Impact of Surface Exchange Coefficients and Sea Surface Cooling on Tropical Cyclone Simulation

The boundary layer is the key region in which tropical cyclones (TCs) interact with the ocean. In this layer, abundant heat and moisture are transported to the low-level atmosphere for TC's development, and the momentum is transported to the ocean to excite ocean currents. The warm ocean at the lower boundary is what supplies the moist static energy to maintain the latent heat release in the eyewall. Any change or perturbation of this lower boundary can potentially greatly affect TC intensity and structures. The thermodynamic and dynamic structure of the lowest part of hurricanes has a large impact on the intensification of storms. This region of a storm is directly affected by the surface processes (friction, fluxes, etc.) to adjust to the changes in the surface properties, but it also affects the evolution of these surface properties. Thus, as hurricanes and typhoons are an extreme case of air-sea interaction, it is crucial to understand the processes happening at the interface.

Since hurricane boundary layer (HBL) is a layer which connects sea surface to TC vortex, controls the radial distribution of moisture and vertical motion, and brings in the momentum that ascends into the eyewall. The physical processes of air-sea interaction associated with the HBL have been investigated in previous studies. On the one hand, earlier studies (Large and Pond^[1]; Smith^[2]; Geernaert^[3]) evaluated the 10-m wind drag coefficient (C_d) for wind speed up to 25 m s^-1 in the HBL of the open ocean. They found a linear increase of the C_d with wind speed. Frank ^[4] performed a budget study of the hurricane boundary layer, which suggested that C_d given by Large and Pond^[1] was too large if extrapolated to high winds. Simulation results with an axisymmetric TC model showed that both the maximum azimuthal wind speed and the central pressure deficit of TC depend on the ratio of enthalpy to momentum exchange coefficients (C_k / C_d) (Emanuel^[5]). His study showed that the ratio C_k / C_d must be above 0.75 to have TC development. However, the C_k / C_d ratio estimates from the Coupled Boundary Layer Air-sea Transfer (CBLAST) measurements are around 0.7 for tropical storm conditions (Black et al.^[6]). Andreas and Emanuel^[7] suggested that the C_d values might increase simultaneously at the wind values during the CBLAST. However, the CBLAST experiment seems to indicate that C_d does not increase without limit with increasing wind speed. An observational study (Powell et al.^[8]), using over 331 wind profiles from global positioning system dropwindsondes of the mean boundary layer in the vicinity of hurricane eyewall, seems to indicate that the drag coefficient is much less than previously thought in winds above 33 m s^-1. By estimating the drag coefficient in a wave tank, Donelan et al. ^[9] found that C_d approaches an asymptotic limit for winds over 30 m s^-1. A measurement of C_d in hurricane conditions shows that the momentum exchange coefficient levels off at wind speed around 23 m s^-1 (French et al.^[10]) which is about 10-12 m s^-1 less than the hurricane force threshold of 33 m s^-1 obtained by Powell et al.^[8] (2003) and Donelan et al.^[9]. The current observations do not support the increasing C_d and C_k with high wind speed.

On the other hand, some studies show that the intensity of TCs is controlled by the dynamic and thermodynamic properties of the atmosphere and upper ocean along the storm track (Emanuel^[11]; Bender and Ginis^[12]; Wada et al.^[13]; Karnauskas et al.^[14]). It has been recognized that the fundamental source of energy for hurricanes is heat transfer from the ocean, but the wind stress imposed on the upper ocean by the storm can limit the intensification through the surface cooling due to the entrainment of subsurface cooler water into the upper ocean mixed layer (OML). The storminduced upper ocean responses have been described by a lot of observational and numerical studies. The first simulation of a hurricane using a coupled oceanatmosphere model showed little effect of the ocean feedback on storm intensity (Chang and Anthes^[15]). Price^[16] explained the mechanism of storm-induced sea surface temperature (SST) cooling as a result of vertical entrainment associated with wind-driven vertical current shear in the upper ocean. Typically, 60%-80% of TC-forced SST cooling results from the entrainment of deeper cold water into the OML due to shear-driven turbulence base resulting from the strong baroclinic near-inertial currents forced by the storms. As this near-inertial current veers to the right, it is mostly aligned with the wind stress in rear-right quadrant relative to a storm motion, thus causing the strongest cooling there. In this regard, the storminduced cooling and its associated effect are asymmetrical. Following Price' s work, several numerical studies have found that such surface cooling is a self-limiting factor for TC intensification by reducing surface enthalpy fluxes (Schade and Emanuel^[17]; Bender and Ginis^[12]). The study on the ocean feedback, which used an advanced higher resolution coupled model showed that ocean feedback has a first-order effect on hurricane intensity (Schade and Emanuel^[17]). Upper ocean processes cause the SST to cool mostly through a combination of mixing and upwelling processes, which in turn alters available heat for the storm's maintenance. The SST field under the tropical cyclone is often not uniform spatially either.

