1. Introduction
Parameterizations of boundary layer turbulent processes play an important role in governing the evolution of tropical cyclone (TC) structure and intensity (e.g., Braun and Tao 2000; Hill and Lackmann 2009; Nolan et al. 2009a,b; Smith and Thomsen 2010; Bryan 2012; Zhang et al. 2015; Bu et al. 2017; Zhang and Pu 2017; Chen et al. 2021b). Continuous development of planetary boundary layer (PBL) schemes, especially for high-wind, nearly neutral TC boundary layers, is critical to further improving forecasts of TC structure and intensity, as well as the global impact of TCs.
NOAA’s Hurricane Analysis and Forecast System (HAFS; e.g., Hazelton et al. 2021) is a hurricane application of the cubed-sphere finite-volume dynamical core (FV3)-based Unified Forecast System (UFS). One of the model physics upgrades in HAFS is replacing the hybrid eddy-diffusivity mass-flux (EDMF) PBL scheme with a scale-aware turbulence kinetic energy (TKE)-based moist EDMF PBL scheme (EDMF-TKE hereafter; Han and Bretherton 2019). Recently, the shear impact on vertical mixing (Rodier et al. 2017) was included in EDMF-TKE.
In the EDMF-TKE PBL scheme, the downgradient transport is parameterized by a TKE-based eddy-diffusivity approach; the counter-gradient transport by large eddies is parameterized by a mass-flux approach that is applicable to all unstable boundary layer conditions. Additionally, parameterizations of mixing length and dissipation length scale in EDMF-TKE follow Bougeault and Lacarrere (1989), and their study showed that these length scales work well in low-wind, convective boundary layers. Given that the EDMF-TKE scheme is not specifically designed for high-wind conditions like hurricanes, this study is motivated to evaluate this new scheme in hurricane conditions, using an evaluation framework tailored to the hurricane boundary layer proposed by Chen et al. (2021a). It is worth noting that the parameterized mass fluxes in EDMF-TKE are scale-aware to horizontal grid spacings (Δ), i.e., mass fluxes decrease with decreasing horizontal grid spacings if 0.1 < Δ/h < 1 (i.e., the model gray zone, Arakawa et al. 2011), where h is boundary layer depth. In this study, we focus on mesoscale grid spacings comparable to those used in HAFS, which are beyond gray-zone resolutions (Δ > h). For the effect of scale-awareness on TC simulations, we refer interested readers to Chen et al. (2021b).
2. Methods and model setup
a. An evaluation framework for PBL schemes in high-wind conditions
In this study, we evaluate the EDMF-TKE scheme that is targeted for version 17 of the Global Forecast System (GFS)1 by using a numerical modeling framework tailored to the hurricane boundary layer (Chen et al. 2021a). In short, this framework allows for either a small-domain [O(5) km] large-eddy simulation (LES) or a single-column modeling (SCM) simulation using the EDMF-TKE PBL scheme under the same controlled thermodynamic conditions. For LES, there are 528 × 528 grid points horizontally, and the horizontal grid spacing is 10 m. We use 500 vertical levels, with the model top of 3 km. The vertical grid spacing is 5 m below 2 km and increases to 15 m between 2 and 3 km. For SCM simulations, a very similar model setup is used except that there is only one single column and the vertical grid spacing is 20 m below 2 km. As in Chen et al. (2021a), domain-averaged turbulence properties from the LES are treated as the benchmark to evaluate the SCM simulations with the EDMF-TKE scheme. The controlled vertical profiles of thermodynamic variables come from dropsonde composites of category-4–5 hurricanes from 1999 to 2010. Using vertical profiles of thermodynamic variables outside the eyewall where the 10-m tangential wind is roughly 25 m s−1 (V25, hereafter), 35 m s−1 (V35, hereafter), and 45 m s−1 (V45, hereafter), respectively, three sets of experiments are performed. We use version 20 of Cloud Model 1 (CM1; Bryan and Fritsch 2002) for both LES and SCM simulations. The LES domain or SCM grid point is located due east to the TC center, and hereafter u and υ denote radial and tangential winds, respectively. For more details of this framework and the related model setup, we refer interested readers to Chen et al. (2021a).
b. Model setup for idealized 3D simulations
To test the robustness of results based on the comparisons of two experiments, we performed other pairs of sensitivity experiments using the original and modified EDMF-TKE by varying Vm, decay rate of the tangential wind outside the RMW, and sea surface temperature. The findings in these sensitivity experiments are consistent with the findings from the above two simulations (not shown), and we focus only on the analyses of these two simulations in section 4b.
c. Model setup for HAFS forecasts of Hurricane Michael (2018)
To examine the effect of the modified EDMF-TKE on real hurricanes, we also perform two sets of 5-member ensemble HAFS forecasts of Hurricane Michael (2018) using the original and modified EDMF-TKE schemes. Hurricane Michael rapidly intensified while over the eastern Gulf of Mexico into a category-5 hurricane at landfall. It defied some forecasts which projected steady state or even some weakening under moderate vertical wind shear (Beven et al. 2019). Hazelton et al. (2020) studied the rapid intensification of Michael using an ensemble of a high-resolution nested-FV3 model (similar to HAFS) simulations, initialized at 1800 UTC 7 October 2018, when Michael was over the northwestern Caribbean Sea and approximately 3 days before it made landfall. In this study, the 5 ensemble members in each set were initialized at −12, −6, 0, +6, and +12 h relative to 1800 UTC 7 October 2018, respectively. The 2021 baseline version of the stand-alone-regional HAFS (HAFS-SAR, Dong et al. 2020) is used. HAFS-SAR features a large static nest over the North Atlantic, Gulf of Mexico, Caribbean Sea, and eastern United States, with a horizontal grid spacing of ∼3 km. The version of HAFS-SAR analyzed here uses 91 vertical levels. The references above describe some of the key model physics. This version of HAFS-SAR is coupled to the Hybrid Coordinate Ocean Model (HYCOM; Bleck 2002).
