PUBLICATIONS. Journal of Advances in Modeling Earth Systems

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1 PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE /2016MS Key Points: Eye excess energy results predominantly from surface entropy flux in the eye region of a TC Eye excess energy contributes insignificantly to convective bursts and rainfall in the inner core region Eye excess energy initiates convection near the inner edge of the eyewall and facilitates eyewall contraction and intensification of a TC Correspondence to: Y. Wang, yuqing@hawaii.edu Citation: Wang, Y., and J. Heng (2016), Contribution of eye excess energy to the intensification rate of tropical cyclones: A numerical study, J. Adv. Model. Earth Syst., 8, , doi: /2016ms Received 10 MAY 2016 Accepted 16 NOV 2016 Accepted article online 21 NOV 2016 Published online 22 DEC 2016 Contribution of eye excess energy to the intensification rate of tropical cyclones: A numerical study Yuqing Wang 1,2 and Junyao Heng 1 1 Key Laboratory of Meteorological Disaster of Ministry of Education, Pacific Typhoon Research Center, Nanjing University of Information Science and Technology, Nanjing, China, 2 Department of Atmospheric Sciences, International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii, USA Abstract Contribution of the near-surface high energy air in the eye region to tropical cyclone (TC) intensification rate (IR) has been evaluated based on idealized numerical experiments using a cloud-resolving, nonhydrostatic atmospheric model. The results show that when the surface entropy flux was turned off in the eye region, the equivalent potential temperature and convective available potential energy in the eye were largely suppressed while the IR of the simulated storm was reduced by about 30% in the rapid intensification (RI) phase. This suggests that the near-surface high energy air in the eye region contributed about 42% to the IR of the simulated storm. The results also showed that the number of convective bursts and the rainfall rate averaged in the inner-core region did not display significant differences. This suggests that the effect of the near-surface high energy air in the eye region on the simulated TC IR was not through the modifications to the overall strength of eyewall convection as previously hypothesized. It is found that the removal of surface entropy flux in the eye region resulted in a slower eyewall contraction and the larger radius of maximum wind (RMW). The results suggest that the near-surface high energy air in the eye region can initiate convection near the inner edge of the eyewall and facilitates eyewall contraction, leading to higher inner-core inertial stability and thus higher dynamical efficiency of eyewall heating in spinning up the tangential winds near the RMW and larger IR of the simulated TC. VC The Authors. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. 1. Introduction Tropical cyclones (TCs) form over tropical oceans with sea surface temperature (SST) higher than 268C and a well mixed layer extending from the surface to a depth about 60 m [Gray, 1968]. Both high SST and deep oceanic mixed layer are necessary to ensure sufficient energy supply in terms of entropy flux from the underlying ocean surface for the development and maintenance of a TC [Malkus and Riehl, 1960]. Although it is not necessary [Montgomery et al., 2009; Montgomery et al., 2015, the wind-induced surface heat exchange (WISHE) is viewed as a major mechanism contributing to the intensification of a TC [Emanuel, 1986; Rotunno and Emanuel, 1987; Zhang and Emanuel, 2016]. WISHE describes a positive feedback between the increase in surface entropy flux and the increase in surface wind speed under the eyewall of a TC. At the intensification stage, the energy input due to surface entropy flux dominates the energy loss due to surface friction [Wang and Xu, 2010]. The former increases linearly with surface wind speed while the latter increases with the cubic power of surface wind speed. When the energy input from the ocean is balanced by the energy loss due to surface friction, the TC could not intensify further and thus reaches its maximum potential intensity (MPI) if there is no any other detrimental environmental effect [Emanuel, 1997; Wang, 2012]. An assumption of the local balance under the eyewall, namely near the radius of maximum wind (RMW), allows Emanuel [1995, 1997] to get an MPI formula (E-MPI) in a very simple form, which was well verified against numerical simulations. However, the maximum intensity of simulated TCs in very high-resolution models often exceeds the E-MPI by as much as 10 50% [Persing and Montgomery, 2003; Cram et al., 2007; Yang et al., 2007; Bryan and Rotunno, 2009; Wang and Xu, 2010; Xu and Wang, 2010a, 2010b]. Some observational studies also show that maximum intensity of observed TCs can also be considerably larger than the E-MPI [Montgomery et al., 2006]. Persing et al. [2003]andCram et al. [2007] proposed that the near-surface high-entropy air in the eye could be a surplus energy source to increase the TC intensity if the air was transported (entrained) into the eyewall. Bryan WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1953

2 and Rotunno [2009], in their axisymmetric model simulations, found that the total magnitude of entropy transport from the eye to the eyewall was less than 3% of the total surface entropy flux under the eyewall and thus is negligible to the entropy budget in the eyewall because of the small volume of the eye region. They showed that the removal of high entropy anomaly in the eye by setting the surface entropy flux in the eye region to be zero resulted in a reduction of about 4% in the maximum tangential wind speed of the simulated storm at the mature stage. This was far too small to explain the more than 40% higher maximum intensity in their simulation than that estimated by the E-MPI. The results were confirmed by Wang and Xu [2010] in their three-dimensional cloud-resolving model simulations. Wang and Xu [2010] further demonstrated through sensitivity experiments that the only additional energy source for the TC intensity was the energy transport from outside of the eyewall. They showed that the frictional dissipation rate was generally