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

Transcription

1 Journal of Oceanography, Vol. 61, pp. 41 to 57, 2005 Numerical Simulations of Sea Surface Cooling by a Mixed Layer Model during the Passage of Typhoon Rex AKIYOSHI WADA* Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Ibaraki , 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 sea surface temperature (SST) observed by R/V Keifu Maru, the ocean response to Typhoon Rex is simulated using a mixed layer model. The rapid decrease of the maritime SST is successfully simulated with realistic atmospheric forcing and an entrainment scheme of which sources of turbulent kinetic energy (TKE) are production due to 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 by instant atmospheric forcing but is mainly produced by entrainment on the right side of the running typhoon as a part of cooling area during its passage, and remained during a few days. The sea surface cooling (SSC) is evident along the track and on the right side of the running typhoon, which is similar to the SSC of satellite observation by TRMM/TMI. The conspicuous SSC produced by both entrainment and upwelling is 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 the wide region. In contrast, the effect of current shear at the mixed layer base is related to the amount of SSC and the sharp horizontal gradient of SSC. The entrainment scheme including all three TKE sources has the best performance for SSC simulation. Keywords: Mixed layer model, typhoon, sea surface cooling, entrainment scheme, upwelling, atmospheric forcing. 1. Introduction Genesis and development of a tropical cyclone are sensitive to upper ocean heat potential where sea surface temperature (SST) is over C (Palmén, 1948). A tropical cyclone produces local cooling of the sea surface (SSC) after its passage. The ocean response of a tropical cyclone has been investigated through observational approaches (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 of the effective ways to understand the upper ocean response during the passage of a tropical cyclone. One of the oceanic variations after the passage of a tropical cyclone is caused by turbulent mixing in the entrainment zone. Jacob et al. (2002) and Jacob and Shay * address: awada@mri-jma.go.jp Copyright The Oceanographic Society of Japan. (2003) investigated effects of an entrainment scheme on the ocean mixed layer response during the passage of Hurricane Gilbert in 1988 using four kinds of entrainment schemes. According to Jacob and Shay (2003), mixed layer temperatures simulated by the scheme using the bulk Richardson number shows the best performance for the observed temperatures of four kinds of entrainment schemes, although the overall pattern remained qualitatively similar. Intercomparison of mixed layer models with different entrainment schemes has been performed for cases of diurnal cycle or seasonal cycle of SST (e.g. Kantha and Clayson, 1994; Large et al., 1994; Anderson and Weller, 1996). Ginis (1995) conducted intercomparison of three different entrainment schemes of a moving idealized storm, which translation speed was 5 m/s. However, realcase simulation during the passage of a tropical storm was very few in number. Besides, it is difficult to validate the result of a mixed-layer model due to poor observation during and even after the passage of a tropical cyclone. The numerical simulation of the upper ocean re- 41

2 sponse to a tropical cyclone with real-case forcing field has hardly ever been performed. Even in the numerical experiment of Jacob et al. (2002) and Jacob and Shay (2003), constant air temperature and humidity were assumed to estimate the surface heat fluxes. The role of the surface heat fluxes was in fact small for local SSC during the passage of a tropical cyclone (Price, 1981; Bender et al., 1993). After the passage of the tropical cyclone, however, surface heat fluxes might play an important role to simulate an increase of SST. A mixed-layer model has been often used to investigate 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). The mixed-layer model is still available in view of computational efficiency or saving memory and storage area. In addition, it is easy to understand the physics of the mixed layer. However, it was difficult to simulate a diurnal cycle of SST and a variation of mixed layer depth because the mixed-layer model simply consists of a mixed layer, a thermocline and undisturbed layers. As a consequence detailed of the inside of the mixed layer could not be simulated. In fact, observation by air-deployed deep floats suggested that the seawater could be cooled at the surface, at the bottom of the trajectories by entrainment, and in occasional mid-depth events by horizontal mixing beneath a hurricane (D Asaro, 2003). For the purpose of simulating the detail of the mixed layer, K-Profile (Large et 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 circulation model. In the present study, numerical simulations were carried out to investigate the ocean response to Typhoon Rex of 1998, using a mixed-layer model with a realistic forcing field based on global analysis data, best track data of Typhoon Rex, and ship observation. The relationship between stages of the typhoon and the ocean response to the typhoon (SSC and deepening of the mixed layer depth) was examined in this paper. This paper is organized as follow: An outline of the mixed layer model and the way of estimation of sea surface fluxes are reported in Section 2. Section 3 describes results of SSC observations during the passage of Typhoon Rex by R/V Keifu Maru and TRMM/TMI. Section 4 presents an outline of a numerical experiment concerning with the ocean response to the passage of Typhoon Rex. In section 4, the formation mechanism of rapid decrease of the SST is discussed using nondimensional numbers. Section 5 describes results of intercomparison of four entrainment schemes of which sources of turbulent kinetic energy (TKE) are respectively different. Section 6 is devoted to summary and discussion. 2. Numerical Model and Sea Surface Fluxes 2.1 Basic equations A mixed layer model, which is an updated version of Wada (2002a), is based on a slab model used for a hurricane-ocean coupled model developed by Bender et al. (1993). Prognostic variables of the model are horizontal current velocity in longitude and latitude, layer thickness of all layers plus sea temperature and salinity in a mixed layer and a thermocline. The model is formulated with hydrostatic and Boussinesq assumption, a reduced gravity approximation, and a flat bottom in the ocean of which depth is 1,500 m. The model consists of equations of motion, thermodynamic, salinity, and continuity equations. Unlike the equations of motion described by Bender et al. (1993), calculation of horizontal viscosity by Smagorinsky (1963) from deformation fields is added to the equations of motion. In addition, the friction terms expressed as a function of an entrainment rate are modified to those of Ginis (1995). A horizontal grid resolution is 0.25 by 0.25 with a longitude-latitude coordinated system. The model has eight vertical layers, including a mixed layer (30 m), a thermocline (170 m), and undisturbed layers (100 m, 100 m, 100 m, 200 m, 300 m, and 500 m), which the last layers are controlled only by the pressure gradient term. The number of the layers is the same as those reported by Bender et al. (1993). 2.2 Sea surface processes In the present study, we estimated solar and longwave radiations and turbulent fluxes by empirical formulas. The momentum, sensible and latent heat fluxes are calculated according to Kondo (1975). The downward solar radiation is defined by Reed (1977) and its coefficients are referred to the results of Schiano (1996). Because Reed s formula does not include the cloud cover, the formula with the cloud cover is used for estimation of the downward solar radiation. The upward solar radiation is determined as a function of downward solar radiation and albedo of the surface. The downward longwave radiation for the temperature range between 275 K and 302 K under the clear sky is specified as described by Swinbank (1963). Using the longwave radiation under the clear sky, the longwave radiation under the cloudy sky is derived from Bignami et al. (1995). The upward longwave radiation was a summation of radiation with a black body temperature and the reflectance of downward longwave radiation. The longwave radiation, which penetration depth is about 10 µm (Fairall et al., 1996), is presumed to leave directly from the sea surface. The physical property of sensible and latent heat fluxes is similar to that of longwave radiation (Price et al., 1986). On the other hand, solar radiation is absorbed within the water column with double exponential depth dependence (Kraus, 1972; Price 42 A. Wada