Hereafter, we refer to the SCM and idealized 3D simulations as well as HAFS forecasts using the original EDMF-TKE as the CTL experiments, and those simulations or forecasts using the revised EDMF-TKE scheme as the REV experiments. The revisions to the original EDMF-TKE scheme are detailed in the next section. Of note, all of the experiments in this study use the same GFDL surface-layer scheme and the formulation of surface drag coefficient as a function of 10-m wind is shown in Fig. 1.
The surface drag coefficient under neutral conditions as a function of 10-m surface wind in the GFDL surface-layer scheme. Adapted from Fig. 4a in Chen et al. (2021a).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
The surface drag coefficient under neutral conditions as a function of 10-m surface wind in the GFDL surface-layer scheme. Adapted from Fig. 4a in Chen et al. (2021a).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
The surface drag coefficient under neutral conditions as a function of 10-m surface wind in the GFDL surface-layer scheme. Adapted from Fig. 4a in Chen et al. (2021a).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
3. Improvement of EDMF-TKE
EDMF-TKE is a TKE-based (i.e., 1.5-order) turbulence scheme, and it is important to understand whether EDMF-TKE can produce an accurate vertical profile of TKE in hurricane conditions. Figure 2a shows TKE profiles from a SCM test using the original EDMF-TKE PBL scheme (i.e., CTL) and a LES benchmark run for V35. TKE from LES is defined as
(a) Vertical profile of TKE (m2 s−2) from LES (black) and CTL (blue) for V35. (b) Vertical profile of cm from the CTL (blue) experiment for V35. The levels of 0.1h and h are marked by gray dashed lines in (b).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a) Vertical profile of TKE (m2 s−2) from LES (black) and CTL (blue) for V35. (b) Vertical profile of cm from the CTL (blue) experiment for V35. The levels of 0.1h and h are marked by gray dashed lines in (b).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a) Vertical profile of TKE (m2 s−2) from LES (black) and CTL (blue) for V35. (b) Vertical profile of cm from the CTL (blue) experiment for V35. The levels of 0.1h and h are marked by gray dashed lines in (b).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
a. Matching PBL and surface-layer formulations
To improve the vertical profile of TKE, a closer examination of the TKE budget equation near the surface is performed in this section. Furthermore, we note that the proper matching of a PBL code with a surface-layer code is essential for providing expected results near the surface (Kepert 2012), where the surface layer is defined approximately as the lowest 10% of the boundary layer. Given that hurricane boundary layers, especially the lower portion, are essentially neutrally stratified in high wind speeds despite the existence of substantial surface heat fluxes (e.g., Kepert 2012; Foster 2013; Chen et al. 2021a), we assume neutral boundary layer conditions in the following derivations.
This is the well-documented “mixing length” hypothesis of Prandtl (1925), as also noted by Kepert (2012). We note that the length scale in the EDMF-TKE scheme, (A6), is equivalent to (10) for neutral conditions near the surface.
Han and Bretherton (2019) used Cd = 0.7 and Cm = 0.4, which is not consistent with (13), suggesting a mismatch between PBL and surface-layer parameterizations. In the original EDMF-TKE code we use for this study, Cd = 0.4, and Cm is 0.4 in the surface layer and then decreases linearly with height to the diagnosed boundary layer height (Fig. 2b); these values in the surface layer are also inconsistent with (13).
Following the studies cited above, we assume
b. Other changes to EDMF-TKE
The mass-flux part of EDMF parameterizes the nonlocal turbulent transport by thermal plumes in low-wind and unstable boundary layer conditions (Siebesma et al. 2007). In EDMF-TKE, the triggering criteria for the surface-driven mass flux [i.e., the second term on the right-hand side of (A1)] is ζ = zs/L < −0.02, where L is Monin–Obukhov length. In hurricane boundary layers, strong vertical wind shear within the boundary layer can distort and tear apart the rising thermal plumes, causing a nonnegligible reduction in mass fluxes. Given this, we curtail mass fluxes based on 10-m wind speed magnitudes—mass fluxes are linearly tapered when V10 ≥ 20 m s−1 and turned off when V10 ≥ 30 m s−1, following the MYNN code from version 4.2 of WRF. Note that this change is applicable to other high-wind boundary layers too.