larger than the energy production rate under the eyewall at the mature stage of their simulated storm and part of the former was balanced by the inward energy transport by the boundary layer inflow from outside of the eyewall. Although the near-surface high energy air in the eye region has been shown to contribute little to the maximum intensity of a TC, some studies have hypothesized that the near-surface high energy air in the eye region can serve as a boost for eyewall convective bursts (CBs) and thus the onset of the RI of a TC [Barnes and Fuentes, 2010; Rogers, 2010; Chen and Zhang, 2013; Miyamoto and Takemi, 2013; Wang and Wang, 2014]. In an observational study for Hurricane Lili (2002), Barnes and Fuentes [2010] defined an eye excess energy as the difference in equivalent potential temperature (u e ) between the eye and the eyewall and in the depth over which u e in the eye is larger than that in the eyewall. They found that the eye excess energy was large at the beginning of RI while became small during RI. They hypothesized that the eye excess energy might serve as a boost for deep convection in the eyewall and the onset of RI. In a three-dimensional cloud-resolving model, Miyamoto and Takemi [2013] found that high convective available potential energy (CAPE) appeared in the eye region prior to RI of their simulated TC and suggested that the high CAPE was accumulated due to the long residence time of boundary-layer air inside the RMW where inertial stability was high. They proposed that high CAPE triggered deep convection inside the RMW and the onset of RI. Studies by Chen and Zhang [2013] and Wang and Wang [2014] found that CBs played an important role in the RI onset of Hurricane Wilma (2005) and Typhoon Megi (2010), respectively. They found that the RI onset was triggered by CBs in the eyewall, which penetrated into the upper troposphere and triggered the formation of the upper tropospheric warm core. As hypothesized by Miyamoto and Takemi [2013], Wang and Wang [2014] found that slantwise CAPE accumulated in the eye region contributed to slantwise eyewall convection and CBs and thus the RI onset of Typhoon Megi. However, once RI started, although the convective area-coverage in the inner core region increased while the updraft velocity in the upper troposphere decreased and both the slantwise CAPE in the eye and the number of CBs decreased during RI. The above studies seem to suggest that the near-surface high energy air in the eye region might be a trigger for the onset of RI but might play a secondary role in the subsequent intensification of a TC. However, from the balanced dynamics point of view, the intensification rate depends strongly on the radial location of diabatic heating. Vigh and Schubert [2009] found that the response of the upper-tropospheric warming to diabatic heating in a balanced TC vortex reaches the maximum when diabatic heating is inside the RMW where the inertial stability is high. Since the eye is often a reservoir of warmest u e (high energy air) in the boundary layer not only during the onset of RI but also throughout the subsequent intensification of a TC, a question arises as to whether the near-surface high energy air plays any role in the intensification of a TC. The main objective of this study is to address whether and to what degree the near-surface high energy air inside the RMW due to surface entropy flux may contribute to convective activity in the eyewall and thus the intensification rate of a TC based on idealized numerical experiments. The rest of the paper is organized as follows. Section 2 briefly describes the numerical model and experimental design. The intensity evolution of the simulated storms is discussed in section 3. Eye thermodynamics and convective activity in the eyewall in different experiments are analyzed in section 4 and a new hypothesis is elaborated in section 5. Main conclusions are drawn in the last section. 2. Model and Experimental Design The model used in this study is the fully compressible, nonhydrostatic TC model TCM4 developed by Wang [2007]. A full description of TCM4 can be found in Wang [2007], and its applications to the studies of TC WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1954

3 Table 1. Summary of the Numerical Experiments Conducted in This Study a Experiments CTRL IE36 DE36 Modification to the Exchange Coefficient for Surface Entropy Flux Calculation in the Eye Region Default exchange coefficient C k in TCM4 C k 5 0 for r 0.9RMW after 36 h run of CTRL C k is doubled for r 0.9RMW after 36 h run of CTRL a Note that C k is the exchange coefficient for surface entropy flux calculation in the model, and RMW is the azimuthal mean radius of maximum tangential wind, r is the radius from the TC center in the model. dynamics can be found in Wang [2008a, 2008b, 2009], Wang and Xu [2010], Xu and Wang [2010a, 2010b], Fudeyasu and Wang [2011], Li and Wang [2012a, 2012b], and Xu and Wang [2013]. Only some major features of the model are summarized below. The model atmosphere is formulated in the mass vertical coordinate and is bounded between a flat surface with the unperturbed surface pressure of 1010 hpa and at the height of about 38 km. The model domain is quadruply nested with two-way nesting and with all three inner meshes automatically moving to follow the model TC [Wang, 2001]. The model has 32 vertical levels with relatively high resolution both in the lower troposphere and near the tropopause. The four meshes have their horizontal grid intervals of 67.5, 22.5, 7.5, and 2.5 km and domain sizes of , , , and grid points, respectively. The model physics [Wang, 2002] include an E-e turbulence closure scheme for subgrid scale vertical turbulent mixing, a modified Monin-Obukhov scheme for surface flux calculations, an explicit treatment of mixed-phase cloud microphysics, a nonlinear fourth-order horizontal diffusion for all prognostic variables except for that related to the mass conservation equation, and a simple Newtonian cooling term to mimic radiative cooling [Rotunno and Emanuel, 1987]. Since no large-scale environmental flow was included in this study, convection occurred mainly in both the inner-core region and the spiral rainbands within about 250 km from the TC center and was covered