Effect of planetary boundary layer schemes on the development of intense tropical cyclones using a cloud-resolving model

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011jd016582, 2012 Effect of planetary boundary layer schemes on the development of intense tropical cyclones using a cloud-resolving model Sachie Kanada, 1 Akiyoshi Wada, 2 Masuo Nakano, 1 and Teruyuki Kato 3 Received 20 July 2011; revised 8 December 2011; accepted 8 December 2011; published 2 February [1] We studied the role of the planetary boundary layer (PBL) in intensity and inner core structure of extremely intense tropical cyclones (TC) using a 2 km mesh nonhydrostatic atmospheric model (NHM2) developed for operational use by the Japan Meteorological Agency. To investigate the effects of the PBL on simulated TCs, we used four PBL schemes: level 2.5 and level 3 Mellor-Yamada-Nakanishi-Niino closure schemes, a nonlocal scheme, and the Deardorff-Blackadar scheme. The numerical results indicated that the subgrid-scale mixing length determined by the PBL scheme plays a critical role in the determination of maximum TC intensity and inner core structure, even when the same expressions are provided for surface roughness lengths and the air-sea momentum and heat transfer coefficients. Different vertical eddy-diffusivity coefficient values derived from the PBL schemes cause differences in the TC intensity, inner core structure, and the relationship between maximum wind speed (MWS) and central pressure (CP). In particular, large vertical eddy diffusivities in lower layers (height <300 m) lead to large heat and water vapor transfers, resulting in extremely intense TCs accompanied by an upright, contracted eyewall structure. We also conducted numerical experiments using a 5 km mesh nonhydrostatic atmospheric model (NHM5) and the same PBL schemes to investigate the effect of horizontal resolution on simulated TCs. The NHM5 was insufficient to accurately represent the MWS or CP of an extremely intense TC, suggesting that NHM2 is required to simulate an extremely intense TC characterized by an upright, contracted eyewall structure. Citation: Kanada, S., A. Wada, M. Nakano, and T. Kato (2012), Effect of planetary boundary layer schemes on the development of intense tropical cyclones using a cloud-resolving model, J. Geophys. Res., 117,, doi: /2011jd Introduction [2] Extremely intense tropical cyclones (TC) are a major concern worldwide. It is well known that during the 2005 TC season, the North Atlantic experienced three extremely intense TCs in the Gulf of Mexico, Hurricanes Katrina, Rita, and Wilma, all with minimum central pressures (MCP) lower than 905 hpa. Those extremely intense TCs caused large losses of human life and socioeconomic damage in coastal regions and islands [Knabb et al., 2005]. Other such extremely intense TCs have been reported in the western North Pacific Ocean (e.g., Typhoon Nida, MCP 905 hpa, in 2009; Typhoon Megi, MCP 885 hpa, in 2010). In response to these recent extremely intense TCs, the Hong Kong observatory now classifies such typhoons in the western North Pacific Ocean as super typhoons, and that term is also used by the Joint Typhoon Warning Center. 1 Independent Administrative Institution, Japan Agency for Marine- Earth Science and Technology, Tsukuba, Japan. 2 Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan. 3 Japan Meteorological Agency, Tokyo, Japan. Copyright 2012 by the American Geophysical Union /12/2011JD [3] There is considerable interest in the potential for extremely intense TC activity in the future, because super typhoons could trigger more devastating natural disasters. Assessment of future TC activity is necessary to avoid or diminish the impacts of future natural disasters. Many studies have attempted to project TC frequency and intensity numerically, and several future climate experiments have suggested that global warming is likely to result in an increased frequency of intense TCs [Kitoh et al., 2009; Knutson et al., 2010]. However, the horizontal resolution of current global climate models is relatively coarse (greater than several tens of kilometers), whereas recent studies have suggested that a nonhydrostatic atmospheric model (NHM) with a grid spacing of less than 1 to 2 km is required to resolve the dynamics of the inner core structure of a TC, such as eye-eyewall mixing processes and vortex Rossby waves [e.g., Chen et al., 2007; Nolan et al., 2009b]. These inner core processes are known to be closely related to the MCP via air-sea interactions [Wada, 2009]. The following question then arises: can we validate the projections of global climate models by using fine-mesh cloud-resolving models that are capable of resolving internal TC dynamics? In other words, can we simulate an extremely intense TC and its inner core structure using fine-mesh cloud-resolving models when future atmospheric environments at the 1of13

2 occurrence of the TC are provided by the global climate model projection? [4] Despite steady advances in our ability to predict TC tracks, considerable uncertainty remains in predictions of TC intensity [Braun and Tao, 2000]. This uncertainty is partly because inner core dynamics and the relationship of inner core dynamics to atmospheric [Davis et al., 2008] and oceanic [Wada and Usui, 2010] environments are important for resolving the eyewall, the eye, and the inner spiral rainbands near the eyewall and thus for predicting TC intensity. Moreover, several physical processes such as vertical turbulent mixing in the upper ocean [e.g., Wada et al., 2010] and sea spray at the air-sea interface [e.g., Wang et al., 2001; Bao et al., 2011] are known to play crucial roles in the determination of TC intensity and structural dynamics [Wang and Wu, 2004]. [5] One of crucial physics is the planetary boundary layer (PBL) that is known to play an important role in the development and maintenance of a TC. PBL processes facilitate interconnections between air-sea interactions with the moistconditionally symmetrical neutral upward flow in the eyewall through the secondary circulation of a TC [Emanuel, 1986]. Observational studies include that of Powell [1982], who compiled numerous observation data over land and water to show the PBL structure and characteristics around the center of Hurricane Frederic before