Vertical profiles of mixing length from LES output averaged over t = 4–6 h. Black, blue, and red lines denote the results for V25, V35, and V45, respectively. Black dots denote in situ aircraft observations from Zhang and Drennan (2012). The LES results are from Chen et al. (2021a).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Vertical profiles of mixing length from LES output averaged over t = 4–6 h. Black, blue, and red lines denote the results for V25, V35, and V45, respectively. Black dots denote in situ aircraft observations from Zhang and Drennan (2012). The LES results are from Chen et al. (2021a).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Vertical profiles of mixing length from LES output averaged over t = 4–6 h. Black, blue, and red lines denote the results for V25, V35, and V45, respectively. Black dots denote in situ aircraft observations from Zhang and Drennan (2012). The LES results are from Chen et al. (2021a).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
4. Evaluation of the modified EDMF-TKE scheme
a. Single-column model tests
In this section, we conduct three sets of SCM tests (i.e., V25, V35, and V45, indicating the approximate values of 10-m wind speed) using the original (CTL) and modified EDMF-TKE (REV) schemes and compare the SCM results against LES benchmark runs. Consistent with Fig. 2a for V35, the CTL experiments using the original EDMF-TKE show a much larger TKE below 500 m than LES in other high-wind conditions (Figs. 4a–c). In contrast, the REV experiments using the modified EDMF-TKE exhibit a much-improved TKE profile, and differences in the magnitude of TKE between REV and LES are <1 m2 s−2 above z = 50 m and ∼3–4 m2 s−2 below z = 50 m. The slightly larger error in the near-surface layer (below 50 m) is partly attributable to relatively coarse vertical grid spacings used in SCM tests than in LES, which may cause an underestimation of vertical wind shear near the surface and thereby the shear production of TKE. Figures 4d–f compare the vertical profile of mixing length lk from the CTL and REV experiments. The maximum value of lk above the surface layer in the REV experiments is capped at 40 m, as discussed in section 4, which is more than a factor of 2 smaller than the maximum lk in CTL. For a reference, Fig. 4d also shows available observations (see black dots) at a similar high-wind condition (Zhang and Drennan 2012). For V25, lk from REV agrees well with these observation data below 800 m height, while lk from CTL exceeds the maximum value of observations by approximately a factor of 2 in the 200–800-m layer.
(a)–(c) Vertical profile of TKE (m2 s−2) from LES (black), CTL (blue), and REV (red) for V25, V35, and V45, respectively. (d)–(f) As in (a)–(c), but for mixing length (m). Black dots in (d) represent observations from Zhang and Drennan (2012).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a)–(c) Vertical profile of TKE (m2 s−2) from LES (black), CTL (blue), and REV (red) for V25, V35, and V45, respectively. (d)–(f) As in (a)–(c), but for mixing length (m). Black dots in (d) represent observations from Zhang and Drennan (2012).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a)–(c) Vertical profile of TKE (m2 s−2) from LES (black), CTL (blue), and REV (red) for V25, V35, and V45, respectively. (d)–(f) As in (a)–(c), but for mixing length (m). Black dots in (d) represent observations from Zhang and Drennan (2012).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
With smaller TKE and lk profiles in REV, it is not surprising to see that REV produces smaller Km than CTL in different high-wind conditions, and the level of maximum Km in REV is closer to the surface than in CTL (Figs. 5a–c). Both of these characteristics in REV agree better with the LES results. With improved Km profiles, the REV experiments reproduce the LES inflow layer depth (∼1 km) and inflow strength (Figs. 5d–f). In comparison, the inflow layer in CTL is deeper than in LES in different high-wind conditions. Figures 5g–i further show that the tangential wind profiles in REV also agree well with the LES results. In short, the SCM tests demonstrate that the modified EDMF-TKE is capable of capturing similar profiles of turbulence properties and winds compared to LES in hurricane conditions, with a notably improved performance compared to the original EDMF-TKE.
As in Fig. 4, but for (a)–(c) Km (m2 s−1), (d)–(f) radial wind u (m s−1), and (g)–(i) tangential wind υ (m s−1).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
As in Fig. 4, but for (a)–(c) Km (m2 s−1), (d)–(f) radial wind u (m s−1), and (g)–(i) tangential wind υ (m s−1).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
As in Fig. 4, but for (a)–(c) Km (m2 s−1), (d)–(f) radial wind u (m s−1), and (g)–(i) tangential wind υ (m s−1).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
As discussed in section 3, the modified EDMF-TKE incorporates four changes: 1) determining values of Cd and Cm that are needed to match the surface-layer and PBL parameterizations, 2) reducing the maximum allowable mixing length from 300 to 40 m, 3) implementing a new definition of the PBL height based on the bulk Richardson number that has been found to perform better in high-wind conditions, and 4) tapering and then turning off mass fluxes from the nonlocal portion of the PBL scheme in high-wind conditions. As the four changes are in tandem with each other and the results in REV show their combined effect, we further examine which changes have the largest impact on the improvements. We perform four additional SCM tests based on REV by removing one of the four changes in each test. Figure 6 compares the results of these SCM tests against the LES for V35. The SCM tests without the changes to mass fluxes (dashed red line in Figs. 6a–d) match well with the LES results. This finding is attributable to the fact that the mass-flux parameterization is not activated with ζ ≈ −1 × 10−3 for V35 and also for V45 and V25 experiments, and stratocumulus-top driven mass fluxes [third term on the right-hand side of Eq. (A1)] are turned off for these SCM tests. Thus, the dashed red lines in Figs. 6a–d are essentially the same as the REV experiment. Due to the special model setup in SCM tests, one cannot draw the conclusion that mass fluxes in EDMF-TKE are unimportant in hurricane conditions, as three-dimensional CM1 tests indicate that the surface-driven mass fluxes and downgradient momentum fluxes can be of comparable magnitude at hurricane-force wind speeds (not shown).