3 et al., 1986). In this study, formulation used in Price et al. (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 to sea temperature at any depths near the surface, a preliminary level model with a vertical resolution of 1 m is configured within the mixed layer. This enables to express the vertical gradient of sea temperature caused by solar absorption that declines exponentially near the surface. In contrast, the longwave radiation, sensible and latent heat fluxes are released directly on the surface. Therefore, a vertical profile of sea temperature may be unstable in the case that seawater at the surface becomes cool during the night. Otherwise, seawater near the surface is also stirred by wind. In the present study, stability criteria for static stability and mixed layer stability in the vertical profile of level model are taken into account within the mixed layer. The following criterion by Price et al. (1986) is used to comprise static and mixed layer stability, ρ 0 z () 1 for convective and stabilizing the buoyancy flux, and R b = g ρh ρ 0 V ( ) ( ) for mixed layer stability, where ρ is the density of seawater, z is the vertical coordinate, ρ 0 is the reference density (1024 kg/m 3 ), V is the horizontal current velocity, h is the thickness in the mixed layer, g is the acceleration of gravity, and ( ) indicates the difference between 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 conservation of ocean heat content in the mixed layer. Subsequently, the temperature at the mixed layer base and thickness in the thermocline are modified in a similar way due to the conservation of the ocean heat content above the thermocline base. 2.3 Entrainment rate In an integral sense, the sources of turbulent kinetic energy in the mixed layer are: 1) production due to wind stress, which is proportional to the frictional velocity to the 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 proportional to the current shear square at the mixed-layer base (Niller and Kraus, 1977; Price et al., 1978). The entrainment scheme used in this study is the entrainment parameterization by Deardorff (1983). This scheme was also used in Bender et al. (1993) although salinity was assumed to be constant in their numerical experiment. Here, not only prognostic sea temperature but also prognostic salinity is used to determine sea water density, which is used to define a velocity scale in the entrainment zone just below the mixed layer. The other refinement is the way of estimation of current shear. Because this model has been developed as a part of the atmosphere-ocean coupled model for a tropical cyclone prediction, computational time of spin-up procedure should be shortened as completely as possible to save computational time. That is the reason why geostrophic current at the initial field is calculated in advance. Current shear is estimated as the summation of diagnostic current (geostrophic current) shear and prognostic current shear. This ingenuity should be abolished if sufficient spin-up procedure is feasible. Performance of a mixed layer model depends on the way of entrainment scheme. As for the ocean response to tropical cyclones, many schemes of entrainment rate have been proposed. Chang and Anthes (1978) included the source 1) described above, which was a modified parameterization of the Kraus and Turner (1967) formulation (hereafter CA). Elsberry et al. (1976) assumed that mixed layer turbulence was generated only by frictional velocity and negative heat flux at the surface (hereafter EL). The parameterization took account of the source 1) and 2). In contrast, estimating the entrainment rate Price (1981) (hereafter PR) assumed that only velocity shear mechanism corresponded to source 3).The concept of this Price s scheme was similar to Pollard et al. (1973). The entrainment scheme by Deardorff (1983) (hereafter DF) took account of sources 1), 2), and 3) described above. This entrainment parameterization is equivalent to that described by Chen et al. (1994), based jointly on the Kraus-Turner type mixed layer (Kraus and Turner, 1967) and Price s dynamical instability model (Price et al., 1986). A brief description how to estimate the entrainment rate by DF is as follows: Assuming horizontally uniform, the second-moment turbulent equations for density flux and density variation are integrated throughout the mixed layer; Each term of integrated equations such as TKE variation, buoyancy flux, velocity jump at the mixed layer base, turbulent transport, and dissipation, is respectively parameterized and then a parameterized equation is formulated; The entrainment rate is repeatedly solved from the parameterized equation; After the convergence, the entrainment rate is determined. 3. Observation A tropical depression was generated in the south of Numerical Simulations of Sea Surface Cooling of Typhoon Rex 43