Since this shear-induced mixing is a onedimensional (1D) process, some studies suggest that coupling a 1D ocean model to a hurricane model may be sufficient for capturing the storm-induced SST cooling in the region providing heat energy to the hurricane (Anderson et al.^[18]; Lin et al.^[19]; Bender et al.^[20]; Davis et al.^[21]). Both the initial SST and the magnitude of the wind-induced sea surface cooling below the hurricane can modulate the intensity of hurricane (Shay et al.^[22]; Cione and Uhlhorn^[23]; Liu et al.^[24]; Balaguru et al.^[25]). The SST cooling was tightly related to the wind-induced mixing (Ginis^[26]; Sun et al.^[27]; Wei et al.^[28]; Liu et al.^[29]). As the winds increase, the surface stress and the vertical mixing in the upper ocean increases, leaving a stronger SST cooling. As illustrated by the recent CBLASTHurricane measurements in Hurricane Frances (2004), from oceanic floats, after the passage of the strong winds over the ocean surface, the horizontal heat fluxes in the upper ocean tend to reduce the deepening of the mixed layer, indicating a transition of the boundary layer heat budget from vertical to threedimensional (Black et al.^[6]). The reduction of the upper ocean temperatures via surface heat fluxes and vertical mixing under the hurricane passage reduces the available heat energy for further intensification of the storm. During the CBLAST-Hurricane experiment, Black et al.^[6] found the most intense cooling to the right of the center of Hurricane Frances (2004) with a cold wake spreading outward behind this region. The leading edge of this wake forms an SST front approximatively 50 km wide, which moves with the storm. The SST cooling rate depends on factors such as upper-ocean warm-layer thickness, upper-ocean stratification, and storm propagation speed. Consequently, both the initial temperature and the thickness of the upper-ocean warm layer are important factors in determining the oceanic contribution to TC intensity. Furthermore, the numerical study by Chan et al.^[30] indicates that the TC intensity is more sensitive to the OML depth if it is less than 50 m. The OML depth of the ocean model coupled should be set to appropriate value to capture the effect of SST cooling induced by wind forcing of TC. Noting that the OML in the coastal region is less than 50 m.

Upper ocean structures and exchange coefficients are particularly important to the evolution and maintenance of TCs. It is necessary to understand the impact of air-sea interaction on the simulations of TCs. The purpose of this study is to investigate the impact of exchange coefficient and the feedback of upper ocean on the intensity and structures of Typhoon Saomai (2006). The paper is organized as follows. The description of Typhoon Saomai and the numerical experiments are introduced in Section 2. Section 3 verified the numerical results to various observations, and Section 4 presents the simulated typhoon intensity and structure. Section 5 gives the discussion and conclusion.

On 4 August 2006, a tropical depression near the southeast of Guam grew to a tropical depression, which is the precursor of Typhoon Saomai (2006). Then the tropical depression moved northwestward over the Northwest Pacific. Under the support of warm water of the Northwest Pacific, it intensified quickly and strengthened to typhoon at 0600 UTC 7 August. The typhoon continued to intensify rapidly, and became a super typhoon with the maximum wind speed of 51.4 m s^-1 on 0600 UTC 9 August. Subsequently, Saomai made a landfall on Cangnan of Zhejiang Province at 11 UTC 10 August as a super typhoon with the minimum sea level pressure (MSLP) of 920 hPa and maximum surface wind speed of 60 m s^-1. After moving westward and moving through Fujian and Jiangxi Provinces, Saomai finally decayed in Hubei Province. The best track of Saomai (2006) from the Japan Meteorological Agency (JMA) is shown in the black line of Fig. 1.

Figure 1.  Tracks of Typhoon Saomai from the best track analysis (every 6-h) by the JMA and the model simulations (every 6-h) from 0000 UTC 08 August to 1200 UTC 10 August 2006.

For numerical simulations, the Advanced Research Weather Research and Forecasting Model (ARW) modeling system version 3.1 is used (Skamarock et al.^[31]). The three-dimensional simulations use two-way interactive nesting in two domains with the outer domain called D1 and the inner domain called D2. Detailed information about the grid and parameterization schemes can be found in Table 1. The integral period of the outer domain D1 covers the entire period from the time when Saomai reached typhoon intensity to its landfall, and D2 starts one day later than D1. D2 is an automatic vortex-following moving nest grid so that the center of the domain is always located at the center of the typhoon. Details of the vortex in D2 is the same with the setting in Ming et al.^[32].