(a)–(c) Vertical profile of (a) TKE (m2 s−2), (b) Km (m2 s−1), (c) radial wind u (m s−1), and (d) tangential wind υ from LES (black line), CTL (dashed blue), and REV-based sensitivity tests for V35. The red, orange, green, and gray lines denote the REV experiment except changes to nonlocal mass fluxes are removed, changes to the Cd and Cm are removed, changes to the maximum allowable lk are removed, and changes to the PBL height definition are removed, respectively. (e) Vertical profile of cm from the REV experiment (red) and the REV-based sensitivity test excluding the changes to PBL height definition (gray) for V35.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a)–(c) Vertical profile of (a) TKE (m2 s−2), (b) Km (m2 s−1), (c) radial wind u (m s−1), and (d) tangential wind υ from LES (black line), CTL (dashed blue), and REV-based sensitivity tests for V35. The red, orange, green, and gray lines denote the REV experiment except changes to nonlocal mass fluxes are removed, changes to the Cd and Cm are removed, changes to the maximum allowable lk are removed, and changes to the PBL height definition are removed, respectively. (e) Vertical profile of cm from the REV experiment (red) and the REV-based sensitivity test excluding the changes to PBL height definition (gray) for V35.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a)–(c) Vertical profile of (a) TKE (m2 s−2), (b) Km (m2 s−1), (c) radial wind u (m s−1), and (d) tangential wind υ from LES (black line), CTL (dashed blue), and REV-based sensitivity tests for V35. The red, orange, green, and gray lines denote the REV experiment except changes to nonlocal mass fluxes are removed, changes to the Cd and Cm are removed, changes to the maximum allowable lk are removed, and changes to the PBL height definition are removed, respectively. (e) Vertical profile of cm from the REV experiment (red) and the REV-based sensitivity test excluding the changes to PBL height definition (gray) for V35.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
In contrast, the most important of the four changes are changes 1 and 2, as removing either change 1 (orange line in Figs. 6a–d) or change 2 (green line in Figs. 6a–d) leads to notably different profiles of TKE, Km, and winds compared to LES. Note that change 1 has a bigger impact on the TKE profile (Fig. 6a), whereas change 2 has a bigger impact on the Km profile (Fig. 6b).
Figure 6e compares the profile of Cm between the REV (red line) and the REV-based sensitivity test excluding the changes to the PBL height (gray line). Including the changes to PBL height notably decreases the diagnosed boundary layer height (i.e., the level of minimum Cm) as well as the value of Cm within the diagnosed boundary layer height. As a consequence, comparison of the red and gray lines in Figs. 6b and 6c indicates that vertical mixing in terms of Km and the inflow layer depth are slightly reduced using the new definition of the PBL height, although these differences are comparably much smaller than those produced by changes 1 and 2.
b. Idealized three-dimensional simulations
This section continues to assess the impact of the modified EDMF-TKE PBL scheme on the evolution of TCs by examining three-dimensional CM1 idealized numerical simulations. Figure 7 compares the evolution of TC intensity and size in the CTL and REV experiments. Compared to the CTL experiment, the simulated TC in REV starts to rapidly intensify at a slightly earlier time, the duration of rapid intensification (RI) in REV lasts slightly longer, and the REV TC attains a stronger intensity in terms of the 10-m maximum azimuthal-mean tangential wind after the RI period (Fig. 7a). The REV TC remains stronger than the CTL TC in the subsequent 6-day simulations. Additionally, the radius of the maximum wind (RMW) of the REV TC is ∼20% smaller than that of the CTL TC during the simulation period (Fig. 7b). Nevertheless, the radius of gale-force wind (R17) in the two experiments is very similar, especially in the first 6 days, suggesting modifications to EDMF-TKE do not have a large impact on the outer-core size of the simulated TCs.
Evolution of (a) 10-m maximum azimuthal-mean tangential wind Vm (m s−1), (b) RMW (km), and (c) R17 (km) from CTL (blue) and REV (red) experiments. The light gray shaded box in (a)–(c) denotes an analysis period. R17 in (c) is shown after the simulated TC reaches hurricane intensity.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Evolution of (a) 10-m maximum azimuthal-mean tangential wind Vm (m s−1), (b) RMW (km), and (c) R17 (km) from CTL (blue) and REV (red) experiments. The light gray shaded box in (a)–(c) denotes an analysis period. R17 in (c) is shown after the simulated TC reaches hurricane intensity.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Evolution of (a) 10-m maximum azimuthal-mean tangential wind Vm (m s−1), (b) RMW (km), and (c) R17 (km) from CTL (blue) and REV (red) experiments. The light gray shaded box in (a)–(c) denotes an analysis period. R17 in (c) is shown after the simulated TC reaches hurricane intensity.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Figure 8 shows the Hovmöller diagram for the azimuthally averaged 1-km radar reflectivity and 10-m tangential wind. While the maximum radar reflectivity within the eyewall (r = 30–50 km) of the two TCs is comparable, large radar reflectivity of >45 dBZ in the eyewall appears at an earlier time and maintains for a longer time over the simulation period in REV than in CTL. This finding is in agreement with the stronger intensity of the REV TC.