4 Aug Aug Aug30 Aug Fig. 1. Map of observed locations by R/V Keifu Maru and central position Typhoon Rex every 6 hours (open) and every 24 hours (shaded). Triangle marks indicate observational stations by R/V Keifu Maru and the circle marks the track of Typhoon Rex. Okinawa Island on August 24, 1998 and developed to Typhoon Rex on August 25. The trajectory of Typhoon Rex was like a trochoid (Fig. 1). Typhoon Rex had been developing to 960 hpa on August 26 and then had sustained its intensity till August 31 (Fig. 2). The minimum sea level pressure (MSLP) was 955 hpa when the translation speed of Typhoon Rex at that time was nearly 1 m/s and the slowest from August 29 to August 30 (Fig. 2). From August 23 to 27, maritime and hydrographic observations at the regular station were implemented around 130 E and N. The hydrographic observation was conducted by conductivity-temperature-depth (CTD) measurement round noon from day to day. The vertical profile of sea temperature in the upper ocean indicates that a mixed layer had been around 30 m in depth (Fig. 3). A gradual decrease of mixed layer temperature shown in Fig. 3 corresponds to that of the SST shown in Fig. 4. Figure 3 also reveals that a variation in the mixed layer temperature is smaller than that in a thermocline, which is defined as a steep gradient of sea temperature below the mixed layer. Occurrence of slight upwelling, probably caused by Typhoon Rex, is observed on August 25. Maritime conditions at the fixed observation had been 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 suddenly decreased and the deviation between air-temperature and dew-point temperature became small on August 24. At the same period, wind velocity temporarily reached 18 m/s. These observational results suggest that precipitation, caused by the passage of rainbands of Typhoon Rex, should have occurred in this region. In fact, light water spread over near the surface was observed at the station (not shown). Except this light layer, however, heavy and vertically homogeneous water lay at around 30 m in depth. Therefore, the mixed layer thickness of the mixed layer model is determined to be 30 m in the later numerical simulation. After the fixed observation was completed, R/V Keifu Maru got on the trail of Typhoon Rex from August 27 to 29. Then, R/V Keifu Maru logged across the track of Typhoon Rex from August 29 to 30. Figure 4 indicates that a sudden decrease of maritime SST occurred where R/V Keifu Maru logs across the track of Typhoon Rex. The SST decreased from 30 C to 27.2 C during several hours. The amount of SSC, nearly 3 C, is in the range of previous observation of Black (1983). However, it should be noticed that a sudden decrease of maritime SST was development sustenance slow Fig. 2. Time series of minimum sea level pressure and translation speed of Typhoon Rex. Closed circles indicate minimum sea level pressure of Typhoon Rex every 6 hours. Cross marks show translation speed of Typhoon REX every 6 hours. 44 A. Wada

5 observed when three days had passed after the passage of Typhoon Rex. In order to investigate how to produce the sudden decrease of SST, a three-day average SST by TRMM/TMI, which can be obtained via a ftp site ftp://ftp.ssmi.com, is used for analysis. Not daily SST but three-day average SST is used because TRMM/TMI can not observe SST directly under cloudy conditions and as a consequence the null region is conspicuous in the case of using daily SST. Horizontal resolution of SST by TRMM/TMI is 0.25 by 0.25, which is covered with a region from 40 S to 40 N. The deviation of TRMM/TMI SST from August 24 is respectively shown in Fig. 5. The day on August 27 corresponds to the stage of Typhoon Rex when the typhoon changed its stage from intensification to sustenance. SSC occurred behind and on the right side of the running typhoon (Fig. 5(a)). The appearance of SSC on the right side of the running typhoon is similar to previous observations (e.g. Black, 1983) and numerical studies (e.g. Price, 1981). However, SSC around the typhoon center can not be observed due to thick clouds of the strong typhoon. The day on August 29 corresponds to the stage of the typhoon when the translation of the typhoon is the slowest. The region of SSC is extended along the track of Typhoon Rex (Fig. 5(b)). In addition, a cooling region at the intersection between the track of Typhoon Rex and the course of R/V Keifu Maru is still remaining. Maximum SSC in Fig. 5(b) is over 6.9 C. The translation speed of Typhoon Rex on August 31 is again faster than that under the slowest translation on August 29. Maximum SSC in Fig. 5(c) is over 7.8 C which appeared at the place where the translation speed is the slowest. In conclusion, SSC under the slowest translation stage is the greatest through the generation, development, and sustenance stages of Typhoon Rex. In contrast, the SST deviation at the intersection becomes smaller after the typhoon passage. This shows that the SST increased in five days after the passage of Typhoon Rex. 4. Numerical Simulation during the Passage of Typhoon Rex Fig. 3. Time series of vertical profiles of sea temperature by CTD measurement at the fixed observed station (130 E, N) during the period from August 23 to August 26, Shaded area represents over 29 C. Contour interval is 0.5 C. 4.1 Initial conditions TRMM/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 SST are created by linear interpolation from Levitus climatology data (Levitus, 1982). Geostrophic currents are primary calculated as the initial ocean currents as described in Subsection 2.1. As for atmospheric initial conditions, global analysis (GANAL) data provided by the Japan Meteorological Agency (JMA), which horizontal resolution is 1.25 by 1.25, are used by linear interpolation. Atmospheric boundary conditions on the surface are updated every 6 hours during the numerical experiment. Atmospheric in- Fig. 4. Time series of maritime SST observed by R/V Keifu Maru during the period from August 24 to August 31. Numerical Simulations of Sea Surface Cooling of Typhoon Rex 45

