1. Introduction
Turbulence within the tropical cyclone (TC) boundary layer is affected by the strong winds and inertial stability (e.g., Eliassen 1971; Kepert 2001), making the TC boundary layer distinct from the traditional convective boundary layer. Growing evidences have shown that parameterized boundary layer turbulent fluxes can impact TC inflow strength and depth and further modulate TC intensity change (e.g., Braun and Tao 2000; Smith and Thomsen 2010; Gopalakrishnan et al. 2013; Zhang et al. 2015). However, accurately representing turbulent fluxes in the planetary boundary layer (PBL) schemes for TC simulations remains challenging. This is in part due to the scarcity of in situ turbulence measurements in high wind conditions, especially those over the ocean, and to the fact that the existing PBL schemes are generally tuned based on observations or large-eddy simulations of convective boundary layers over land.
The issue is further complicated with the increase in computing power, which enables horizontal grid spacings (Δ) of global and regional numerical models at ~1 km or smaller (e.g., Nolan et al. 2009; Miyamoto et al. 2013; Shin and Dudhia 2016; Biswas et al. 2020). Such grid spacings are comparable to the boundary layer height (zi) of TCs (Zhang et al. 2011b), and belongs to the “terra incognita” (Wyngaard 2004), also well known as the model gray zone (Arakawa et al. 2011). While boundary layer turbulence is completely parameterized in coarse-resolution simulations (Δ ≫ zi), it becomes partially resolved by model grid points at gray-zone resolutions. Therefore, neither the traditional PBL schemes nor large-eddy simulations with subgrid-scale (SGS) turbulence closure is appropriate to represent the boundary layer turbulence in the gray zone. The direct use of traditional PBL schemes in the gray zone can result in overestimated turbulent mixing. Many ensuing unrealistic features have been reported in previous studies of the convective boundary layer, including weakened resolved motions (Honnert et al. 2011; Ching et al. 2014) and broken or thinner convective rolls (LeMone et al. 2010; Shin and Hong 2015).
To alleviate the gray-zone issue, several scale-aware PBL schemes have been developed in recent years in the context of the convective boundary layer (Boutle et al. 2014; Shin and Hong 2015; Ito et al. 2015). The core essence of the scale awareness in these PBL schemes is to apply a predefined empirical partition function of the dimensionless grid spacing Δ/zi to down-weight PBL-scheme-parameterized turbulent fluxes in the gray zone. Although these empirical functions generally lack a solid theoretical basis (Zhou et al. 2017), they have been shown to have the desired effects on the convective boundary layer. However, to the best knowledge of the authors, evaluation of the performance of such scale-aware PBL schemes in TC simulations is not found in formal literature.
This study is motivated to investigate the effect of the scale-aware PBL scheme on TC intensification and structural changes within a set of WRF simulations of Hurricane Earl (2010) at subkilometer horizontal grid spacings. The subkilometer grid spacing is selected because observational analysis of in situ dropsondes indicates that the TC boundary layer height in terms of the mixed-layer depth1 is generally less than 1 km (Zhang et al. 2011b). Two PBL schemes are selected in this study, namely, the YSU (Hong et al. 2006) and Shin–Hong (below abbreviated as SH; Shin and Hong 2015) schemes. YSU is one of the most popular PBL schemes used for TC simulations (Kepert 2012), and SH adopts similar parameterization of turbulent fluxes as YSU but with the inclusion of scale awareness. The performance of these two PBL schemes in the gray zone has been evaluated in both the dry and moist convective boundary layers (Xu et al. 2018; Choi and Han 2020) but not for the TC boundary layer. In the TC boundary layer, the adjustment of vertical mixing in the scale-aware PBL schemes may exert an impact on the extent of gradient-wind imbalance as well as vertical profiles of thermodynamic variables in the inflow layer, which may further affect the TC structure and intensity. Given this, the specific scientific questions to be addressed in this study include the following: (i) What is the effect of the scale-aware SH scheme on the structural and intensity changes of TCs at gray-zone resolutions? (ii) When and where does the scale awareness play an important role? (iii) What is the physical mechanism responsible for the differences in the structural and intensity changes?
