The atmospheric boundary layer (BL) in tropical cyclones (TCs) connects deep convection within rainbands and the eyewall to the air–sea interface. Although the importance of the BL in TCs has been widely recognized in recent studies, how physical processes affect TC structure and intensity are still not well understood. This study focuses on a particular physical mechanism through which a TC-induced upper-ocean cooling within the core circulation of the TC can affect the BL and TC structure. A coupled atmosphere–ocean model forecast of Typhoon Choi-Wan (2009) is used to better understand the physical processes of air–sea interaction in TCs. A persistent stable boundary layer (SBL) is found to form over the cold wake within the TC’s right-rear quadrant, which influences TC structure by suppressing convection in rainbands downstream of the cold wake and enhancing the BL inflow into the inner core by increasing inflow angles over strong SST and pressure gradients. Tracer and trajectory analyses show that the air in the SBL stays in the BL longer and gains extra energy from surface heat and moisture fluxes. The enhanced inflow helps transport air in the SBL into the eyewall. In contrast, in the absence of a TC-induced cold wake and an SBL in an uncoupled atmosphere model forecast, the air in the right-rear quadrant within the BL tends to rise into local rainbands. The SBL formed over the cold wake in the coupled model seems to be a key feature that enhances the transport of high energy air into the TC inner core and may increase the storm efficiency.
The atmospheric boundary layer (BL) is a layer that directly links the deep convection in tropical cyclones (TCs) to the underlying sea surface. As the surface enthalpy fluxes from the ocean to the atmosphere are the main energy source for TCs (Emanuel 1986; Rotunno and Emanuel 1987), it is of a particular interest to understand how air–sea coupling affects the BL structure and, ultimately, the evolution of storm structure and intensity.
A majority of previous studies regarding air–sea interaction in TCs focused on the negative impact of the TC-induced ocean cooling on TC intensity. Downward momentum fluxes cause vertical mixing and upwelling that led to the cooling of SST and the upper ocean. The ocean cooling reduces the degree of thermal disequilibrium across the air–sea interface and weakens the storm intensity by reducing the upward enthalpy fluxes (e.g., Schade and Emanuel 1999; Davis et al. 2008). This negative impact has been included as one of the predictors in the operational Statistical Hurricane Intensity Prediction Scheme (SHIPS; DeMaria et al. 2005). In contrast, there are very few studies focusing on the impact of air–sea coupling on the BL and the corresponding TC structure and intensity. Most recently, Chen et al. (2013) show the importance of coupling of surface waves and ocean circulation on the structure and intensity of Hurricane Frances (2004) in a fully coupled atmosphere–wave–ocean model.
By using an axisymmetric hurricane model coupled to an idealized ocean model, Anthes and Chang (1978) documented that storm-induced SST cooling results in reduced mean temperature and moisture in the BL. The cooling is especially significant at the large radii where the BL thermodynamic properties are mainly controlled by the ocean temperature. Using a three-dimensional (3D) ocean model, Price (1981) showed that the TC-induced cooling is strongest in the right-rear quadrant of the storm, which indicates that its impact on BL may be asymmetric. Many observational studies have shown that the TC-induced cold wake is maximized in the right-rear quadrant, including both from ship-based (e.g., Leipper 1967) and satellite observations (e.g., Lin et al. 2003). This persistent cold wake within TCs can result in a shallower BL (atmospheric mixed layer), as well as lower equivalent and virtual potential temperatures in the right-rear quadrant, as shown recently in coupled atmosphere–wave–ocean model simulations and in situ observations (Lee and Chen 2012; Chen et al. 2013). The changes in BL moisture and temperature might change TC vortex structure (Van Sang et al. 2008).
