A High-resolution Simulation of Supertyphoon Rammasun (2014) —— Part I: Model Verification and Surface Energetics Analysis

In the past three decades or so, the forecasting skill for tropical cyclone (TC) tracks has steadily improved, while that for TC intensity still remains low. This is partly due to the fact that the TC track is mainly determined by large-scale environmental circulation, while the TC intensity is controlled by multiscale processes and their interactions, such as sea surface temperature (SST), environmental vertical wind shear (VWS), TC inner-core dynamics, and even cloud microphysics and sea spray processes (Marks and Shay, 1998; Wang and Wu, 2004; Elsberry et al., 2013). Among these processes, some are still poorly understood. The lack of high-resolution observations of TCs, especially in the inner-core region, could be one of the main obstacles for understanding the dynamical/physical processes responsible for TC intensity changes. Fortunately, the use of high-resolution, cloud-resolving models in the last two decades has advanced/ improved our understanding of many aspects of TC intensity and structure changes. It is believed that with improved understanding of TC inner-core dynamics and more advanced data assimilation with high-resolution observations, the forecasting skill of TC intensity and structure changes will continuously improve in the coming decade or so.

Using a three-layer incompressible model, (Ooyama, 1969) successfully simulated the lifecycle of a TC for the first time. Since his pioneering work, remarkable progress has been achieved in numerical model developments and simulations of TCs. In particular, cloud-permitting regional atmospheric models are nowadays widely used in TC simulations. For example, (Liu et al., 1997) simulated Hurricane Andrew (1992) quite realistically using a cloud-resolving model with a finest-mesh resolution of 6 km and suggested that, with high-resolution, realistic model physics and proper vortex initialization, it is possible to predict the track, intensity and inner-core structure of TCs reasonably well. As demonstrated further in their follow-up studies (Liu et al., 1999; Zhang et al., 2000, 2001, 2002; Yau et al., 2004), high-resolution cloud-resolving models can reproduce many fine structures and the dynamics of TCs reasonably well, including the eye, eyewall, and the inner and outer rainbands, as well as their evolutions induced by external environmental forcing and internal dynamics. Based on a 4-km resolution simulation, (Wu et al., 2006) investigated the role of VWS in changes of TC precipitation structure. (Chen et al., 2011) successfully reproduced the rapid intensification (RI) and eyewall replacement cycle in Hurricane Wilma (2005) using the Weather Research and Forecasting (WRF) model with the finest grid length of 1 km. However, improvements in TC simulation depend not only on model resolution but also on many other aspects——in particular, model physics, such as cloud microphysics, planetary boundary layer parameterization, air-sea flux calculation, initial TC intensity and structure, and so on (e.g., Braun and Tao, 2000; Davis and Bosart, 2002; Wang, 2002; Zhu and Zhang, 2006; Li and Pu, 2008; Davis et al., 2010; Cha and Wang, 2013; Deng et al., 2016). Furthermore, the performance of some physical parameterization schemes may also depend on grid size (Zhu and Zhang, 2006; Li et al., 2014; Sun et al., 2014). In addition, (Zhang et al., 2015) found that, in addition to the model's horizontal resolution, the simulated TC intensity and structure could also be sensitive to its vertical resolution.

Another promising advancement in TC research is the theoretical work of Emanuel (1986, 1987, 1988, 1995, 1997) on the maximum potential intensity (MPI) of a TC. The MPI is the intensity a TC can reach given completely favorable environmental oceanic and atmospheric conditions. The theoretical MPI developed by Emanuel, often referred to as E-MPI, has been verified well with axisymmetric model experiments (Rotunno and Emanuel, 1987; Emanuel, 1995). In E-MPI theory, a TC is viewed as a Carnot heat engine, which obtains its energy from the underlying ocean and dissipates its energy to the underlying ocean due to surface friction. Due to different rates of increase in energy production and energy dissipation with wind speed or the intensity of the TC, the TC reaches its MPI as the energy production rate is locally balanced by the frictional dissipation, predominantly under the eyewall or near the radius of maximum wind (RMW) (Emanuel, 1997; Wang, 2012).

However, using the same model of (Rotunno and Emanuel, 1987) but with different model resolutions, (Persing and Montgomery, 2003) found that the peak TC intensity in the model could considerably exceed the E-MPI as the model resolution increased. They called this phenomenon "superintensity". A number of studies hypothesized that the near-surface, high-entropy air in the eye, once entrained into the eyewall, could serve as an additional energy source and increase the TC intensity (Persing and Montgomery, 2003, 2005; Cram et al., 2007). However, (Bryan and Rotunno, 2009a) showed that, because of the small volume of the eye, the high-entropy air transported from the eye to the eyewall could only account for a small portion of the total entropy budget in the eyewall and contributed to less than 4% of the storm's peak intensity. (Wang and Xu, 2010) demonstrated that the underestimation of peak intensity by the E-MPI results mainly from the assumption of the balance of energy production and frictional dissipation near the RMW. They showed that the energy production within a radius of 2-2.5 times the RMW is needed to balance the frictional dissipation under the eyewall at the mature stage, suggesting that radial inward energy transportation from outside the eyewall needs to be incorporated into the E-MPI. (Frisius and Schönemann, 2012) extended the E-MPI by considering an additional energy source outside the eyewall in terms of CAPE (convective available potential energy), while some other studies have attributed the superintensity to unbalanced flow in the boundary layer (Smith et al., 2005, 2009; Bryan and Rotunno, 2009a).