The remainder of the paper is organized as follows. Section 2 provides an overview of the YSU and SH schemes. The data, experiment design, and model setup are described in section 3. A brief overview of the life cycle of Hurricane Earl is presented in section 4. Section 5 analyzes the effect of the scale-aware SH scheme on the TC structural and intensity changes. The related physical mechanisms and additional suggestions to the improvement of PBL schemes for TC simulations are discussed in section 6. Concluding remarks are presented in section 7.
2. A brief comparison between the YSU and SH PBL schemes
(a) Stability dependency function Ccs in the Shin–Hong PBL scheme and (b) nonlocal scale-aware coefficient for momentum (black), and potential temperature (red) flux when Ccs = 1 (solid) or Ccs = 2 (dashed).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
3. Data, experiment design, and model setup
The WRF-ARW Model, version 3.8 (WRF; Skamarock and Klemp 2008) is used in this study. Two-way interactive, quadruple-nested model domains are utilized with horizontal resolutions of 12, 4, 1.33, and 0.444 km, consisting of 502 × 346, 391 × 409, 469 × 487, and 1189 × 1243 horizontal grid points, respectively (Fig. 2). The outermost domain is fixed while the inner three domains move with the model TC. All three domains contain 51 sigma levels with the top level at 50 hPa. There are 18 model levels below 850 hPa. The outer three domains run from 1800 UTC 26 August to 1800 UTC 31 August, while the innermost domain is activated 18 h later and run from 1200 UTC 27 August to 1800 UTC 31 August. The European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim) data are used for the initial and lateral boundary conditions. The grid resolution of the ERA-Interim dataset is 0.702° latitude × 0.703° longitude at 37 pressure levels.
Quadruple-nested model domains for the simulation of Hurricane Earl (2010). The shading denotes the sea surface temperature (°C) at 1800 UTC 26 Aug 2010.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
The WRF model physics configurations used are as follows: the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1993) in the outermost domain, the Thompson microphysics scheme (Thompson et al. 2008), the Dudhia shortwave radiation (Dudhia 1989), and the Rapid Radiative Transfer Model (RRTM) longwave radiation scheme (Mlawer et al. 1997) in all four levels of grid. The Thompson microphysics scheme is selected given recent evaluation studies using polarimetric radars indicated the Thompson scheme outperforms several other microphysics schemes by reasonably capturing raindrop size distributions and surface precipitation in TCs (e.g., Brown et al. 2016; Wu et al. 2021).
The YSU and SH PBL schemes are used in the two control simulations, named CTL-SH and CTL-YSU, respectively, and five additional sensitivity tests (see Table 1). The Revised MM5 Monin–Obukhov (below abbreviated as RMO) surface layer scheme is adopted in both experiments. In the RMO surface layer scheme, the surface drag coefficient Cd in high winds levels off and does not continue to increase for wind speeds greater than 30 m s−1 (Davis et al. 2008), which is in line with the dropsonde and laboratory observations (Powell et al. 2003; Donelan et al. 2004). In all simulations, the first-order Smagorinsky closure is used for the horizontal SGS mixing, which is recommended for real-case simulations. Of note, results from one additional pair of (CTL) experiments using the WDM6 microphysics scheme (Lim and Hong 2010) are consistent with those in CTL-SH and CTL-YSU, and thus are not included in this study.
Numerical experiments design.
4. Overview of the evolution of Hurricane Earl (2010)
Earl (2010) originated from a tropical easterly wave that left the west coast of Africa on 23 August. With continuous convective organization in the central area of the circulation, Earl gradually intensified to a tropical depression by early 25 August and further to a tropical storm by 1200 UTC 25 August. In the next several days, it moved westward to west-northwestward under the steering flow south of the subtropical ridge. Meanwhile, it reached the hurricane intensity at 1200 UTC 29 August in an environment with warm seawater (28°–29°C, see Fig. 2) and weak-to-moderate vertical wind shear. Earl underwent a rapid intensification2 (RI) from 0600 UTC 29 August to 1800 UTC 30 August, as it passed over the very warm seawater (~30°C). It was upgraded into a category-4 hurricane at the end of RI (Fig. 3). A concentric eyewall replacement cycle followed subsequently and the storm intensification paused. Details of the storm evolution have been reported in Cangialosi (2010) and discussed in previous literature (e.g., Montgomery et al. 2014; Rogers et al. 2015; Susca-Lopata et al. 2015; Chen and Gopalakrishnan 2015).