by the innermost domain. Therefore, cumulus parameterization was not included even in the outermost domain. The model was initialized with an axisymmetric cyclonic vortex, which had a maximum tangential wind speed of 12.5 m s 21 at the surface and at the radius of 75 km. The tangential wind decreased sinusoidally with height and vanished at 100 hpa. All simulations were performed on an f plane of 18 o N in a quiescent environment over the ocean with a constant SST of 298C. The initial thermodynamic structure of the unperturbed model atmosphere was defined as the western Pacific clear-sky environment given by Gray et al. [1975]. The mass and thermodynamic fields of the TC vortex were obtained by solving the nonlinear balance equation as described in Wang [2001]. The TC center at a given time was defined as the center of the axisymmetric circulation along which the azimuthal mean tangential wind at the lowest model level (about 26.7 m) reached the maximum in all simulations. Three numerical experiments were performed (Table 1). In the control experiment (CTRL), the model was integrated with all default model settings. In the second (IE36) and third (DE36) experiments, the exchange coefficient for calculating surface entropy flux was artificially set to zero and doubled inside the radius of 0.9 RMW (namely in the eye region), respectively, after the first 36 h integration, which was the initial adjustment period of the model TC, in CTRL. Note that similar experiments were conducted in Xu and Wang [2010a]. However, because they focused on the effect of surface entropy flux in the eye region on the maximum intensity of their simulated TCs, they turned off the surface entropy flux in the eye region after the model TC reached a relatively high intensity. Since the focus of this study was on contribution of nearsurface high energy air in the eye region due to surface entropy flux on the intensification rate of the simulated TC, the surface entropy flux was switched off during the early stage of RI. As indicated in Xu and Wang [2010a], the actual radius of the eyewall in each quadrant could deviate from the azimuthal mean RMW (which varies with time in all simulations) due to the elliptical and polygonal eyewall structures in the simulation, especially in the preintensification stage. An initial examination indicated that the RMW varied in different quadrants with the maximum variances in general less than 15% of the azimuthal mean RMW at the lowest model level in the simulated storms after the first 36 h spinup (not shown) because the model was run on an f-plane in a quiescent environment. As a result, if the surface entropy flux within the azimuthal mean RMW was turned off, part of the flux near the inner edge of the eyewall would be eliminated. Here a factorof0.9wasthususedtoavoidanysignificantmodification to the surface entropy flux under the eyewall and to ensure the removal of (more energetic) near-surface high-entropy air in the eye region in IE36 (DE36). To show the robustness of the results, in addition to the above standard runs, four perturbed runs were conducted for each experiment. Similar to that in Nguyen et al. [2008], the water vapor mixing ratio at the WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1955

4 Figure 1. Time evolutions of the maximum azimuthal mean tangential wind speed (m s 21, solid) and the mean radius of maximum tangential wind (RMW in km, dashed) at the lowest model level (26.7 m above the sea surface) in the three experiments: CTRL (blue), IE36 (green), and EE36 (red) as listed Table 1. Results from the five member runs and the ensemble mean for each experiment are shown in thin and thick curves, respectively. The horizontal dashed line segments indicate the maximum azimuthal mean wind speeds of 25 m s 21 and 45 m s 21, respectively, showing the time periods used in the time average in Figure 5. lowest model level in the innermost domain was perturbed with anomalies of 21.0%, 20.5%, 0.5%, and 1.0% of that in the standard run, respectively, in the four perturbed runs. Note that all the perturbed runs started after the first 36 h integration of the CTRL simulation. Therefore, in total 5 runs were conducted for each of the three experiments. In the following discussions, we will show results from individual runs and also the ensemble mean for each experiment, but with our focus on the ensemble mean. 3. Intensity Evolution of the Simulated Storms Figure 1 shows the time evolutions of maximum azimuthal mean tangential wind and the azimuthal mean RMW at the lowest model level (26.7 m above sea level) in experiments CTRL, IE36, and DE36, including those of individual runs and their ensemble mean for each experiment. As shown in previous studies with idealized simulations of TCs [e.g., Wang, 2007, 2008a, 2008b; Xu and Wang, 2010b], the TC in CTRL experienced an initial weakening for several hours due to the spinup of the frictional boundary layer. The TC then showed little intensity change up to 26 h during which the inner core region of the TC was moistened and saturated (not shown). The RMW experienced some variability in the first 12 h, which was followed by a rapid contraction from 80 km at 12 h to about 20 km by 36 h of simulation, but it varied quite stably afterward. In the following discussion, we will only focus on results from the ensemble runs after the first 36 h of simulation for all three experiments. Note that the spread from the 5 ensemble runs for each experiment was not large in the intensification stage before 144 h of simulation (Figure 1). This suggests that the difference among the three experiments was significant in the intensification stage but less insignificant in the mature stage. Since our interest is on intensification of the simulated storms, we will mainly focus on results of the ensemble means below. The TC in CTRL intensified rapidly from 36 h to about 94 h of simulation with an averaged intensification rate of 18.6 m s 21 d 21 with the peak intensification rate of 25 m s 21 d 21 between 60 h and 79 h in the ensemble mean. Later, the storm intensified with a considerably lower intensification rate of about 10 m s 21 d 21 from 94 h to 136 h. During the RI phase (36 94 h of simulation), the storm showed a very slow contraction