However, most of the above studies were based on idealized conditions or simple numerical models, and focused mainly on the mature stage of TCs. The energetic processes during TC intensification, especially in the RI phase, have not been thoroughly investigated——in particular, for real case simulations. The purpose of this study is to extend the previous work on the energetics in the TC surface layer to a successful high-resolution, real-case simulation of Supertyphoon Rammasun (2014). In this regard, the simulation is first verified against available observations, including environmental flow, synoptic weather systems, and TC structure, such as the storm eye, eyewall, and rainbands. The results are then used to examine the surface energetics during the RI phase, as well as the subsequent intensity evolution. Section 2 provides an overview of Supertyphoon Rammasun (2014) and describes the model configuration. The simulation results, including the TC track and intensity, as well as the TC structure, are verified against available observations in section 3. In section 4, the surface energetics components are examined based on the simulation results. Conclusions are drawn in the last section.

Supertyphoon Rammasun (2014) was the most intense TC over the western North Pacific in 2014. It was the strongest TC that made landfall over the Chinese mainland since 1949. Rammasun (2014) formed at 1800 UTC 13 July in the western North Pacific, with its center at (8.8^°N, 152.3^°E), and moved westwards along the southern edge of the western Pacific subtropical high towards the Philippines. It then intensified to a severe typhoon, before striking the central Philippines at 0900 UTC 15 July, bringing gale force winds and heavy rains over the Philippines. It weakened a little bit after its landfall over the Philippines and then moved into the South China Sea (SCS) and turned northwestwards (Fig. 1). Rammasun (2014) reorganized and reintensified over the SCS from 0000 UTC 16 July to 0000 UTC 19 July.

Figure 1.  The observed (a) track and (b) intensity of Supertyphoon Rammasun (2014). In (b), the dashed curve denotes the minimum central sea level pressure (units: hPa), the solid curve denotes the maximum sustained 10-m wind speed (units: m s^-1), and the gray shading from 0000 UTC 16 July to 0000 UTC 19 July 2014 indicates the simulation period of this study.

Because of high SST and favorable environmental conditions over the SCS, Rammasun (2014) experienced an RI phase in the northern SCS, about 500 km southeast of Hainan Island. During this stage, it reached a peak intensity of 72 m s^-1, shortly before it struck Hainan as the most intense landfalling TC over the Chinese mainland since 1949. Rammasun (2014) struck Wenchang, a city in northern Hainan Island, at about 0700 UTC 18 July, and led to great losses of lives and property. Sweeping over the whole island, Rammasun (2014) moved across the Qiongzhou Strait and continued heading over the Chinese mainland. It eventually dissipated in Guangxi Province near the border between China and Vietnam on 20 July (Fig. 1a).

It is worth noting that Rammasun (2014) experienced two RI phases. The first RI phase was from 1800 UTC 13 to 0600 UTC 15 July, when it was approaching the east coast of the Philippines over the western North Pacific. The second RI phase was from 1800 UTC 16 to 0600 UTC 18 July, over the SCS, before the storm struck Hainan Island (Fig. 1b). The two RI phases caused great challenges for operational forecasting of the storm's intensity. In this study, we focus only on the second RI phase, i.e., the reintensification stage after Rammasun (2014) moved over the SCS.

The high-resolution Typhoon Regional Assimilation and Predication System (T-RAPS) of the State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, was adopted in the simulation. T-RAPS is a real-time forecasting system consisting of a dynamical initialization (DI) scheme for the initial TC vortex (Cha and Wang, 2013), a state-of-the-art atmospheric model in the form of the Advanced Research WRF (ARW) model, version 3.5.1 (Skamarock et al., 2008), and a post-processing module. The DI scheme uses 6-h cycle runs initialized at 6 h prior to the initial time of the forecast/simulation, to spin up the axisymmetric component of the TC vortex (Cha and Wang, 2013; Wang et al., 2013). When the storm intensity is comparable to the best-track intensity, the cycle run is terminated and followed by the model simulation with the so-called warm startup of model dynamics and physics. More details on the DI scheme can be found in (Cha and Wang, 2013) and (Wang et al., 2013). This DI scheme can greatly improve the initial intensity and structure of the targeted TC, as well as the subsequent simulation (Wang and Wang, 2014).

