1. Introduction
The air–sea energy exchange is one of the most important physical processes governing the tropical cyclone (TC) evolution. The ocean state, especially the sea surface temperature (SST), plays a crucial role in determining TC intensity (Fisher 1958; Emanuel 2007). Observations and model simulations have proved that TCs moving over ocean cause a decrease in SST, which is generally asymmetric about the TC track (Price 1981; Stramma et al. 1986; Black and Dickey 2008). The width of the SST cooling may extend to hundreds of kilometers and the maximum SST decrease can reach 9°C as observed during Typhoons T8914, T8915, and Kai-Tak (Sakaida et al. 1998; Lin et al. 2003). In uncoupled atmosphere models, however, SST is usually held constant, which cannot appropriately evaluate the TC-induced SST change. To consider a real ocean state in the TC modeling, it is of great necessity to employ a coupled atmosphere–ocean model.
The earliest numerical TC–ocean interaction experiments were conducted in 1970s by Chang and Anthes (1979). They coupled an axisymmetric TC model with a highly simplified ocean model and the model results reveal negative effects of the ocean feedback. By using a simple coupled axisymmetric TC–ocean model, Schade and Emanuel (1999) demonstrated that the negative effects of the ocean feedback depend on many parameters such as the mixed-layer depth, the translation speed of the TC, and the stratification below the mixed layer. Recent studies using three-dimensional atmosphere–ocean coupled models further clarified the negative effects of ocean response on TC development in detail by considering more realistic and complex coupling processes (e.g., Bender et al. 1993; Bender and Ginis 2000; Chan et al. 2001; Zhu et al. 2004; Chen et al. 2010). With a focus on simulations of four real cases and a statistic of 163 forecasts, Bender and Ginis (2000) showed that the Geophysical Fluid Dynamics Laboratory (GFDL) coupled TC–ocean model evidently improved the prediction skill of storm intensity by imposing a limitation on the storm overintensifying. Zhu et al. (2004) and Chen et al. (2010) found that the storm-induced SST cooling not only weakens the TC intensity but also increases the asymmetry of the storm thermodynamic and dynamic structures. More recently, B. Liu et al. (2011) established a fully coupled three-way atmosphere–wave–ocean model and pointed out that the overall effects of the atmosphere–wave–ocean coupling on TC intensity are modulated by the negative contributions of SST feedback, which is consistent with previous atmosphere–ocean model studies. The TC track, on the other hand, is indicated to be insensitive to SST cooling (Zhu et al. 2004; Chen et al. 2010; B. Liu et al. 2011).
A large number of TCs in the western North Pacific basin confront ocean eddies during their lifetime (Lin et al. 2005; Wu et al. 2007). When mesoscale oceanic eddies are incorporated in the ocean models, the storm simulations are always improved markedly (Hong et al. 2000; Emanuel et al. 2004). The mesoscale oceanic eddies, including the warm core eddies (WCEs) and the cold core eddies (CCEs), have warmer or cooler ocean temperature and thicker or thinner mixed-layer depth than common water and thus can modulate the oceanic response to TCs by affecting the rate of turbulent entrainment and upwelling. It is also found that the presence of a WCE serves as an insulator against the negative feedback of the ocean, and thus as a TC encounters a WCE, the SST cooling is significantly reduced and the storm rapid intensification always occurs (Hong et al. 2000; Lin et al. 2005; McTaggart-Cowan et al. 2007; Wu et al. 2007; Jaimes and Shay 2009).
The present studies of TC–oceanic eddy interactions mainly centralize in the roles of WCEs. Contrastingly, only very limited studies have been conducted to document the significant increase of SST cooling induced by the passage of TC over CCEs (Halliwell et al. 2008; Jaimes and Shay 2009). Detailed roles of the CCE in TC sustaining and intensification, especially the CCE-induced changes of the TC structures have not been well investigated, though CCEs should have the equivalent importance as WCEs during TC evolution. Therefore, it is necessary to systematically evaluate the roles of CCE in TC development, especially its effects on TC intensity and internal structures.
Observations indicate that CCEs, which have opposite thermal features to WCEs, are generally elliptical and have typical diameters from 100 to 300 km, and remarkably negative ocean temperature anomaly between the CCE center and the common water, which can reach 10°C (Doblar and Cheney 1977; Horton and Baylor 1991). Based on these characteristics, an idealized CCE is incorporated in this study to simulate the TC–CCE interaction using a coupled atmosphere–ocean model with idealized atmospheric and oceanic initial conditions. Section 2 describes the coupled model, the idealized initial conditions and the experimental design. The ocean response to the moving TC is discussed in section 3. Section 4 analyzes the TC response to the ocean feedback, with a focus on the impact of the CCE on the intensity and structure changes of the TC. The main conclusions are given in section 5.
2. Descriptions of the coupled model, idealized model initialization, and experimental design
a. The coupled model
The coupled model used in this study has been developed to conduct real-case simulations of the TC–ocean interaction by L. Liu et al. (2011). It comprises the Weather Research and Forecasting Model (WRF) (Skamarock et al. 2008) as the atmospheric component and the Princeton Ocean Model (POM; Mellor 2004) as the oceanic component.