Verification of the simulated (a) track, (b) minimum SLP (hPa), and (c) 10-m maximum wind speed (m s−1). The gray, black, and red lines in each panel represent the best track data from the National Hurricane Center, CTL-YSU, and CTL-SH experiment, respectively.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
5. Results
Figure 3 presents comparisons of track and intensity between the two control simulations (CTL-SH and CTL-YSU) and the best track from the National Hurricane Center. The RI onset in both simulations is approximately 1800 UTC 29 August, 12 h later than that in the best track data. Before RI onset, TCs in both experiments undergo several cycles of slow intensification and weakening (Fig. 3c). The weakening periods are closely related to low-level ventilation (Riemer et al. 2010), i.e., convective downdrafts bring low-θe air parcels from above into the boundary layer and cool the inflow layer (not shown). The low-level ventilation is unfavorable for the maintenance of convective activity within the inner-core region and TC intensification, which has been documented in previous studies for sheared TCs (e.g., Molinari et al. 2013; Chen et al. 2019). These low-θe parcels are subsequently recovered by surface enthalpy fluxes and the TC intensifies again (e.g., Chen et al. 2021). The minimum sea level pressure at the peak intensity in CTL-SH is closer to the best track. During the RI period, the CTL-SH TC has a higher intensification rate than the best track while the CTL-YSU TC intensifies at a lower intensification rate. Nevertheless, both simulations generally reproduce the track, RI, and eyewall replacement cycle (not shown), and the simulation datasets provide a chance to gain insight into the effect of the scale-aware SH scheme on the TC intensity and structural changes.
a. Impact of scale-aware SH PBL scheme on TC intensity and structural changes
Figures 3b and 3c indicate that the intensity evolution between the two control simulations is similar until 0600 UTC 28 August. The CTL-SH TC subsequently becomes stronger than the CTL-YSU TC, and somehow the TC intensity at RI onset in the two experiments becomes comparable. Differences in the minimum sea level pressure or maximum 10-m wind speed notably increase during the RI period, i.e., from 1800 UTC 29 August to 1800 UTC 30 August. Figure 4 shows the results over the period when the innermost domain is activated. Recall that the innermost domain is activated 18 h later than the outer three domains. The evolution of the maximum 10-m axisymmetric tangential wind exhibits a similar phenomenon (Fig. 4a). The stronger CTL-SH TC after 0600 UTC 28 August is accompanied by a more rapid contraction of the radius of maximum wind (RMW) at 10-m height (Fig. 4b). The RMW of the CTL-SH TC is approximately half of the RMW of the CTL-YSU TC over the period from 0700 UTC 28 August to 0400 UTC 29 August. The increase in the TC intensity after 0600 UTC 28 August is accompanied by a steady increase in the mean boundary layer height averaged within the radius of 200 km in both experiments (Fig. 4c). Of note, the large-scale environmental vertical wind shear is very similar in CTL-YSU and CTL-SH over the simulation period (not shown) and is not responsible for driving these differences.
Evolution of (a) maximum 10-m axisymmetric tangential wind (m s−1), (b) 10-m radius of maximum wind (km), and (c) mean boundary layer height (m) in the CTL-YSU (black), CTL-SH (red), and SH-NoSA (green) experiments. Evolution of (d) mean local (black) and nonlocal (red) scale-aware coefficients for momentum (dashed) and θ (solid), (e) mean u*/w* (red) and Ccs (black), and (f) mean w* (m s−1; red) and u* (m s−1; black) in the CTL-SH experiment. The results in (c)–(f) are averaged within r = 200 km. The local scale-aware coefficients in (d) are averaged within the lowest 300 m. The gray dashed line in each panel denotes the time when the TC intensity of the two experiments begins to diverge. The black arrow in (a) denotes the RI onset time.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
Figures 4a–c also show the results from the experiment SH-NoSA in which the scale-aware effect is turned off (i.e., PNL = PL = 1). Since SH differs from YSU in both the inclusion of scale awareness and the formulation of