of the RMW, in sharp contrast to the rapid contraction of the RMW in the first 26 h of simulation. Therefore, the intensification of the simulated TC was not accompanied by a significant eyewall contraction, which is inconsistent with previous findings based on balanced dynamics, which predicts that the intensification of a TC vortex would be accompanied by an eyewall contraction [e.g., Shapiro and Willoughby, 1982]. However, the result here is consistent with recent findings by Qin et al. [2016], who reported that the RI phase of TCs often occurred with constant RMWs after the rapid contraction. Since our main interest in this study was to evaluate the contribution of the near-surface high energy air in the eye region to the intensification rate of the simulated TC, we focused on the RI phase and artificially modified the exchange coefficient for surface entropy flux calculation in the eye region after the first 36 h spinup period. The removal of surface entropy flux in the eye region in IE36 affected the storm evolution immediately (Figure 1). Without surface entropy flux in the eye region, the RMW experienced an adjustment first and then showed a slow contraction during the intensification stage, similar to that in CTRL. However, the ensemble mean RMW in IE36 was consistently about 5 6 km larger than that in CTRL during the RI phase between 36 h and 96 h of simulation. The intensification rate of the simulated storm in IE36 was considerably smaller WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1956

5 than that in CTRL, especially after 48 h of simulation, namely about 12 h after the surface entropy flux was switched off. The ensemble mean intensification rate during the main intensification phase between 36 h and 94 h in IE36 was about 13.1 m s 21 d 21, which is about 30% smaller than that in CTRL (18.6 ms 21 d 21 ). This means that the eye excess energy in CTRL contributed (directly and/or indirectly) to the intensification rate by about 42% during this period. This seems to suggest that the eye excess energy contributed not only to the initial convective boosts and thus the onset of RI as discussed in previous studies [Barnes and Fuentes, 2010; Miyamoto and Takemi, 2013] but also to the subsequent RI even with a relatively small eye volume. However, the difference in the intensification rate between IE36 and CTRL became quite small after 94 h of simulation in the later slow intensification phase (Figure 1). The storm intensity at the mature stage averaged between 192 and 216 h of simulation in IE36 was only about 5% smaller than that in CTRL. This demonstrates that the eye excess energy contributed insignificantly to the maximum intensity of the simulated storm, which is consistent with previous studies [Bryan and Rotunno, 2009; Wang and Xu, 2010]. Note that the difference in the ensemble mean RMW between IE36 and CTRL was reduced to about 2.5 km (15 km in CTRL versus 17.5 km in IE36) after 120 h of simulation and became negligible after 192 h of simulation (Figure 1). With the exchange coefficient doubled for surface entropy flux calculation in the eye region in DE36, the storm intensified more rapidly than that in CTRL up to 72 h of simulation or in the first 36 h after the exchange coefficient being doubled. The 36 h mean intensification rate between 36 h and 72 h of simulation was 22.5 ms 21 d 21 in DE36 compared with 18.8 m s 21 d 21 in the same period in CTRL (Figure 1), about 20% larger in DE36 than in CTRL. This further demonstrates that the eye excess energy due to doubled surface exchange coefficient contributed largely (about 20% here) to the intensification rate in DE36 relative to that in CTRL. This is smaller than the 30% increase in the intensification rate in CTRL relative to that in IE36 averaged between 36 h and 94 h of simulation discussed above. Note that the difference in intensification rate after 72 h between DE36 and CTRL became less systematic although the overall mean intensification rate in DE36 was slightly larger than that in CTRL between 72 h and 96 h of simulation. The doubled exchange coefficient in the eye region resulted in a storm about 5% (averaged in the last 24 h of simulation) stronger in the mature stage. Note that the difference in the ensemble mean RMW between DE36 and CTRL was quite small, in contrast to that between CTRL and IE36. This suggests that artificial removal of surface entropy flux in the eye region in IE36 slowed down the eyewall contraction during the intensification phase of the simulated storm but enhanced surface entropy flux in the eye region in DE36 showed little effect on the variation in the RMW. Note also that the doubled exchange coefficient for surface entropy flux calculation in the eye region did not imply the doubled surface entropy flux therein because the surface entropy flux also depended on the thermodynamic disequilibrium across the air-sea interface. This latter was considerably reduced after the eye region became saturated about 24 h after the exchange coefficient was doubled in the eye region (not shown). Results from the sensitivity experiments discussed above strongly suggest that the eye excess energy contributed to the RMW contraction to some extent while contributed significantly to the TC intensification rate in the RI phase in CTRL. The surface entropy flux in the eye region contributed to the maximum intensity of the simulated storm in the mature stage by only about 5%, consistent with earlier studies. Some previous studies have hypothesized that entrainment of the high entropy air from the eye region could increase buoyancy in the eyewall, favorable for convective bursts in the eyewall and RI of TCs [Rogers, 2010; Chen and Zhang, 2013; Wang and Wang, 2014]. We will show below that the eye excess energy also contributed to the slow contraction of the eyewall during the RI phase, which is responsible for the increased intensification rate of the simulated storm in CTRL compared to that in IE Eye Thermodynamics and Convective Activity in the Eyewall Previous studies have hypothesized that the eye excess energy contributes to TC intensification by entraining/mixing high entropy air from the eye region to the eyewall and thus enhancing buoyancy and convection in the eyewall [Barnes and Fuentes, 2010]. However, since the entrainment/mixing of the near-surface high-entropy air in the eye region into the eyewall is hard to be quantified from observations, the contribution of the eye excess energy to the TC intensification rate has not been evaluated in previous studies. Results from section 3 demonstrate that surface entropy flux in the eye region could contribute as large as about 42% to the intensification rate during the RI period. In this section, we will examine how the change of WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1957