WRF integrates compressive, nonhydrostatic Euler equations using a terrain-following vertical η coordinate. It includes multiple selections of physical schemes for cloud microphysical, cumulus, planetary boundary layer, and radiation processes. The POM is a three-dimensional, free-surface, primitive equation ocean model with a sigma coordinate. The Mellor–Yamada turbulence closure scheme (Mellor and Yamada 1982) is embedded in the model to provide vertical mixing coefficients. An Arakawa-C grid is used as the horizontal finite-difference scheme. The POM has been widely used to model estuaries, coastal regions, and open oceans.
In the coupling procedure, the atmosphere model drives the ocean model through sea surface wind stress, surface sensible and latent heat fluxes as well as the shortwave and longwave radiations. In turn, the SST computed by the ocean model is transferred back to the atmosphere model. Variables are exchanged between the atmosphere and ocean model at every coupling time step. During each coupling time step, the SST is held constant.
b. The idealized model initialization
The intensity of real storms is usually modulated by many environmental factors. For example, Hurricane Opal (1995) is simultaneously affected by a westerly upper-tropospheric trough and a WCE while undergoing rapid intensification (Bosart et al. 2000; Hong et al. 2000); hence, it is difficult to distinguish which factor specifically dominates. To exclude interferences of other factors, the coupled model is initialized with idealized TC and ocean conditions. Both the atmosphere model and ocean model are set on a β plane with the model domain center set at 20°N. The coupling time step is set to be 900 s.
For all experiments, WRF is configured with triply-nested grids, with the inner two following the storm. The three meshes have dimensions of 220 × 220, 202 × 202, and 202 × 202, with horizontal resolution of 15, 5, and 1.667 km, respectively. The outmost domain utilizes the Betts–Miller–Janjic scheme (Betts and Miller 1986) to parameterize the cumulus convection processes due to its coarse resolution. No cumulus parameterization is employed in the two inner meshes. The Yonsei State University (YSU) scheme (Hong et al. 2006) and the Monin–Obukhov scheme (Monin and Obukhov 1954) are chosen as the planetary boundary layer scheme and the surface layer scheme, respectively. The Lin scheme (Lin et al. 1983) is used to model the microphysical processes. The Dudhia shortwave (Dudhia 1989) and Rapid Radiative Transfer Model (RRTM) longwave (Mlawer et al. 1997) schemes are used as the radiation schemes. The model top is set at 50 hPa and the model possesses 36 vertical levels distributed as default in WRF, with nine levels (1, 0.993, 0.983, 0.97, 0.954, 0.934, 0.909, 0.88, and 0.844) in the lowest 150 hPa. The horizontally uniform ambient temperature and humidity profiles in WRF are specified by the mean tropical sounding of Jordan (1958), and the default humidity values above 450 hPa are given by the linear interpolation. The sea level pressure and SST are set uniformly at 1010 hPa and 29°C separately. The uniform easterly winds of 3 m s−1 are specified at all levels, with geopotential heights adjusted at each level according to the geostrophic wind balance. A bogus vortex is implanted in the idealized atmosphere environment with a maximum wind speed of 24 m s−1 at a radius of 125 km. The vortex is initialized with hydrostatic and gradient wind balance. Then WRF is integrated individually for 24 h with SST fixed at 29°C as the model spinup of a TC-like vortex.
The POM is configured with a single domain of 185 × 165 grid points and resolution of approximately 0.2° × 0.2°, covering a region slightly larger than that of WRF; 23 vertical levels are used in the ocean model, with 11 levels placed in the upper 100 m. The time step is 300 s. The horizontally uniform temperature and salinity profiles for POM initialization and boundary conditions are given by the monthly averaged (August) Simple Ocean Data Assimilation (SODA) profiles at (20.25°N, 176.25°E), except that the temperature of the upper-ocean mixed layer and the SST are modified slightly to be 29°C so as to keep equal with the initial SST in WRF. The entire domain is set to be ocean with a uniform depth of 2500 m. For simplicity, the model is initialized with quiescent current to keep the CCE stationary. The initial interfacial heat fluxes and wind stress forcing are derived from WRF.
Because of the lack of subsurface observations, mesoscale eddies in the numerical experiments are usually constructed either by using temperature and salinity profiles at different locations or by assigning a specified departure from the surrounding ocean temperature (Wu et al. 2007; Yablonsky and Ginis 2008). In this study the latter method is adopted to incorporate a CCE in the ocean model for the sensitivity experiment. The temperature profile at the center of the CCE is assigned by reducing the temperature of common water for a specified value referring to the feature-based methodology of Yablonsky and Ginis (2008). The temperature departure is set to be maximal at approximately a depth of 400 m and decreases in the upper and lower levels gradually, so as to keep the temperature horizontally homogeneous at the sea surface and below the depth of 1700 m approximately. The salinity profile in the CCE keeps same as that in the common water. The CCE is then initialized by integrating the POM individually for 96 h without external forcing, to make the density and current geostrophically adjusted to a steady state. The upper 1100 m of the temperature profiles in the steady-state CCE center and the background ocean are shown in Fig. 1. The maximum temperature departure is 8.0°C, suggesting that the constructed CCE is rather strong so as to make impacts of the CCE more evident. The horizontal temperature and current fields of the CCE at 45 m in depth are exhibited in Fig. 2a and the vertical section of the temperature crossing the CCE center is shown in Fig. 2b. The initial CCE has overall typical properties as observed that it is in nearly circular shape, with a diameter of about 280 km and a maximum sea surface current velocity of ~1.2 m s−1.