As the mean boundary layer height in CTL-SH becomes comparable to or larger than the horizontal grid spacing of the innermost domain (i.e., Δ = 444 m), the reduction in the scale-aware coefficients becomes more notable (see discussions in section 2). Figure 4d shows the evolution of local and nonlocal scale-aware coefficients for both momentum and θ averaged within the 0–300-m layer. We select this layer to ensure that the local scale-aware coefficients are averaged within the boundary layer height. Of note, the mean boundary layer height is ~350 m prior to 0600 UTC 28 August. Figure 4d shows that the local scale-aware coefficients decrease slightly as the boundary layer height increases, while the nonlocal coefficients rapidly decrease and reach a minimum of 0.6–0.7 at nearly 1500 UTC 29 August. Given the small difference between the local and nonlocal coefficients for θ when Ccs = 1 (Fig. 1b), the relatively large discrepancy between them in Fig. 4d is indicative of the modulation of the nonlocal scale-aware coefficients by the stability function (Ccs = 2). This hypothesis is confirmed by Fig. 4e. The mean Ccs is ~1.5 before 0600 UTC 28 August and it rapidly increases toward 2.0 afterward. Consistently, the mean
The nonlocal scale-aware coefficient gradually increases after 0300 UTC 30 August (i.e., in the middle of the RI period), since the mean Ccs steadily decreases as the mean
To examine where the scale-aware effect is most significant in the TC circulation, Figs. 5a–d show the plan view of radar reflectivity and boundary layer height at 0700 UTC 28 August for the two experiments. In both experiments, a convective rainband, which is closely related to vortex tilt (not shown), is located in the front half of the storm relative to the storm motion with a left-of-motion maximum in radar reflectivity. Similar location of maximum radar reflectivity was documented in earlier observational studies for mature hurricanes (e.g., Marks 1985; Franklin et al. 1993; Reasor et al. 2000). The strongest convection is also located in the downshear-right quadrant, suggesting both the storm motion and deep-layer shear may play a role in determining the precipitation asymmetry at the early stage. Figures 5b and 5d reveal a front-back asymmetry in the boundary layer height, which agrees with the findings of dropsonde composite analysis for hurricanes (Ren et al. 2019). The dry (i.e., nonprecipitation) region ahead of the storm and radially outward of the convective rainband has the maximum boundary layer height. Accordingly, the nonlocal and local scale-aware coefficients are smaller in the dry region, indicative of a stronger scale-aware effect.
Plan view of (a) radar reflectivity averaged within the lowest 500 m and (b) boundary layer height (m) at 0700 UTC 28 Aug 2010 for CTL-YSU experiment. (c),(d) As in (a) and (b), but for CTL-SH experiment. (e),(f) Plan view of nonlocal and local scale-aware coefficients for wind, respectively. The local coefficient is averaged within the lowest 300 m. Gray and black arrows denote the direction of storm motion and 200–850-hPa vertical wind shear. Dashed lines in (e) and (f) delimit the downshear and upshear semicircles. The thick red circle denotes the RMW, and the thin black circles denote the rings every 50 km.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
The relationship of boundary layer height and scale-aware coefficients in the TC circulation is further examined in Fig. 6, which shows the composite radial profile of their azimuthal mean over three consecutive 18-h periods before RI onset and after the activation of the fourth domain. The mean boundary layer height in CTL-SH is generally shallower than that in CTL-YSU over the three periods, which is consistent with the findings in Choi and Han (2020). The boundary layer height increases with radius and correspondingly the scale-aware coefficients decrease with radius, consistent with the results shown in Fig. 5. Over periods 1 and 2 (i.e., from 1200 UTC 27 August to 0000 UTC 29 August), the radial gradient of the boundary layer height is weak within the innermost 120-km radii (Figs. 6a,c). A strong radial gradient of the boundary layer height builds up over period 3 (i.e., from 0000 UTC 29 August to 1800 UTC 29 August) immediately before RI onset, with lower values of boundary layer height at smaller radii (Fig. 6e). The sharp radial gradient of boundary layer height implies the effect of strong rotation on the mixed-layer depth or thermodynamic stability. A strong radial gradient of the scale-aware coefficients also appears over period 3 (Fig. 6f). The large discrepancy in the azimuthal-mean nonlocal and local coefficients again supports the notion that the scale-aware effect for the nonlocal fluxes is more prominent due to the modulation of the stability function Ccs.