Hovmöller diagram of azimuthally averaged 1-km radar reflectivity (shading; dBZ) and 10-m tangential wind (black contour with values of 5, 10, 20, 30, 40, 50, and 60 m s−1) for (a) CTL and (b) REV experiments. The white line denotes the radius of the maximum wind (km).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Hovmöller diagram of azimuthally averaged 1-km radar reflectivity (shading; dBZ) and 10-m tangential wind (black contour with values of 5, 10, 20, 30, 40, 50, and 60 m s−1) for (a) CTL and (b) REV experiments. The white line denotes the radius of the maximum wind (km).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Hovmöller diagram of azimuthally averaged 1-km radar reflectivity (shading; dBZ) and 10-m tangential wind (black contour with values of 5, 10, 20, 30, 40, 50, and 60 m s−1) for (a) CTL and (b) REV experiments. The white line denotes the radius of the maximum wind (km).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
To understand the differences in the TC intensity and structure between the two experiments, we examine radius–height plots of turbulence properties including TKE and Km averaged over t = 100–120 h (Fig. 9). Over this period, TC intensity and RMW in the two experiments are comparable. One notable difference in the distribution of TKE between the two experiments is that the TKE column (>1 m2 s−2) in the eyewall region of the REV TC extends to higher levels than that of the CTL TC (Figs. 9a,b). The eyewall region is indicated by updrafts with w > 1 m s−1 (see the red contour in Figs. 9a,b). Given advection of TKE is not included in these simulations, differences in the depth of TKE column are attributable to the modifications to EDMF-TKE. Additionally, the REV TC has much smaller TKE values below 500 m height than the CTL TC (Fig. 9c), which is consistent with the findings from SCM tests (e.g., Figs. 4a–c); the difference in TKE attains its maximum near the surface of the eyewall region (>6 m2 s−2, Fig. 9c), where surface winds are the strongest. Differences in the Km distribution between the two experiments resemble the differences in the TKE distribution, with the Km column (>10 m2 s−2) in the eyewall of the REV TC extending to a slightly higher level (Figs. 9d–f). The REV TC has smaller Km within the diagnosed h (the orange line in Figs. 9d–e) and above the near-surface layer than the CTL TC. In contrast, the REV TC has slightly larger Km in the near-surface layer than the CTL TC (Fig. 9f). These findings are quite similar to the results from SCM tests (Figs. 5a–c), where Km in the near-surface layer in REV agrees better with the LES results.
(a),(b) Radial–height plot of azimuthally averaged TKE (shading; m2 s−2) averaged over t = 100–120 h for CTL and REV experiments, respectively. The difference in the distribution of TKE (i.e., CTL − REV) is shown in (c). (d)–(f) As in (a)–(c), but for Km (shading; m2 s−1). In each panel, the red contour denotes w = 1 m s−1, and the black line denotes the mean RMW. In (c) and (f), the w contours are from CTL, and the black and dashed gray lines denote RMW from CTL and REV, respectively. The orange line in (a) and (b) and (d) and (e) denotes the mean h. In (a) and (b), the dashed gray line denotes hRic.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a),(b) Radial–height plot of azimuthally averaged TKE (shading; m2 s−2) averaged over t = 100–120 h for CTL and REV experiments, respectively. The difference in the distribution of TKE (i.e., CTL − REV) is shown in (c). (d)–(f) As in (a)–(c), but for Km (shading; m2 s−1). In each panel, the red contour denotes w = 1 m s−1, and the black line denotes the mean RMW. In (c) and (f), the w contours are from CTL, and the black and dashed gray lines denote RMW from CTL and REV, respectively. The orange line in (a) and (b) and (d) and (e) denotes the mean h. In (a) and (b), the dashed gray line denotes hRic.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a),(b) Radial–height plot of azimuthally averaged TKE (shading; m2 s−2) averaged over t = 100–120 h for CTL and REV experiments, respectively. The difference in the distribution of TKE (i.e., CTL − REV) is shown in (c). (d)–(f) As in (a)–(c), but for Km (shading; m2 s−1). In each panel, the red contour denotes w = 1 m s−1, and the black line denotes the mean RMW. In (c) and (f), the w contours are from CTL, and the black and dashed gray lines denote RMW from CTL and REV, respectively. The orange line in (a) and (b) and (d) and (e) denotes the mean h. In (a) and (b), the dashed gray line denotes hRic.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Figures 9a and 9b also compare the diagnosed h (the solid orange line; see definition in the appendix) and hRic (the dashed gray line) between the two experiments. With the inclusion of a modified PBL height definition, the diagnosed hRic in REV is ∼600 m shallower than that in CTL. Using hRic as a first guess, h is further determined by taking the smaller value between hRic and the diagnosed boundary layer height of updraft velocity wu = 0. The reduced h compared to hRic indicates that the diagnosed boundary layer height of wu = 0 is shallower than hRic. Nevertheless, h in REV remains shallower than that in CTL, which is expected based on the SCM tests, and the largest difference of ∼1 km appears within 1–2 × RMW.