and after its landfall. Drennan et al. [2007] and French et al. [2007] reported the first direct measurements of latent heat and momentum flux in high winds, obtained during the Coupled Boundary Layer Air-Sea Transfer (CBLAST) project sponsored by the U.S. Office of Naval Research. From observational data collected by research aircraft, Zhang et al. [2011a] estimated the parameters associated with turbulent characteristics such as turbulent momentum flux, turbulent kinetic energy (TKE), and vertical eddy diffusivity, and Zhang et al. [2011b] investigated boundary layer depth characteristics by using 794 GPS dropsonde data collected from 1997 to However, such observations of turbulence in the inner core region of an intense TC are difficult because of safety constraints. [6] Numerical studies have addressed the importance of inflow [Wang and Xu, 2010] and the turbulent length scale [Bryan and Rotunno, 2009] in the PBL on the development of TCs, maximum TC intensity, and the dynamics of the inner core structure. Other relevant factors include horizontal resolution of the model [Braun and Tao, 2000; Davis et al., 2008; Gentry and Lackmann, 2010], exchange coefficients for momentum and enthalpy transfers, and roughness lengths [Nolan et al., 2009a, 2009b]. Nolan et al. [2009a, 2009b] compared non-local-type Yonsei University and Mellor-Yamada-Janjic parameterizations and indicated that both schemes could reasonably reproduce the observed PBL of Hurricane Isabel (2003). However, Nolan et al. [2009b] extended the definition of the PBL to include both surfaceboundary processes and turbulent mixing in the PBL. Therefore, the effects of turbulent mixing alone on TC intensity and structural changes have not been investigated. In addition, Nolan et al. [2009a, 2009b] focused on TCs after their most intense phase so that they could compare their numerical results with airborne observations obtained during the same phase. Different from their work, we focus here on the effects of the PBL on TC intensity and relevant structural changes that occur from the last rapid intensification phase to the time when maximum intensity is reached in the mature phase. [7] The purpose of this study is to clarify how different PBL schemes influence the calculated structure and intensity of an intense TC, such as a super typhoon, and to obtain a better understanding of the roles of vertical turbulent mixing, particularly the mixing length scale, and the horizontal resolution of the numerical model in TC calculations. We conducted numerical sensitivity experiments using a 2 km mesh NHM (hereafter NHM2) with four PBL schemes. We also conducted sensitivity experiments with a 5 km mesh NHM (hereafter NHM5). As the target for this study, we chose an extremely intense TC obtained in a future projection experiment (MCP, 904 hpa) by an atmospheric general circulation model with a horizontal resolution of 20 km (AGCM20) [Kitoh et al., 2009]. Initial and boundary conditions for the numerical experiments conducted with NHM2 and NHM5 were extracted from the AGCM20 output. [8] The remainder of this paper is organized as follows. Section 2 documents and describes the models used in the study and the experimental design, and section 3 presents the numerical results. In section 4, we discuss the effects of subgrid-scale vertical turbulent mixing lengths on the dynamics of the inner core structure of simulated TCs. Finally, a summary is provided in section 5. The terminology used for TC structure in this study is from the review by Houze [2010]. 2. Model Descriptions and Experiment Design 2.1. Model Descriptions and Initial Conditions [9] Downscaling numerical experiments for an extremely intense TC simulated by AGCM20 [Kitoh et al., 2009] were conducted with NHM2 and NHM5. NHM5 is operationally used for weather predictions by the Japan Meteorological Agency [Saito et al., 2007]. It uses the Kain-Fritsch convective parameterization scheme [Kain and Fritsch, 1990] in conjunction with a bulk-type microphysics scheme that includes an ice phase [Lin et al., 1983; Murakami, 1990]. Both a clear-sky radiation scheme [Yabu et al., 2005] and a cloud radiation scheme [Kitagawa, 2000] are used. This study used the surface boundary schemes proposed by Beljaars and Holtslag [1991] and Beljaars [1995] to estimate surface fluxes and the surface roughness length (z 0 )in all numerical experiments. NHM2 and NHM5 both used similar settings, except that NHM2 did not use a convective parameterization scheme. [10] Both NHM2 and NHM5 were nested directly in the 6 hourly output of AGCM20. In AGCM20, sea surface temperature (SST), which was provided to both NHM2 and NHM5 as an initial condition (Figure 1), was calculated by summation of the following: (1) the linear trend in the multimodel ensemble mean (MMEM) of SST projected using phase 3 multimodels of the Coupled Model Intercomparison Project (CMIP3), (2) future changes in the MMEM of SST, and (3) detrended observed SST anomalies. Future changes in the MMEM of SST were calculated from the difference in the results between twentiethcentury experiments and projected future experiments under the A1B scenario in the Special Report on Emissions 2of13

3 Figure 1. Computational domains and horizontal distributions of surface temperature (color shading, degrees Celsius) and sea level pressure (contours, hpa) in the initial conditions for (a) NHM5 and (b) NHM2. (c and d) Enlarged views of the area within the black square in Figures 1a and 1b are shown. Contour interval is 4 hpa. Horizontal wind vectors (in meters per second) at 10 m height are depicted for every 20 km mesh. (e) Domain-averaged vertical profiles of temperature (solid line, degrees Celsius) and dew point temperature (dotted line, degrees Celsius) in the area shown by the dashed rectangle in Figure 1b are shown. Scenarios [Nakicenovic and Swart, 2000]. Detailed descriptions are given by Kitoh et al. [2009]. SST in AGCM20 was provided to both NHM2 and NHM5 every 6 h. The computational domains of NHM2 and NHM5 covered an area of 2400 km 2200 km and 3350 km 2650 km, respectively, centered at 22 N, 132 E (Figure 1). The domain of NHM2 was somewhat smaller than that of NHM5 (Figure 1) because CPU time increased more than tenfold from NHM5 to NHM2. Time steps were 10 s and 20 s for NHM2 and