6 (a) (b) (c) 150 deg deg deg Fig. 5. Horizontal distribution of SST deviation from the initial time, August 24 by TRMM/TMI. (a): SST deviation on August 27, (b): August 29, and (c): August 31. Open and shaded, circle and triangle marks are the same as Fig. 1. gredients using as initial and boundary conditions are air temperature, sea level pressure, and wind velocity in north-south and east-west components, which north and east components are positive. In fact, GANAL data can not reproduce realistic MSLP of Typhoon Rex due to the coarse resolution, which is the reason why we merged the typhoon-like vortex into the GANAL field (Wada, 2002a). In a practical sense, the typhoon-like vortex is created using a Rankin vortex introduced by Chang and Anthes (1978). Horizontal distribution of surface wind is primarily determined based on the maximum wind velocity of Typhoon Rex recorded by JMA best track data. Cloud cover, which is observed by R/V Keifu Maru every 3 hours, is used in the numerical experiment, assuming horizontally uniformly. Precipitation occurring concurrently with Typhoon Rex is neglected in this numerical experiment because rainfall around the eyewall and rainband of the typhoon is presumed to be rather heavy in comparison to the rainfall observed by R/V Keifu Maru. In addition, presumption of horizontal distribution of precipitation is difficult even in the atmospheric model. In fact, no precipitation data is supported by the GANAL dataset. 4.2 Numerical simulation A numerical experiment, which target is simulation of SSC during and subsequent to the passage of Typhoon Rex is performed using a mixed layer model. Detailed targets of the numerical simulation are the following: 1) To investigate a gradual decrease of maritime SST at the fixed station observed from August 24 to 27. 2) To investigate a rapid decrease of maritime SST observed at the intersection between the track of Typhoon Rex and the course of R/V Keifu Maru. 3) To reproduce a horizontal distribution of the cooling region on the sea surface along the track of Typhoon Rex. Time variations of observed and simulated SSTs at observational stations of R/V Keifu Maru are represented in Fig. 6. As for the target 1), a gradual decrease of SST observed from August 24 to 27 can not be simulated by the model of Wada (2002a) and the model in the present study compared to the observed SST. However, the gradual decrease of observed SST can be successfully simulated by the 1-dimensional mixed layer model by Wada (2002b) with observed atmospheric forcing at a 10- minute interval. Therefore, the unsuccessful simulation for the gradual decrease of SST is considered to be caused by the difference between GANAL wind velocities and observed ones. It is noted that wind-induced mixing hardly works well in the numerical experiment during the period of the target 1). As for the target 2), on the other hand, a rapid decrease of SST observed at the intersection between the track of Typhoon Rex and the course of 46 A. Wada

7 Fig. 6. Time series of maritime SST observed by R/V Keifu Maru (open circle), simulated SST by a mixed layer model (close circle), and simulated SST by Wada (2002a) (open triangle). Time unit is JST. (b) Fig. 7. Time series of atmospheric forcing at the observed station of R/V Keifu Maru. (a): Wind stresses in north-south (open circle) and ease-west (shaded circle) directions of which unit is N/m 2, (b): Solar insolation (shaded circle) in the right vertical axis, longwave radiation (open circle), sensible heat (square), and latent heat (cross) fluxes in the left vertical axis of which unit are all W/m 2. Downward radiation and fluxes show heating in the ocean. Numerical Simulations of Sea Surface Cooling of Typhoon Rex 47

8 Fig. 8. Contribution of the terms in the thermodynamic equation in the mixed layer to a SST variation at the observed station by R/V Keifu Maru. Open circles indicate an SST variation per hour caused by the sea surface flux. Cross marks indicate an SST variation caused by the divergent term. Shaded triangles indicate an SST variation caused by entrainment. The unit of the vertical axis is expressed as C per hour (a) (c) (b) (d) Fig. 9. Results of numerical simulation at 08 JST on August 31 during the passage of Typhoon Rex. (a) Horizontal distribution of SSC ( C) from the initial time, August 24. (b) Horizontal distribution of SSC ( C), (c) horizontal distribution of the depth of a mixed layer (m), and (d) horizontal distribution of depth at the base of a thermocline (m). 48 A. Wada