The eddy viscosity Km in the boundary layer is known to affect boundary layer inflow structure, with smaller Km typically resulting in stronger inflow strength and a shallower inflow depth (e.g., Foster 2009; Gopalakrishnan et al. 2013; Zhang et al. 2015). This finding is supported by a comparison of inflow structure averaged over t = 100–120 h in Figs. 10a and 10b. The inflow layer depth (inflow depth indicated by u = −1 m s−1) of the REV TC is ∼500 m shallower than that of the CTL TC within 1–3 × RMW. The REV TC has stronger boundary layer inflow than the CTL TC beneath the eyewall, while it is difficult to see the differences clearly radially outward due to the differences in the RMW of the CTL and REV TCs over this period (Figs. 10a,b). Given this limitation, we adopt another insightful measure of inflow strength, i.e., surface inflow angle, defined as tan−1(u10/υ10), where u10 and υ10 are the radial and tangential velocities at 10-m height, respectively.
(a),(b) Radial–height plot of azimuthally averaged radial velocity u (shading; m s−1) averaged over t = 100–120 h for CTL and REV experiments, respectively. The red contour denotes w = 1 m s−1, and the black line denotes the mean RMW. The orange line denotes the mean h, and the dashed blue line denotes u = −1 m s−1 (c),(d) Composite 10-m radial profile of inflow angle (°) as a function of normalized radius R* (=R/RMW) for CTL (blue) and REV (red) over t = 100–120 h in (c) and t = 25–45 h in (d). The 10-m radial profile of inflow angle from a dropsonde composite of category-1–5 hurricanes (Zhang and Uhlhorn 2012) is shown for a reference (gray); the gray bar denotes 95% confidence intervals. The maximum intensity of simulated TCs averaged over each period is shown on the top of (c) and (d).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a),(b) Radial–height plot of azimuthally averaged radial velocity u (shading; m s−1) averaged over t = 100–120 h for CTL and REV experiments, respectively. The red contour denotes w = 1 m s−1, and the black line denotes the mean RMW. The orange line denotes the mean h, and the dashed blue line denotes u = −1 m s−1 (c),(d) Composite 10-m radial profile of inflow angle (°) as a function of normalized radius R* (=R/RMW) for CTL (blue) and REV (red) over t = 100–120 h in (c) and t = 25–45 h in (d). The 10-m radial profile of inflow angle from a dropsonde composite of category-1–5 hurricanes (Zhang and Uhlhorn 2012) is shown for a reference (gray); the gray bar denotes 95% confidence intervals. The maximum intensity of simulated TCs averaged over each period is shown on the top of (c) and (d).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
(a),(b) Radial–height plot of azimuthally averaged radial velocity u (shading; m s−1) averaged over t = 100–120 h for CTL and REV experiments, respectively. The red contour denotes w = 1 m s−1, and the black line denotes the mean RMW. The orange line denotes the mean h, and the dashed blue line denotes u = −1 m s−1 (c),(d) Composite 10-m radial profile of inflow angle (°) as a function of normalized radius R* (=R/RMW) for CTL (blue) and REV (red) over t = 100–120 h in (c) and t = 25–45 h in (d). The 10-m radial profile of inflow angle from a dropsonde composite of category-1–5 hurricanes (Zhang and Uhlhorn 2012) is shown for a reference (gray); the gray bar denotes 95% confidence intervals. The maximum intensity of simulated TCs averaged over each period is shown on the top of (c) and (d).
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Figure 10c shows the composite radial profile of inflow angle averaged over t = 100–120 h. The REV TC has larger inflow angles than the CTL TC outside the RMW, with the largest differences of ∼4°, suggesting inflow outside the RMW is stronger in REV. For reference, Figs. 10c and 10d also show a radial profile of observed inflow angle based on a composite of 1600 global positioning system (GPS) dropsondes collected in 18 different hurricanes (Zhang and Uhlhorn 2012). The median storm intensity for the dropsonde data is 56.7 m s−1, which fits in the category-3 hurricane intensity and is similar to the intensity of the simulated TCs over t = 100–120 h (Fig. 10c). Possibly due to the similar TC intensity, the inflow angle in both CTL and REV is encouragingly comparable to observations over t = 100–120 h. To examine the robustness of this finding as well as the variability of inflow angle to TC intensity, radial profiles of inflow angle over t = 25–45 h are also shown in Fig. 10d. Over this period, the mean TC intensity in terms of the 10-m maximum tangential wind is ∼40 m s−1 (category-1 hurricane) in both experiments. Compared to the results over t = 100–120 h, the magnitude of inflow angle increases by ∼2°–3° within 1–3 × RMW in REV while it generally decreases by 2°–3° outside the RMW in CTL over t = 25–45 h. Therefore, the inflow angle in REV becomes even larger than in CTL over t = 25–45 h, with the largest differences of ∼10° within 1–2 × RMW. Additionally, compared to the results over t = 100–120 h, the peak inflow angle in CTL is shifted radially outward to 2 × RMW over t = 25–45 h (Fig. 10b); the notable weakening of radial inflow within 1–2 × RMW may account for a tendency of RMW expansion in CTL over the same period (Fig. 6b). These findings suggest that radial profiles of inflow angle depend on TC intensity and structure. Examining the variability of inflow angle to TC intensity and structural changes using observations or modeling output will be an interesting topic to pursue for future work.