A 72-h cloud-resolving simulation of Rammasun (2014) is performed using T-RAPS in this study. The initial time of the simulation is 0000 UTC 16 July 2014. Three two-way interactive nests are employed in the simulation, with horizontal resolutions of 18, 6 and 2 km and domain sizes of 310× 250, 270× 270 and 210× 210 grid points (lat × lon), respectively. The model is run with 50 vertical levels between the model top at 10 hPa and the surface. The outermost domain is stationary with center at (19^°N, 116.9^°E), while the two inner nests move with the TC during the simulation. The Kain-Fritsch cumulus parameterization scheme (Kain, 2004) is used in the outermost domain only. Other physical parameterizations include the WSM6 microphysics scheme (Hong and Lim, 2006), the BouLac scheme (Bougeault and Lacarrere, 1989) for the planetary boundary layer, the Monin-Obukhov surface-layer scheme (Paulson, 1970), and the Dudhia cloud radiation scheme (Dudhia, 1989). The initial and lateral boundary conditions are interpolated in both time and space from the six-hourly FNL (final analysis) data of the National Centers for Environmental Prediction. The SST is specified using the Optimum Interpolation Sea Surface Temperature (OISST) dataset (Reynolds et al., 2002). The model outputs, including the simulated track, intensity, and all related variables from the innermost domain, are saved every 15 minutes.

The simulation reproduces the TC track and intensity well (Fig. 2), as compared with the best track of the Joint Typhoon Warning Center (JTWC). Track errors are generally less than 90 km during the entire 72-h simulation. The simulated TC center is located slightly east of that observed between 24 h and 48 h of simulation. A large area of warm water is apparent in the northern SCS, with averaged SST over 302 K, which is favorable for TC intensification. The simulated storm intensity is comparable to that observed, either in terms of maximum sustained 10-m wind speed or central sea level pressure. Note that although the central sea level pressure in the model simulation is higher than the observed before 0000 UTC 18, the simulated maximum surface wind speed agrees much better with the observed. More importantly, the RI phase from 1800 UTC 16 to 0600 UTC 18 July is also well simulated. Therefore, the cloud-resolving simulation not only reproduces the track, but also captures the intensity changes, including the second RI phase of Supertyphoon Rammasun (2014).

Figure 2.  (a) Observed (black) and simulated (blue) TC track and observed SST at 0000 UTC 16 July 2014. (b) Observed (solid) and simulated (dashed) TC intensity, in terms of maximum sustained 10-m wind speed (black; units: m s^-1) and central minimum sea level pressure (gray; units: hPa).

Nevertheless, there are a number of deficiencies in the simulation that should be noted. Observationally, from 1800 UTC 17 to 0600 UTC 18 July, the intensification of the storm slowed down a little bit, which is also apparent in the model simulation, but for a relatively shorter duration than observed. This slight slowdown of intensification could result from the SST cooling induced by ocean upwelling, which is not included in the simulation. We can also see that the simulated TC decays more rapidly than that observed after landfall. This could be related to other factors, such as the inaccuracy in representing land surface processes in the model, errors in the environmental VWS in the model simulation, and so on. Since our interest lies chiefly in the structure and intensity over the ocean, the intensity bias after landfall is not a great barrier for our following analysis.

Geostationary satellites are commonly used to monitor TCs because of their coverage of vast areas in the tropics and continuous observations at high temporal resolutions. To evaluate the overall model performance in simulating the storm structure, we construct synthetic images and compare them with the geostationary satellite observations from the Multifunctional Transport Satellites 2 (MTSAT2). The synthetic images are produced by the Community Radiative Transfer Model (CRTM), which simulates satellite-observed brightness temperatures by considering the emission and extinction at the surface and in the atmosphere, given the simulated atmospheric profiles and surface conditions in the numerical model (Weng, 2007). Using the synthetic images, we evaluate the model performance not only in terms of cloud features, but also the circulations beneath these features (Hasler et al., 1998; Grasso et al., 2014; Jin et al., 2014). Figure 3 shows images from MTSAT2 in the infrared window channel with a central wavelength of 10.8 μm (Figs. 3a and c), and the corresponding synthetic images based on our simulation (Figs. 3b and d). Note that the spatial resolution of the MTSAT2 images is 4 km, and that of the synthetic images varies with model configuration (18 km for Fig. 3b and 6 km for Fig. 3d). As we can see from Fig. 3, the model reproduces the synoptic- and mesoscale cloud systems, including the mei-yu cloud belt extending from the Japan Sea to Southwest China, the cloud features of Supertyphoon Rammasun (2014), the incipient TC (Matmo) disturbance southeast of Rammasun (2014), and the cloud clusters in the monsoon flow south-southwest of Rammasun (2014) (Figs. 3a and b). This indicates that the large-sale circulation is reasonably simulated.

Figure 3.  Brightness temperature (units: K) of the MTSAT2 infrared channel at 10.8 μm from the observation (left) and model simulation (right) at 0000 UTC 17 July 2014. The upper panels (a, b) are for the outermost domain and the lower panels (c, b) are for the second model domain. The red dots in (c) show the locations of four radiosonde stations whose data are used in the verification of the simulation in this study: A, Haikou; B, Xisha; C, Laoag; D, Tanay.