One of the interesting features in the TC BL associated with air–sea interaction is the development of a stable boundary layer (SBL), which has been documented by Black and Holland (1995), in which they observed a SBL near the TC-induced cold wake within TC Kerry (1979). Reports of fog over the cold wake in earlier studies by Ramage (1972) could be seen as an indication of the SBL in a TC. Warm air over cooler SST in a TC can result in formation of a SBL, which is consistent with one of the mechanisms described in Stull (1988). A review of the SBL over SST fronts in the midlatitudes by Small et al. (2008) concluded that the response of the flow in the atmospheric BL to the cold SST front is a weakening of the surface winds. Such a wind reduction results in momentum imbalance and the wind turning toward the background pressure gradient. These changes include the following: 1) the development of an internal SBL that is usually shallower than the surrounding BL, 2) a decrease in the downward momentum fluxes from the top of the BL due to the increased thermal and moisture stratification and the suppressed turbulent activity in the BL, 3) a reduction in surface fluxes due to the SST cooling, and 4) the formation of hydrostatic pressure anomalies (Wallace et al. 1998; Small et al. 2008). Among all the factors, the decrease of the turbulent mixing and the downward momentum fluxes over the cold SST front is thought to be the primary causes of wind reduction under the moderate to high wind regime. The changes in surface fluxes and hydrostatic pressure gradient due to cold SST play minor roles because of the smaller adjustment period. In an idealized atmospheric modeling experiment of a TC with a specified SST patch, Chen et al. (2010) showed that the near-surface wind responds to the specified “cold wake” in a manner similar to that of the midlatitude cold SST front. Lin et al. (2003) showed a modulation of surface winds by the poststorm cold wake using satellite data. The question of how the SBL affects TC convection and structure remains unresolved.
In this study, we focus on examining the impact of the cold-wake-induced SBL within the TC core circulation on the physical properties of the TC BL, and on convection that may affect the TC structure and intensity. A high-resolution, coupled atmosphere–ocean model forecast of Typhoon Choi-Wan (2009) will be used to investigate the physical mechanism(s) responsible for the formation of the SBL and its influence on the TC structure, especially the eyewall and rainbands. A detailed description of the coupled model and numerical experiments will be given in section 2. To follow the evolution of the BL airflow in the model forecast, we developed tracer and trajectory analyses in the atmospheric model, which will be described in section 3. Section 4 presents comparisons of the model forecasts and some limited observations of Choi-Wan. In sections 5 and 6, the coupled atmosphere–ocean model forecast will be compared with the uncoupled atmosphere model forecast to isolate the effects of the air–sea coupling on the formation of the cold wake and the SBL as well as their impact on the TC structure and intensity. Finally, conclusions will be given in section 7.
2. Coupled model and configurations
The University of Miami coupled atmosphere–wave–ocean modeling system (UMCM) includes three model components: the atmospheric, surface wave, and ocean circulation models (Chen et al. 2007, 2013). UMCM can be configured using various component models. In this study, UMCM consists of the Weather Research and Forecasting Model (WRF; Skamarock et al. 2008) and the three-dimensional Price–Weller–Pinkel (3DPWP) upper-ocean circulation model (Price 1981; Price et al. 1994), which will be referred to as UMCM-WP. In UMCM-WP, 3DPWP is designed to share the same horizontal grids as WRF, including the nesting domains, and there is no interpolation required when these two components exchange information. The time steps of WRF and 3DPWP models can be specified according to the desired coupling interval. In this study, the time steps of the outermost domain of WRF and 3DPWP, as well as the coupling interval are set to be 1 min.
WRF is configured with triply nested grids with 12-, 4-, and 1.3-km resolutions, respectively. The inner two nests are storm-following moving grids (Tenerelli and Chen 2001) while the outermost domain is fixed. The number of grid points in the 12-, 4-, and 1.3-km domains are 400 × 300, 202 × 202, and 283 × 283, respectively. There are 36 vertical levels with 10 levels in the lowest 1 km. The microphysical scheme used is the WRF single-moment 5-class microphysics scheme (WSM5; Hong et al. 2004) and the boundary layer scheme is the Yonsei University (YSU; Hong et al. 2006) for all three nested grids. On the 12-km outer domain, the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1993) is used in addition to WSM5. The surface roughness and heat and moisture exchange coefficients are based on Donelan et al. (2004) and Garratt (1992).
The 3DPWP model is configured with nested 12- and 4-km domains matching that of WRF. The ocean fields on the 1.3-km domain are linearly interpolated from the 4-km domain. 3DPWP is a full-physics 3D ocean circulation model with the exception of bathymetry (Price et al. 1994). There are 30 layers in 3DPWP with vertical resolution varying from 5 m in the mixed layer to 20 m below down to 390-m depth. The computational time of the 3D ocean model is usually a small fraction of that of WRF.