The composite radial profile of (left) azimuthal-mean boundary layer height (m) and (right) scale-aware coefficients over (a),(b) 1200 UTC 27 Aug–0600 UTC 28 Aug, (c),(d) 0600 UTC 28 Aug–0000 UTC 29 Aug, and (e),(f) 0000 UTC 29 Aug–1800 UTC 29 Aug, respectively. The shading in (a), (c), and (e) represents ±1 standard deviation of the boundary layer height, and the black (red) line denotes CTL-YSU (CTL-SH). In (b), (d), and (f), PL for momentum (black) and potential temperature (red) is averaged within the lowest 300 m. The dashed and solid lines denote PNL and PL, respectively.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
Figure 7 presents the radial profiles of azimuthal-mean tangential wind, radial wind, and horizontal convergence over the same three periods. Over period 1, the profiles of tangential and radial winds in the two experiments are very similar except for the innermost 50-km radii. In CTL-SH, the tangential wind is slightly weaker and radial wind is slightly stronger within r = 50 km (Figs. 7a,d), and the stronger inflow corresponds to the stronger convergence therein (Fig. 7g). The stronger convergence in CTL-SH precedes stronger diabatic heating at 2-km height over period 2 (Fig. 8), indicating the role of boundary layer convergence in initiating the convection therein. The RMW of the CTL-SH TC contracts inward more rapidly and the tangential wind increases at a higher rate within r = 50 km (Fig. 7b) over period 2, which can be explained by a response to the stronger diabatic heating near and inside the RMW according to balanced dynamics (e.g., Shapiro and Willoughby 1982; Chen et al. 2018; Xu and Wang 2018).
Radial profile of composite (a)–(c) tangential wind, (d)–(f) radial wind (m s−1), and (g)–(i) divergence (10−3 s−1) averaged within the lowest 300 m over the same three periods as in Fig. 6. The legend for these plots is shown in (c). Note the y axis is different between (g) and (h)–(i).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
Hovmöller diagram of the azimuthal-mean diabatic heating at z = 2 km (shading; K h−1) and horizontal convergence (black contours with values of −2, −1, −0.5, −0.1 × 10−3 s−1) at z = 0.25 km for (a) CTL-YSU and (b) CTL-SH. The thick white line in each panel denotes the RMW at z = 0.25 km. The white dashed lines delimit three periods before RI onset.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
The discrepancy in the magnitude of radial inflow (Fig. 7e) and convergence (Fig. 7h) between the two experiments significantly increases over period 2. The maximum convergence near the TC center in CTL-SH is nearly 2 times of that in CTL-YSU over period 2. The averaged diabatic heating near the RMW at 2-km height over period 3 (i.e., 0000 UTC 29 August–1800 UTC 29 August) is smaller than that over period 2 (Fig. 8), and the radial wind and convergence averaged in the lowest 300-m layer in CTL-SH are weaker than that over period 2 (Figs. 7f,i). Nevertheless, the CTL-SH TC still has a smaller inner core and stronger intensity than the CTL-YSU TC over period 3 (Fig. 7c).
Given that the differences in the radial inflow, horizontal convergence, and diabatic heating near the TC center between CTL-YSU and CTL-SH increase with the increasing discrepancy in vortex structure and intensity, Fig. 9 compares the vertical profiles of azimuthal-mean radial wind, specific humidity, and θ in the two experiments averaged within r = 200 km over period 1, when notable differences in the vortex structure and intensity have not emerged (Figs. 4a,b and 7a,d). This comparison provides a chance to identify the impact of vertical turbulent mixing on the boundary layer structure. Figure 9a shows that the radial inflow is enhanced within zi (≈ 350 m) (Fig. 9a), consistent with the response of the radial inflow to weaker vertical viscosity in previous studies (e.g., Gopalakrishnan et al. 2013; Zhang et al. 2015). Meanwhile, more water vapor is retained in the boundary layer of the CTL-SH TC (Fig. 9b). In CTL-SH, the stronger radial inflow carries more water vapor inward, inducing stronger horizontal convergence and diabatic heating near the TC center, as seen in Fig. 8b. Although this effect is relatively smaller over period 1, it gradually accumulates with time as the discrepancy in the vortex structure and intensity magnifies.