The simulated cloud features of Rammasun (2014) generally resemble the observed. The sizes of the central overcast areas in the simulation are similar to but slightly smaller than those in the observation. The locations of the outer spiral cloud bands in the simulation also agree well with those observed. In the southwestern quadrant of the TC outer-core region, feathery cirrus clouds radiating out to the southwest indicate strong outflow from the northeast to the southwest, which resulted from the interaction between the TC and the monsoon circulation (Figs. 3c and 3d). Namely, the large-scale northeasterly VWS associated with the low-level southwesterly monsoon flow predominantly configured the outflow layer cloud features. There were two outer rainbands at this time: one spiraled outwards to the southeast; and the other, originating from the west, spiraled to the north of the TC (Fig. 3c). The rainband to the east was much weaker than that to the west and is not well simulated in the model (Fig. 3d). With the intensification of the storm, the rainband to the west grew to become a primary rainband, while the one to the east dissipated eventually (not shown). The above comparison between the MTSAT2 observation and synthetic images suggests that the simulation reproduces the large-scale circulation and the primary cloud systems reasonably well. The model also captures the mesoscale structure of Rammasun (2014) to a certain degree, including the outer spiral rainbands.

Because the infrared channels onboard MTSAT2 are sensitive to clouds, the products cannot be used to infer the structure under clouds. Since microwaves have the ability to penetrate non-precipitating clouds, microwave products can provide useful information on cloud and precipitation structures. The Advanced Technology Microwave Sounder (ATMS), one of the main sensors onboard Suomi-NPP, which is a new generation polar-orbiting meteorological satellite developed in the United States, has 22 channels in bands from 23 GHz through 183 GHz. Via the CRTM, we can also obtain synthetic images of ATMS from our model simulation. Figure 4 shows the observation (Fig. 4a) and synthetic images (Fig. 4b) of ATMS in channel 1 (23.8 GHz). This channel is sensitive to cloud water and precipitation, with high brightness temperatures indicating high cloud water content. The TC eye is very clear in Fig. 4a, with the center at (15.6^°N, 116.9^°E). In the MTSAT2 cloud image (Fig. 3c), the TC eye is covered by thick cloud and cannot be identified, even six hours later (0000 UTC 17 July). According to the synthetic image, the simulated TC eye is larger than the observed, while the eyewall in both the observation and simulation shows a significant asymmetric structure, with strong convection located in the south-southwest quadrants, as we can see from Fig. 4. This is consistent with the prevailing environmental northeasterly VWS as mentioned above; namely, convection was enhanced downshear and downshear-left (Wang and Holland, 1996; Reasor et al., 2004; Chen and Gopalakrishnan, 2015; Gu et al., 2015, 2016). Moreover, the two outer rainbands, as mentioned above, can also be detected from the ATMS images. In particular, the rainbands to the southeast can now be clearly seen in the model simulation (Fig. 4b). Note that the outer rainband to the east breaks upshear and dissipates more rapidly in the simulation (Fig. 3d). These results suggest that the asymmetric structure of the eyewall and outer rainbands are reasonably captured in the simulation.

Figure 4.  Brightness temperature (units: K) of ATMS channel 1 with a central frequency of 23.8 GHz from the (a) observation and (b) simulation. The validated time of observation is 1755 UTC 16 July 2014, and that of the simulation is 1800 UTC 16 July 2014.

Figure 5.  The (a) observed and (b) simulated composite reflectivity (units: dBZ) at 0600 UTC 18 July 2014, and height-latitude cross sections of reflectivity in the (c) observation and (d) simulation across the TC center, which is shown as the dashed line AB in (a). The black pentagrams in (a) and (b) denote the location of the Doppler radar at Haikou.

Figure 6.  The observed (black) and simulated (red) radiosonde profiles at 0000 UTC 17 July 2014 at (a) Haikou, (b) Xisha, (c) Laoag, and (d) Tanay. Solid lines denote temperature and dashed lines denote dew-point temperature.

As Rammasun (2014) approached Hainan Island, its inner core structures were well captured by Doppler radar at Haikou. Composite reflectivity maps based on observations and the simulation are shown in Figs. 5a and b, respectively. The validated time is 0600 UTC 18 July, shortly before the TC made landfall. The primary rainband with high reflectivity in the southwest quadrant of the TC observation is reasonably simulated. However, there are still some deficiencies in the model simulation. The simulated eyewall is much wider and the corresponding reflectivity is considerably higher than observed. Observationally, the eye and eyewall were surrounded by a weak-echo annulus (i.e., moat), with averaged reflectivity less than 30 dBZ. The moat is often associated with eyewall replacement (Houze et al., 2007; Houze, 2010). (Wang, 2008) demonstrated that the moat is mainly controlled by subsidence associated with the overturning flow from eyewall convection and stratiform precipitation outside the eyewall. The simulation fails to reproduce the moat. Moreover, the simulated eye is too large, with a distinctly polygonal structure, which might be due to strong potential-vorticity mixing (Schubert et al., 1999) and wave breaking caused by barotropic instability (Itano and Hosoya, 2013). The height-latitude cross sections of reflectivity across the TC center, compared in Figs. 6c and d, suggest that the model reproduces the vertical structure of the TC reasonably well. Note that some blind areas in both the lower and upper levels in Fig. 6c are due to the limitation of the radar elevation angle. Besides the discrepancies mentioned above, the simulated eyewall tilts more outwards with height than observed, in particular above 6 km. This might be associated with the larger size of the RMW in the simulation (Stern et al., 2014) and interaction between the TC vortex and environmental VWS (Hazelton et al., 2015). These results suggest that, although the model reproduces the track, intensity, and both the symmetric and asymmetric structures of the TC reasonably well, there are still considerable deficiencies in the simulation, especially with respect to the size of the eye and the width of the eyewall, due to the model's resolution and/or imperfect physical parameterizations.