To isolate the physical processes leading to the formation of the SBL due to the storm-induced SST cooling and its impact on the storm structure, we conduct an uncoupled atmosphere (UA) WRF forecast and a coupled atmosphere–ocean (AO) WRF-3DPWP forecast of Supertyphoon Choi-Wan (2009). The WRF configuration is the same for both the coupled and uncoupled forecasts.
b. Initial and lateral boundary conditions
The models are initialized at 0000 UTC 13 September 2009. A 96-h forecast is made over a period of time when Choi-Wan intensified from a tropical storm to a supertyphoon and then reached a relatively steady-state stage. The two inner domains start at 0600 UTC after a short spinup period with the outermost 12-km domain. The Global Forecast System (GFS) 1° × 1° forecast fields are used as the initial and lateral boundary conditions for WRF. The 3DPWP is initialized with the global Hybrid Coordinate Ocean Model (HYCOM) real-time forecast fields and the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager/Advanced Microwave Scanning Radiometer for Earth Observing System (TMI/AMSR-E) SST data from the Remote Sensing Systems (http://www.remss.com/measurements/sea-surface-temperature/oisst-description) on 12 September. A blended satellite observed SST with HYCOM subsurface temperature is used in 3DPWP, which provides the best initial ocean field for UMCM-WP.
3. Analysis of BL and airflow in TCs
a. Stable boundary layer
Historically, several stability parameters have been used to characterize the BL properties. In this study we define the surface stability S as the Monin–Obukhov stability index:
where the Obukhov length is given by
In Eq. (1), k is the Von Kármán constant, w is the vertical velocity, g is the gravity, and is the frictional velocity. All of the fields can be separated into mean (overbar) and perturbation (prime) components. The positive and negative values of S represent stable and unstable surface layer, respectively. The Monin–Obukhov stability index is calculated in WRF.
Here the BL is defined as the well-mixed layer (e.g., Lee and Chen 2012). The BL height is where is 0.5 K higher than its value at the surface. The static stability of the BL is computed at each grid point. An SBL is defined as a BL within which every model level is statically stable.
b. Forward Lagrangian trajectory and tracer analysis
To quantify the source of airflow originating in the BL that may go into the convection in TC rainbands and/or the eyewall, we use both the Lagrangian trajectory and tracer analyses. A Lagrangian trajectory is an undiluted air parcel that is advected by flow resolved by the model, which can be integrated forward with time:
where represents the location of the trajectory in the i direction at time t, and is the displacement of the trajectory advected by over a period . This approach works well in the free atmosphere and strongly forced convection. However, it cannot represent the mixing processes in the BL, as shown in Romps and Kuang (2010), which are important in this study. Here we use a tracer analysis to represent air parcels that are subjected not only to advection but also mixing and diffusion:
where c is the concentration of a passive tracer, is again the location in the i direction, u is the wind in the i direction, and is the molecular diffusivity. The total fields can be separated into mean (overbar) and perturbation (prime) components. The terms on the right-hand side are the mean molecular diffusion, the divergence of turbulent tracer flux, and a source/sink term, which is set to be 0 in this study.
The tracer calculation uses the same scalar variables as in WRF-chem with the turbulent mixing processes added in the YSU PBL scheme. Special care is given in both tracer and trajectory calculations related to the moving nested grids, particularly when the air parcels travel across between nested domains. The across-domain entrainment/detrainment of a tracer is handled by the WRF numerical schemes. For trajectories, we calculate each new location, , in all nested grids at every model time step, but save the one from the finest model resolution grid. In UMCM-WP, is not limited to be an integer (i.e., the location of each trajectory is not constrained to be at the model grid point). At each time step t, is linearly interpolated onto the trajectory position from eight surrounding grid points. The advantage of this new trajectory calculation described here is the improved accuracy. It avoids the potential error when using a relatively infrequent model output to calculate trajectories as pointed out by Dahl et al. (2011). However, one drawback is that backward trajectories cannot be computed using this method.