NHM5, respectively. NHM2 and NHM5 each used 50 vertical levels with variable height, from 40 m for the lowermost layer near the surface to 904 m for the uppermost layer. The top height was nearly 22 km. With regard to the vertical level settings, we conducted sensitivity experiments using the same settings with NHM2 with 56 stretched vertical layers and a top height of 24 km and with NHM2 with 50 stretched vertical layers with a top height of 22 km, and found no significant difference between the numerical results obtained with 50 or 56 vertical layers. The output interval was every hour for precipitation, sea surface pressure, and surface wind speeds, and 3 h for three-dimensional elements. The center of the calculated TCs was determined for each output time every hour, using the method proposed by Braun [2002]. The horizontal distribution of sea level pressure was used to determine the approximate geometric center (centroid) of the pressure field. The geometric center differs from the central pressure (CP) location. [11] The integration period used with the two NHMs was the 4 days from 12:00 UTC, 2 June 2087, to target a TC (MCP, 904 hpa) that was projected by AGCM20 to be most intense at 12:00 UTC on 5 June. During the experimental period, SST around the TC was about 30 C. The incipient vortex projected by AGCM20, with a CP of 961 hpa at 12:00 UTC on 2 June, was nested into the initial conditions of NHM2 and NHM5. AGCM20 did not calculate a rapid drop of CP (51 hpa in 48 h) until nearly a day after the initial time. The incipient vortex developed in a warm, moist environment (Figure 1e). Domain-averaged specific humidity in the NHM2 domain (Figure 1b) at the initial time exceeded 21 g kg 1 near the surface PBL Schemes [12] The PBL schemes used in the experiments of this study (Table 1) included two versions of the Mellor- Yamada-Nakanishi-Niino (MYNN) scheme [Nakanishi and Niino, 2004]: level 2.5 (2MY2.5 experiment) and level 3 3of13

4 Table 1. List of Control and Sensitivity Experimentsa Experiment Horizontal Resolution (km) CNTL2 2MY2.5 2NL0.2 2NL0.1 2D 2D2 CNTL NKF AGCM PBL Schemes Mellor-Yamada-Nakanishi-Niino level 3 [Nakanishi and Niino, 2004] Mellor-Yamada-Nakanishi-Niino level 2.5 [Nakanishi and Niino, 2004] non-local-type scheme [Sun and Chang, 1986] Cm = 0.2, lx = dx, ly = dy, lz:nonlocal, Ds = dz nonlocal scheme [Sun and Chang, 1986] Cm = 0.1, lx = dx, ly = dy, lz:nonlocal, Ds = dz lz: Deardorff [1980] and Blackadar [1962] lx = ly = lz, Ds = (dx dy dz)1/3, Cm = 0.1 lz: Deardorff [1980] and Blackadar [1962] lx = dx, ly = dy, Ds = dz, Cm = 0.1 Mellor-Yamada-Nakanishi-Niino level 3 [Nakanishi and Niino, 2004] Kain-Fritsch convective parameterization scheme no use of convective parameterization scheme Mellor-Yamada level 2 a Variables are as follows: Cm, coefficient; lx, subgrid-scale mixing length for x direction; ly, subgrid-scale mixing length for y direction; lz, subgrid-scale mixing length for z direction; Ds, grid scale. (CNTL2). The MYNN is a second-order turbulence closure scheme. In the level 2.5 model, second-order moments, except TKE, are determined diagnostically by neglecting the time tendency and diffusion terms. Nakanishi and Niino [2004] describe the level 2.5 and level 3 schemes in detail. Two other PBL schemes were also used, a non-local-type scheme and the Deardorff-Blackadar scheme, which are 1.5order turbulence closure schemes. The coefficient of vertical momentum diffusion (Kmz) was estimated as Kmz = Cm lz E0.5, where E is the TKE, Cm is a coefficient, and lz is the subgrid-scale vertical mixing length. In this study, different experiments conducted with the NHMs estimated lz differently: the non-local-type scheme [Sun and Chang, 1986] was used with two different Cm values (experiments 2NL0.2 and 2NL0.1) and the Deardorff-Blackadar scheme [Blackadar, 1962; Deardorff, 1980] was used with two different grid scales (Ds, defined below) (2D and 2D2) (see Table 1). The methodology used to estimate lz in each scheme is summarized below. [13] The non-local-type scheme preliminarily calculated the depth of the PBL as the height at which the virtual potential temperature (qv) above the lowermost level matched qv at the lowermost level. According to Sun and Chang [1986], lz increases from the lowermost level and peaks at the middle level in the PBL. With the non-local-type scheme the values Cm = 0.1 [Deardorff, 1980] (experiment 2NL0.1) or Cm = 0.2 [Klemp and Wilhelmson, 1978] (2NL0.2) were adopted. Because Kmz is estimated as Kmz = Cm lz E0.5, when Figure 2. Horizontal distributions of hourly precipitation amounts in the 1 h preceding the most intense phase of the TC: (a and b) CNTL2, (c) 2NL0.2, (d) 2D, (e) 2D2, (f) CNTL5, and (g) AGCM20. The time (day and hour) of the most intense phase and the minimum central pressure (hpa) are indicated. 4 of 13

5 Figure 3. Radial profiles of (a) azimuthally averaged hourly precipitation (millimeters per hour) and (b) maximum wind speed (meters per second) at the most intense phase. Red, pink, black, purple, and blue lines and circles indicate CNTL2, 2NL0.2, 2D, 2D2, and CNTL5, respectively. C m = 0.2 the value of K mz is twice that obtained when C m = 0.1. Both Deardorff [1980, formula (10)], and Sun and Chang [1986, formula (14)], assumed that l z ¼ min 0:76E 0:5 N 1 ; Ds for N 2 > 0; otherwise l z ¼ Ds; where N is the Brunt-Väisälä frequency. Considering the anisotropy in the lower layers, the equations Ds x ¼ Dx; Ds y ¼ Dy; and Ds z ¼ Dz were adopted for Ds in experiment 2D2 on the basis of the work by Sun and Chang [1986]. In the original formulation by Deardorff [1980] and Klemp and Wilhelmson [1978], Ds was assumed as ð1þ Ds ¼ ðdx Dy DzÞ 1=3 ; ð2þ and this formulation was used in experiment 2D in this analysis. Experiments CNTL5 and 5NKF both used the MYNN level 3 scheme (Table 1), but only the CNTL5 experiment used the Kain-Fritsch convective parameterization scheme. 