In addition to the above comparisons with remote sensing observations, data from four sounding stations (Fig. 3c)——Haikou (station number: 59758), Xisha (59981), Laoag (98223) and Tanay (98433)——are also used to verify the vertical profiles of temperature and humidity in the model simulation (Fig. 6). Haikou and Xisha are situated to the west of the TC, while Laoag and Tanay are to the east. The low-level monsoonal flow transported large amounts of moisture from the Indian Ocean, all the way towards the periphery of the TC, leading to much higher humidity at stations B, C and D than at station A. Station A was in a clear-sky region outside the TC's clouds (Fig. 3c) and was controlled by subsidence and, thus, a deep dry layer. Although a similar situation occurred for stations C and D, because of the low-level moisture advection, dry layers at both stations were shallow and remained only at the upper levels. The temperature profiles in the simulation at all stations are comparable to those based on observations. The relatively larger errors appear in the dew-point temperatures. Nevertheless, the comparison of the sounding profiles suggests that our model captures the main features in the middle and low levels, and simulates the vertical structure of temperature better than that of humidity.

Figure 7.  Radius-time Hovmöller diagrams of the azimuthal mean (a) C _k/C _d, (b) SH flux (units: W m^-2), and (c) LH flux (units: W m^-2). The black curve in each panel shows the azimuthal mean RMW at the lowest model level, which is calculated based on model output every 15 minutes and smoothed by five points running average for 10 times.

The above model verification using geostationary satellite observations in the infrared channel, polar orbiting satellite observations in the microwave channel, Doppler radar reflectivity, and radiosonde data, confirms that our simulation captures the main features of the synoptic-scale weather systems and the overall structure of Supertyphoon Rammasun (2014). Although there are some discrepancies, the simulation can at the very least be used to understand the intensification processes of the storm.

The high-resolution simulation results are used to evaluate the surface energetics under the TC. Following (Wang and Xu, 2010), the energy production rate (P _r) and the frictional dissipation rate (D _i) can be written as \begin{equation} P_{\rm r}=2\pi\int_0^{r_0}P_{\rm D}r{\rm d}r , (1)\end{equation} and \begin{equation} D_{\rm i}=2\pi\int_0^{r_0}D_{\rm S}r{\rm d}r , (2)\end{equation} where \begin{eqnarray} P_{\rm D}&=&\varepsilon({\rm SH+LH})=\varepsilon\Bigg[\dfrac{1}{2\pi}\int_0^{2\pi}\rho C_{p}C_{\rm k}|{V}|(T_{\rm s}-T_{\rm a}){\rm d}\lambda\nonumber\\ &&+\dfrac{1}{2\pi}\int_0^{2\pi}\rho L_{\rm v}C_{\rm k}|{V}|(q_{\rm s}-q_{\rm a}){\rm d}\lambda\Bigg] ,\ \ (3)\end{eqnarray} SH and LH are sensible heat and latent heat fluxes respectively and \begin{equation} D_{\rm S}=\dfrac{1}{2\pi}\int_0^{2\pi}\rho C_{\rm D}|{V}|^3{\rm d}\lambda . \ \ (4)\end{equation} In the above, ε denotes the thermodynamic efficiency, which is determined by temperatures at the ocean surface and in the outflow layer; C_p is the specific heat of dry air at constant pressure; L _v is the latent heat of vaporization; T _s is the SST; q _s is the saturation mixing ratio of water vapor at SST; T _a and q _a are air the temperature and water vapor mixing ratio at the lowest model level, which is about 38 m in our simulation; |V| is the lowest model level wind speed; C _k and C _d are the surface exchange and drag coefficients at the lowest model level as well; Λ is the azimuth, r is the radius; and ρ denotes the air density at the lowest model level. P _D and D _S are the azimuthal mean energy production and frictional dissipation rates at a given radius. Here, P _D includes only the sensible and latent heat fluxes. In their idealized simulation, (Wang and Xu, 2010) also included the dissipative heating and radiative cooling. In our simulation, dissipative heating is not included; and radiative heating/cooling, which is much smaller than the sensible and latent heat fluxes, is thus not included in our analysis. Furthermore, the mean state of the summer SCS conditions implies a thermodynamic efficiency of 0.34 in our calculation below. We further introduce a net rate of energy gain (ε _g), which is defined as the residual between the energy production rate and the frictional dissipation rate at a given radius: \begin{equation} \varepsilon_{\rm g}=P_{\rm D}-D_{\rm S} .\ \ (5) \end{equation} All calculations discussed below are conducted in cylindrical coordinates following the storm center based on the model outputs at every 15 minutes. To exclude the influence of complex interactions with the land surface when the storm is approaching land, calculations are performed only when the TC is moving over water in the SCS.