6 Figure 2. (a) The lowest 0.5 km mean equivalent potential temperature (EPT, h e in K) and (b) convective potential energy (CAPE, J kg 21 ) averaged within the RMW in the three experiments CTRL (blue), IE36 (green), and DE36 (red) as listed in Table 1. Results from the five member runs and the ensemble mean for each experiment are shown in thin and thick curves, respectively. surface entropy flux affected the eye thermodynamics, convective activity in the eyewall, and the size of the eyewall, leading to the different intensification rate of the simulated storms discussed in section 3. Equivalent potential temperature (h e ) is often used to represent the thermodynamic feature of air and convective available potential energy (CAPE) is used as a measure of convective instability or the maximum kinetic energy per unit mass that a buoyant parcel could obtain by ascending from a state of rest at the level of free convection to the level of neutral buoyancy near the tropopause. We calculated h e following Bolton [1980] and CAPE with the hourly model outputs from all member runs in the three experiments listed in Table 1. Figure 2 shows the time evolutions of the mean h e in the lowest 500 m of the model atmosphere and CAPE, both averaged in the eye region (namely within the RMW) in five member runs and their ensemble mean in each experiment. In CTRL, as the storm intensified after the initial 36 h spinup the ensemble mean near-surface h e in the eye region increased rapidly by about 15 K in the RI phase from 36 h to 96 h of simulation (Figure 2a). Overall, the near-surface h e in the eye region continued increasing until 132 h of simulation but with a much reduced rate, which was consistent with the slow intensification of the simulated storm in the same period. The results seem to suggest that the highentropy air in the eye region contributed to the intensification rate of the simulated storm in CTRL (Figure 1). The immediate response to the removal of surface entropy flux in the eye region in IE36 was an initial decrease for 6 h and then a much reduced rate of increase in the near-surface h e in the eye region, in sharp contrast to the rapid increase in CTRL. As a result, the near-surface h e in the eye region in IE36 was about 12 K lower than that in CTRL by 96 h of simulation (Figure 2a) and the difference remained through the end of the 240 h simulation, consistent with the reduced intensification rate of the simulated storm in IE36. In contrast, the near-surface h e in the eye region in DE36 increased more rapidly than that in CTRL up to 72 h during the RI phase (Figure 2a) and was about 6 K higher by 72 h of simulation and remained larger afterward. Note that the difference in the near-surface h e in the eye region between DE36 and CTRL was 50% smaller than that between CTRL and IE36. This is mainly due to the reduced thermodynamic disequilibrium in DE36 due to the saturation of air in the eye region as already mentioned in section 3. Nevertheless, the similarity in the evolutions of the near-surface h e in the eye region (Figure 2a) and the intensity of the simulated storms (Figure 1) in all three experiments implies a positive contribution of the near-surface h e air in the eye region to the simulated TC intensification rate. The CAPE averaged in the eye region in CTRL became very high in the first 6 h of simulation and then decreased rapidly from the maximum value of over 2600 J kg 21 to about 900 J kg 21 (Figure 2b) as the eyewall sharply contracted from 80 km at 6 h to 12.5 km at 30 h of simulation. However, the storm intensity WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1958

7 Figure 3. (a) Numbers of grid points where CBs occurred and (b) the area-averaged rain rate (mm h 21 ) within a radius of 60 km from the storm center in experiments CTRL (blue), IE36 (green), and DE36 (red) as listed in Table 1. Results from the five member runs and the ensemble mean for each experiment are shown in thin and thick curves, respectively. changed little during the period of the rapid CAPE decrease. After the first 36 h spinup, the ensemble mean CAPE in the eye region in CTRL increased to a moderate value of about 1500 J kg 21 by 69 h of simulation during which the storm intensified rapidly. Then, the CAPE in the eye region decreased to about 400 J kg 21 by 144 h and remained at this level afterward through the end of 240 h of simulation. Since the near-surface h e in the eye region increased with time (Figure 2a), the decrease of CAPE in the eye region can be considered as a result of the increase in static stability due to the formation of the warm core structure (not shown). Nevertheless, the accumulation of CAPE in the eye region also played a positive role in triggering the onset of RI and the subsequent RI of the simulated storm in CRTL. This is consistent with the hypothesis of Miyamoto and Takemi [2013] and the results for Typhoon Megi (2010) studied in Wang and Wang [2014]. The removal of surface entropy flux in the eye region in IE36 (Figure 2b) resulted in an immediate decrease of CAPE in the eye region. The CAPE in the eye region decreased to less than 50 J kg 21 after 96 h of simulation, suggesting that the contribution by buoyancy in the eye region was negligible in IE36. With the exchange coefficient doubled for surface entropy flux calculation in the eye region in DE36, the CAPE in the eye region increased rapidly and reached a maximum value of 2300 J kg 21 in the ensemble mean by 69 h of simulation and then decreased until 144 h and remained at a value of about 420 J kg 21 afterward, slightly higher than that in CTRL in the same period. This seems to suggest that the CAPE and thus buoyancy in the eye region are