In short, the stronger boundary layer inflow in REV contributes to stronger convergence beneath the eyewall, which contributes to a more sustained eyewall convective activity in REV (Fig. 8b). The relationship of the enhanced convergence within the eyewall and stronger diabatic heating was also suggested in an observational study of Hurricane Allen (1980) (see Fig. 15 in Marks 1985). These physical processes account for the stronger TC with a smaller RMW in REV than in CTL.
c. HAFS forecasts of Hurricane Michael (2018)
To test the robustness of the findings from idealized simulations, we examine two sets of 5-member ensemble HAFS forecasts of Hurricane Michael (2018) using the original and modified EDMF-TKE schemes, respectively. Figure 11 compares the evolution of TC track, intensity, and RMW from the CTL (blue lines) and REV (red lines) experiments against best track data from NOAA’s National Hurricane Center (dashed gray line). Figures 11a and 11b suggest that compared to best track data the simulated TCs in the two sets of ensemble experiments move faster and thereby make landfall at an earlier time (t ≈ 60 h) than in the best track (t ≈ 72 h). However, Fig. 11b shows that the REV TCs remain stronger than the CTL TCs prior to landfall, as the CTL TCs generally remain in steady state or intensify very slowly until t = 48 h. The averaged maximum intensity of the REV TCs is ∼63 m s−1, approximately 13 m s−1 stronger than that of the CTL TCs, but is very close to the maximum intensity indicated by the best track (∼70 m s−1). Prior to landfall, the contraction of RMW is more notable in REV than in CTL (Fig. 11c), especially early in these forecasts; the smaller RMW in REV agrees better with the best track data. The R17 is very similar between the two sets of ensemble experiments and is not shown.
Two sets of 5-member ensemble HAFS forecasts of Hurricane Michael (2018) initialized at −12, −6, 0, +6, and +12 h relative to 1800 UTC 7 Oct, respectively, showing evolution of (a) TC track, (b) 10-m maximum wind (m s−1), and (c) RMW (km). The dashed gray line denotes best track; blue and red lines denote CTL and REV experiments, respectively. The thick red and blue lines in (b) and (c) denote the experiments initialized at 1800 UTC 7 Oct, and the gray arrow in (b) denotes the bifurcation point of the two experiments.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Two sets of 5-member ensemble HAFS forecasts of Hurricane Michael (2018) initialized at −12, −6, 0, +6, and +12 h relative to 1800 UTC 7 Oct, respectively, showing evolution of (a) TC track, (b) 10-m maximum wind (m s−1), and (c) RMW (km). The dashed gray line denotes best track; blue and red lines denote CTL and REV experiments, respectively. The thick red and blue lines in (b) and (c) denote the experiments initialized at 1800 UTC 7 Oct, and the gray arrow in (b) denotes the bifurcation point of the two experiments.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Two sets of 5-member ensemble HAFS forecasts of Hurricane Michael (2018) initialized at −12, −6, 0, +6, and +12 h relative to 1800 UTC 7 Oct, respectively, showing evolution of (a) TC track, (b) 10-m maximum wind (m s−1), and (c) RMW (km). The dashed gray line denotes best track; blue and red lines denote CTL and REV experiments, respectively. The thick red and blue lines in (b) and (c) denote the experiments initialized at 1800 UTC 7 Oct, and the gray arrow in (b) denotes the bifurcation point of the two experiments.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Figure 12 shows the CTL and REV experiments initialized at 1800 UTC 7 October 2018 and compares their composite radial wind structure over t = 18–24 h, which centers on the bifurcation point for the evolution of TC intensity, after which the REV TC intensifies faster than the CTL TC (see Fig. 11b). Clearly, the REV TC has stronger boundary layer inflow than the CTL TC, especially within 1–3 × RMW (see Fig. 12c), which is particularly consistent with the findings of the idealized simulations over t = 25–45 h (Fig. 10d), when the simulated TCs have comparable intensity. The stronger boundary layer inflow and smaller RMW contribute to the earlier RI onset timing in REV, which is consistent with the findings in Chen et al. (2018). Comparison of the diagnosed hRic (gray lines in Figs. 12a,b) shows that hRic is reduced by 300–500 m in REV than in CTL, reminiscent of results of the idealized simulations (e.g., Figs. 9a,b), which would contribute to a reduction of the vertical turbulent mixing in REV as discussed in section 3b. Comparison of inflow layer depth, indicated by dashed blue and gray lines in Fig. 12c, shows that the inflow layer depth in REV is similar between the two experiments except near the RMW, where the inflow layer depth in REV is 200–300 m shallower than in CTL. The relatively large discrepancy in the inflow layer depth near the RMW is also seen in Figs. 10a and 10b.