The initial and boundary conditions for numerical experiments are provided by the JMA Regional Spectral Model's (RSM) reanalysis field with a horizontal resolution of 20 km × 20 km and a time interval of 6 hour (JMA^[39]; Hosomi^[40]). Because the analysis does not contain an adequate representation of the initial hurricane vortex, a bogusing technique, which is provided by the ARW modeling system, is used. The TC bogusing scheme can remove an existing tropical storm, and bogus in a Rankine vortex for the new tropical storm. The values of maximum wind speed, and radius of maximum wind prescribed for the bogus vortex are 38.5 m s^-1 and 25 km. The model physics options are the same for two domains. There are no cumulus parameterization schemes for two domains.

In this study, four experiments are designed to examine the effects of exchange coefficients and airsea interaction on the typhoon intensity and structures. Details of four experiments are listed in Table 2. In the first experiment (i. e., CTL), the Charnok formula for the surface roughness (z₀) is used to account for the effects of increasing roughness on the turbulent boundary layer over the ocean (Charnok^[41]). The Charnok formula is defined as:

where c_z0=0.0185 and o_z0= 1.59 × 10^-5; u_* is the friction velocity; g is the gravitational acceleration. Then the drag coefficient in the neutral condition can be defined as:

where k is the Von-Kármán's constant. The 10-m drag coefficient increase as the wind speed increases. Furthermore, the formula of enthalpy exchange coefficient (C_k) is:

where z₀ is roughness length, z_0q is thermal roughness length, and k is the Von-Kármán's constant. C_k is parameterized through z₀ and a separate thermal roughness length z_0q with different formulas which are Carlson-Boland scheme (Carlson and Boland^[42]). The Carlson-Boland scheme is defined as:

where xka is a constant that equals 2.4 × 10^-5 and u_* is the friction velocity. The changing rate at which C_k varies with wind speed is slower than that of C_d because that the thermal roughness length is more slowly varying than the roughness length does.

In the second experiment (i.e., TC1), an alternate drag formulation based on the high-wind laboratory studies of Donelan et al.^[9] was adopted. It produces values of C_d lower than those from the Charnok relation for low winds with a linear increase up to a maximum near 0.0024 at about 35 m s^-1. The roughness length can be defined as:

where z₀ is limited to within the range of values 1.27 × 10^-7 ≤ z₀ ≤ 2.85 × 10^-3. Furthermore, the thermal roughness length uses the ramped formula (Dudhia et al.^[43]). The ramped formula is defined as:

C_k is almost linearly with wind exceeding the value of C_d beyond about 50 m s^-1. Hence the ratio C_k / C_d exceeds one as the wind speeds increase much above 50 m s^-1. As expected, this has an effect of significantly intensifying the storms where wind speeds may exceed 70 m s^-1 (Dudhia et al.^[43]).

In the third and fourth experiments, the ARW is coupled with a simple mixed layer ocean model and uses the same formula of roughness length and thermal roughness length as the second experiment. The ocean mixed-layer model is based on Pollard et al.^[44] and is designed for hurricane modeling in order to simulate the cooling of the ocean underneath hurricanes. Each column is independently coupled to the local atmospheric column, so the ocean model is onedimensional (1D). The ocean part consists of a timevarying layer, representing the variable-depth mixed layer over a fixed layer acting as a reservoir of cooler water with a specified thermal lapse rate. In the mixed layer, the prognostic variables are mixed layer depth, vector horizontal current, and mean temperature taken to be the SST. The hurricane winds drive the current, which in turn leads to mixing at the base of the mixed layer when the Richardson number becomes low enough. This mixing deepens and cools the mixed layer, and hence the cooler SST impacts the heat and moisture fluxes at the surface, and has a negative feedback on hurricane intensity. The model includes Coriolis effects on the current, which are important in determining the location of maximum cooling on the right side of the hurricane track. It also includes a mixed-layer heat budget, but the surface fluxes and radiation have much less impact than the hurricaneinduced deep mixing on the thermal balance at the time scales considered during a forecast. The ocean mixed layer model is initialized using the observed SST for the mixed layer. The initial current is set to zero, which is a reasonable assumption given that the hurricane-induced current is larger than pre-existing ones.