Vertical profiles of the temperature (°C) in CCE center and the common water.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
(a) The horizontal temperature (°C, contour) and ocean current (m s−1, vector) at 45 m in depth and (b) vertical section of the temperature (°C) across the CCE center.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
c. Experimental design
Several numerical experiments are conducted to explore ocean coupling effects on TC evolution, especially under CCE conditions. Table 1 shows a summary of these experiments. The experiment using the coupled WRF and POM model without CCE incorporated in the ocean model is considered as the control run, denoted as CTRL. The experiment with CCE considered in the coupled model is denoted as CLD24. The experiment using the single WRF with SST fixed at 29°C is denoted as UNCP. In CLD24 it is designed that the TC center passes over the CCE center at 24 h, and the CCE position is primarily determined by the TC position at 24 h in CTRL. All runs are integrated for a total of 120 h.
List of numerical experiments.
3. Ocean response
The patterns of SST at 24 h for CTRL and CLD24 are displayed in Fig. 3. Each TC leaves behind a cold wake located at the right rear of the TC, with similar strength of −1.5°C and a width of about 200 km. The maximum SST cooling of the cold wake is outside the range of eyewall indicated from the surface winds (shaded). The characteristics of the cold wake are mainly determined by the temperature profile in the upper ocean and the TC translation speed, and the right bias of the cold wake is primarily due to the asymmetric turning of wind stress arisen from the translation of a vortical wind pattern (Price 1981; Price et al. 1994, 2008). Because of the presence of the CCE in CLD24, the mixed-layer depth under the TC center is much thinner than the common water (Fig. 2b), and thus the SST response tends to be stronger (Schade and Emanuel 1999). For CLD24, in addition to the cold wake, there also exists pronounced cooling of the ocean in a nearly circular area beneath the TC core, with the lowest SST less than 26°C. Since the symmetric component of the SST cooling can weaken the TC intensity more effectively (Wu et al. 2005), the CCE-induced nearly symmetric SST cooling pattern under the TC center as well as its much lower value could significantly block the TC intensification.
Plan views of the SST (contour, °C) and the 10-m surface winds (shaded, m s−1) at 24 h for (a) CTRL and (b) CLD24. The black spots denote the simulated storm track at 3-h interval.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Figure 4 shows the evolution of the averaged upper-ocean temperature around the TC center for two coupled experiments. The SST in CTRL decreases steadily and the ocean water under the mixed layer is also cooled gradually because of the vertical mixing and upwelling associated with the strengthened surface winds. With the TC moving over the CCE, the ocean temperature around TC center in CLD24 drops down rapidly from 12 to 24 h and then increases gradually until 36 h. Afterward, the TC exits the CCE regime and the ocean temperature variation exhibits a similar trend with that in CTRL.
Time series of the azimuthally and radially averaged ocean temperature (°C) within a radius of 100 km from the storm center for (a) CTRL and (b) CLD24.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
where H26 is the depth of the 26°C isotherm, ρ is the ocean density taken as 1 g cm−3, cp is specific heat at constant pressure taken as 1 cal g−1 K−1, T is the ocean temperature, and 26°C is recognized as the minimum temperature beneficial for TC intensification. Figure 5 shows the temporal variations of the averaged OHC. The OHC in CTRL decreases gradually owing to the stronger cooling of the upper ocean with the storm intensification (Fig. 6). CLD24 exhibits otherwise consistent trend of the OHC with CTRL except that at around 24 h there exists a sharp decrease. At 24 h the OHC in CLD24 exhibits its minimum value of 56 kJ cm−2 due to the existence of the CCE, 59% less than that in CTRL, which shows a value of 136 kJ cm−2. The much smaller value of OHC for CLD24 lasts from approximately 12 to 36 h, which limits the energy supplied from the ocean to power the TC strengthening. During the time from 84 to 114 h, CLD24 gives somewhat larger OHC than CTRL, which is beneficial for the storm reintensification.
Time series of the averaged oceanic heat content (kJ cm−2). The averaging is done within a radius of 100 km from the storm center.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Time evolution of (a) the minimum sea level pressure (hPa) and (b) the maximum azimuthal mean 10-m wind speed (m s−1).