important for RI but less crucial for the slow intensification at the later stage of the simulated storms. Previous studies have hypothesized that the near-surface high u e air in the eye region, if being mixed into eyewall updrafts, could increase the eyewall buoyancy and trigger/enhance convective bursts (CBs) in the eyewall, favorable for the formation of warm core in the upper troposphere and the onset of RI and subsequent RI [Chen and Zhang, 2013; Wang and Wang, 2014] or increase the maximum potential intensity (MPI) of a TC [Holland, 1997; Braun, 2002; Persing et al., 2003]. It is thus our interest to examine CBs in the inner core region of the simulated storms in the three experiments. Although there have been different definitions of CBs in the literature (see a discussion in Wang and Wang [2014]), we found that the results were consistent in general. Therefore, we only focus on the results with CBs defined as the grid points where the maximum vertical velocity between 5 and 15 km was 5 m s 21 or larger. Figure 3a shows the time series of the numbers of CBs in a radius of 60 km from the storm center in all five member runs and their ensemble mean in each experiment. We can see that the number of CBs in the inner core region showed a general increasing trend throughout the 240 h of simulations in all experiments but with large variability (Figure 3a). Similar to the number of CBs, the area-averaged rain rate in the inner core region (within a radius of WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1959

8 Figure 4. Radial distribution of (a) total numbers of grid points where CBs occurred in each annulus of 10 km averaged between 54 h and 96 h of simulations and (b) the corresponding averaged area coverage in percentage by CBs (%) in experiments CTRL (blue), IE36 (green), and DE36 (red) as listed in Table 1. Results from the five member runs and the ensemble mean for each experiment are shown in thin and thick curves, respectively. 60 km from the storm center) also showed a general increasing trend throughout the 240 simulations (Figure 3b). Note that the differences in the total number of CBs and the area averaged rain rate in the inner core region were much smaller than those in the near-surface e h e and CAPE in the eye region among the three experiments. Although the difference in the total number of CBs in the inner core region among the three experiments looks small in Figure 3a, a close examination indicates systematic differences in the radial distributions of the total number of CBs and the averaged percentage area coverage by CBs. Figure 4 shows the number of CBs and their percentage area coverage in each 10 km annulus averaged in the RI phase between 54 h and 96 h of simulation for all individual member runs and their ensemble mean in each experiment. We can see that the total number of CBs peaked in the outwardly tilted eyewall region, namely slightly outside the RMW at the lowest model level while inside the RMW at the 12 km height (Table 2), in all experiments. Overall, the ensemble mean CB number was the largest (19) in CTRL and smallest (12) in IE36. The percentage area coverage by CBs was the largest (12%) in DE36 and smallest (3.5%) in IE36. Note that the larger difference in the percentage area coverage by CBs than that in the total CB number among the experiments was due to the difference in the radial location where the peak CB number occurred. Note that although the difference in the percentage area coverage was consistent with the difference in the intensification rate of the simulated storm among the three experiments, we found that the difference was largely attributed to the difference in storm intensity in the averaged period. This is confirmed by the radial distributions of the CB number and the percentage area coverage by CBs averaged in the period when the storms had their intensity between 25 m s 21 and 45 m s 21 in the three experiments, namely between 54 h and 75 h in CTRL, 60 h 94 h in IE36, and 52 h and 71 h in DE36 (Figure 1). As we can see from Figure 5, differences in both the CB number and the percentage area coverage by CBs among the three experiments were much smaller than those in Figure 4. This strongly suggests that the differences in the CB number and percentage area average by CBs (as well the area averaged rain rate) in the inner core region were mainly related to the difference in Table 2. The Ensemble Mean Radius of Maximum Wind (RMW) at the Lowest Model Level (26.7 m Above the Surface, Ave_RMW_26.7m) and That at the Height of 12 km (Ave_RMW_12Km) During h of Simulations in All Three Experiments Experiment Ave_RMW_26.7m Ave_RMW_12Km CTRL IE DE storm intensity and could not explain the large difference in the intensification rate of the simulated storms among the three experiments. Note that the second maxima in both the CB number and the percentage area coverage by CBs around 100 km radius were related to the activity of outer spiral rainbands, which showed little differences WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1960

9 Figure 5. Radial distribution of (a) total numbers of grid points where CBs occurred in each annulus of 10 km averaged during the period when the ensemble mean axisymmetric tangential wind speeds between 25 m s 21 and 45 m s 21 in simulations (see Figure 1) and (b) the corresponding averaged area coverage in percentage by CBs (%). The average periods are, respectively, between 54 h and 75 h in CTRL (blue), between 60 h 94 h in IE36 (green), and between 52 h and 71 h in DE36 (red). Results from the five member runs and the ensemble mean for each experiment are shown in thin and thick curves, respectively. among the three experiments. Note again that similar to the results shown in Figure 4 the total number of CBs peaked slightly outside the RMW at the lowest model level while inside the RMW at the 12 km height in all experiments (Table 3), indicating the outwardly tilted eyewall of the simulated storms. The above results demonstrate that the high near-surface u e air in the eye region had little effects on the number of CBs and the amount of condensational heating in the inner core region. We showed that the differences among the three experiments resulted mainly from the difference in storm