3. Results 3.1. General Features [14] CNTL2 calculated an extremely intense TC with a MCP of 895 hpa at 15:00 UTC on 5 June The distribution of hourly precipitation amounts indicated that the TC consisted of an eye, eyewall, inner core rainbands, and distant rainbands (Figure 2a). The inner core rainbands consisted of primary and secondary rainbands (Figure 2b), indicating that CNTL2 could resolve the inner core structure of a TC. In all experiments (Table 1), horizontal distributions of hourly precipitation amounts were concentrated in the inner core of the TC and showed an annular pattern around the center (Figures 2b 2g). However, the distribution of hourly precipitation amounts, particularly in the inner core, showed large differences among the experiments conducted with NHM2, NHM5, and AGCM20. The AGCM20 result (Figure 2g) showed an asymmetric pattern of hourly precipitation amounts accompanied by a broad highprecipitation area. A region of intense precipitation (exceeding 60 mm h 1 ) was located on the eastern side of the TC center. In the AGCM20 result, the eye was relatively larger and more blurred compared with the NHM2 and NHM5 results, which all showed a contracted and concentric precipitation pattern (Figures 2b 2f). In U.S. Air Force aircraft reconnaissance observations of 66 TCs in the northwestern Pacific Ocean [Weatherford and Gray, 1988a, 1988b], the eyes of extremely intense TCs with MCP lower than 910 hpa all had a relatively small radius. The observed radius of maximum wind speed (MWS) of Typhoon Kim (1980; MCP, 908 hpa) was 20 km [Weatherford and Gray, 1988a]. Weatherford and Gray [1988b] also reported that the eyewall size, determined as the distance from the TC center to the beginning of eyewall convection, of extremely intense TCs (MCP < 910 hpa) was between 7 and 20 km, whereas that of medium TCs (MCP, hpa) ranged from 5 km to more than 80 km. [15] We focused in this study on the inner core region, defined as the area within a radius of 100 km (R = 100 km) from the TC center and examined the differences in the inner core components (eye, eyewall, and primary and secondary rainbands) according to the PBL scheme. The eyewall and rainbands in the inner core were broader in 2NL0.2 (Figure 2c) than in CNTL2 (Figure 2b), and 2NL0.2, but not CNTL2, showed a double eyewall structure. Hourly precipitation was more narrowly distributed in 2D (Figure 2d) than in CNTL2, although the eyewall width was approximately the same in both 2D and CNTL2. Comparison of the hourly precipitation distribution between 2D2 (Figure 2e) and 2D showed that the eyewall width was narrower in 2D2 than in 2D, and in 2D2 the primary rainband appeared thin and sharp. The primary rainband was also thin and sharp in 2NL0.1 (not shown). Comparison of the inner core structures in CNTL2 (Figure 2a) and CNTL5 (Figure 2f) showed a wider eyewall in CNTL5 than in CNTL2. The hourly precipitation distribution in CNTL5 showed no remarkable distinction between the eyewall and the rainband region (Figure 2f). The radius of the maximum azimuthally averaged hourly precipitation at the most intense phase was 30 km in CNTL2, 50 km in 2NL0.2, 30 km in 2D, 15 km in 2D2, and 40 km in CNTL5 (Figure 3a). In both CNTL2 and 2D, the maximum precipitation amounts at around R = 30 km were the highest obtained and exceeded 80 mm h 1. The highest MWS at the most intense phase was 99 m s 1 at R = 23 km in 2D (Figure 3b), and the second-highest MWS was 70 m s 1 in 2NL0.2 at R = 30 km. The differences in the precipitation and wind speed distributions among PBL 5of13

6 Figure 4. (a) Time variations of CP and (b) the relationship between MWS and CP. The (10 min) wind pressure analytical relationship for northwest Pacific TCs [Koba et al., 1990] is represented by solid black circles in Figure 4b. schemes revealed that the inner core structure of the simulated TC at the most intense phase was affected not only by the horizontal grid resolution but also by the choice of PBL scheme. [16] The CP evolution (Figure 4a) also varied among the experiments (Table 1). At the most intense phase, MCP was 895 hpa in CNTL2, 921 hpa in 2NL0.2, 895 hpa in 2D, 899 hpa in 2D2, 929 hpa in CNTL5, 925 hpa in 5NKF, and 904 hpa in AGCM20. Note that MCP in 2NL0.2 was substantially higher than that in AGCM20 even though the horizontal grid resolution in 2NL0.2 was 2 km and that in AGCM20 was 20 km. The difference in MCP between CNTL5 (928 hpa) and 5NKF (925 hpa) was only 3 hpa, which was within the range of error. This result indicates that the Kain-Fritsch convective parameterization scheme, used in CNTL5 but not in 5NKF, played a minor role in the TC intensity calculation. Most precipitation around the eyewall in CNTL5 was caused not by the convective parameterization but by large-scale condensation due to the cloud microphysics process (not shown). In this study, regardless of the PBL scheme used, MCP was never as low as 920 hpa in the NHM5 simulations (not shown). [17] Figure 4b indicates the CP-MWS relationships obtained in our experiments comparing with the relationship between pressure and 10 min winds derived from an observational analysis in the northwestern Pacific Ocean [Koba et al., 1990]. Note that MWS in this study was defined not as the maximum azimuthally averaged wind speed but as the maximum wind speed in the grid within the inner core. We divided the experimentally obtained relationships into three categories: those showing (1) excessive MWS (100 m s 1 ) relative to the CP values (2NL0.2 and 2D); (2) reasonable agreement with observed wind-pressure relationships (CNTL2 and 2MY2.5); and (3) underestimation of MWS relative to the CP values (CNTL5, 5NKF, 2D2, 2NL0.1 (not shown), and AGCM20). Although the MCP was reached earlier in 2MY2.5 than in CNTL2 (Figure 4a), the hourly precipitation distributions and the inner core structures before the mature phase did not differ markedly between 2MY2.5 and CNTL2. The shapes of the hourly precipitation distribution and the CP evolution were almost the same in 2NL0.1 and 2D2. Therefore, in the following analysis we focus on the results of CNTL2, 2NL0.2, 2D, 2D2, and CNTL5. The most notable characteristic of CP evolution in 6of13