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
4. Atmosphere response
a. TC intensity and size
The TC tracks simulated by three experiments show little difference (not shown) and all move northwest under the easterly steering flow and the beta effects (Fig. 3). However, the TC intensities in terms of the minimum sea level pressure (MSLP) and the maximum surface wind (MSW) for different runs show great discrepancies (Fig. 6). During the early period of simulations, when the cold wake has not been well strengthened, the model storms in both UNCP and CTRL develop rapidly and the differences of the MSLP and MSW are relatively small. With the development of the cold wake (Fig. 4a), their difference enlarges steadily after about 24 h. The TC in CTRL experiences an intensification period until 72 h, and then it basically reaches maturity, with its lowest MSLP of 923 hPa and largest MSW of 47 m s−1. Contrastingly, the TC in UNCP undergoes a more rapid and longer intensification period, which lasts until about 96 h. As a result, the intensity difference between CTRL and UNCP becomes more significant as the TC in CTRL reaches a steady state in advance. At the end of the simulation the MSLP difference is as large as 21 hPa, and the MSW difference reaches 8 m s−1. It indicates that the ocean coupling has notably negative impacts on the storm intensification rate and thus its final intensity since the TC intensity is proportional to the efficiency of the intensification (Nolan et al. 2007). The large changes in storm intensity while high similarities in storm track caused by the coupling effects are well consistent with the results in other coupled systems (Bender and Ginis 2000; Zhu et al. 2004; Chen et al. 2010).
A comparison of CLD24 and CTRL is further made to clarify the effect of the CCE. Before 12 h, when the TC in CLD24 has not been affected by the CCE, the MSLP and MSW of CLD24 are nearly the same as that of CTRL. Afterward, the TC in CLD24 is weakened progressively as it enters the CCE region, in contrast with the continuous intensification in CTRL. The intensity difference between CLD24 and CTRL enlarges steadily until approximately 30 h, shortly after the TC passes over the CCE center, when the MSLP reduction caused by the CCE attains a maximum value of 12 hPa. It seems that negative effects of the CCE accumulate as the TC crosses over the CCE and reach a maximum before the TC leaves the CCE. The storm reintensifies again and undergoes a period of recovery after departure from the CCE. During this time the MSLP and MSW discrepancies between CLD24 and CTRL decrease gradually. The storm in CLD24 returns to its steady state at 72–84 h, suggesting that the recovering period lasts about 36–48 h, which should be dependent on some parameters such as the OHC, the TC size and strength, and so on. The continual effects of the CCE may be achieved by changing the internal structures of the TC. After the storms in CTRL and CLD24 reach maturity, they possess the similar but not identical intensity, which could be due to their somewhat different asymmetric features. Although the CCE can directly affect the inner core of the TC while the cold wake only works in the right rear of the TC, the effect of the CCE on TC intensity still seems to be less significant than the cold wake, which could be because the interaction between the TC and the CCE is short term but impacts of the cold wake are permanent.
Figure 7 exhibits the evolution of the radius of hurricane-force wind to denote the TC size. Evidently the storm circulation enlarges with the storm development for all runs. CTRL shows progressively smaller storm size than UNCP, especially after 72 h. At the end of the simulation the storm in CTRL is about 24.7 km (14%) smaller than that in UNCP. It suggests that the cold wake has hindered the outward expansion of storm wind fields, which has been obtained by Chen et al. (2010) in their simulations. The CCE has also notably affected the TC size, though not as great as the cold wake. CLD24 exhibits a smaller storm size ever since 18 h, as the storm intensity appears to be weakened. Of interest is that despite the TC returns to its steady-state intensity sometime after it leaves the CCE, the TC size is unanimously smaller throughout the remainder of the simulation. This at least implies that the recovery of the storm size requires much longer time compared with that of the storm intensity, if not permanent, and verifies that the ocean state could be one of the potential factors determining the TC size. Nevertheless, although the correlation between TC intensity and size should be weak (Chan and Chan 2012), the variation of the storm size seems to show a close relationship with the TC intensity (Fig. 6), suggesting that the TC size change in this case may be partly due to the intensity change.
Time evolution of the azimuthally averaged radius (km) of hurricane-force (33 m s−1) winds.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
b. TC symmetric structures
Considering the surface latent heat fluxes are several times larger than the surface sensible heat fluxes and both have the similar trends (not shown), the surface latent heat fluxes are shown in Fig. 8 on behalf of the total surface heat fluxes. The temporal variation of the surface latent heat fluxes demonstrates a trend corresponding to ocean response fairly well that CTRL gives dramatically lowered surface heat fluxes than UNCP throughout the simulation, and considerably larger values than CLD24 during passage over the CCE. The lowest value in CTRL is 605 W m−2 at 113 h, when UNCP gives a value of 982 W m−2, suggesting that nearly 40% of the surface heat fluxes have been eliminated by the cold wake. The presence of the CCE limits the upward surface enthalpy fluxes from the ocean to a great extent as well, that at 24 h the surface latent heat flux in CLD24 is 75 W m−2 (11%) less than that in CTRL. It should be noted that the averaged surface heat fluxes do not always increase with storm strengthening (e.g., CTRL throughout the simulation), which could be because the eye size is evidently amplified during the simulation (which will be discussed later) so that less eyewall and rainband regions are included within the radius of 200 km, or the water vapor mixing ratio (and the potential temperature) difference between the surface and the lowest half-η level is reduced by cooler SST. Since the TC is thermodynamically maintained by the upward surface fluxes of higher equivalent potential temperature air from the underlying warm ocean (Emanuel 1986), the greatly diminished surface heat fluxes caused by the ocean response result in significant changes in TC structure. Figures 9 and 10 show details of the storm symmetric structures including the evolution of the warm core and the height–radial plots of the azimuthally averaged tangential flows and secondary circulation. Without considering ocean feedback, the warm core in UNCP strengthens steadily with time, and the height of the warm core elevates from 4–6 to 14–16 km after 72 h. Although the change in the height of the warm core does not necessarily imply changes in the storm intensities (Stern and Nolan 2012), the strength of the warm core is generally believed to be well correlated with the TC intensity. The warm core in CTRL, as expected, is evidently weaker than that in UNCP. The warm core in CLD24 begins to strengthen merely after 36 h, apparently delayed by the CCE. When the storm in CLD24 has completely recovered its intensity, that is, approximately after 72 h, it possesses the similar warm-core strength as that in CTRL.