intensity and was not related to the intensification rate of the simulated storms. This is in sharp contrast to the previous hypothesis, which assumes that once the eye energetic air is transported or mixed into the eyewall, it can enhance eyewall updrafts and convection, and thus contributing to TC intensification rate [Barnes and Fuentes, 2010; Chen and Zhang, 2013; Miyamoto and Takemi, 2013; Wang and Wang, 2014]. We argue that since the eye volume is so small, even though part (or most) of the high near-surface u e air in the eye region was transported/mixed into the eyewall, it contributed only a very small portion to the entropy budget in the eyewall and thus had insignificant effect on the eyewall buoyancy and convection. This is the same as the fact previously used to explain little contribution of the high near-surface u e air in the eye region to the MPI of a TC [Bryan and Rotunno, 2009; Wang and Xu, 2010]. We found that the large difference in the intensification rate of the simulated storms among the three experiments was largely contributed by the difference in the radial location of CBs as already seen in Figures 4 and 5 and thus the radial distribution of diabatic heating as will be discussed in the next section. 5. A New Hypothesis Considering the small eye volume in the boundary layer, we can hypothesize that the eye excess energy contributed to the intensification rate of the simulated storm by setting the eyewall convection at relatively smaller radii with the smaller RMW and Table 3. The Ensemble Mean Radius of Maximum Wind (RMW) at the Lowest Model Level (26.7 m Above the Surface, Ave_RMW_26.7m) and That at the Height of 12 km (Ave_RMW_12Km) During the Period With the Wind Speed Increased From 25 m s 21 to 45 m s 21 in All Three Experiments Experiment Ave_RMW_26.7 m Ave_RMW_12 km CTRL (54 75 h) IE36 (60 94 h) DE36 (52 71 h) higher inertial stability, making the eyewall heating more effectively in spinning up the inner core tangential wind, and thus increasing the intensification rate of the storm. This means that the nearsurface high u e air entrained/mixed from the eye region into the eyewall either was very limited and could not significantly WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1961

10 Figure 6. Time-radius cross section of the azimuthal mean equivalent potential temperature (K) averaged in the lowest 0.5 km of the (a c) model atmosphere and (d f) vertical velocity (m s 21 ) averaged between 3 km and 5 km height in experiments (a, d) CTRL, (b, d) IE36, and (c, f) DE36. The solid black curve shows the radius of the azimuthal mean tangential wind at the lowest model level (26.7 m). Results are the ensemble mean for each experiment. affect the amount of buoyancy and the number of CBs in the eyewall, rather it could increase the buoyancy and thus initiate convection near the inner edge of the eyewall, leading to eyewall convection slightly shifted inward. This may have two consequences: one was to make the convective heating in the eyewall closer to the storm center where the inertial stability was very high and the other was to make a relatively faster contraction of the eyewall and thus the reduced RMW and increased inertial stability inside the RMW. Both would increase the dynamical efficiency of diabatic heating in the eyewall in spinning up tangential wind in the inner core region [Vigh and Schubert, 2009; Rogers et al., 2013]. To verify our hypothesis, we examined the radial distribution of the azimuthally averaged near-surface u e, eyewall updrafts, diabatic heating, and inertial stability in the three experiments to demonstrate the validity of the proposed mechanism as discussed below. First, we show in Figure 6 the time-radius cross sections of the azimuthally averaged near-surface u e and the vertical velocity averaged between 3 and 5 km heights in the three experiments. Consistent with the WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1962

11 near-surface u e averaged in the eye region shown in Figure 2a, near-surface high u e in the eye region in CTRL (Figure 6a) disappeared with the removal of surface entropy flux in the eye region through the end of simulation in IE36 (Figure 6b). However, the removal of surface entropy flux in the eye region had little effect on near-surface u e outside the RMW. The eyewall upward motion averaged between 3 km and 5 km heights was slightly larger, in particular during the RI phase, and occurred at slightly smaller radii in CTRL than in IE36 (Figures 6d and 6e). This suggests that the eye excess energy led to the eyewall convection closer to the storm center, resulting in about 5 km (25%) smaller mean RMW of the simulated storm in CTRL than in IE36 averaged during the RI phase (Figures 1, 6a, and 6b). Consistent with the smaller difference in the intensification rate between DE36 and CTRL than that between CTRL and IE36, the differences in the radial location of eyewall upward motion and the RMW between DE36 and CTRL were also smaller (Figures 6d and 6f). This was mainly due to the fact that doubling the exchange coefficient for surface entropy flux calculation would not imply doubling the surface entropy flux itself as the flux was also determined by the thermodynamic disequilibrium at the air-sea interface as mentioned in section 3. Nevertheless, the above results strongly suggest that the near-surface high entropy air in the eye region would lead to the eyewall heating closer to the storm center and the smaller RMW, enhancing dynamical efficiency of eyewall heating in spinning up tangential wind in the inner core, consistent with our hypothesis above. To further verify the above hypothesis, we compared in Figure 7 the time evolution of the azimuthal mean diabatic heating rate and inertial stability in experiments CTRL and IE36 temporarily averaged for ensemble mean between 6 h centered at the time given at the top right of each panel. We can see from Figure 7 that the difference in the radial distribution and magnitude of diabatic heating rate became visible between CTRL and IE36 shortly after the removal of surface entropy flux in the eye region in IE36. For example, averaged in 6 h after the removal of surface entropy flux in the eye region, the eyewall heating was mainly located between 