The ocean mixed-layer model initialized with two variables: the mixed layer depth and the ocean lapse rate beneath the mixed layer. In the third experiment (i. e., TC1 COUPLED 70), these two variables are initialized with constant value across the domain. The mixed layer depth is 70 m, which is used in Nolan et al.^[45]. And the value of ocean lapse rate beneath the mixed layer is 0.14 K m^-1, which was used by Davis et al. ^[21] in their evaluation of the ocean mixed layer model. The SST is initialized with daily TRMM (the tropical rainfall measuring mission) TMI (microwave imager)/ AMSR-E (the advanced microwave scanning radiometer for the earth observing system) data combined with weekly optimum interpolation SST analysis. In the fourth experiment (i. e., TC1 COUPLED), the mixed layer depth is not a constant. The mixed layer depth can be calculated using the three-dimensional data from the Hybrid Coordinate Ocean Model (HYCOM, Bleck et al.^[46]). The data from HYCOM is a global analysis field with data assimilation at 1 / 12° resolution. Fig. 2 displays the distribution of mixed layer depth on 07 July 2006. It has more realistic structures than the constant mixed layer depth, especially in the coastal region. The SST and the value of ocean lapse rate beneath the mixed layer are the same as the third experiment.

Figure 2.  The initial mixed layer depth (m) from HYCOM on 07 August 2006. The magenta line shows the track of Saomai (2006) from the best track data by the JMA.

Figures 1 and 3 compare the simulated track and intensity (including the minimum sea level pressure (MSLP) and the maximum surface wind speed) from all four experiments with the JMA best track from 0000 UTC 08 August to 1200 UTC 10 August. The simulated tracks in four experiments almost overlap and show the same west-northwestward track as the JMA best track. However, all the tracks are shifting a slightly northward (Fig. 1). Given that the track of TC is dominated by the steering flow produced by the background circulation on the upper layer, the similar simulated tracks mean that the large scale circulation is similar in all four experiments. Overall, the simulations of tracks are not sensitive to new formula of exchange coefficient and coupling processes between the atmosphere and the ocean in the ARW model. However, the simulation of intensity forecasts are significantly different after the maximum wind speed exceeds 40 m s^-1, where the new formula has effect on the intensity (Fig. 3). Before the wind speed exceeds 40 m s^-1, storms in all four experiments intensify rapidly. Afterward, the storms of TC1 and TC1 COUPLED 70 experiments over-intensify when they move into the coastal region. But CTL and TC1 COUPLED experiments produce similar MSLP and closed to the best track. Especially the MSLP of TC1 COUPLED has the same trend as the best track data. Furthermore, the maximum wind speed of four experiments has the same feature as the MSLP. In the coastal region, TC1 COUPLED experiment has the ability to reproduce the intensity of typhoon. By comparing the intensity of CTL and other three experiments, it can be concluded that the new formula of roughness length and thermal roughness length used in later three experiments tends to strengthen the storm, especially when the wind speed exceeds 45 m s^-1 in this case. Moreover, given that the storms in TC1 COUPLED and TC1 COUPLED 70 are weaker than TC1, the feedback of upper ocean responses to TC intensity can be seen clearly. However, there is tiny difference between TC1 and TC1 COUPLED 70, suggesting a weak feedback of upper ocean on the storm in TC1 COUPLE 70. The depth of mixed layer depth is 70 m, and thus the cooler water beneath mixed layer cannot be mixed with warm water. The mixed depth from the HYCOM data in Fig. 2 also shows that the 70 m depth of mixed layer in research area is too deep and unrealistic. The effect of upper ocean, especially the SST cooling, will be discussed in the next paragraph in detail.

Figure 3.  Time series of (a) maximum surface wind speed (m s^-1) and (b) minimum sea level pressure (hPa) of Saomai in model simulations and the best analysis by the JMA.

Figure 4 shows the SST anomaly at 0000 UTC 10 August 2006 in observation and coupled model simulations. A well-defined cold wake approximately 150 km in width is created, as the observed SST anomaly from TRMM TMI/AMSR-E data, to the right of the storm track during the first day of the TC1 COUPLED simulation. When the storm moved into coastal region, the cold wake becomes widely distributed. The maximum SST cooling is almost 4℃ and occurs to the right of the storm track. The maximum cooling in TC1 COUPLED is stronger than the observation. Furthermore, the model-simulated lateral width of the cold wake is somewhat larger than observation before the storm landfall. It should be noted that the range of SST cooling is not confined to the right side of track but extends to the left of the track in both observation and TC1 COUPLED. It is similar as the traditional opinion of the cooling should be shifted to the right of the storm track (Price^[16]), and the rightward bias in the SST cooling is a result of the rightward bias in the shear induced turbulent mixing in the water column. As for TC COUPLED 70, it is not surprising that the SST cold wake is weak and tiny, because the value of mixed layer depth is set to 70 m everywhere in the domain. It is too deep to be penetrated by the wind-driven mixed layer current and limit the SST cooling especially in the coastal region where the mixed layer is much shallower than 70 m. Thus, the intensity in this experiment is closed to that of TC1 experiment due to weak SST cooling.