7 Figure 5. Time variations of (a) cumulative precipitation amounts and (b) cumulative sensible (dotted line) and latent (solid line) heat fluxes within a radius of 100 km until 12:00 UTC on 6 June. MDDHH is shown on the horizontal axis, where M is the month, DD the day, and HH the hour. the experiments in which MCP was below 900 hpa was the rapid decrease in the CP (Figure 4a). Therefore, we divided the analysis period into two: period I consisted of the first 24 h of continuous decrease of the CP, and period II consisted of the 24 h from the end of period I, including the time of the MCP (see Figure 4a). [18] Braun and Tao [2000] conducted numerical sensitivity experiments using a 4 km mesh model and suggested that simulated TC intensity was largely determined by surface heat fluxes rather than by vertical turbulent mixing in the PBL. Therefore, we investigated the effect of surface heat fluxes on hourly precipitation amounts and the MCP. The time variations in the hourly precipitation amounts and surface heat fluxes accumulated within R = 100 km during the calculation period of NHM (Figure 5) showed that the differences in the hourly precipitation amounts among the experiments were within 400 mm except in the 2D2 experiment (MCP, 899 hpa), which showed a large decrement over time compared with the values obtained in other experiments. The largest cumulative amount was recorded in CNTL5 (MCP 929 hpa), followed by 2NL0.2 (MCP 921 hpa). We used the schemes of Beljaars and Holtslag [1991] and Beljaars [1995], in which surface heat fluxes depend on wind speed, to determine the surface roughness length (z 0 ) and exchange coefficients for momentum, heat, and water vapor in all experiments (Table 1). As a result, hourly precipitation amounts and MCP calculated by NHM2 changed (MCP by up to 26 hpa) depending on the PBL scheme used and its specifications Vertical Structures [19] In section 3.1, we showed that both the PBL scheme and the horizontal resolution could have large impacts on MCP and hourly precipitation. In this section, we examine their impacts on the vertical structure of an intense TC during its rapid development phase. Three hourly outputs of the updraft and the radial (V r ) and tangential (V t ) winds are averaged during period II (see Figure 4a for the period) to investigate the representative averaged structure of an axisymmetric TC during its rapid development phase. Note that our focus here is on the results of the NHM2 and NHM5 experiments because, as described in section 3.1, AGCM20 could not resolve the inner core structure owing to its coarse horizontal resolution. In section 3.1, we showed that the MCP in CNTL2, 2D, and 2D2 was lower than 900 hpa, whereas in 2NL0.2 and CNTL5 it was higher than 920 hpa. In the 24 hourly mean azimuthally averaged vertical cross sections of the vertical winds (Figure 6), intense updrafts and upright eyewall profiles are seen in CNTL2 (Figure 6a), 2D (Figure 6d), and 2D2 (Figure 6e). In contrast, the vertical 7of13

8 Figure 6. Radial-vertical cross sections of 24 hourly mean azimuthally averaged vertical winds (shading, in millimeters per second), tangential wind speed (V t, contours, in meters per second), and wind fields (vectors) in (a) CNTL2, (b) 2NL0.2, (c) CNTL5, (d) 2D, and (e) 2D2 during period II (see Figure 4a). The thick contours represent V t = 60 and 70 m s 1.(f j) Same as Figures 6a 6e but for vertical winds (shading, in meters per second), radial (V r ) and tangential (V t ) wind speeds (thick and thin contours, in meters per second), and wind fields (vectors) below 2000 m height. White crosses and circles indicate the positions of the maximum updrafts and wind speeds below 2 km height, respectively. The contour interval for both V r and V t is 10 m s 1. cross sections show an eyewall profile that slants outward with increasing height in 2NL0.2 and CNTL5 (Figures 6b and 6c, respectively). [20] In CNTL2 (Figure 6a) and 2D (Figure 6d), the intense updraft and upright eyewall are located at R 30 km in the lower layers, below a height of 2 km (Figures 6f and 6i), whereas in 2D2 they are located at R = 20 km below 2 km height (Figure 6j). The updraft peaks between 8 and 10 km in height. In contrast, below the height of 2 km the intense updraft and the slanted eyewall are located at R = 40 km in 2NL0.2 (Figure 6g) and CNTL5 (Figure 6h). Thus, the radius of eyewall in 2NL0.2 and CNTL5 is much larger than that in CNTL2, 2D, or 2D2. In 2NL0.2, the lower part of the intense updraft region, where the wind speed exceeded 1.5 m s 1, is separated from an upper intense updraft region; between these two intense updraft regions, between 3 and 6 km height, is a branching moderate updraft region (wind speeds exceeding 0.8 m s 1 ). Note that replacements of the updraft region indeed occur in 2NL0.2 (not shown). [21] Next, we investigated the impact of the PBL scheme on the 24 hourly mean azimuthally averaged vertical cross sections of V r and V t, focusing on differences in the lower layers, below the height of 2 km (Figures 6f 6j). All of the numerical results show typical radial inward airflow near the surface (inflow is represented by a positive V r value). The inflow layer in CNTL2 extends to 1500 m at R = 60 km, with the height decreasing toward the TC center. V r exceeds 20 m s 1 between 100 and 200 m height (Figure 6f). In CNTL2, V t exceeds 72.5 m s 1 at 600 m height and R = 30 km, corresponding to the leading edge of the inflow. This structure is consistent with the observational structure obtained from the analysis of data from the 794 GPS dropsondes from 13 hurricanes [Zhang et al., 2011b]. In CNTL2, updrafts exceeds 1.0 m s 1 around the eyewall, just above the leading edge of the inflow. In CNTL5 (Figure 6h), the inflow layer depth at R = 60 km is the same as that in CNTL2. However, V t in the inner core in CNTL5 is relatively weak; the maximum V t of 67.5 m s 1 occurs at 1000 m height and R = 40 km. A strong outflow exceeding 5ms 1 above 1700 m height is found between R = 35 km and R = 50 km. [22] The height of the inflow layer at R = 60 km is 1300 m in both 2NL0.2 (Figure 6g) and 2D (Figure 6i). The height is lower than those in CNTL2 and CNTL5. In contrast, V r in 8of13