4. Supertyphoon Choi-Wan (2009)
Choi-Wan (2009) was a supertyphoon with a maximum wind speed (MWS) >100 kt (1 kt = 0.5144 m s−1) in the western North Pacific based on the Joint Typhoon Warning Center (JTWC) best track estimates. It formed on 11 September as a tropical depression and quickly intensified to a tropical storm on 12 September. Choi-Wan tracked westward along the southern edge of a strong subtropical high pressure system over the warm ocean in the west Pacific (Fig. 1a). Choi-Wan became a category-4 supertyphoon on 14 September (Fig. 1b) and was still steered by the subtropical ridge toward the northwestward. The storm reached its maximum intensity later on 15 September as a category-5 supertyphoon. The environmental vertical wind shear was lower than 4 m s−1, based on the Statistical Typhoon Intensity Prediction Scheme (STIPS; Knaff et al. 2005). The upper-ocean condition can be characterized by a depth-averaged temperature T100 (Price 2009). In this study T100 is computed from the initial HYCOM analysis field along the storm track (Fig. 2b). T100 was above 28°C when Choi-Wan reached its peak intensity (Fig. 3). With the help of favorable atmospheric environment and ocean conditions, Choi-Wan remained near its peak intensity, 140 kt, until late on 16 September. The official best track data provided by the Japan Meteorological Agency (JMA) had Choi-Wan as a category-3 supertyphoon. The difference between the JTWC and JMA best track data is due in part to the different definitions of the maximum surface wind they used (Harper 2010; Nakazawa and Hoshino 2009). JMA uses a 10-min sustained wind speed, whereas JTWC a 1-min sustained wind. In general, the storm intensity issued by JTWC is about 10% stronger than that of JMA (Lander 2008). However, for Choi-Wan, the peak intensity estimated by JTWC is 40% higher than that of JMA. This uncertainty should be considered when comparing model forecast to these best track data. We include both best track intensity estimates in Fig. 1b. With the strong surface wind and slow storm translation speed (2–4 m s−1), Choi-Wan induced a relatively strong SST cooling of more than 3°C during 13–17 September (Fig. 3c).
b. Model forecasts of Choi-Wan
The UA and AO model forecast tracks and intensities are compared with the best track data from JMA and JTWC (Fig. 1). The model forecast tracks in both AO and UA have a southward bias. By comparing the 500-hPa geopotential height field in these two forecasts to that in the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis field (not shown), we found that such a southward bias is due to an overpredicted ridge northeast of the storm in the models. The track error may affect the model forecasted storms as they experience slightly different upper-ocean conditions than those of Typhoon Choi-Wan (Figs. 2a,b and 3).
Both UA and AO forecasts capture the intensification of Choi-Wan from 13 to 16 September (Fig. 1b). The environmental vertical wind shear in the model forecasts varies from 2 to 6 m s−1 during this period. Although the large-scale environment is about the same for both UA and AO, the storm intensity in UA and AO starts to evolve differently late on 14 September. UA intensifies more rapidly than that of AO. They both reach a quasi–steady state early on 16 September and start to weaken late on the same day.
Given that the main focus of this study is to investigate the physical processes associated with the storm-induced ocean cooling and its impact on the BL and storm structure, we will analyze the UA and AO model forecasts and contrast their distinct features due to the air–sea coupling in the model. The strong ocean cooling in AO developed after the initial intensification period will be the focus of the analysis. Unfortunately, there is no in situ collocated atmospheric and ocean observations in Choi-Wan during 13–17 September. Nevertheless, the differences between the UA and AO model forecasts can provide some physical insight into the effects of air–sea coupling on the TC structure and intensity.
5. Stable boundary layer in Typhoon Choi-Wan
One of the most robust features that coupled models and observations have consistently shown is a relatively shallow BL over the storm-induced cold wake in the right-rear quadrant of TCs (e.g., Lee and Chen 2012). This feature is also presented in the coupled AO model forecast in Choi-Wan, which is located outside of the eyewall extending out to about 350-km radius (Fig. 4a). It is absent in UA where there is no storm-induced SST cooling (Fig. 4b). The stability analysis based on Eqs. (1) and (3) shows that the surface layer and BL are stable over this region in AO (Fig. 5a). The area of the stable surface layer is larger than that of the SBL. The formation of a stable surface layer and an SBL is likely the result of warm air being advected over the cold water from upstream of the cold wake in the coupled model. In contrast, there is no SBL or stable surface layer in UA (Fig. 5b). Although there is no direct observation of an SBL in Typhoon Choi-Wan, observations using the GPS dropsondes collected in three Atlantic hurricanes by Barnes (2008) showed that 10% of the dropsonde data have a stable thermal profile. Whether these stable profiles were over cold SST is unknown because there was no collocated ocean measurement. Barnes (2008) found that the stable profiles mostly had a surface wind speed less than 30 m s−1, which is consistent with the fact that the SBL is away from the center of the storm in Choi-Wan (Fig. 5a), where the wind speeds are less than 25 m s−1 (not shown).