Figure 8.  Radius-time Hovmöller diagrams of the azimuthal mean (a) P _D (units: W m^-2), (b) D _S (units: W m^-2) and (c) ε _g (units: W m^-2). The black curve in each panel is the same as in Fig. 7.

Previous studies have already demonstrated that the TC MPI is very sensitive to C _k/C _d (Emanuel, 1995; Bryan and Rotunno, 2009b; Montgomery et al., 2010; Emanuel and Rotunno, 2011). Therefore, we first examine this parameter and SH as well as LH in our model simulation. Figure 7 shows the radius-time cross sections of the azimuthal mean C _k/C _d, SH and LH. The ratio C _k/C _d shows a decreasing trend as the near-surface wind speed increases, and ranges from 0.7 to 0.5 near the RMW (Fig. 7a). This is smaller than what is implied by the E-MPI (Emanuel, 1995), but is comparable with more recent observations and other modeling studies (Black et al., 2007; Montgomery et al., 2010; Zeng et al., 2010; Andreas, 2011; Bryan, 2012). Note that the large C _k/C _d (greater than 0.9) in the eye region is due to the weak wind speed, since the drag coefficient often increases with wind speed for winds less than about 30-35 m s^-1 and changes little as wind speed further increases (Powell et al., 2003; Donelan et al., 2004; Black et al., 2007; Zeng et al., 2010). The SH and LH show large values in regions with high wind speeds near and slightly outside of the RMW. In the eye region, both the LH and SH decrease rapidly towards the storm center. In the inner-core region, the LH is about an order of magnitude larger than the SH, indicating that LH is the primary energy source for TC intensification and maintenance (Figs. 7b and c). Note that, as the TC intensifies, the RMW first keeps shrinking until 1800 UTC 17 July, and then almost remains constant thereafter. This is consistent with recent observations and numerical studies of TCs (Stern et al., 2015; Qin et al., 2016).

Figure 8 shows radius-time cross sections of the azimuthally averaged P _D, D _S and ε _g. Since the LH is much larger than the SH within the TC inner-core region, the overall evolution and radial distribution of the P _D (Fig. 8a) is very similar to that of the LH (Fig. 7b). Since the D _S is proportional to the cube of the near-surface wind speed, it increases rapidly as the storm intensifies (Fig. 8b). In particular, large D _S appears in a narrow area across the RMW and increases rapidly as the TC intensifies (Figs. 2b and 8b). Unlike the radial distribution of P _D and D _S, the rate of net energy gain, ε _g, shows a generally increasing trend radially outwards until 1500 UTC 17 July. However, as the storm further intensifies, the ε _g near the RWM decreases with time and becomes negative from 1800 UTC 17 July. This is consistent with the results of (Wang and Xu, 2010) in their idealized TC simulations. In the eye region, the ε _g remains moderate (about 40-80 W m^-2) and contributes to the high-entropy air in the eye (Xu and Wang, 2010). The negative ε _g near the RMW from 1800 UTC 17 to 0600 UTC 18 July implies that the P _D becomes less than the D _S under the eyewall. Since the storm is still intensifying, this result suggests that radially inward transport of energy is required to balance the energy dissipation locally under the eyewall as demonstrated by (Wang and Xu, 2010).

Figure 9 shows the radial profiles of the azimuthal mean P _D and D _S at four given times, for a more subtle comparison of their radial dependence in the simulated TC during the intensification stage. As already seen from Fig. 8, the P _D is generally larger than the D _S at all radii in the early stage of the simulation, when the storm had a maximum wind speed of less than 63 m s^-1, before 1800 UTC 17 July (Figs. 2 and 9a, b). After 1800 UTC 17 July, the D _S becomes larger than the P _D in the narrow radial range across the RMW (Figs. 9c and d). During 0000 UTC to 0600 UTC 18 July, as the TC approaches close to its peak intensity, the D _S is about 19.5% larger than the P _D near the RMW (Fig. 9d). (Emanuel, 1997) assumed that a TC reaches its MPI as the P _D and D _S are approximately balanced near the RMW. The negative ε _g near the RMW in our simulation implies that the storm intensity, in terms of the maximum near-surface wind, exceeds the E-MPI, or the simulated storm is superintense (Persing and Montgomery, 2003). This imbalance of energy production and dissipation under the eyewall was also noticed by (Wang and Xu, 2010) in their idealized simulations at the mature stage. They attributed their simulated superintensity of TCs to the radially inward transport of energy from outside of the eyewall.

Figure 9.  Radial distribution of the six-hourly averaged P _D (units: W m^-2) and D _S (units: W m^-2) during different time periods: (a) 0600-1200 UTC 17 July 2014; (b) 1200-1800 UTC 17 July 2014; (c) 1800 UTC 17 to 0000 UTC 18 July 2014; (d) 0000-0600 UTC 18 July 2014.