Time series of the surface latent heat fluxes (W m−2). The averaging is done within a radius of 100 km from the storm center.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Time series of the azimuthally and radially averaged temperature anomaly (K) within a radius of 30 km from the storm center for (a) UNCP, (b) CTRL, and (c) CLD24.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Height–radius cross sections of the temporally and azimuthally averaged radial winds (contour, m s−1) and vertical motion (shaded, m s−1) for (a) UNCP, (c) CTRL, and (e) CLD24 and tangential winds (m s−1) for (b) UNCP, (d) CTRL, and (f) CLD24 from 42–48 h.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
By diagnosing the three-dimensional winds, all runs exhibit typical secondary circulation structure: the radial outflow in the upper troposphere, radial inflow in the boundary layer, and slantwise upward motion. UNCP produces a much stronger secondary circulation than CTRL, which is beneficial for the strengthening of the primary circulation through advecting angular momentum inward in the inflow layer. In UNCP there also exists a relatively stronger outflow jet near the top of the planetary boundary layer, which helps maintain the local maximum in tangential winds (Kepert and Wang 2001). During 42–48 h the storm in CLD24 is still in its recovering period and thus gives weaker secondary circulation. The weakening of the low-level radial inflow seems to be more evident than that of the upper-level outflow. The maximum tangential velocity occurs at about a height of 1 km and UNCP gives again the strongest tangential winds. CLD24 presents a smaller value than CTRL, yet the radius of the maximum tangential velocity seems to be slightly larger, suggesting that the eye size is somewhat broadened by the CCE.
c. TC asymmetric structures
To further understand the effects of ocean feedback, the changes in storm asymmetric features are primarily diagnosed in this section. The plan views of surface latent heat flux differences between UNCP, CTRL, and CLD24 are shown in Fig. 11. Corresponding to the ocean response, the reduced surface heat fluxes in CTRL are distributed well above the cold wake. As expected, the CCE-induced changes in the distributions of surface heat fluxes are mainly concentrated in the inner core of the storm, while in the outer region of the storm the CCE shows little impact. Figure 12 shows the Hovmöller diagrams of the azimuthally averaged 2-m temperature for UNCP, CTRL, and CLD24 as well as the radius of maximum surface winds (RMW) for each case. The RMW and thus the eye size in all runs show no evident contraction with the continual intensifying of the storm. Instead, they increase considerably after about 48 h. Similar results have also been shown by Hill and Lackmann (2009), who attribute it to “breaking vortex Rossby waves in the eyewall” as the possible mechanism. The relatively cold zone just outside the RMW in UNCP could be produced by convective downdrafts driven by precipitation as reviewed by Houze (2010). The downdraft zone narrows and weakens probably as a result of increased relative humidity under the eyewall (not shown) or lowered cloud base with the storm strengthening as explained by Yang et al. (2007). Because of the contributions of the cold wake, CTRL shows contrastingly an enlarged cold zone under the eyewall, which is located slightly inward relative to UNCP. Compared with CTRL, CLD24 shows a notably cooler area during 12–36 h under influences of the CCE. The cooler area extends from the outer region to the storm center rapidly with the TC passing over the CCE center and attains a lowest temperature at 24 h, which is situated just under the RMW due to the upwelling of cold ocean water induced by the maximum wind speed. The secondary minimum value of air temperature is located at the TC center, just under the eye. As the TC leaves the CCE and enters similar underlying ocean surface as CTRL, the cooled air is warmed up gradually. It indicates that a portion of the effects of the CCE as well as the cold wake are to cool the boundary layer inflow air just under the eyewall, which limits its unstable energy and the upward transport of water vapor. Additionally, the CCE can also cool the storm eye directly, which may be less efficient in deepening the storm central pressure (Zhang and Chen 2012) but could serve as a negative role as it flows outward and mixes with the eyewall air (Willoughby 1998).