To further examine the vertical structure of the BL in and out of the region of the SBL, we divide the vertical profiles of into four groups based on the corresponding SST values in both AO and UA (Fig. 6). The profiles are sampled outside of the eyewall/inner-core region and rainbands to ensure that they are not in convection. Because the SST is kept constant in time in UA forecast, profiles in UA represent a BL without storm-induced cooling with SST ranging from 28.5° to 29.5°C (Fig. 6b). Profiles with SST below 28.5°C from AO are likely affected by the storm-induced ocean cooling in the coupled model (Fig. 6a). In addition, some profiles with SST values from 28.5° to 29.0°C in AO may also be cooled from higher SST values at the model initial time. The SBL profiles are found in three of the four groups in AO with SST < 29°C (red profiles in Fig. 6a). They are mostly from the cold-wake region in AO (Fig. 5a). Although there is a large variability within each SST group, the main characteristics of in the BL are distinct between different groups. When SST > 29°C (in both UA and AO), the mean profile (thick black line) can be separated into three layers from the surface upward: an unstable layer in which decreases with height, a well-mixed layer right above the unstable layer with almost constant with height, and another stable layer with increases with height. As SST decreases, some profiles display a stable layer near the surface and in the BL in AO (red lines in Fig. 6a). For the group with 28.5° < SST < 29.0°C, the mean profile in UA is more unstable than AO near the surface. The unstable layer disappears in some profiles in AO.
6. Impact of SBL on near-surface airflow
An SBL may affect both thermodynamic and dynamic properties of the flow near the surface and/or throughout the BL. To understand the impact of the SBL on the airflow and convection in Choi-Wan, we conduct trajectory and tracer analyses as described in section 3b. Both trajectories and tracers are released at 0000 UTC 16 September in AO and UA forecasts. We track the trajectories and tracers over the next 6 h when the model forecast storms are in a relatively steady state in term of intensity (Fig. 1b). The total amount of tracer is conserved during this 6-h period when the air parcels have sufficient time going into either the inner core or the outer regions in the TC. In AO, the tracers are released between the 150- and 350-km radii away from the storm center in three locations: 1) the SBL over the cold wake, 2) the region 90° upstream of the cold wake, and 3) the region 90° downstream of the cold wake (Fig. 7a). For convenience, we refer to the tracers released from the three areas as cold-wake tracer, upstream tracer, and downstream tracer. The size and shape of these three areas are the same. All tracers are released at the 80-m level that is the first model layer above the surface layer in WRF. Within each area, the tracer concentration is set to 1, while everywhere else is set to 0. Note that the tracers from different areas do not interact/mix with each other. We also release 86 trajectories in the SBL over the cold-wake region at the 80-m level as indicated by the blue dots in Fig. 7a. For comparison, the tracers and trajectories are also released in the same storm relative locations in UA as in AO (Fig. 7b).
a. Enhanced near-surface airflow into the inner core
The cold-wake tracers in the right-rear quadrant in AO evolved in a rather distinct manner compared to that in UA. Figure 8 shows the 0.05 isosurface of the cold-wake tracer at various times after the tracers are released, ttracer = 0, 20, 60, and 120 min. The tracers are well mixed in the BL within 20 min due mostly to the turbulent mixing. At ttracer = 60–120 min, the difference between cold-wake tracers in AO and that equivalent location in UA becomes apparent. There is less vertical transport and faster inward spiraling airflow from the cold-wake area in AO compared to that in UA. More tracers in AO are transported into the eyewall than in UA. The tracers in UA mostly go upward into the rainband convection (Fig. 8).
The azimuthally integrated tracer concentration from ttracer = 3–6 h is shown in Fig. 9. The concentration in the BL in AO is higher than in UA, especially at ttracer = 3–4 h. Unlike tracers being transported into local rainbands in UA, the cold-wake tracers in AO are transported horizontally into the inner core and carried upward with the convective updraft in the eyewall. The cold-wake tracer concentration in the eyewall in AO is much higher than that in UA at ttracer = 6 h. Identical analyses for the upstream and downstream tracers are conducted (not shown). There is no major difference between AO and UA in the upstream and downstream locations. The upstream tracers are strongly affected by the primary rainbands in both cases. They are entrained quickly into the rainband convection with little entering the eyewall.
b. Effects on TC convection
To understand the effects of the SBL on the convection in TCs, we compare the convective organization between UA and AO forecasts. Figure 10 shows the model-simulated radar reflectivity from AO and UA at the 1-km level for the same time period as the tracer and trajectory analysis at 0000 and 0600 UTC 16 September. Although the main convective features in UA and AO are similar, including the size and shape of the eyewalls, the locations of the primary rainbands in the south side, and the persistent outer rainbands southeast of the storm center, there are a few important differences. The overall rainbands are slightly less and more confined in AO than those in UA, which is similar to the result in Chen et al. (2010). The main difference in convection between UA and AO seems to be in the northeastern quadrant, downstream of the cold wake in AO, as highlighted in the wedged boxes in Fig. 10. There are less rainbands in AO downstream of the cold wake with the SBL compared to the same storm-relative location in UA where there is no cold wake and the BL is mostly unstable or neutral. This result indicates that the SBL in AO suppresses the convective activities downstream of the cold wake.