15 and 30 km radii in CTRL while between 20 and 30 km radii in IE36 (Figures 7a and 7b), indicating convection occurring near the inner edge of the eyewall in CTRL. This feature became more pronounced as time proceeded (Figures 7c 7h) and resulted in the smaller RMW in CTRL than in IE36, consistent with the results shown Figures 1 and 6. More importantly, inertial stability in the inner core region was considerably higher in CTRL than in IE36 and the large eyewall heating rate was located in smaller radii with higher inertial stability in CTRL than in IE36 in all given time averages (Figure 7). This implies higher dynamical efficiency of diabatic heating in the eyewall in spinning up tangential wind in the inner core region [Schubert and Hack, 1982; Vigh and Schubert, 2009]. Note that the differences in the RMW and the radial location of eyewall heating were not related to the storm intensity in the particularly chosen period but a robust consequence of the difference in the near-surface entropy in the eye region. The results thus suggest that the near-surface high entropy air in the eye region contributed to the eyewall contraction by initiating convection near the inner edge of the eyewall, favorable for RI of the simulated storm. To further demonstrate the above mechanism, we examined several key variables and their differences in their ensemble means averaged between 48 h and 60 h of simulation in CTRL and IE36 as shown in Figure 8. Note that the background shading in Figure 8 shows the variables corresponding to the results from IE36 while the overlapped contours show the differences between the corresponding variables between CTRL and IE36 except for Figure 8b in which the background shading shows the difference in u e between CTRL and IE36. As mentioned above, vertical motion in the eyewall in CTRL showed an inward shift relative to that in IE36 as inferred from the positive (negative) difference in vertical motion in Figure 8a. This vertical motion difference was rooted in the boundary layer near the inner edge of the eyewall with low-level high u e anomalies and thus could be attributed to the possible forcing of the near-surface high u e air in the eye region near the inner edge of the eyewall in CTRL (Figure 8b). The inward shift of eyewall updrafts led to the inward shift of diabatic heating to the region with higher inertial stability (Figure 8d), implying higher dynamical efficiency of diabatic heating in the eyewall in spinning up tangential winds in the inner core region in CTRL (Figure 8e). Note that the radial wind was affected very marginally as we can see from the difference in radial wind between CTRL and IE36 (Figure 8f), suggesting that the tangential wind spin-up in the inner core resulted mainly from the increased inertial stability (and thus the absolute vorticity) inside the RMW as will be discussed below. Since the inertial stability in the inner core region increases with TC intensity, the above process would be expected to become more significant as the simulated storm intensified, resulting in the increasing difference in intensification rate of the simulated storm between CTRL and IE36. This indeed was true up to 96 h WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1963

12 Figure 7. Azimuthal mean inertial stability (normalized by square of the Coriolis parameter f, contours) and condensational heating rate (shading, K h 21 ) averaged in 6 h centered at the time given at the top-right of each plot in experiments (left) CTRL and (right) IE36. Results are the ensemble mean for each experiment based on hourly model outputs. of simulation as we can see from Figure 1. An example is shown in Figure 9, which is similar to Figure 8 but shows results averaged between 60 h and 72 h of simulations. Now the differences in those variables between CTRL and IE36 seen in Figure 8 all became larger although their patterns are quite similar (Figure 9). As we can see from Figure 9e, during this time period, the maximum tangential wind was over 10 m s 21 larger in CTRL than in IE36. Note that the simulated storms in both experiments were experiencing rapid intensification and consistently eyewall heating was well collocated with high inertial stability in this time WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1964

13 Figure 8. Azimuthal mean (a) vertical motion (m s 21, shading) averaged between 48 h and 60 h of simulation in IE36 overlapped by the difference in vertical motion between CTRL and IE36 (contours with interval of 0.1 m s 21 ), (b) differences in equivalent potential temperature (EPT, h e ) between CTRL and IE36 (K, shading) overlapped by the difference in vertical motion (contours with interval of 0.1 m s 21 ) as in Figures 8a, (c) as in Figure 8a but for condensational heating rate (K h 21 ), (d) as in Figure 8a but for inertial stability (normalized by the square of the Coriolis parameter), and (e) as in Figure 8a but for tangential wind (m s 21 ), and (f) as in Figure 8a but for radial wind (m s 21 ). Results are the ensemble mean for each experiment based on hourly model outputs. period. The storm in CTRL intensified more rapidly than that in IE36 because of the contribution of the nearsurface high entropy air in the eye region in CTRL. Our azimuthal mean tangential wind tendency budget analysis (not shown) also confirmed that the more rapid intensification in CTRL resulted mainly from higher inertial stability (larger absolute vorticity and thus larger radial inward angular momentum transport) near and inside the RMW in CTRL than in IE36, further supporting our hypothesis regarding the role of eye excess energy in TC intensification elaborated above. 6. Conclusions Although the near-surface high energy air in the eye region has been shown to contribute little (about 5%) to the maximum intensity of a TC in previous studies, some studies have proposed that the near-surface high energy air and CAPE accumulated in the eye region due to the long residence time associated with high inertial stability can serve as a boost for eyewall CBs and could contribute positively to the onset of RI and the subsequent intensification rate of a TC. However, this hypothesis has never been verified in a WANG AND HENG CONTRIBUTION OF EYE EXCESS ENERGY TO TCs 1965