Figure 4.  (a) SST anomaly (℃) fields from TRMM TMI/AMSR-E data; The simulated SST anomaly (℃) and 10-m wind vector (m s^-1) in experiments (b) TC1 COUPLED 70 and (c) TC1 COUPLED between 0000 UTC 7 August to 0000 UTC 10 August 2006. The solid line shows the track of Typhoon Saomai (2006) in the best analysis of the JMA and two model simulations.

Figure 5 shows the relationship between C_d, C_k and 10-m wind speed valid at 0000 UTC 10 August 2006. In CTL, the Charnok formula is used and C_d is increasing linearly with 10-m wind speed, because of increasing of the surface roughness. The C_k increases with wind speed at a lower changing rate. When the Charnok formula is changed to the new formula of Donelan in TC1 and TC1 COUPLED, C_d levels off when 10-m wind speed is greater than 28 m s^-1. The new formula produces stronger surface wind and smaller C_d, especially when surface wind speed is greater than 50 m s^-1. Furthermore, ramped formula for C_k is used in experiments other than the CTL; the results suggest that, in the low wind regime (below 30 m s^-1), C_k with Carlson-Boland formula is larger than that with the ramped formula, while in the high wind regime (above 30 m s^-1, which usually occurs in the eyewall) it is reversed, where C_k is increasing faster with 10-m wind speed. Both new formula of roughness length and thermal roughness length produce smaller C_d and bigger C_k while in the high wind regime. They induce stronger surface wind and get more enthalpy flux from the underlying ocean surface, then intensify the storm.

Figure 5.  The variations of the simulated (a) drag coefficient and (b) enthalpy exchange coefficient with 10-m wind speed (m s^-1) at 0000 UTC 10 August 2006 from all three experiments: CTL (blue), TC1 (red), and TC1 COUPLED (magenta).

The observed and the simulated 2-km radar reflectivity image at 1900 UTC 09 August are compared in Fig. 6 (Zhao et al.^[47]). The results of TC1 COUPLED 70 are omitted in the following comparison because the structures of storm in this experiment is closed to that in TC1 experiment. All the experiments have relatively big eyes compared to the observation. CTL has looser and almost closed eyewall with intermittent high echo region in the northwest part outside of eyewall. TC1 and TC1 COUPLED have closed eyewall with high reflectivity and a spiral rainband located in the southeast quadrant which is similar as the observation. TC1 COUPLED has boarder eyewall and inboard eyewall is smoother compared to other experiments. The southwest part of eyewall is weaker compared to other parts. The reasons of this feature are discussed in the later section. The rainband in the southeast part is similar to the observation. Similar to other modeling experiments, peak reflectivity values are higher in the simulations than observations by 10-15 dBZ, which is similar as Rogers et al.^[48].

Figure 6.  The (a) observed 2-km radar reflectivity (dBZ) at 1903 UTC 09 August, and the simulated 2-km radar reflectivity (dBZ) at 1900 UTC 09 August 2006 from three experiments: (b) CTL, (c) TC1, and (d) TC1 COUPLED.

Figure 7 provides a more detailed look at the three dimensional statistical properties of inner core structures by showing contoured frequency by altitude diagrams (CFADs, Yuter and Houze^[49]) of radar reflectivity with 1.75 dBZ bin. The inner core region is an area of 225 km×225 km centered at the typhoon's surface minimum pressure. CTL experiment has a region of enhanced reflectivity between 30-40 dBZ below 6 km. TC1 and TC1 COUPLED have similar structures and they have two regions of enhanced reflectivity between 30-40 dBZ and 40-50 dBZ. The new roughness formula reduces the roughness with the high wind speed, then reduce the effect of drag and induce the convective cells in the inner core region which produce high radar reflectivity regions. Compared to TC1, the TC1 COUPLED has different feature with lower percentage of 40-50 dBZ points from 1 to 5-km height level, and higher percentage of 30-40 dBZ points from 1 to 5 km height level. Storm induced SST cooling limits the convective cell in the inner core region and reduced the points radar reflectivity at lower levels. In the observation, high percentage points are between 30 and 40 dBZ at lower levels. All the experiments are about 10 dBZ higher than the observation. At higher level, there is a striking region of enhanced reflectivity above 5-km altitude in the observation. This region, clearly seen in the 1.2%- 1.6% contour, is likely due to enhanced precipitated ice supported by the stronger low-level updraft. TC1 COUPLED experiment has similar feature above 5km, except the magnitude of contour is smaller than observation. However, CTL and TC1 experiments have different structures in the upper level, where the proportion of points at weak reflectivity is higher.