Previous studies have shown that convection/rainfall asymmetry in TCs may be affected by other factors such as environmental vertical wind shear and storm motion (e.g., Black et al. 2002; Rogers et al. 2003; Chen et al. 2006). We compute the vertical wind shear in both the UA and AO model forecasts using a similar method as in Chen et al. (2006) (i.e., the difference between 200 and 850-hPa winds). The shear in UA and AO is very similar (Figs. 10a–d). Furthermore, the storm translation speeds in both forecasts are almost identical as shown in Fig. 1a. These analyses confirm that the difference in rainbands downstream of the cold wake in the right-rear quadrants in UA and AO cannot be attributed to the environmental shear or storm motion.
To further quantify this result, we compute the number of grid points that are convective in nature within the rainbands downstream of the cold-wake region. We use a similar method from Rogers (2010). Briefly, it defines a convective cell that satisfies two conditions: 1) the mean vertical velocity within the layer from the 1–2-km level is greater than 0.5 m s−1 at a grid point, and 2) reflectivity >40 dBZ at the 3-km level within a 10-km radius of the grid point. This analysis shows that the rainband convection downstream of the cold wake in AO is 40%–50% less than that in the similar region in UA (highlighted in the red wedge in Fig. 10). For the overall rainband convection outside of the eyewall, AO is about 20%–25% less than UA. The reduction in the convective rainbands downstream of the cold wake is twice of the storm overall value. Furthermore, a satellite-observed microwave image of Choi-Wan at about 0600 UTC 16 September shows a similar suppressed convective region in the right quadrants downwind of the cold wake (Fig. 10e) as in the coupled model simulation from AO (Figs. 10a,c).
The thermodynamic forcing of the SBL in AO seems to have two main effects on the near-surface flow and convection in TCs: 1) suppresses convection over and downstream of the cold wake (Fig. 10); and 2) constrains the air within the BL, which increases the amount of near-surface air from the cold-wake region entering the eyewall/inner core (Figs. 8 and 9).
c. Dynamic enhancement of near-surface inflow
The tracer analysis shown in Fig. 8 indicates that the airflow from the cold-wake region in AO wraps around farther inward than that in UA from the same storm-relative location, which resulted in a larger radial flux of tracer into the eyewall in AO. This phenomenon may be associated with changes in wind speed across the SBL, as shown in Small et al. (2008) and Spall (2007) for midlatitude SST front and Chen et al. (2010) in an idealized TC simulation. The wind speed is usually reduced when the air goes from a neutral/unstable BL to SBL because of the decrease in turbulent mixing from the top of the BL (Spall (2007)). In a TC, if the wind speed decreases at a distance from the center of the storm, the gradient wind imbalance would result in further inward turning, and therefore a larger inflow angle. This feature can be seen clearly in a comparison of the 10-m wind vectors in AO (red) and UA (blue) in Fig. 11. Because storm intensity in UA is 5–10 kt stronger than that in AO at this time, the overall inflow angles around the storm are expected to be stronger in UA than AO. We computed the inflow angles using tangential and radial winds in the earth-relative coordinate. The mean inflow angle over the whole domain is 21.4° in UA and 19.0° in AO. Over and near the cold wake (shaded gray in Fig. 11), there is an apparent further inward turning of 10-m wind in AO than UA (cf. the red and blue arrows). The area-averaged inflow angle over the cold wake is 21.6°, which is 2.6° larger than the mean inflow angle over the entire storm in AO. There is no such difference in the same relative region in UA.