9 Fig. 10. Map of locations where the maximum SSC occurred. Shaded circle indicates the place where the maximum SSC occurred 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 Keifu Maru. R/V Keifu Maru is successfully simulated in comparison to the result of Wada (2002a). However, both computed SSTs under-evaluate compared to the observation because the location of Typhoon Rex in the GANAL data on August 24 is erroneous. Atmospheric forcing at the observed stations of R/V Keifu Maru is shown in Fig. 7. Wind stresses were comparably stronger on August 24, which were caused by generation of Typhoon Rex. However, wind stresses were less than 0.1 N/m 2 from August 26 to 31 (Fig. 7(a)). Solar radiation varied with diurnal cycle, while longwave radiation and latent heat fluxes were less than 200 W/m 2 and sensible heat fluxes were much less than latent heat fluxes (Fig. 7(b)). As for the net heat flux, solar radiation is more dominant during the day than any other fluxes on the surface. In order to check each contribution of physical processes, the amount of SST variations per hour at the observed station by entrainment, heat flux and divergence terms is investigated in Fig. 8. The SST rose during the day with the diurnal cycle of solar radiation. In contrast, the entrainment works well during the night and probably deepen the mixed layer. The net heat flux without solar radiation works as an enhanced SSC. This implies that the unstable vertical profile by buoyancy flux inside the mixed layer is responsible for enhancing an entrainment process. Heat loss on the sea surface drives penetrative convection that deepens the mixed layer thickness, while mixing depth is progressively inhibited by solar heating during the day (Denman and Gargett, 1995). The rest of the physical processes expressed as the divergence term is called advection in this study. This is too small compared to that of the net heat flux and entrainment, which is consistent with the result of idealized numerical experiments by Wada (2002a). To sum up the results at the observed station of R/V Keifu Maru, nevertheless, it is found that the rapid decrease of SST at the intersection between the track of Typhoon Rex and the course of R/V Keifu Maru can not be produced by instant atmospheric forcing. As for target 2), therefore, it was considered that the rapid decrease of SST was already been produced before R/V Keifu Maru arrived at the place. For the purpose of verifying target 3), horizontal distributions on August 31 of the SST deviation from the initial time (Fig. 9(a)), the SST itself (Fig. 9(b)), the mixed layer depth (Fig. 9(c)), and the depth at the base of a thermocline (Fig. 9(d)) are represented. The maximum negative deviation of simulated SST from the initial time was nearly 6 C around E and N, which was smaller than that of the observed SST by TRMM/TMI (Fig. 5(c)). Characteristic of the distribution of SST deviation shown in Fig. 5(c), namely appearance of a region where salient SSC occurred, is similar to Fig. 9(a). Figures 9(a) and (b) indicate that SST anomalies are located on and around the track of Typhoon Rex, in particular on the right side of the running typhoon. At the same time, a mixed layer on and around the track of Typhoon Rex deepened, in particular on the right side of the running typhoon (Fig. 9(c)). It is considered that a variation of mixed layer thickness corresponds to that of the SST under an enhanced entrainment process. Not only the entrainment process but also an upwelling process is important for producing SSC (Chang and Anthes, 1978; Price, 1981; Wada, 2002a). The elevation at the base of the thermocline shown in Fig. 9(d) reveals the upwelling region where maximum SSC occurred. This upwelling region is related to the slow translation stage of Typhoon Rex. How salient SSC observed by R/V Keifu Maru and by TRMM/TMI was produced? Figure 10 represents the positions where the maximum SSC occurred in the numerical simulation. In the early integration, when the stage of Typhoon Rex is a tropical depression, the positions of maximum SSC is far from the track of Typhoon Rex because wind velocity of GANAL is greater than that of Rankin vortex. As the integration goes on, the positions of maximum SSC are situated just under the track. Then, the positions are shifted on the right side of the running typhoon. As the typhoon moves slower, the position again turns to be situated just under the track. Finally, the position hardly changes although the typhoon moves with a faster translation. At the position of maximum SSC, a contribution of the entrainment term is dominant for SSC, in particular on August 26 and 27, which is in agreement with the place where the positions of maximum SSC are situated on the right side of the typhoon (Fig. 11). The place is also including the intersection between the track Numerical Simulations of Sea Surface Cooling of Typhoon Rex 49