Figure 7.  Contoured frequency by altitude diagrams of (a) observed radar reflectivity (dBZ) at 1903 UTC 09 August, and simulated radar reflectivity (dBZ) at 1900 UTC 09 August 2006 from three experiments: (b) CTL, (c) TC1, and (d) TC1 COUPLED.

Figure 8 shows the vertical velocity at 1 km level with the same level radar reflectivity of 30-dBZ contours overlaid at 0000 UTC 10 August, and the cross section of vertical velocity with radar reflectivity of 30-dBZ. The contours of radar reflectivity denote the eyewall and spiral rainbands. There is a high upward vertical motion ring with different structures around it in all three experiments. The spiral bands of vertical motion located cyclonic around the high upward vertical motion regions in CTL and TC1 experiments are characterized by numerous small scale patches of updrafts and downdrafts, especially couples of updrafts and downdrafts in the north part. There are some downdrafts inside the high upward motion ring, which could produce the warm core in the eye. The high upward vertical motion ring in TC1 experiment is smaller and the patches of updrafts and downdrafts is less than that of CTL experiment. In the cross section, the updrafts in the eyewall originate from low level and extend to the upper level, and the downdrafts are between the convective cells. However, the TC1 COUPLED experiment produce different structures of vertical motions. The magnitude of upward motion is smaller and downdrafts inside the eye is weaker than the other two experiments. There are almost none spiral bands in the northwest part of the storm, and less small scale patches of updrafts and downdrafts around the high upward motion ring. In the cross section, a primary updrafts originate from low level, but almost none small downdrafts exist. The storm already moves into the coastal region, and model produce strong SST cooling with the shallow mixed layer in the TC1 COUPLED experiment. The strong SST cooling located in the rear-right quadrant reduces the surface fluxes from the ocean and suppresses the convective cell from the low level. The relative stable air with less fluxes can influence the whole eyewall structures with the main spiral flow. It results in less convection in the north part of the storm and reduces the width of the high radar reflectivity region in the eyewall. At last, the negative feedback of SST cooling has effect on the intensity of the typhoon.

Figure 8.  (a-c) Vertical velocity (m s^-1) at 1 km (red and blue lines) overlaid with radar reflectivity of 30-dBZ contours (gray solid lines) from three experiments: (a) CTL, (b) TC1, and (c) TC1 COUPLED at 0000 UTC 10 August. (d-f) The cross section of vertical velocity (m s^-1) from three experiments: (d) CTL, (e) TC1, and (f) TC1 COUPLED at 0000 UTC 10 August. The red solid lines in (a-c) denote the location of cross section. Red (blue) lines are for the positive (negative) vertical velocity, which means the updrafts (downdrafts). The values of vertical velocity contours are (±) 1, (±) 2, (±) 3, (±) 4, (±) 5, and (±) 6.

The boundary layer heights of the storms are plotted in Fig. 9. Because of the highly rotational wind with strong horizontal gradient in a typhoon, definition of boundary layer height is more complex than that of the planetary boundary layer. For a nearly neutral or convective boundary layer, a common method is to define the boundary layer height as the atmospheric mixed layer depth based on the virtual potential temperature profile. We take the top of the atmospheric mixed layer to be defined the thermodynamic boundary layer height as where θ_v increases by 0.5 K from its mean value in the lowest 150 m (Anthes and Chang^[50]). A radial-height cross-section diagram of azimuthally averaged thermodynamic boundary layer height over quadrants at 0000 UTC 10 August 2006 are shown in Fig. 10. In the rear-left (RL) and rearright (RR) quadrants, the boundary layer height is close to each other among all three experiments. In the front-left (FL) and front-right (FR) quadrants, the mean boundary layer heights of CTL and TC1 are close to 500 m, but that of TC1 COUPLED is lower than the other two. Strong SST cooling in the TC1 COUPLED clearly limits the flux from ocean surface. The air rotates with the highly rotational wind and lower the mean boundary layer height in the front half of the storm. Apparently, the asymmetry of boundary layer height is not significant in CTL and TC1 experiment, whereas it is consistently lower in the front two quadrants in TC1 COUPLED experiment.

Figure 9.  The quadrant-mean virtual potential temperature increases by 0.5 K from the lowest level 150-m on 0000 UTC 10 August 2006. Colors indicate three experiments: CTL (blue), TC1 (red), and TC1 COUPLED (magenta).

Figure 10.  The quadrant-mean Richardson number with value of 0.25 on 0000 UTC 10 August 2006. Colors indicate three experiments: CTL (blue), TC1 (red), and TC1 COUPLED (magenta).