9 Figure 7. Twenty-four hourly averaged mean vertical profiles in eyewall regions of (a) sensible heat flux (SH, kw m 2 ) and (b) latent heat flux (LH, g m 2 s 1 ) during period I (see Figure 4a). (c and d) Same as Figures 7a and 7b but during period II. Also shown are the 24 hourly mean radial-vertical profiles in the eyewall region for (e) the momentum diffusion coefficient (K m,m 2 s 1 ) and (f) the heat diffusion coefficient (K h,m 2 s 1 ) during period I. (g and h) Same as Figures 7e and 7f but during period II. 2NL0.2 and 2D exceeds 30 m s 1 near the surface and is greater than that in CNTL2 or CNTL5. The regions where V t exceeds 70 m s 1 extends to lower levels in 2NL0.2 and 2D (300 and 100 m height, respectively), whereas V t exceeds 72.5 m s 1 and is stronger in a lower layer in 2D (200 m) than in 2NL0.2 (600 m). In addition, differences between 2NL0.2 and 2D are large in the mean updraft below a height of 2 km. In 2NL0.2, the maximum updraft (1.7 m s 1 )is reached at 1.6 km height and R = 42 km (white cross in Figure 6g), corresponding to a strong outflow exceeding 5ms 1, whereas in 2D, the updraft is maximal (2.2 m s 1 ) at the lower height of 1.3 km, below a region with a strong outflow exceeding 5 m s 1 (Figure 6i). The maximum updraft also coincides with a region of strong outflow exceeding 5 m s 1 in CNTL5 (Figure 6h). The maximum updraft and strong outflow are considered to play a crucial role in the formation of the slanted eyewall structure in 2NL0.2 and CNTL5. Zhang et al. [2011b] reported a clear difference in the heights of the thermodynamical boundary layer (the mixed layer) and the dynamical boundary layer (the inflow depth), with the thermodynamical boundary layer height being much shallower than the dynamical boundary layer height. In our experiments, the thermodynamic boundary layer heights around the eyewall, 310 m (CNTL2), 300 m (2D), 310 m (2NL0.2), 250 m (2D2), and 420 m (CNTL5), were also shallower than the inflow depths. [23] The wind field in 2D2 is quite different from those in the other experiments and in observations (described in section 1). V t exceeds 80 m s 1 at 200 m height, even though MWS is weaker than 60 m s 1 (Figure 4b). The difference between V t and MWS causes a strong vertical shear from the surface to 200 m height. The inflow layer in 2D2, just below 600 m at R = 60 km, is shallowest among all of the experiments. This shallow boundary layer might have been responsible for the maintenance of an extremely strong V t at 200 m height and the low V t near the surface around the eyewall region Role of the PBL [24] Vertical turbulent mixing in the PBL is one of the essential processes that strengthen secondary circulation and accelerate air-sea turbulent heat and water vapor fluxes and moisture convection around a slanted eyewall [Emanuel, 1986; Nolan et al., 2009b]. Calculated turbulent heat fluxes accumulated within R = 100 km showed a similar time evolution to hourly precipitation amounts at the eyewall (Figure 5). Thus, differences in cumulative turbulent heat fluxes among the numerical experiments were small except in 2D2 (Figure 5b). Even though MCP in 2D2 was less than 900 hpa, the cumulative turbulent heat flux was about 50% smaller than that in the other experiments. The decrease in the magnitude of the cumulative turbulent heat flux within the inner core of the TC in 2D2 was related to the contraction of the eyewall, which narrowed the precipitation region at the eyewall. We examined the roles of vertical heat flux (sensible heat flux) and water vapor flux (latent heat flux) in the development of the TCs, focusing on the differences between intense TCs, with MCP lower than 900 hpa (CNTL2 and 2D) and nonintense TCs, with MCP higher than 920 hpa (CNTL5 and 2NL0.2). 9of13

10 Figure 8. Radial-vertical cross sections of 24 hourly azimuthally averaged mean angular momentum (color shading, 10 5 m 2 s 1 ), vertical wind speed (contours), and wind fields (vectors) for (a) CNTL2. Figures 8b 8e are the same as Figure 8a but for the difference in momentum compared with CNTL2 (color shading, 10 5 m 2 s 1 ): (b) 2NL0.2, (c) CNTL5, (d) 2D, and (e) 2D2. [25] We show vertical transport of sensible and latent heat fluxes around the eyewall during the two periods, during the early period of development (period I) and during rapid development (period II), described in section 3.1 (Figure 7). We defined the eyewall region at each vertical level as the region between the innermost position of upward vertical velocity greater than 0.2 m s 1 and that of the maximum azimuthally averaged tangential wind. The vertical transport of the sensible heat flux shows that the downward sensible heat flux is large in 2NL0.2 (Figures 7a and 7c). During period II, downward sensible heat transport occurs even near the surface in 2NL0.2 and is clearly different from sensible heat transport in CNTL2 and 2D2. In 2D, upward sensible heat flux occurs below the height of 100 m during period II (Figure 7c). In CNTL2, upward sensible heat transport occurs near the surface during both periods. [26] The upward latent heat flux due to eddy diffusion reaches a maximum at 600 m height in 2NL0.2 (Figures 7b and 7d); however, the upward transport rapidly diminishes below 100 m height. The upward latent heat flux is larger between 100 and 300 m and below 100 m height in 2D and CNTL2, respectively, compared with that in 2NL0.2. Those larger upward latent heat fluxes in the lower layers might have contributed to the development of CNTL2 (MCP 895 hpa) and 2D (MCP 895 hpa). Magnitudes of vertical sensible and latent heat fluxes are smaller than other experiments except 2D2 during period II in CNTL5. In 2D2, they are the smallest among the experiments during both periods. The first direct measurements of latent heat and momentum flux in high winds, obtained by the CBLAST experiment, indicated that the latent heat flux below 400 m height was between 300 and 1200 W m 2 [Drennan et al., 2007]. Our period I results, except those in 2D2, are comparable. [27] Differences of l z and Ds among the PBL parameters are responsible for differences in the eddy-diffusivity coefficients for momentum (K m ) and water vapor (K h ; see Figures 7e 7h), resulting in differences in the vertical transports in each experiment. From flight-level data collected by a research aircraft that penetrated the eyewall, Zhang et al. [2011a] estimated that K m within the eyewall of Hurricane Hugo (1989), a category 5 storm, was around 120 m 2 s 1 at 436 m height, when the CP was around 940 hpa and the mean wind speed was 59 m s 1. The value of K m in this study is 130 m 2 s 1 in CNTL2 when CP was around 940 hpa and the mean wind speed was 55 m s 1, results that are fairly comparable to the findings of Zhang et al. [2011a]. Large values of K m, particularly in the lower layer, enhance vertical momentum transport in CNTL2 and 2D; by contrast, K m values in 2D2 are