainment schemes by Changand Anthes (1978), Elsberry et al. (1976), Price (1981),and Deardorff (1983) is implemented using a mixed layermodel in the case of Typhoon Rex. The computed SSTsare compared with the observed time series of SST vari-ation by R/V Keifu Maru and horizontal distribution of

SST deviations derived from TRMM/TMI satellite SST.The result reveals that the Deardorff’s entrainment schemehas the best performance of the four examined entrain-ment schemes. In addition, contributions of three sourcesof turbulent kinetic energy for the ocean response to Ty-phoon Rex are investigated. The sources are frictionalvelocity, buoyancy flux, and current shear. The entrain-ment scheme derived from frictional velocity and buoy-ancy flux is responsible for the wide area of SSC. In con-trast, the scheme derived from current shear at the baseof the mixed layer can simulate a realistic amount of SSCand a sharp horizontal gradient of SST distribution formedalong the track of typhoon. These features are in agree-ment with those reported by Jacob and Shay (2003), how-ever Jacob and Shay (2003) do not include the atmos-pheric radiation effect.

In the Deardorff’s entrainment scheme, these threephysical effects are incorporated into the scheme. There-fore, both wider and greater SSCs can be simultaneouslyreproduced by the Deardorff’s model. Note that the en-trainment scheme derived from only current shear likePrice (1981) can produce the realistic horizontal gradientof SST deviation, which is more similar to that by TRMM/TMI than that by Deardorff’s model. D’Asaro (2003) sug-gested from the observation that much more coolingshould occur because of much larger inertial currents andshear on the right side of the running storm. This meansthat the entrainment rate derived from current shear maybe under-evaluated when the current velocity is unsuc-cessfully simulated. In other words, more realistic SSCsimulation can be realized in the present study if the cur-rent velocity is successfully simulated. Nonetheless, theeffect of the frictional velocity and the buoyancy flux isrequired for entrainment parameterization to express thewider deviation of SSTs.

In order to improve the prediction of ocean currentsusing the present model, more accurate atmospheric forc-ing, sufficient spin-up time, installation of realistic to-pography, and high accuracy of advection scheme will berequired. In addition, atmospheric forcing updated everysix hours except around the typhoon obtained fromGANAL data is too coarse in temporal and spatial reso-lution. Weak wind stresses are responsible for under-vali-dation of ocean currents and current shears. The horizon-tal structure of a typhoon such as the size of the eye andthe radius of maximum wind velocity is important for theocean response to a typhoon. Otherwise, if spin-up pro-cedure is made complete with realistic topography andhigh accuracy of advection scheme, the interaction be-tween the ocean response to a typhoon and a westernboundary current like Kuroshio can be clarified.

The effect of precipitation on the sea surface requiredfor a variation of salinity is important for the upper oceanresponse to a typhoon. According to Pudov and

56 A. Wada

Petrichenko (2000), salinity anomalies in the trail of theTyphoon Flo are highly informative. Light water producedby heavy rainfall stabilizes the upper ocean, while heavywater on the surface is caused by release of latent heatflux. The heavy water is responsible for mixing in theupper layer so that sea temperature in the upper layershould decrease. Nonetheless, estimation of precipitationis difficult because the effect of ocean coupling to hori-zontal distribution of the rainfall is still uncertain. In thefuture, the ocean response to a typhoon will be investi-gated using an atmosphere-ocean coupled model withfiner grid resolution. Even in that case, results in this pa-per will link to the development of not only a regionalcoupled model but also a global coupled model.

AcknowledgementsMaritime and hydrographic data by R/V Keifu Maru

were acquired by the staff and crew of R/V Keifu Maruin the Japan Meteorological Agency. Two anonymous re-viewers provided useful comments on an earlier versionof this manuscript. The author thanks Prof. T. Awaji, edi-tor of Journal of Oceanography, and Dr. M. Kamachi forgiving useful suggestions. The original source code ofthe mixed layer model was provided by Prof. I. Ginis atthe University of Rhode Island.

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