Vertical profile of azimuthal-mean (a) radial wind (m s−1), (b) specific humidity (g kg−1), and (c) potential temperature (K) averaged within r =200 km over the period from 1200 UTC 27 Aug to 0600 UTC 28 Aug 2010. The legend for these plots is shown in (a).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
The stronger moisture convergence and diabatic heating at smaller radii in CTL-SH benefits a faster contraction of the low-level RMW preceding RI onset (Figs. 4b and 8). While the low-level RMW in CTL-YSU manages to contract to a similar size as that in CTL-SH at RI onset, the mean RMW of the CTL-SH TC is smaller during the RI (Fig. 4b). The faster intensification rate during the RI period in CTL-SH can be explained by the stronger boundary layer inflow and stronger diabatic heating within the more compact inner core based on an existing theory: diabatic heating at smaller radii can draw large absolute angular momentum inward to smaller radii and thereby spin up the storm circulation above the boundary layer more effectively than diabatic heating at larger radii (Smith and Montgomery 2016).
b. Sensitivity to the vortex structure at RI onset
Previous studies highlighted the importance of the inner-core structure at RI onset in the subsequent intensification (e.g., Carrasco et al. 2014; Miyamoto and Nolan 2018; Chen et al. 2018, 2019). At RI onset (i.e., 1800 UTC 29 August), the RMW in CTL-SH and CTL-YSU is very similar (Fig. 10c), while the CTL-SH TC has a much larger (~40 km) radius of gale-force winds (R17) (Fig. 10d). The different R17 may also exert an additional impact on the subsequent intensification rate and vortex structure evolution (e.g., Xu and Wang 2018). To exclude the effect of the vortex structure and clearly identify the effect of the scale-aware SH scheme in the intensity and structural evolution during the RI period, two sensitivity experiments, namely, the YSU2SH and SH2YSU (see Table 1), are performed. In experiment YSU2SH, the YSU scheme is switched to SH scheme at RI onset, and it is vice versa in SH2YSU.
Evolution of the simulated (a) minimum SLP (hPa), (b) 10-m maximum wind speed (m s−1) from 1800 UTC 26 Aug to 1800 UTC 31 Aug; evolution of (c) RMW (km) and (d) radius of gale-force winds (km) from 1800 UTC 29 Aug to 1800 UTC 31 Aug. The legend for these plots is shown in (a). The gray shading in (a) and (b) denotes the analysis period in (c) and (d).
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
The RI period in YSU2SH extends to 0300 UTC 31 August (Fig. 10b), approximately 9 h longer than in CTL-YSU, and maximum 10-m wind is ~10 m s−1 stronger at the end of the RI. Compared to CTL-YSU, the RMW and R17 in YSU2SH further decrease by ~4 km and ~10 km, respectively, during the RI period (Figs. 10c,d). In parallel, the comparison between CTL-SH and SH2YSU indicates that the TC intensification rate in SH2YSU is slightly reduced (Figs. 10a,b). The RMW in SH2YSU increases by ~5 km, and the R17 in SH2YSU increases by ~10 km compared to those in CTL-SH during the RI period (Figs. 10c,d). These results and the analyses in section 5a consistently show that the SH PBL scheme tends to produce a stronger vortex with smaller inner-core size throughout the early stage to the end of RI. However, differences in the TC intensification rate by switching the PBL scheme at RI onset is much smaller than those between the two control simulations, suggesting that the vortex structure at RI onset is the main controlling factor in the rate of intensification.
Additionally, the larger radius of gale-force winds in CTL-SH than in CTL-YSU during the RI period is attributed to the differences in the vortex structure at RI onset, while the SH scheme itself tends to produce a smaller R17 if the same vortex structure as in CTL-YSU is provided at RI onset.
c. Sensitivity to different start time
To further test the robustness of the findings, we also run other pairs of simulations with the start time 12 h (i.e., late-R1 experiments) and 24 h (i.e., late-R2 experiments) later than the control simulations (see Table 1). The late-R1 experiments do not show a RI until near the end of the simulations and thereby the maximum intensity of the simulated TCs is much weaker than the best track. However, at the end of the simulations, the maximum wind of the SH TC is 12 m s−1 larger than that of the YSU TC and the RMW of the SH TC is also smaller (not shown). The late-R2 experiments exhibit a similar RI onset timing as in CTL experiments (Fig. 11). Results consistently show that the SH TC has a smaller RMW (Fig. 11c) and exhibits higher intensification rate (Figs. 11a,b) during RI (i.e., from 0000 UTC 30 August to 0600 UTC 31 August) than the YSU TC. After 0900 UTC 31 August, the SH TC undergoes an inner-core process similar to eyewall replacement (not shown) with the RMW expanding and the intensification paused. This accounts for the fact that the SH TC is slightly weaker than the YSU TC near the end of the simulation. Nevertheless, results of the late-start simulations are generally consistent with those of the CTL simulations.