relatively small. In 2NL0.2 and 2D, K h values are remarkably large below 500 m height, which possibly accounts for the intense convective activity at the eyewall that result in relatively large low-level updrafts in these experiments (Figures 6g and 6i). In CNTL5, the values of K m and K h are similar to those in CNTL2 during period I, but during period II they remain relatively small instead of increasing like those of CNTL2. [28] Vertical cross sections of 24 hourly azimuthally averaged mean angular momentum (MAM) show that the inner core structure of TCs depends largely on the PBL scheme and the horizontal resolution (Figure 8). In general, frictional forcing is responsible for a large decrease in MAM near the surface. In CNTL2, an updraft occurs along the constant MAM isopleths above 1000 m height at R = 20 km (Figure 8a). The decrease in MAM in 2NL0.2 (Figure 8b), 2D (Figure 8d), and 2D2 (Figure 8e) is larger near the surface than that in CNTL2 (Figure 8a), and these large decreases in MAM correspond to the relatively large inflows in those experiments. In particular, we attributed vertical turbulent mixing in the lower layers to weak vertical eddy diffusion in 2D2, which was responsible for the maintenance of a strong inflow near the surface and the large MAM at around 200 m height. The large-mam region extends to R = 20 km in 2D and to R = 15 km in 2D2 from the surface to the upper layers along the updraft isopleths at the eyewall. Note that MCP was lower than 900 hpa in both 2D and 2D2, similar to MCP in CNTL2. In contrast, the values of MAM around the eyewall are relatively small in 2NL0.2 and CNTL5 (Figures 8b and 8c, respectively), in which the MCP was higher than in the other experiments. According to Wang [2002], there was substantial grid-scale transport in the eyewall region of TCs. Further analysis is needed to estimate the contributions of both subgrid- and grid-scale transport to the rapid development of an extremely intense TC. 4. Discussion [29] First, we discuss the effect of the subgrid-scale vertical mixing length on the inner core structure of TCs. 10 of 13

11 Previous studies have reported that an increase in horizontal resolution leads to improved boundary layer expression around the eyewall [e.g., Nolan et al., 2009b]. However, the results of this study suggest that both finer horizontal resolution and optimal PBL parameters are required to simulate a reasonable boundary layer structure. It is true that in this study we cannot validate a realistic boundary layer structure of TCs using observational evidence because we use a projection of a future TC. However, we obtain an azimuthally averaged radial-vertical wind field structure consistent with observational structure [Zhang et al., 2011b]. We base the validity of the calculated inner core boundary layer structure in this study on MWS-CP relationships derived from observational analysis of TCs in the western North Pacific Ocean [Koba et al., 1990]. The analyzed MWS-CP relationship is based on the wind speed averaged over 10 min intervals. If the representative timescale of the calculated MWS are shorter than 10 min, then all experiments except 2NL0.2 would lead to further underestimation of MWS. However, the results of this study will contribute to the improvement of this issue by providing insight into how to improve PBL schemes. [30] In this study we demonstrate that eddy diffusivity, that is, the diffusion of a conservative property by eddies in a turbulent flow, plays a critical role in determining the intensity and inner core structure of the calculated TCs because of the large upward latent heat flux that occurs below 300 m height (Figures 7b and 7d). By contrast, vertical sensible and latent heat fluxes in the higher layers are not effective in the experiment when these values are small near the surface (2NL0.2; see Figure 7b). The large vertical upward transport with a smaller upward or a downward transport near the surface might have led to the formation of a slanted structure of the eyewall in 2NL0.2, resulting in the upwind transport at a higher level where the outflow is strong. [31] The values of both Ds and C m affect the intensity and structure of the calculated TCs. For example, the sensitivity experiments (Table 1) showed that the difference in the results of experiments 2D and 2D2 can be attributed to the difference in the formulation of Ds, by equation (1) or equation (2), and the resultant difference in l z between them. In fact, l z is longer in 2D than in 2D2. The differences in Ds result in clear differences in the horizontal scales of the eyewall, MWS, MCP, and the azimuthally averaged mean vertical structure of the TCs, because the differences in l z and eddy diffusivity are responsible for changes in vertical heat and water vapor transport. Note that the 2NL0.1 results show characteristics that are similar not to 2NL0.2 but to 2D2, which use the same Ds settings. The azimuthally averaged mean radial-vertical wind field at the eyewall in 2D2 and 2NL0.1 is unrealistic compared with that derived from the observational analysis. However, MCP in 2D2 and 2NL0.1 is lower than 900 hpa even though MWS is still smaller than 57 m s 1. Some studies have defined TC intensity on the basis of MWS or MCP [Wang and Wu, 2004]. We must pay attention to discuss on the relationships between those properties and TC intensity. [32] Not only the horizontal resolution and the PBL scheme but also SST plays a crucial role in the calculation of TC intensity because SST directly affects the sensible and latent heat fluxes at the air-sea interface. In this study, SST was provided by AGCM20. Our results in this study may have been affected by the SST conditions at the initial time. In addition, the roughness lengths associated with momentum and heat and water vapor fluxes were uniquely calculated by empirical bulk formulas that depend on the surface frictional wind velocity. As described in section 1, surface boundary layers and air-sea interactions are important for strengthening secondary circulation and convective activity within the eyewall. However, in this study, we demonstrated only that MWS and MCP are very sensitive to the characteristics of PBL parameters. The PBL scheme is responsible for resolving the inner core structure of a TC. In the