The other definition of dynamic boundary layer height is related to the bulk Richardson number (R_ib). The bulk Richardson number represents the ratio of shear and buoyancy forcing which are responsible for generating and reduces turbulence. It can be defined as:

where R_ib is the Richardson number between the surface and an atmospheric level z, θ is potential temperature, and V represents the wind speed. Using the model output, we calculate the Richardson number as a function of height and define the boundary layer height as the height at which Richardson number equals to 0.25 (Holtslag et al. ^[51]). The quadrant mean dynamic boundary layer height is shown in Fig. 11. The dynamic boundary layer heights are lower than 500 m in all the experiment and they change a lot in the eyewall region where the convection exist, especially in the front-left quadrant of CTL and TC1. The boundary layer heights are close to each other in the rear two quadrants same as the thermodynamic boundary layer height. The height of TC1 COUPLED is lower than those of the other two experiments in the front two quadrants. It means that this part of storm is relative stable for turbulence and less mixing compared to that of other experiments.

Figure 11.  Model simulated (a-c) sensible heat flux (W m^-2), (d-f) latent heat flux (W m^-2) and 10-m wind vectors (m s^-1) at 0000 UTC 10 August 2006 from (a, d) CTL, (b, e) TC1 and (c, f) TC1 COUPLED. The thick arrow with a long shaft stands for the motion of storm.

Figure 11 depicts the horizontal distribution of sensible heat flux and latent heat flux from all the experiments at 0000 UTC 10 August 2006. In CTL, high sensible heat flux occurs in the eyewall where stronger surface wind happens. However, the sensible flux in TC1 experiment is stronger than that in CTL experiment because the new formula of C_d reduces the roughness in the high wind regime and increase the surface wind speed. In the TC1 COUPLED experiment, a significant reduction of sensible flux in the right part, especially the right rear of storm, where the storm induced SST cooling is the strongest even underneath the eyewall and the primary rainband. The high latent flux occurs in the eyewall and primary rainband where stronger surface wind and large C_k happens. According to the new formula, C_k is larger in the high wind regime so the latent heat is larger in the TC1 experiment compared to that in CTL experiment. The significant change happens in the TC1 COUPLED experiment. The closed high flux ring is open due to the reduction in the front-right and rear-right quadrant. The results indicate that the asymmetric ocean response causes an asymmetry in the surface fluxes. This feature is more prominent in TC1 COUPLED due to a stronger SST cooling.

The direct effect of the new formula and ocean coupling is to change the magnitude and spatial distribution of air-sea fluxes. Fig. 12 shows the areaaveraged SST and air-sea fluxes in the inner core region during the lifecycle of Saomai. The SST is the same in CTL and TC1, because there is no ocean model in these two experiments. Comparison between TC1 COUPLED and TC1 COUPLED 70 shows that the SST is similar in the one and half day, afterward the mean SST cools with the ocean coupling. Due to the unrealistic 70-m depth mixed layer in TC1 COUPLED 70 experiment, the SST cooling is very weak. There seems to be no change compared to other two uncoupled experiments. The sensible heat flux is close to each other in CTL and TC1 experiment. The latent heat and moisture fluxes in CTL is similar to that in TC1 experiment. Furthermore, the latent heat and moisture fluxes of TC1 COUPLED is smaller than those of TC1 and CTL experiments because of the negative feedback of SST cooling. Given that the new formula reduce the C_d compared to Charnok formula, the momentum flux of TC1 is smaller than that of CTL, but TC1 produces high wind speed, brings more flux from the underlying ocean surface, and gets the storm stronger. The feedback of SST cooling can be seen when TC1 is compared with TC1 COUPLED. About 2 K of SST cooling can cause more than 300 W m-2 reductions in mean latent heat fluxes, about 100 W m-2 reductions in sensible heat fluxes, and about 40% reduction in the upward moisture flux. However, the momentum flux changes little because they have same calculation of C_d, and the difference is related to the wind speed. When the ocean surface cools down, the surface specific humidity is reduced, leading to a lower evaporation rate and hence a reduction of surface latent heat fluxes. Furthermore, the surface fluxes depend on not only the thermodynamic disequilibrium but also the surface wind strength. Once the storm receives less energy flux, it grows weaker with lower surface wind speed, which results in positive feedback to the latent heat flux. Therefore, ocean coupling can decrease the energy from ocean to TC, and cause the weaker surface wind and its associated smaller mean momentum fluxes. For the same reason, the sensible, latent and momentum fluxes in experiments with simple ocean coupling are smaller than those in CTL experiment.