Plan views of the differences of surface latent fluxes (W m−2) at 24 h for (a) CTRL − UNCP and (b) CTRL − CLD24.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Hovmöller diagram of azimuthally averaged 2-m temperature (K) for (a) UNCP, (b) CTRL, and (c) CLD24. The radius of maximum azimuthal mean surface wind is also shown by the dashed line.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Figure 13a displays the temporally and azimuthally averaged temperature difference between CLD24 and CTRL from 18–30 h. The boundary layer in CLD24 is obviously cooled by the CCE, especially in the inner core of the storm, as already shown in Fig. 12c. The most striking feature is the distinctly negative temperature difference (~2.5 K) centered at 2–4 km in altitude within a radius of 30 km from the TC center. The warm core height in both CTRL and CLD24 during this time is 4–6 km (Fig. 9), indicating that this negative temperature difference is not simply a reflection of the warm core strength associated with the storm intensity. This could not be the direct propagation of the low-level eye air cooled by the CCE since it barely exists under a height of 0.5 km and the eye region is generally dominated by subsidence flow. Corresponding to the temperature difference, there is also a moist core centered at 2–4 km high in the storm center from the difference between CLD24 and CTRL (Fig. 13b), probably as a result of the same inducement. The relative cooler and moister core in CLD24 vanishes gradually after 36 h, when the storm has left the CCE (not shown). Another distinctive feature is a much dryer boundary inflow layer in CLD24, which is detrimental for supplying moisture to the upper eyewall region. The radius of maximum vertical velocity at each level is also superposed in Fig. 13. As implied from Fig. 10, the eye size is broadened for several kilometers by the CCE, which is most evident in the lower troposphere.
Height–radius cross sections of the temporally and azimuthally averaged (a) temperature (K) and (b) water vapor mixing ratio (10−4) difference between CLD24 and CTRL from 18–30 h. The radius of maximum azimuthal mean vertical velocity at each level is also shown with the solid line denoting CTRL and dashed line denoting CLD24.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
It seems that under influences of the CCE, the eye air at 2–4 km in altitude, located just under the height of the warm core, becomes distinctly cooler and moister. To explore what physical mechanism works behind this phenomenon, the water vapor mixing ratio qυ budget is conducted for further analysis (see the appendix). The local change in azimuthally averaged qυ is determined by four processes: the mean horizontal advection (HADV) and mean vertical advection (VADV) by the symmetric flow, the diabatic processes including evaporation, condensation and turbulent diffusion (DISS), and the horizontal and vertical eddy processes (EDDY). Figures 14 and 15 show these terms for CTRL and the difference between CLD24 and CTRL. The qυ budget in the boundary layer is dominated by the radial inward advection (Fig. 14a), which is partly offset by upward transfer of the surface enthalpy flux (Fig. 14c). The upward advection of the qυ covers a large area, especially in the eyewall. In the eye region VADV is negative above the boundary layer as a result of compensating subsidence. DISS shows considerably negative values in the eyewall region, which primarily offset the vertical qυ advection, an indication of the water vapor condensation and thus the formation of eyewall clouds. The eddy term contributes positively in the eyewall region, though quite small and mainly negative in the boundary inflow layer. Compared with CTRL, the inward radial advection of qυ in the boundary layer is somewhat weaker in CLD24 (Fig. 15a), and the upward surface enthalpy fluxes are also diminished indicated from Fig. 15c. The vertical advection of qυ, determined by azimuthal mean vertical winds and vertical gradient of qυ, is much smaller in the eyewall region in CLD24 (Fig. 15b) as the consequence of its undermined upward motion (Fig. 10e), and correspondingly the condensation is less significant (Fig. 15c). Since the primary change in qυ caused by the CCE is the moist core in the eye region at 2–4 km in altitude (Fig. 13b), by examining the local qυ tendency due to each term, it is the vertical advection that could play a major role, which should be attributed to changes in the eye subsidence. Other terms have little or negative contributions in this region. These results imply that as a storm passes over a CCE, the updraft and moisture condensation in the eyewall are inhibited probably as a result of reduced upward surface enthalpy fluxes, weakened boundary layer inflow, and cooled low-level eye air flowed into the eyewall. Therefore, the eye subsidence is suppressed since less intense eyewall convection tends to result in a raised inversion and thus abated descent in the eye (Willoughby 1998). The subsidence-induced adiabatic warming is thus diminished and less dry air aloft is transported into the lower layer, and as a result, the low-level air in the eye becomes cooler and moister, as inferred from Fig. 13.
Height–radius cross sections of the temporally and azimuthally averaged qυ budget (10−7 s−1) for CTRL due to (a) horizontal advection, (b) vertical advection, (c) diffusion, and (d) eddy from 18–30 h.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
As in Fig. 14, but for CLD24 − CTRL.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
The moist static energy, or equivalently the equivalent potential temperature θe, has a close relationship with the TC evolution. Figure 16 shows the height–radius cross sections of θe, defined as θe = θ exp(Lqυ/CpT) by Rotunno and Emanuel (1987), which have the typical pattern as shown in previous observations and numerical simulations (Hawkins and Imbembo 1976; Wang and Xu 2010). In the boundary layer θe increases steadily inward to a maximum in the storm center, an indication of the inflow air acquiring energy because of the upward transport of surface enthalpy fluxes from the underlying ocean. The great radial gradient in the eyewall region suggests intense updraft there since θe in an air parcel is nearly conserved above the boundary layer. Another distinct feature is the lowered value of θe in the storm center above 2 km in altitude, which is the evidence of eye subsidence (Houze 2010). The difference of θe between CLD24 and CTRL is highly similar to the difference of qυ (Figs. 13b and 16b), suggesting the change of θe is mainly determined by the moist processes. The lower θe of CLD24 in the boundary layer is caused by the diminished upward surface enthalpy fluxes due to the presence of the CCE (Fig. 8). The θe following the eye air parcel is much larger above 1 km in CLD24 (Fig. 16b), which further evidences the suppressed eye subsidence. It also indicates that increase of θe in the lower eye region above the boundary layer contributes little to the storm intensification.