Figure 10.  Changes in energy production (red curve) and energy dissipation (blue curve) with maximum sustained 10-m wind speed (units: m s^-1), (a) schematically shown in Wang (2012) and (b) fitted from our simulation. In (b) the points represent the simulation result at each 15-min interval from 1200 UTC 16 to 0600 UTC 18 July 2014.

The different dependence of the surface energy production and frictional dissipation on surface wind speed has been used to explain not only the E-MPI (Emanuel, 1997), but also a TC's intensification (Wang, 2012). The latter study schematically represented changes in the P _D and D _S as functions of the near-surface wind speed near the RMW and viewed TC intensification as the stage with positive ε _g in the area between the two curves, as shown in Fig. 10a. It is interesting to examine this schematic diagram based on our simulation results, and Fig. 10b shows such a plot, with each point representing the P _D (red) or D _S (blue) at the RMW every 15 min from 1200 UTC 16 to 0600 UTC 18 July. We can see from Fig. 10b that the E-MPI predicts an MPI of about 63 m s^-1, while the peak intensity of the simulated TC is about 14% higher than the E-MPI. This suggests that the energy production deficits near the RMW during the RI phase (Figs. 8c and 9c, d) must be supplemented either from the eye region or from outside of the RMW. Although the contribution by the high-entropy air in the eye region to the peak intensity at the mature stage is marginal (Bryan and Rotunno, 2009a; Wang and Xu, 2010) and the energy deficit under the eyewall is balanced by the inward energy transport (Wang and Xu, 2010), a recent study by (Wang and Heng, 2016) demonstrated that the near-surface high-entropy air could contribute significantly to the intensification rate of TCs by promoting convection near the inner edge of the eyewall and the inward shift of the RMW. Therefore, here, we may hypothesize that the intensification of the simulated Rammasun (2014) could also be contributed by the high-entropy air in the eye, since the eye size in the simulation is not that small. At 0600 UTC 18 July, during the mature stage, the area-integrated P _D and D _S can reach a balance within a radius of 86 km from the storm center, i.e., about 2.3 times the RMW. This means that the energy production from surface sensible and latent heat flux in the inner core, including the area outside the RMW, is important for TC intensification.

According to the conceptual model shown in Fig 10a, during the TC intensification stage, the P _D should be larger than the D _S, while their difference, the ε _g, should increase with TC intensity first, and then decreases after the storm reaches a certain intensity. The turning point where the ε _g reaches the maximum is roughly at 60% of the E-MPI. Although the ε _g might not directly determine the intensification rate of the TC, it may be closely related to TC intensification. To examine this possible relationship, we calculate the intensity change of the simulated TC in 12-h intervals, as given below: \begin{equation} I_{\rm t}=\dfrac{V_{\max,_{t+12{\rm h}}}-V_{\max,_t}}{12} . (6)\end{equation} Here, V_max denotes the maximum near-surface wind speed. Figure 11 shows the variations of I _t and the area-integrated ε _g (ε _ga) within an 80-km radius from the TC center. In the early intensification stage, I _t increases until 1200 UTC 17 July and reaches its peak when V_max is about 52 m s^-1. After this stage, TC intensification slows down, possibly due to the outer circulation affected by the land. The ε _ga in the inner-core region starts to increase at 1600 UTC 16 July, shortly before the onset of RI, and increases slowly until 0800 UTC 17 July and decreases rapidly shortly before I _t reaches its peak. This suggests that the intensification of the simulated storm is highly correlated with the ε _ga in the inner-core region. Namely, the ε _g integrated in the TC inner-core region roughly determines the subsequent TC intensification. However, during 0200 UTC 17 to 0800 UTC 17 July, although the ε _ga does not change much, the I _t increases significantly, indicating that other factors might be at work or the response of TC intensity change lags the ε _ga in this case. In addition, since the ε _ga remains steady, the increasing I _t could imply a large dynamical efficiency for the potential energy to be converted to mechanical energy in the TC system. (Schubert and Hack, 1982), based on balanced dynamics, demonstrated that as a TC intensifies, the inner-core inertial stability will increase, making diabatic heating in the eyewall convection more efficiently, to spin up the tangential wind; namely, a faster intensification of the storm. This means that, with the increase of inertial stability in the inner core, the efficiency of energy conversion should be improved as well. Therefore, it is not surprising that the intensification rate of the simulated storm and the peak in ε _ga do not match well with the peak in intensification rate, with the latter lagging the former in the simulation. This suggests that the schematic view on TC intensification based on surface energetics as shown in Fig. 10a needs to be modified to include the effect of dynamical efficiency. This should be a topic for a future study. Nevertheless, the analysis in this study provides a preliminary evaluation for the possibility to develop a theoretical energetics model of TC intensification, and to help understand TC intensification based on the energetics point of view, in future studies.