The composited horizontal maps of inflow angle and velocity from 0000 to 0600 UTC 16 September show the strong inflow in the inner core/eyewall is located in the front (west-northwest) of the storm (Fig. 11), which is consistent with previous idealized modeling study of Shapiro (1983) and observational studies (Powell 1982; Barnes and Dolling 2013). Outside of the inner-core region, the larger inflow angles are found in the left and left rear (south) of the storm center in Choi-Wan. Note that various factors can influence inflow angles in a TC, including environmental mean flow, wind shear, storm motion, intensity, and so on. The horizontal pattern of inflow angles can vary from storm to storm. Such variability is especially significant for a slow-moving storm like Choi-Wan. Using Earth-relative data (same framework as used in our modeling analysis), Powell (1982) showed that the larger inflow angles in Hurricane Frederic (1979) are in the rear and rear left. In a fully coupled atmosphere–wave–ocean modeling study by Chen et al. (2013), they showed that one of the effects of wind–wave coupling on surface stress patterns is to shift the larger inflow angles toward rear and rear-left region of Hurricane Frances (2004), which may in part explain the location of large inflow angles in the left could be farther to the rear if coupling to the surface waves were included in the model.
To address the impact of the cold wake and SBL due to the coupling to the ocean on the inflow angle of Choi-Wan in AO, we computed the difference fields between AO and UA. The differences in both the inflow angle (Fig. 12c) and wind speed (Fig. 12f) between AO and UA show the enhanced inflow angle and speed downstream of the cold-wake region.
d. Thermodynamic enhancement of near-surface air into the eyewall
To better understand the impact of the SBL on the energetic of TCs, thermodynamic properties of the near-surface air parcels in the SBL in AO are compared with those from the same storm-relative region in UA but with the unstable/neutral BL. We compute the equivalent potential temperature based on Bolton (1980) along all the trajectories1 from the cold wake in AO and the equivalent region in UA shown in Fig. 7. Figure 13 provides a 3D view of the trajectories with color-coded values using a subset of the trajectories. The trajectories are divided into two groups: trajectories going into the eyewall/inner core and trajectories in the rainbands/outer regions. The former tends to stay near the ocean surface longer than the latter before entering the eyewall/inner core, which allows them to gain extra energy from the warm ocean downstream away from the cold wake in AO with higher θe values on its way to the eyewall/inner core (Fig. 13a). In contrast, trajectories that go into the outer rainbands lose the initial high energy while being transported upward. Although the air parcels have higher values initially in UA, because of the higher SST than in AO (Fig. 5), more trajectories initialized in SBL over the cold wake go into the eyewall/inner core in AO than in UA at the equivalent region (Fig. 13). This result is confirmed using all 86 trajectories from the SBL or equivalent regions in each of the model forecasts over the same 6-h period in AO and UA (Fig. 14). There are 22 trajectories entering the eyewall/inner core in AO (Fig. 14a) while there are only 15 in UA (Fig. 13b).
It is also important to note that the initial average θe value near the surface for trajectories went into the eyewall/inner core from the SBL over the cold wake in AO is about 358 K, ~2 K lower than that in UA (red thick lines in Fig. 14). This relatively low θe air in AO increases its value to >365 K quickly before rising in the eyewall/inner core (Fig. 14a). This result is consistent with the 3D trajectories shown in Fig. 13a. A possible explanation for this increase of θe along the trajectories near the surface is due to the enhanced air–sea enthalpy flux when the relative cooler air over the cold wake advected over the warmer water downstream. Another important difference between AO and UA is that the average θe value in the lowest 2 km from trajectories went into the eyewall/inner in AO is higher than that in UA (Fig. 14), which shows the impact of the air–sea coupling on the lower-tropospheric property in TCs. There are some extreme high θe trajectories in UA due to the unrealistic high SST without storm-induced ocean cooling. Although there is no direct observation in Typhoon Choi-Wan, the extreme high value of >368–370 K in the eyewall in UA is higher than in situ observations from TCs with similar intensity (e.g., Lee and Chen 2012).
Another interesting difference between AO and UA is in the outer rainband region. Aside from more trajectories go into the outer rainbands in UA than AO, the rainband convection in UA is as deep as the eyewall convection as shown by the heights of trajectories reached (blue lines in Fig. 14b). In contrast, the rainband convection in AO is shallower than the eyewall convection (Fig. 14a), which is consistent with observations described in Didlake and Houze (2009). They showed that the convection in the rainbands is capped vertically by the outflow from the eyewall, which limit the vertical extend of convection in the rainbands. In other words, the convection in UA is unrealistically strong due to the lack of storm-induced ocean cooling in the uncoupled model without the air–sea coupling. There are more trajectories in the rainbands with lower θe values in the lower troposphere in UA than AO, which may be a result of stronger convective downdraft in UA than AO over these regions.
e. Energetic efficiency in TCs
A TC can be viewed as a heat engine converting heat energy extracted from the ocean into the kinetic energy (KE) through the diabatic heating in the moist convection in the eyewall (Emanuel 1986). From an energetic point of view, the intensity of the TC in AO should be weaker than UA because of the storm-induced ocean cooling and the reduced overall enthalpy fluxes from the ocean surface in AO. However, the TC-induced cold wake and SBL in the right-rear quadrant in AO can increase the amount of high air near the surface entering the eyewall as shown in the previous sections. This mechanism may increase the efficiency of the storm in AO, and help offset the negative impact from SST cooling.