10 Fig. 11. Same as Fig. 8 except for the location where the maximum SSC occurred in the results of the simulation during the passage of Typhoon Rex by the mixed layer model. of Typhoon Rex and the course of R/V Keifu Maru taken as target 2). In contrast, contributions of the net heat flux term and the advection term are smaller than that of the entrainment term. In contrast, even under conditions of strong intensity of Typhoon Rex and enhanced SSC, a contribution of the entrainment term at the slower translation stage is comparably smaller than that on August 26 and 27. We must emphasize the contribution of upwelling at this stage for producing salient SSC shown in Fig. 9(d). The upwelling is also related to the position of the maximum SSC. Leipper (1967) reported that SSC by Hurricane Hilda appeared on the left side of the moving direction. 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 direction. In the present paper, the position of the maximum SSC caused by Typhoon Rex depends on its stages. In each stage of the typhoon, the contribution of entrainment and upwelling for SSC is different. 4.3 Nondimensional analysis As described earlier, physical processes of SSC during the passage of a tropical cyclone are caused by entrainment and upwelling (Price, 1981; Wada, 2002a). In this section, the relationship between the ocean response during the passage of the typhoon and internal (oceanic) or external (atmospheric) factors is investigated using three nondimensional variables: a nondimensional storm speed, a Burger number, and a Rossby number, which are all introduced by Price et al. (1994). Price et al. (1994) suggested a representative value for each hurricane. However, the nondimensional variables should be changed in response to the stage of a tropical cyclone because a tropical cyclone has various stages of genesis, development, sustenance, and lysis (change to extratropical cyclone). The nondimensional storm speed (S) is S πu 4 fr = H, () 3 max where U H is a translation speed, f is the Colioris parameter, and R max is a radius of maximum wind velocity. For example, typical values of U H = 5 m/s and R max = 50 km imply that S is O(1). This variable represents a ratio of a local inertial period to a tropical cyclone residence time. Wind stresses observed from the ocean change on a time scale comparable to the local inertial period (Price et al., 1994). The lower S implies that the size of a tropical cyclone is larger or the translation is slower. In the case of a larger and slower tropical cyclone, we expect that the ocean response will be stronger. On the other hand, a tropical cyclone with a smaller size or a faster translation speed has a larger S, which characterizes strong inertial and asymmetric motions across the track (Wada, 2002a). In the case of Typhoon Rex, S has the maximum value on August 28 of which maximum value is 1.9. It is lower than 2.4 in Hurricane Norbert and is higher than 0.8 and 1.1 in Hurricane Josephine and Hurricane Gloria, which were all investigated by Price et al. (1994) (Fig. 12(a)). Roughly the value S is lower from August 29 to August 30 when the translation of Typhoon Rex becomes slower and its intensity becomes stronger. During the time, the additional SSC of nearly 1 C is simulated (Fig. 12(a)). On the other hand, Fig. 12(a) implies that the value S is irrelevant to the rapid decrease of the SST that occurred from August 26 to 28. Therefore, the additional SSC of nearly 1 C from August 29 to August 30 can be explained by the effect of the typhoon translation although we can not explain the salient SSC from August 26 to 28 using the nondimensional storm speed S. In order to resolve the mechanism of the salient SSC, another factor is required. 50 A. Wada

11 (a) (b) (c) Fig. 12. Time series of (a) the nondimensional storm speed S, (b) the Berger number B, and (c) the Rossby number Q. The cross indicates the amount of maximum SST cooling. The left axis indicates the scale of S, B, and Q while right axis indicates deviation of SST from the initial condition for the comparison. The Burger number (B) is B gh 4 f R max =, ( 4 ) where g is the reduced gravity and h 1 is a mixed layer thickness where the maximum SSC occurred. The Burger number B represents a direct measure of the pressure coupling between currents in the mixed layer and those in the thermocline. The large number of B is an evidence of enhanced pressure coupling connected with the dynamics at the relaxation stage. Stronger wind stresses are required for a mixed layer to become deepening. Therefore, the Burger number B is considered to represent a scale of turbulent mixing due to entrainment. In the case of Typhoon Rex, the Burger number increases from August 25 till August 27, which agrees to the period when SST suddenly decreases from August 26 to 28 (Fig. 12(b)). The maximum Burger number of Typhoon Rex is nearly 0.12, which is higher than that in Hurricane Josephine (0.04) and Hurricane Gloria (0.02), and is lower than that in Hurricane Norbert (0.37) (Price Numerical Simulations of Sea Surface Cooling of Typhoon Rex 51

12 Fig. 13. Time series of SST deviations from the observation by R/V Keifu Maru. The shaded circle indicates SST deviations derived 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). et al., 1994). The Burger number is maintained from 0.06 to 0.12 from August 28 to 30. Note that the Burger number decreases after 18 JST on August 28. It is because Typhoon Rex moves far away that the region of SSC is irrelevant to in-situ atmospheric forcing. The Rossby number (Q) is Q τ, 5 ρ 0 hu 1 f = ( ) where τ is magnitude of the wind stress. Q represents a ratio of horizontal momentum wind forcing to the Coriolis force. The higher Rossby number represents the ocean response 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 to that of enhancing upwelling. Figure 12(c) shows that the Rossby number has a maximum value of 1.2 on August 30, which is higher than a value of 0.7 in Hurricane Norbert and 0.2 in Hurricane Josephine and Hurricane Gloria (Price et al., 1994). The maximum value of Rossby number occurred during the period when SST suddenly decreases again. Therefore, this sudden decrease of SST from August 29 to 30 is caused by upwelling, while the upwelling does not play a significant role in the sudden decrease of SST from August 26 to 28. The nondimensional storm speed S, the Burger number B, and the Rossby number Q all depend on both stages of Typhoon Rex. In the case of Typhoon Rex, there are two stages when the ocean response during and subsequent to the typhoon is enhanced. One stage is linked H to intensification of Typhoon Rex. The other stage is related to the slowest translation of Typhoon Rex. In the stage when Typhoon Rex becomes stronger, a contribution by entrainment for SSC is dominant. However, the area where maximum SSC occurred shifts to the running direction as Typhoon Rex is moving. On the other hand, the Burger number and the Rossby number keep high values under the low nondimensional storm speed S under the slowest translation of Typhoon Rex. Under the slow translation, the depth in the mixed layer deepens nearly at the same place. At that time, upwelling is enhanced just behind Typhoon Rex in spite of simultaneously occurrence of the entrainment process. Once SSC is enhanced by upwelling, a cooling area is still remaining, even when Typhoon Rex moves far away with a low Berger number. 5. Intercomparison of Entrainment Schemes In this section, intercomparison of entrainment schemes introduced in Subsection 2.3 is implemented applying the mixed layer model to the case of Typhoon Rex under the same atmospheric and oceanic conditions. Actually, the entrainment rate plays an important role in the ocean response to a typhoon. Figure 13 shows deviations of SSTs simulated by the mixed layer model with different entrainment schemes from the maritime SST by R/V Keifu Maru at the equivalent time. All entrainment schemes used in this study tend to numerically evaluate the SSTs higher till August 27, and lower from August 29 than the maritime SSTs. The former corresponds to the period of target 1) described in the previous section. In the latter period, R/V Keifu Maru went back to Japan across the Kuroshio region. The deviation in Fig. 13 var- 52 A. Wada