future, the impact of SST, roughness lengths, and PBL parameters on the calculation of TCs should be explored separately. Apart from this issue, AGCM20 was able to calculate an extremely intense TC with a MCP of 904 hpa even though it apparently could not sufficiently resolve the inner core structure of TCs because of its coarse horizontal resolution of 20 km. This AGCM20 result is difficult to understand if inner core dynamics and thermodynamics are necessary to accurately calculate TC intensity. How is AGCM20 able to predict an intense TC without resolving the inner core structure? The AGCM20 result suggests that the relationship between the inner core structure and TC intensity continues to be uncertain, or that TC intensity is determined from dynamics and thermodynamics other than the dynamics of the inner core structure of the TC, such as eye-eyewall mixing processes and vortex Rossby waves, as described in section 1. [33] Note that our aim here is not to confirm the future occurrence of super typhoons. Rather, our purpose is to point out the large variance in TC intensity and the possible sensitivity of TC intensity to PBL parameters in a projected atmospheric environment by using fine-mesh models already in operational use. Further studies are required to project future changes in the intensity of extremely intense TCs as well as their frequency. [34] At this time, it is hard to determine which PBL scheme is best for simulation of an extremely intense TC. Observational analysis has shown that the boundary layer can be clearly separated into thermodynamic and dynamic boundary layer heights [Zhang et al., 2011b]; however, we cannot recommend a PBL scheme in which the depth of the PBL must be preliminarily calculated before l z can be estimated (i.e., the scheme used in 2NL0.2 and 2NL0.1). 5. Summary [35] To explore the effect of the PBL scheme on TC intensities and inner core structures, we conducted numerical experiments using an NHM with a horizontal resolution of 2 km (NHM2) or 5 km (NHM5), in combination with various PBL schemes, namely, the Mellor-Yamada-Nakanishi-Niino Level 3 (CNTL2 and CNTL5) and Level 2.5 (2MY2.5) schemes, a nonlocal scheme with a large coefficient (2NL0.2), and the Deardorff-Blackadar scheme with two different grid scales (2D and 2D2). From a future projection of AGCM20, we selected as a target TC an extremely intense TC with a calculated MCP of 904 hpa for simulations conducted with NHM2 and NHM5 in combination with one of the four PBL schemes. The AGCM20 results were used to obtain initial and boundary conditions for the NHM simulations. [36] From the viewpoint of the wind-pressure relationship, our numerical results can be divided into three categories: excessive MWS (100 m s 1 ) relative to the CP values (2NL0.2 and 2D), reasonable agreement between the results 11 of 13

12 and the observed wind-pressure relationships [Koba et al., 1990] (CNTL2 and 2MY2.5), and underestimation of MWS relative to the CP values (CNTL5, 5NKF, 2D2, 2NL0.1, and AGCM20). These results indicate that the wind-pressure relationship obtained from the numerical simulations is sensitive to the PBL scheme used. The results for the windpressure relationship in CNTL2 and 2MY2.5 are in close agreement with the observed relationship in the western North Pacific Ocean [Koba et al., 1990]. There appears to be no markedly difference between MCP in CNTL5 and 5NKF, which indicates that the Kain-Fritsch convective parameterization scheme used in CNTL5, but not in 5NKF, plays a minor role in calculating the TC intensity. [37] The subgrid-scale mixing length and its associated eddy diffusivity, calculated in the PBL schemes, plays critical roles in the maintenance of an upright updraft within an eyewall through the upward latent heat flux from the lower layers (<300 m); the upward latent heat flux from the lower layers is responsible for the formation of an intense TC with an MCP lower than 900 hpa. In addition, a horizontal resolution of 2 km is required to simulate the inner core structure of a TC. The choice of PBL parameters is very important for the proper representation of the TC eyewall structure and the wind-pressure relationship. [38] Therefore, the intensities and structures of TCs calculated by the numerical models used in this study are highly sensitive to not only the horizontal resolution of numerical models but also the choice of PBL scheme and the values of the parameters in the PBL scheme used. However, large uncertainties remain in the PBL schemes and parameters. Here we only demonstrate the effects of the PBL scheme on TC intensity and inner core structure, but unlike the effects of horizontal resolution, the reasons for the PBL scheme effects cannot be easily understood. Nevertheless, this study provides insight into possible mechanisms of excessive MWS, given a certain CP value, and an explanation for the underestimation of MWS relative to the CP value from the viewpoints of PBL physics and wind-pressure relationships. In addition, we successfully calculated some representative inner core structures and relevant processes associated with observed TCs, such as a slanted eyewall structure and outflows just above the boundary layer. These results contribute to the clarification of boundary layer processes within the inner core of a TC. In the future, numerical experiments to reproduce real TCs and their verification against field observations are needed to improve our understanding of inner core mechanisms and TC development in relation to PBL physics. [39] Acknowledgments. This study was supported by the Ministry of Education, Culture, Sports, Science and Technology of Japan under the framework of the Kakushin Program. Numerical simulations were performed using the Earth Simulator. We greatly appreciate the thorough reviews and constructive comments of three anonymous reviewers. The authors gratefully acknowledge the Kakushin 3 modeling group for conducting the project, as well as M. Nakamura, S. Hayashi, and H. Tsuguti of the Meteorological Research Institute and T. Hara of the Japan Meteorological Agency for valuable discussions. A. Wada was supported by the Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C) ( ). References Bao, J.-W., C. W. Fairall, S. A. 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