Radial–height plot of azimuthally averaged radial wind (shading; m s−1) averaged over t = 18–24 h for the (a) CTL and (b) REV experiments of Hurricane Michael (2018) initialized at 1800 UTC 7 Oct. (c) The difference in radial winds (i.e., CTL − REV). In (a) and (b), the dashed blue line denotes u = −1 m s−1, and the gray line denotes hRic. The red contour in (a) and (b) denotes w = 0.3 m s−1, and the black line denotes the mean RMW. In (c), the RMW and w contours are from CTL, and the dashed blue and gray lines denote the inflow layer depth from CTL and REV, respectively.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Radial–height plot of azimuthally averaged radial wind (shading; m s−1) averaged over t = 18–24 h for the (a) CTL and (b) REV experiments of Hurricane Michael (2018) initialized at 1800 UTC 7 Oct. (c) The difference in radial winds (i.e., CTL − REV). In (a) and (b), the dashed blue line denotes u = −1 m s−1, and the gray line denotes hRic. The red contour in (a) and (b) denotes w = 0.3 m s−1, and the black line denotes the mean RMW. In (c), the RMW and w contours are from CTL, and the dashed blue and gray lines denote the inflow layer depth from CTL and REV, respectively.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
Radial–height plot of azimuthally averaged radial wind (shading; m s−1) averaged over t = 18–24 h for the (a) CTL and (b) REV experiments of Hurricane Michael (2018) initialized at 1800 UTC 7 Oct. (c) The difference in radial winds (i.e., CTL − REV). In (a) and (b), the dashed blue line denotes u = −1 m s−1, and the gray line denotes hRic. The red contour in (a) and (b) denotes w = 0.3 m s−1, and the black line denotes the mean RMW. In (c), the RMW and w contours are from CTL, and the dashed blue and gray lines denote the inflow layer depth from CTL and REV, respectively.
Citation: Weather and Forecasting 37, 6; 10.1175/WAF-D-21-0168.1
In summary, differences in TC intensity, size, boundary layer height, and inflow structure from two sets of ensemble HAFS forecasts are generally consistent with those from idealized 3D simulations, confirming that the modified EDMF-TKE tends to produce stronger boundary layer inflow, stronger TC intensity, and a smaller RMW than the original EDMF-TKE.
5. Conclusions
A TKE-based eddy-diffusivity mass-flux (EDMF) PBL scheme (EDMF-TKE) is used in NOAA’s Global Forecast System (GFS) model as well as the next-generation hurricane forecast model, the Hurricane Analysis and Forecast System (HAFS). Given this PBL scheme is not specifically designed for the hurricane boundary layer, this study evaluates and improves a new version of this PBL scheme (targeted for version 17 of GFS model) in hurricane conditions using a recently developed evaluation framework proposed by Chen et al. (2021a).
Evaluation results show that the original EDMF-TKE substantially overestimates TKE below 500-m height in hurricane conditions compared to LES; additionally, EDMF-TKE overpredicts the diagnosed boundary layer height and inflow layer depth. To improve the results, four changes are made: 1) the coefficients used to determine eddy viscosity and TKE dissipation are modified to ensure a match between the PBL and surface-layer parameterizations; 2) the maximum allowable value of mixing length is reduced from 300 to 40 m based on LES results and observational estimates; 3) a different PBL height definition is adopted that works well in the hurricane boundary layer; and 4) nonlocal turbulent mass fluxes in high-wind conditions are reduced, given the impact of strong vertical wind shear on damping rising thermal plumes. SCM tests using the modified EDMF-TKE demonstrate that vertical profiles of TKE, eddy viscosity, and winds are substantially improved and match well with the LES results. Among the four changes, the first two changes were found to have the largest impact on the improvements.
Comparisons of three-dimensional idealized simulations using the original (i.e., the CTL experiment) and modified EDMF-TKE (i.e., the REV experiment) show that the modified EDMF-TKE tends to produces a stronger vortex with a smaller radius of maximum wind (RMW). However, these experiments produce a similar radius of gale-force wind (R17), suggesting the TC outer-core size is unaffected. The smaller eddy viscosity in the boundary layer in REV results in stronger boundary layer inflow outside the RMW. The enhanced convergence beneath the eyewall is thereby enhanced in REV, supporting a more sustained convective activity in the eyewall. Two sets of ensemble HAFS forecasts of Hurricane Michael (2018) using the two PBL schemes nicely agree with the results of idealized simulations.
As a concluding note, the modified EDMF-TKE substantially improves the turbulence properties and wind profiles in the hurricane boundary layer, and also shows encouraging promise to improve the forecasts of rapid intensification of hurricanes under sheared environments. Future work will further assess the impact of the modified EDMF-TKE on the model forecast skills of hurricane intensity/structure change by testing more cases over a wide range of intensities during the 2021 Atlantic hurricane season.
This code was provided by Drs. Jongil Han and Chunxi Zhang at NOAA/EMC.
In this study, Cd does not denote a surface drag coefficient; instead, it is a coefficient used in the TKE dissipation term following Han and Bretherton (2019).
Equation (A3) slightly differs from (4) in Han and Bretherton (2019) in that
Acknowledgments.
We would like to acknowledge high-performance computing support from Cheyenne (doi:10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. The authors appreciate Dr. Jun Zhang for generously sharing the inflow angle data and Dr. Scott Braun for the conversation regarding the new definition of PBL height. The constructive suggestions and comments from Dr. Kyle Ahern, Dr. Gus Alaka, and three anonymous reviewers improved the clarity of the method and quality of the analysis. Xiaomin Chen is supported by Award NA21OAR4320190 to the Northern Gulf Institute at Mississippi State University from NOAA’s Office of Oceanic and Atmospheric Research, U.S. Department of Commerce. George Bryan is supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977, and by Office of Naval Research Grant N00014-20-1-2071.
Data availability statement.
The LES and single-column modeling experiments using the CM1 model are available on NCAR’s Cheyenne supercomputer. The HAFS simulations of Hurricane Michael (2018) are available on the NOAA RDHPCS computer system, or by request.
APPENDIX
A Brief Overview of the EDMF-TKE PBL Scheme
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