Evolution of (a) minimum SLP (hPa), (b) 10-m maximum wind speed (m s−1), and 10-m RMW from lateR2-YSU (black) and lateR2-SH (red) experiment. The gray line in (a) and (b) denotes the best track data from the National Hurricane Center.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
6. Discussion
a. Related mechanisms and additional discussions
The analysis in section 5 demonstrates that the scale-aware effect in SH can impact both TC intensity and structure evolutions at gray-zone resolutions. The related physical mechanism is summarized in Fig. 12. In SH, the response of the scale-aware coefficients to the changing boundary layer height leads to a dynamical adjustment of the vertical diffusivity at different stages of the TC evolution. The associated weakening in vertical turbulent mixing or increase in frictional deceleration induces stronger boundary layer inflows due to the gradient-wind imbalance in the boundary layer. The stronger radial inflows advect larger absolute angular momentum to smaller radii, which facilitates the spinup of tangential winds at smaller radii as well as a more notable RMW contraction in the TC boundary layer. Meanwhile, the weakened vertical turbulent mixing helps retain more water vapor within the boundary layer. The resulting stronger moisture convergence and diabatic heating near the TC center also help draw the large absolute angular momentum inward and spin up the TC circulation above the boundary layer more efficiently (Smith and Montgomery 2016). These physical processes account for the smaller inner core and faster intensification of the TC in CTL-SH. Of note, previous modeling studies that directly changed the vertical eddy viscosity (e.g., Gopalakrishnan et al. 2013; Zhang et al. 2015) indicated very similar physical processes.
Schematic of the effect of scale-awareness on TC intensification and structural changes based on the comparison of simulations with the SH and YSU PBL schemes. The Vmax represents the maximum TC intensity, |Vr| denotes the inflow strength, and qυ denotes the specific humidity.
Citation: Monthly Weather Review 149, 7; 10.1175/MWR-D-20-0297.1
In addition to the scale-aware effect, the weaker vertical turbulent mixing in CTL-SH is also in part attributed to the slightly lower zi (Fig. 4c), especially before RI onset, since the maximum value of Km is proportional to the zi in the KPP PBL schemes (e.g., Kepert 2012). The parameterization of nonlocal vertical heat fluxes
b. Suggestions for the improvement of YSU and SH schemes in TC simulations
This study takes a preliminary step toward the understanding of scale-aware PBL parameterizations at gray-zone resolutions for TC simulations. Several potential issues of using the SH PBL schemes in the TC simulations should be noted. First, similar to YSU (Hong et al. 2006), the vertical viscosity and nonlocal turbulent fluxes in SH was formulated based on the LES of a typical convective boundary layer over land (Shin and Hong 2015), and its suitability in TC simulations is still uncertain.
Second, the enhancement of scale-aware effect within a specific range of
Third, given that the scale-awareness parameterization in SH and the maximum vertical eddy viscosity depend crucially on the diagnosed boundary layer height (i.e., mixed-layer depth), whether the mixed-layer depth can represent the top of the boundary layer in hurricane environments is another important issue needing further investigation. In the convective boundary layer, the dominant length scale of the flow is typically assumed comparable to the boundary layer height. In this study, the mixed-layer depth in the eyewall is generally less than 800 m, while observations at the low levels of the eyewall of mature hurricanes show that the estimated horizontal length scale of the dominant turbulent eddies is mostly between 800 and 3000 m (Zhang et al. 2011a). Several earlier studies recommended using the inflow layer depth to represent the boundary layer height in hurricanes (e.g., Smith et al. 2009; Zhang et al. 2011b). This recommendation is supported by in situ momentum flux measurements (Zhang et al. 2009) in which the vertical transport of momentum flux is found to mainly occur within the inflow layer. The dropsonde composite analysis for hurricanes pointed out that the inflow layer depth is more than a factor of 2 greater than the mixed-layer depth (Zhang et al. 2011b), with a mean inflow layer depth of 1–1.5 km. The large discrepancy in the mixed-layer depth and inflow layer depth suggests choosing an appropriate TC boundary layer height in the formulations of the turbulent fluxes and scale-awareness functions is a key element in the future development of KPP PBL schemes for the TC boundary layer.