Here we define the term efficiency as a ratio between the change of mass-weighted KE and the mass-weighted surface enthalpy fluxes within a control volume (a cylinder with a radius of 350 km).2 KE is calculated based on the difference of the kinetic energy per mass between 0000 and 0600 UTC 16 September, the same time period as the tracer and trajectory analyses. The surface enthalpy flux is computed by averaging the 10-min instantaneous surface enthalpy fluxes per mass over the same period. The mass-weighted calculation takes into account the change of the total mass associated with the storm intensity changes. We have done the same analysis by varying the radius from 300 to 700 km, which does not change the outcome.
The results are shown in Table 1. The TC efficiency is 2.95% and 3.44% in UA and AO, respectively. So AO is about 20% more efficient than UA in converting additional enthalpy flux to kinetic energy. The higher efficiency in AO can also be shown by the larger inward moist-static energy fluxes at the outer edge of the eyewall within the BL in AO than UA (Table 1). However, a comprehensive study is needed to better understand this complex problem related to TC energetics. The generality of the simple calculation presented here remains an open question for future studies.
A fully coupled atmosphere–ocean model forecast of Typhoon Choi-Wan (2009) has been used to better understand the physical processes of air–sea coupling in TCs. Comparisons of the coupled atmosphere–ocean (AO) model with the uncoupled atmospheric (UA) model forecasts have provided new physical insights into how air–sea coupling affects the TC structure and intensity. While the TC-induced ocean cooling in AO reduces overall TC intensity than using an unrealistic constant SST with time in UA, the storm-induced cold wake in AO leads to the formation of a stable surface layer (SBL) that contributes to the transport of high-energy air near the surface into the eyewall.
Two main effects of the SBL can be summarized here in Fig. 15. First, the tracer and trajectory analyses show that the thermodynamic effect of the SBL is to suppress the convection and prevent the air in the SBL from going into the rainbands over and downstream of the cold wake. At the same time, the SBL keeps the air in the BL longer to gain extra energy from the enhanced enthalpy flux from the ocean. Second, the dynamic effect of the SBL is to enhance the inward turning of the BL air due to the momentum imbalance caused by the suddenly reduced wind speed over the SBL. The enhanced inflow helps transport air in the SBL into the eyewall. In contrast, in the absence of the TC-induced cold wake and the corresponding SBL in the UA model forecast, the air in the right-rear quadrant in the BL tends to rise into the local rainbands. The SBL formed over the TC-induced cold-wake region in AO seems to be a key feature that enhances high energy air into the TC inner core.
In summary, this study shows that, while the TC-induced ocean cooling reduces the overall storm intensity that is usually overpredicted by uncoupled atmospheric models with unrealistic constant SST with time, the storm-induced cold wake and the SBL in the right-rear quadrant within the TC core circulation can offset some of the overall negative impact on the storm intensity through the enhanced inflow with high energy air into the TC inner core. This mechanism may increase the efficiency in TC intensification. To represent these important physical processes for TC intensity prediction, numerical models need to be able resolve the TC eyewall and TC-included cold wake/SBL with a high grid resolution (1–2 km) and full coupling to the ocean. However, as expected, the relative importance of this mechanism may vary from storm to storm because of the variability of other environmental and internal factors affecting TC intensity. More comprehensive observational and modeling studies are needed.
We thank Drs. Brandon Kerns of UM and Jimy Dudhia of NCAR for their assistance during the course of this study. Comments from three anonymous reviewers helped improve the manuscript. This research was supported by research grants from the Office of Naval Research under Impact of Typhoon on Ocean in the Pacific (ITOP) N000140810576, the National Ocean Partnership Program (NOPP) N000141010162, and the Gulf of Mexico Research Initiative (GoMRI) SA1207GOMRI1005.
The radial advection of moist static energy is close to zero beyond the 300-km radius. Thus, we use 350 km as the radius of the cylinder to be consistent with the tracer analysis.