13 CA CA (a) (a) EL EL (b) (b) PR PR (c) (c) Fig. 14. Same as Fig. 9(a) except for (a) entrainment parameterization by Chang and Anthes (1978) (CA), (b) by Elsberry et al. (1978) (EL), and (c) by Price (1981) (PR). Fig. 15. Same as Fig. 9(c) except for (a) entrainment parameterization by Chang and Anthes (1978) (CA), (b) by Elsberry et al. (1978) (EL), and (c) by Price (1981) (PR). Numerical Simulations of Sea Surface Cooling of Typhoon Rex 53

14 ies from August 28 to 29 when Typhoon Rex has gone on the left side of the ship track of R/V Keifu Maru (Fig. 1). During this period, two peaks of the minimum SST deviation are easily recognized. One peak implies that the model with EL entrainment scheme can not simulate sudden cooling of the sea surface at around 00 JST on August 29. The other peak means that the computed SST by PR scheme is recovered to warmer water earlier than the maritime SST. As for target 1) and target 2), the model with DF entrainment scheme has the best performance, although the model with CA entrainment scheme provides comparative results. As for target 3), Fig. 14 indicates respectively horizontal distributions of SST deviation on August 31 from August 24 by CA, EL, and PR schemes. The distribution by 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 and the area where SSC is produced. In the case of the EL scheme (Fig. 14(b)), the cooling area is comparable to that by DF, CA, and TRMM/TMI. Nevertheless, the magnitude of maximum SSC is too small against that by DF, CA, and TRMM/TMI. As for the small evaluation of SSC in the EL entrainment scheme, the mixing factor of CA is approximately double compared to that of EL according to Chang and Anthes (1978). In other words, SSC by EL is under-evaluated compared to that by CA. In the case of PR scheme (Fig. 14(c)), the magnitude of maximum SSC is plausible, while the cooling area is too narrow and 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 important factor to evaluate the performance of the entrainment scheme because the mixed layer deepens due to entrainment. Figure 15 indicates horizontal distributions of 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)), but the magnitude of mixed layer thickness by CA is deeper than that by DF. As for the mixed layer depth, no observed data can verify the validity of the entrainment scheme in the present study. In the case of the EL scheme (Fig. 15(b)), not only magnitude of the mixed layer thickness is smaller but also the horizontal distribution of the depth in the mixed layer is different from the typical pattern introduced by Ginis (1995). In the case of PR schemes, the deepest area in the mixed layer is concentrated along the track of Typhoon Rex so that this is different from the typical pattern by Ginis (1995), too. The latter result suggests that the PR scheme can not simulate the salient rightward bias of the mixed layer depth. However, Price (1981) suggested that a PR scheme somewhat enhanced the asymmetry in the SST response, while a CA scheme yielded a symmetric SST response to a symmetric storm. This implies that the ocean response to a typhoon depends not only on its stages but also on the horizontal structure of wind velocity including the size of the eye and the distance of maximum wind velocity, which is related to the distribution of current shears. These factors can also influence the estimation of nondimensional numbers shown in the previous section. The above examination shows that the DF scheme is the best performance of four schemes in target 3) introduced in the previous section. As for target 1), frictional velocity and buoyancy effects included in the CA, EL, and DF schemes are significant to evaluate not only the gradual SST variation, but also the SST deviation widely recognized around the Typhoon Rex. The wide area of SSC, which is similar to the area shown in Fig. 5(c) or Fig. 9(a) can be simulated in the cases of CA and EL schemes. However, the rapid SST decrease on August 29 (Fig. 13) can not be quantitatively simulated due to overdeepening of the mixed layer in the case of the CA scheme. On the other hand, as for target 2), the effect of current shear included in PR and DF contributes to the sudden SSC and horizontal sharp gradient of SSC. In fact, the magnitude of SSC by PR scheme is the greatest of four schemes. In addition, a cooling region by the passage of Typhoon Rex is too narrow in comparison to the region by TRMM/TMI. However, the wide area and asymmetric distribution of SSC shown in Fig. 5(c) can not be simulated in a PR entrainment scheme. As for target 3), both factors of target 1) and target 2) are required so that the DF scheme has the best performance for the SSC simulation by the passage of Typhoon Rex. These results are in agreement with those described by Jacob and Shay (2003), i.e., the DF scheme predicted intense entrainment due to enhanced shears; whereas the response is broader and weaker in a CA-like scheme. However, the effect of radiation fluxes on the sea surface is not included in the result of Jacob and Shay (2003). In addition, the priority of this study for Jacob and Shay (2003) is reliable evaluation of contribution of the sources of turbulent kinetic energy to each entrainment scheme for the SSC, using not only the computed SSTs but also ship and TRMM/TMI SST data. Note that no salient difference of elevation at the base of the thermocline is detected by four schemes (not shown). This reveals that the vertical velocity of four schemes at the base of the thermocline is all almost alike in Fig. 9(d). This result is in agreement with that of O Brien and Reed (1967). The strong upwelling caused by wind stresses is irrelevant to the entrainment process. 6. Summary and Discussion Numerical simulations during the passage of Typhoon Rex by a mixed layer model were carried out to investigate the ocean response to Typhoon Rex using the 54 A. Wada