7. Conclusions
This study examines the effect of a scale-aware PBL scheme on the tropical cyclone (TC) intensification and structural changes in the gray zone by performing a set of WRF-ARW simulations of Hurricane Earl (2010) at a subkilometer grid spacing (i.e., 444 m on the innermost two-way interactively nested grid). Two K-profile parameterization PBL schemes including nonlocal terms, i.e., the YSU and Shin–Hong (SH) schemes, are used in these simulations. SH includes the parameterization of scale dependency of the subgrid-scale (SGS) turbulence flux in the gray zone and is considered a scale-aware variation of the more traditional YSU. The essence of the scale-awareness in SH is to reduce the SGS vertical turbulence mixing in the gray zone by multiplying a function of dimensionless grid spacing (i.e., the horizontal grid spacing normalized by the boundary layer depth), since more turbulent fluxes can be explicitly resolved at finer horizontal resolutions.
Results show that the experiments using SH and YSU (i.e., CTL-SH and CTL-YSU, respectively) are capable of reproducing the rapid intensification (RI) of Earl at the gray-zone resolutions. However, the CTL-SH TC undergoes a faster intensification during the RI period and reaches a much stronger intensity after RI than the CTL-YSU TC. Additionally, the contraction of the radius of maximum wind (RMW) in CTL-SH is faster preceding RI onset, and the inner-core size remains smaller during the RI period.
Further analysis reveals that the scale-awareness starts to play a role as the diagnosed boundary layer height increases to a scale comparable with the subkilometer horizontal grid spacing. The scale-aware effect is most prominent through the early stage to the middle of RI, when nonlocal turbulent fluxes are substantially reduced due to the effect of parameterized convective rolls. In the late RI and subsequent eyewall replacement, the scale-aware effect dwindles as the nonlocal scale-aware coefficients increase. This is mainly due to the rapid increase in the surface frictional velocity during RI such that the large ratio of
While both the scale awareness and different parameterization of the nonlocal turbulent heat flux in SH reduce the vertical turbulent mixing, the scale awareness plays a dominant role in reducing the TC inner core size and increasing the TC intensity. The reduced vertical mixing induces stronger radial inflows and helps retain more water vapor in the lower boundary layer. The resulting stronger moisture convergence and convective diabatic heating closer to the TC center benefit faster RMW contraction before RI onset and higher intensification rates during RI. Additional sensitivity experiments that switch the PBL scheme at RI onset confirm that SH tends to produce a stronger TC with a smaller RMW during the RI period than YSU, while the vortex structure at RI onset is the controlling factor in the intensification rate during RI.
To our knowledge, this study presents a first look into the effect of a scale-aware PBL scheme on the TC intensity and structural evolution in the gray zone. As model grid spacings keep decreasing, results in this study can provide guidance for physics development of global and regional models for TC forecast purposes. Recognizing that the existing scale-aware PBL schemes are generally developed in the context of non-TC conditions, we hope this study will promote interests and attention toward the PBL scheme development for the TC boundary layer, which is quite different from the traditional continental convective boundary layer due to its predominance of shear-driven turbulence mechanisms in the lower-to-middle boundary layer (Bryan et al. 2017) as well as the effect of strong rotation on the boundary layer dynamics (Eliassen 1971; Kepert 2001) and turbulence characteristics (Cione et al. 2020). Last, we should note that this study is based on a single case and limited model physics configurations; similar comparisons should be performed with more cases and with different model configurations to test the robustness of the results. This is a topic for future studies.
Acknowledgments
This study had been supported by the National Key R&D Program of China under Grant 2017YFC1501601 and the Natural Science Foundation of China Grant 41775056. The authors want to acknowledge Drs. Gus Alaka and Xuejin Zhang for their suggestions to improve the early version of this manuscript. The authors are also grateful for the helpful comments from two anonymous reviewers. The first author, Xiaomin Chen, is currently supported by the NRC Research Associateship Programs. Numerical simulations were performed at the High Performance Computing Center (HPCC) of Nanjing University.
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In both YSU and SH, the boundary layer height is defined as the mixed-layer depth where positive surface heat fluxes exist.
The RI is defined as the maximum 10-m wind increasing by 15 m s−1 over 24 h (Kaplan and DeMaria 2003).