In addition, our analysis above is based on the azimuthal mean or the axisymmetric component of the TC. The TC intensity change could be considerably affected by asymmetric processes, particularly in the early development stage. Since the TC in our simulation period is already quite strong, with a maximum near-surface wind speed of about 40 m s^-1, this means that the intensification in the simulation could be largely controlled by axisymmetric processes. Nevertheless, it is necessary to further study to what extent the surface asymmetric energetics may affect the TC intensity change. Figure 12 shows the spatial distribution of the ε _g at two given times (1800 UTC 17 and 0000 UTC 18 July), overlapped by model reflectivity at an altitude of 1 km (shading) and wind vectors at the lowest model level. We can see that large ε _g is located slightly outside the eyewall, as already seen in Fig. 8c, and in the outer rainband to the south. Previous studies have emphasized the importance of the outer rainband to TC structure and intensity in terms of heating and cooling due to cloud microphysical processes (Wang, 2009; Li and Wang, 2012; Li et al., 2015), while our study indicates that the outer rainband might play an additional important role in providing the ε _g. However, it is unclear whether and to what degree the asymmetric distribution of the ε _g could affect the TC intensification, which will be a topic for a future study.

Figure 11.  Temporal evolution of the storm intensification rate (black; units: m s^-1 h^-1) and net energy gain (area-integrated ε _g) within an 80-km radius from the TC center (red; units: 10¹² W). Note that all data are calculated based on model output every 15 minutes and smoothed with a five-point running average for 10 times .

Figure 12.  Radar reflectivity at an altitude of 1 km (shading; units: dBZ), wind vectors (units: m s^-1) at the lowest model level, and the ε _g (>200 W m^-2; contours), at (a) 1800 UTC 17 and (b) 0000 UTC 18 July 2014.

Rammasun (2014) was one of the most intense landfalling TCs over China since 1949. In this study, a 72-h high-resolution simulation of Rammasun (2014) is conducted using T-RAPS. The track errors are less than 90 km during the whole simulation period. The model also satisfactorily simulates the evolution of the storm's intensity, as compared with the best-track data of the JTWC, in terms of both maximum surface wind speed and minimum sea level pressure. Moreover, the RI phase is well captured in the simulation.

The simulated storm structure is verified based on remote sensing and conventional observations, including MTSAT2 infrared cloud images, microwave images of the ATMS onboard Suomi-NPP, the reflectivity of the Doppler radar at Haikou, and four stations' sounding data. The CRTM is used to construct synthetic images using the model outputs. The comparison between the synthetic infrared images and the corresponding satellite observations indicates that the simulation captures the large-scale circulation and dominant synoptic-scale weather systems reasonably well, including the mei-yu front, Rammasun (2014), an incipient TC [Matmo (2014)], and convective clusters embedded in the East Asian summer monsoon. The model also roughly captures the main inner-core features and active outer spiral rainbands in Rammasun (2014). In particular, a strong southwestward outflow channel enhanced by the monsoonal circulation and the associated strong northeasterly VWS is simulated in the model. The asymmetric cloud features induced by the environmental VWS are simulated well, as compared with the microwave images. However, there are still many deficiencies in the simulated TC inner-core structure, such as the absence of the moat, polygonal eyewall, and excessive outward tilting of the eyewall, which may be attributable to imperfections in the physical schemes of the model, as well as its resolution. In addition, the sounding profiles at four observational stations are used to verify the vertical structure of the simulated temperature and humidity. The results show that the model simulates the environmental vertical structure around the TC reasonably well, especially in the mid-lower troposphere. The model performs better in simulating the vertical structure of temperature than that of humidity.

Based on the high-resolution model outputs, the surface energetics in the simulated Rammasun (2014) are examined. The energy production and frictional dissipation rates are analyzed. It is shown that the P _D reaches its maximum near the RMW and decreases both inwards towards the TC center and outwards. The D _S is more concentrated near the RMW. The distributions of the P _D and D _S lead to an ε _g that is quite uniform in the inner-core region, except in the eye. As the TC continues to intensify, the ε _g becomes negative under the eyewall when the simulated TC reaches its superintensity stage, i.e., the TC intensity exceeds the E-MPI. The results show that, before the TC reaches its peak intensity, the D _S exceeds the P _D by 19.5% near the RMW, which is mainly balanced by the inward energy transport from outside of the eyewall, i.e., in a radius of 86 km from the storm center, or roughly 2.3 times the RMW. This is consistent with results from idealized simulations in (Wang and Xu, 2010).

A hypothesized connection between intensification and the ε _ga in the inner core is also evaluated. The results show that, initially, both the ε _ga in the inner-core region and the TC intensification rate increase as the TC intensifies. Shortly after the ε _ga reaches its maximum, it starts to decrease as the TC continues to intensify. Subsequently, the TC's intensification rate experiences a lagged decrease. We hypothesize that, in addition to the net energy gain, the dynamical efficiency, which is determined mainly by inertial stability in the inner-core region, also plays important roles. It is suggested that a conceptual view on TC intensification based on surface energetics needs to include the effect of dynamical efficiency. Nevertheless, this study provides a preliminary evaluation for the possibility to develop such a theoretical energetics model of TC intensification. Note that more real-case simulations could be performed in future studies to confirm the results from what is only one case simulation in this study.