15 realistic forcing field based on global analysis data, best track data of Typhoon Rex, and ship observation. The formation 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 this study. Applying the mixed layer model with a realistic atmospheric 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, can be much improved compared to results by Wada (2002a). The horizontal distribution of SSC by the mixed layer model is similar to the distribution of SST observed by TRMM/TMI. Local SSC along the track of Typhoon Rex is quite evident in the simulated and observed distribution of SST deviations. A rapid decrease of maritime SST by R/V Keifu Maru at the intersection between the track of Typhoon Rex and the course of R/V Keifu Maru is not produced by instant atmospheric forcing at the observational station but is produced by strong wind during the passage of Typhoon Rex and remaining at that place after its passage. The place of the maximum SSC varied from just under the typhoon to the right side of the typhoon in accordance with the stage of Typhoon Rex, i.e., intensification or maintenance stages. From the analyses of three kinds of nondimensional number, formation mechanism of SSC in the case of Typhoon Rex is proposed. A rapid SST decrease observed by R/V Keifu Maru is caused by enhanced entrainment, while SSC under the slow translation is induced not only by entrainment but also by upwelling. In the area where upwelling is greatly enhanced, maximum SSC is remaining in a sustainable way. In contrast, the area of maximum SSC moved to the right side of the typhoon when entrainment is greatly enhanced. Under a non-stormy condition, solar radiation dominates a variation of SST directly. However, the contribution of heat fluxes for SSC is comparably small under a stormy condition. The results are consistent with the idealized numerical experiment (Price, 1981; Wada, 2002a) and the observation (D Asaro, 2003). The transition of physical processes from only entrainment to both entrainment and upwelling is determined by the stage of a typhoon, intensification or maintenance stages. Not only the amount of SSC but also the place of the maximum SSC is related to the stage of a typhoon. Intensification and translation of a typhoon play an important role for the ocean response to the typhoon. Intercomparison of entrainment schemes by Chang and Anthes (1978), Elsberry et al. (1976), Price (1981), and Deardorff (1983) is implemented using a mixed layer model in the case of Typhoon Rex. The computed SSTs are compared with the observed time series of SST variation 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 scheme has the best performance of the four examined entrainment schemes. In addition, contributions of three sources of turbulent kinetic energy for the ocean response to Typhoon Rex are investigated. The sources are frictional velocity, buoyancy flux, and current shear. The entrainment scheme derived from frictional velocity and buoyancy flux is responsible for the wide area of SSC. In contrast, the scheme derived from current shear at the base of the mixed layer can simulate a realistic amount of SSC and a sharp horizontal gradient of SST distribution formed along the track of typhoon. These features are in agreement with those reported by Jacob and Shay (2003), however Jacob and Shay (2003) do not include the atmospheric radiation effect. In the Deardorff s entrainment scheme, these three physical effects are incorporated into the scheme. Therefore, both wider and greater SSCs can be simultaneously reproduced by the Deardorff s model. Note that the entrainment scheme derived from only current shear like Price (1981) can produce the realistic horizontal gradient of SST deviation, which is more similar to that by TRMM/ TMI than that by Deardorff s model. D Asaro (2003) suggested from the observation that much more cooling should occur because of much larger inertial currents and shear on the right side of the running storm. This means that the entrainment rate derived from current shear may be under-evaluated when the current velocity is unsuccessfully simulated. In other words, more realistic SSC simulation can be realized in the present study if the current velocity is successfully simulated. Nonetheless, the effect of the frictional velocity and the buoyancy flux is required for entrainment parameterization to express the wider deviation of SSTs. In order to improve the prediction of ocean currents using the present model, more accurate atmospheric forcing, sufficient spin-up time, installation of realistic topography, and high accuracy of advection scheme will be required. In addition, atmospheric forcing updated every six hours except around the typhoon obtained from GANAL data is too coarse in temporal and spatial resolution. Weak wind stresses are responsible for under-validation of ocean currents and current shears. The horizontal structure of a typhoon such as the size of the eye and the radius of maximum wind velocity is important for the ocean response to a typhoon. Otherwise, if spin-up procedure is made complete with realistic topography and high accuracy of advection scheme, the interaction between the ocean response to a typhoon and a western boundary current like Kuroshio can be clarified. The effect of precipitation on the sea surface required for a variation of salinity is important for the upper ocean response to a typhoon. According to Pudov and Numerical Simulations of Sea Surface Cooling of Typhoon Rex 55