Height–radius cross sections of the temporally and azimuthally averaged equivalent potential temperature (K) for (a) CTRL and (b) CLD24 − CTRL from 18–30 h.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
The asymmetry of the storm structure is confirmed to be a limiting factor for TC strengthening, no matter that it is generated by environment forcing or internal dynamical process (Peng et al. 1999; Nolan and Grasso 2003; Nolan et al. 2007; Yang et al. 2007). Since the asymmetric structures are dominated by low-number waves (Wang 2002), the azimuthal wavenumbers-1–3 maximum radar reflectivity difference between CLD24 and CTRL is shown in Fig. 17 to analyze the evolution of the CCE induced asymmetry. The calculation is taken along the RMW since the eye and eyewall size varies much with time, though a fixed radius in the inner core gives similar results (not shown). From Fig. 17a, the changes of the wavenumber-1 structure caused by the CCE increase steadily as the storm encounters the CCE and reach a maximum at around 30 h, when the CCE-induced weakening of the storm intensity is also most significant (Fig. 6). After 36 h the storm exits the CCE regime, and the asymmetry difference becomes smoother with time but remains significant until about 84 h. The wavenumber-2 and -3 structures show similar changes but with smaller magnitudes. It indicates that the CCE drives the generation of significant inner-core asymmetries, which greatly prevents the storm intensification. After the storm leaves the CCE, the residual asymmetry still works, so that the storm remains weaker for a certain time period. However, when the CCE-induced asymmetry has been basically eliminated by storm axisymmetrization, the storm recovers to its steady state completely and possesses similar intensity as the control run.
Azimuth–time Hovmöller diagram of the (a) wavenumber-1, (b) wavenumber-2, and (c) wavenumber-3 maximum simulated radar reflectivity (dBZ) difference between CLD24 and CTRL along the RMW.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
Both the simulations conducted by Zhu et al. (2004) and Chen et al. (2010) show that the strongest convergence in the boundary layer rotates counterclockwise when including the cold wake feedback. In this study there is also a counterclockwise shift in the strongest convergence in CTRL compared with UNCP (Fig. 18), but not as dramatic as shown by Zhu et al. (2004). In some other times this rotation is even not evident (not shown), suggesting it is not an inevitable result of the ocean feedback. CLD24 also shows slightly counterclockwise rotation of the strongest convergence compared with CTRL (Fig. 18c), but the result may be different if the storm moves toward different directions (e.g., northeast) or the CCE is located at the right or left side of the storm. Nevertheless, the shift of the convergence fields indicates that the horizontal patterns of the vertical motion in the boundary layer have been altered by the cold wake and CCE, and thus changes in low-level asymmetric structures occur.
Plan views of the temporally averaged divergence (10−4 s−1) at 10 m in altitude from 54–60 h for (a) UNCP, (b) CTRL, and (c) CLD24. Values smaller than 15 × 10−4 s−1 are contoured by an interval of 3 × 10−4 s−1 to highlight the maximum convergence.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
d. Dependence on the horizontal resolution
The above discussions are based on high-resolution (1.67 km) simulations. For coarser resolution, or if the cumulus convection processes are represented implicitly, it is important to diagnose whether the ocean feedback in terms of the cold wake and CCE has a similar effect. Therefore, two additional groups of experiments are conducted with identical model configurations as illustrated in section 2, but with different horizontal resolutions. One group is conducted without the innermost 1.67-km mesh, that is, a highest resolution of 5 km. The other one uses only the outmost domain, with a resolution of 15 km. The simulated storm intensities by two groups are shown in Figs. 19a,b separately. By a comparison of Figs. 6a and 19, it is evident that the storm intensity increases greatly with improving horizontal resolution, which could be due to changes in the representation of physical processes important to storm intensity (Gentry and Lackmann 2010). All the runs show remarkably negative impacts of the cold wake. The TC response to the CCE shows great similarities between 1.67-km runs and 5-km runs, including the similar time period of recovery, which indicates that changes in the storm intensity caused by the CCE are mainly controlled by the low-number asymmetries since higher-number asymmetries cannot be sufficiently resolved by 5-km resolution (Gentry and Lackmann 2010). For 15-km runs, the changes in the storm intensity caused by the CCE show some discrepancies with the former two groups of runs. The most significant weakening of the storm intensity occurs much later and the weakening seems to be long lasting. The storm basically recovers its intensity only after 96 h, about 12–24 h delayed relative to the 1.67- and 5-km runs. This difference should be due to the implicit parameterization of the cumulus convections or poor representation of the storm structures such as the eyewall and spiral rainbands. It seems that the 5-km resolution is adequate to reproduce the storm intensity response to the CCE, though a higher resolution is required to resolve more detailed structures. However, too coarse resolution may lead to a somewhat unrealistic response of the TC to the CCE.