Figure 12.  Time series of (a) SST (K), (b) latent heat flux (W m^-2), (c) sensible heat flux (W m^-2), (d) momentum flux (kg m^-1 s^-2), and (e) moisture flux (W m^-2) averaged over the inner-core region. Different color represents four experiments: CTL (blue), TC1(red), TC1 COUPLED (magenta), and TC1 COUPLE 70 (green).

The momentum, heat and moisture exchange in atmospheric boundary layer play a vital role in TC development. It is essential to understand the effect of air-sea interaction on simulations of hurricanes or typhoons. Based on the numerical simulation of Typhoon Saomai (2006), this study investigates the impact of exchange coefficients and upper ocean responses on the intensity and structure of Saomai (2006).

By changing the formula of roughness length and thermal roughness length at the same time, the present study conducts two numerical experiments (CTL and TC1) to illustrate the impact of exchange coefficient related to the momentum and enthalpy fluxes on development of TC. In CTL, the Charnok formula is used and C_d is increasing linearly with 10-m wind speed due to the increasing surface roughness. The C_k with Carlson-Boland formula also increases with wind speed at a smaller increasing rate than C_d. In TC1, a new formula of Donelan and ramped formula are used for C_d and C_k respectively. The new formula allows C_d to keep constant when 10-m wind speed exceeds 28 m s^-1 and produces stronger surface wind. And the C_k in TC1 is larger (smaller) than CTL at the high (low) wind regime. The significant difference in intensity forecasts appears when the maximum wind speed exceeds 40 m s^-1 because the new formula produces a smaller C_d and larger C_k. Then the surface wind and enthalpy fluxes increase and promotes the storm to intensify. Both the sensible and latent heat fluxes in TC1 experiment is stronger than that in CTL experiment because of the reduced roughness and increased C_k at the high wind regime. As a result, the simulated intensity of storm in TC1 is stronger than CTL. Based on the structure of TC from different experiments, it can be found that the eyewall in TC1 is closed and the surrounding spiral rainband is complete and well-organized. Moreover, the updrafts ring in TC1 is smaller and the patches of updrafts and downdrafts are less than that of CTL, while the thermodynamic and dynamic boundary layer height has few difference between CTL and TC1.

Two more coupled experiments (TC1 COUPLED, TC1 COUPLED 70), which sshare the same configuration with TC1 except for the ocean coupling, can illustrate the feedback of upper ocean on evolution of TC. The only difference between the two coupled experiments lies in the mixed layer depth. A rightwardbiased cold wake along storm track occurred in both coupled experiments. Compared to the TC1 COUPLED that uses the input mixed layer depth from HYCOM data, the cooling in TC1 COUPLED 70 is weaker and is restricted in a narrower area because of the unrealistic deep mixed layer of 70 m in this experiment. The 70-m depth of mixed layer is too deep to breakthrough by the wind-driven mixing, thus leaving a weaker SST cooling and smaller impact on storm structure and intensity. The storm intensity in TC1 COUPLED is significantly weaker than TC1 and TC1 COUPLED 70 because of the negative feedback of strong SST cooling. Both the intensity and the symmetry of the structure are modified by SST cooling. In TC1 COUPLED, a significant reduction of sensible and latent flux appear in the right part of Saomai (2006), where the storm induced SST cooling is the strongest.

The negative feedback of SST cooling can be concluded as the following: When the ocean surface cools down, the sensible heat fluxes decreases with the reduction of the air-sea temperature difference instantly. Then the latent heat fluxes also decreases with the reduced specific humidity. The energy supply from the ocean to the storm decreases, resulting in weaker surface wind speed, which in turn reduces the sensible and latent heat flux further. Therefore, ocean coupling can decrease the energy exchange in the airsea interface, cause a weaker surface wind and its associated weaker mean momentum and enthalpy fluxes, and finally affects the intensity and structure of a storm.

This study emphasizes the effect of exchange coefficients and air-sea interaction on TC intensity and structure. However, there still exists some interesting phenomena that need to be handled in the future. It should be noted that the magnitude of simulated SST cooling in TC1 COUPLED is stronger than the observation. That is because of that the ocean model coupled with WRF is only a one-dimensional model, which lacks complicated ocean processes such as mesoscale ocean eddies, tides, background ocean circulation and so on. Besides, there are three dynamic processes (vertical mixing, horizontal advection, and vertical advection related to upwelling and downwelling) that induce the cooling of SST, but the one-dimensional model lacks the horizontal advection which can modulate the pattern and magnitude of SST response. Moreover, under the condition of high wind speeds, a complicated air-sea interface full of bubbles and sea spray is formed and will affect the surface flux exchange. Thus, it is necessary to study the numerical simulation of TC with coupled atmosphere-ocean-wave models and new flux parameterization that considers the effect of sea surface state in the future.