Time evolution of the minimum sea level pressure (hPa) for (a) 5-km horizontal resolution and (b) 15-km horizontal resolution.
Citation: Monthly Weather Review 141, 4; 10.1175/MWR-D-12-00123.1
5. Summary and conclusions
In this study the effects of CCE on TC evolution are investigated by using a coupled atmosphere–ocean model with idealized atmospheric and oceanic environment. A rather strong CCE is constructed for experiments to make the effects of the CCE more salient and prone to be isolated.
The interaction between the storm and the background ocean is consistent with previous studies. The TC leaves behind a cold wake with the maximum SST cooling located outside the radius of the maximum surface winds. The storm track shows little sensitivity to ocean coupling, while the storm intensification rate and final intensity are greatly influenced. The cold wake also produces notable influences on the TC structures that the warm core strength is clearly undermined and the secondary circulation is weakened as well. The outward expansion of storm circulation is also hindered, which leads to a decrease of the storm size.
Although the initial SST is kept homogeneously to be 29°C, presence of the CCE has led to both thinner mixed-layer depth and lowered OHC. As the storm passes over the CCE, the SST cooling induced by surface winds is dramatically increased, and this conversely suppresses the storm development. The impacts of the CCE have some differences with the cold wake since the CCE can influence the storm eye directly and the interaction only occurs when the storm passes over it. The storm begins to weaken as it reaches the edge of the CCE, and the weakening reaches a maximum shortly after the storm moves over the CCE center. As the storm exits the CCE regime, it undergoes a period of recovering time, which lasts about 36–48 h. During this time the storm intensity gradually recovers, and eventually it reaches its steady state as the control run, with similar but not identical intensity. The CCE has broadened the eye size during the passage of the storm. The storm size is reduced by the CCE as well, though less distinct than the cold wake. Despite the storm intensity completely recovers after a time period, the storm size is unanimously smaller throughout the remainder of the simulation, which at least implies that the recovery of the storm size requires much longer time than that of the storm intensity.
The CCE has also produced profound influences on the storm symmetric and asymmetric structures. The development of the warm core and three-dimensional winds are suppressed consistently with the storm intensity. The boundary layer inflow is weakened to a much greater extent than the upper-level outflow. In the lower eye region the CCE has induced notably negative temperature difference and positive moisture difference centered at 2–4 km, just below the warm-core height. It is proved not to be the upward propagation of the boundary layer eye air cooled by the CCE since it merely stays under a height of 0.5 km, though the cooled eye air may play a negative role when flowed outward and mixed with the eyewall air. The water vapor mixing ratio budget is conducted to explore the possible mechanisms. The vertical advection process is identified to play a major role, that is, the undermined subsidence occurred in the eye region as a response to the suppressed eyewall convection by the CCE. As a result, less downward dry air from the upper eye region is transported into the lower troposphere and the subsidence-induced adiabatic warming is reduced consequently; therefore, the eye air in the lower troposphere tends to be moister and cooler. The undermined subsidence also leads to distinctly increased θe in this region. By diagnosing the evolution of the wavenumber-1 to -3 asymmetric structures of the storm, the CCE-induced asymmetries grow steadily as it encounters the CCE. After the storm leaves the CCE, the asymmetries become smoother gradually but remain significant for about 36–48 h, which results in a storm with still weakened intensity. After the CCE-induced asymmetries have basically eliminated by the storm axisymmetrization, the storm recovers to its steady state completely. Consistent with previous studies, the cold wake causes a counterclockwise shift in the strongest convergence, and a similar effect is produced by the CCE. It indicates that the horizontal patterns of vertical motion in the boundary layer and thus the low-level asymmetries in the inner core have been altered by the cold wake and CCE. The 5-km resolution seems to be adequate to reproduce the effect of the CCE on TC intensity, while too coarse resolution may lead to an unrealistic result.
Finally, this work is conducted toward a detailed understanding of the effect of the CCE on storm intensity and internal structures. The results highlight the necessity to incorporate subsurface mesoscale cold eddies in the coupled models for improving TC intensity prediction. It should be noted that the conclusions obtained in this study are under the frame of atmosphere–ocean coupling, which does not include the processes of wave feedback and wave–ocean interaction. It should be also noted that this study utilizes a rather strong CCE so as to isolate its roles more easily. For a weaker CCE, its effects are foreseeable to be less influential. Impacts of the CCE should be also dependent on some parameters such as the storm size, translation speed, and the CCE size and location, etc. These issues will be specially explored in the future study.
Acknowledgments
We thank Ron McTaggart-Cowan and two anonymous reviewers for their constructive and detailed comments. This work is supported by the National Public Benefit (Meteorology) Research Foundation of China Grant GYHY201106004, and the National Natural Science Foundation of China with Grants 41005029 and 41105065.
APPENDIX
Equations for Water Vapor Mixing Ratio Budget Analysis
The four terms on the right-hand side of (A2) represent contributions to the azimuthal mean local qυ budget by the mean horizontal advection and mean vertical advection by the symmetric flow; the diabatic processes including evaporation, condensation, and turbulent diffusion; and the horizontal and vertical eddy processes.
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