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Article

Effects of Surface Layer Physics Schemes on the Simulated Intensity and Structure of Typhoon Rai (2021)

by
Thi-Huyen Hoang
,
Ching-Yuang Huang
* and
Thi-Chinh Nguyen
Department of Atmospheric Sciences, National Central University, Taoyuan City 320317, Taiwan
*
Author to whom correspondence should be addressed.
Atmosphere 2024, 15(9), 1140; https://doi.org/10.3390/atmos15091140
Submission received: 31 July 2024 / Revised: 26 August 2024 / Accepted: 19 September 2024 / Published: 20 September 2024
(This article belongs to the Section Meteorology)
Browse Figures
Figure 1
<p>The WRF model domains for Rai at the initial time. The outermost box (d01) denotes the outermost domain, while the red and blue boxes (d02 and d03, respectively) denote the two inner moving domains. The dashed black line (JMA) with cycles at intervals of 24 h indicates the best track from JMA from 0000 UTC 14 December to 0000 UTC 18 December 2021.</p> "> Figure 2
<p>(<b>a</b>) Tracks of Typhoon Rai, including the best track data from JTWC (dashed black line) and JMA (solid black line), as well as simulated tracks for CTL (red line), MM5 (blue line), and MYNN (green line), during the period from 0000 UTC 14 December to 0000 UTC 18 December 2021. Circle symbols in (<b>a</b>) indicate the time every 24 h. (<b>b</b>) as in (<b>a</b>), but for the 10-m maximum wind speed (V<sub>max</sub>, m s<sup>−1</sup>).</p> "> Figure 3
<p>12-h accumulated precipitation (mm) during 48–60 h from (<b>a</b>) multi-satellite precipitation product GSMaP, (<b>b</b>) CTL, (<b>c</b>) MM5, and (<b>d</b>) MYNN. (<b>e</b>), (<b>f</b>), (<b>g</b>), and (<b>h</b>) as in (<b>a</b>), (<b>b</b>), (<b>c</b>), and (<b>d</b>), respectively, but during 60–72 h. (<b>i</b>), (<b>j</b>), (<b>k</b>), and (<b>l</b>) as in (<b>a</b>), (<b>b</b>), (<b>c</b>), and (<b>d</b>), respectively, but during 72–84 h.</p> "> Figure 4
<p>Simulated ratio of enthalpy exchange coefficient to drag coefficient (C<sub>K</sub>/C<sub>D</sub>) as a function of 10-m wind speed for CTL (red line), MM5 (blue line), and MYNN (green line) at 54 h.</p> "> Figure 5
<p>Time evolutions of (<b>a</b>) friction velocity (m s<sup>−1</sup>), (<b>b</b>) surface sensible heat flux (W m<sup>−2</sup>), and (<b>c</b>) surface latent heat flux (W m<sup>−2</sup>) for CTL (red line), MM5 (blue line), and MYNN (green line), averaged within the area of 300 × 300 km around the typhoon center from 24 h to 72 h.</p> "> Figure 6
<p>Horizontal distribution of 10-m wind speed (shaded color, m s<sup>−1</sup>) for (<b>a</b>) CTL, (<b>b</b>) MM5, and (<b>c</b>) MYNN at 54 h. (<b>d</b>), (<b>e</b>), and (<b>f</b>) as in (<b>a</b>), (<b>b</b>), and (<b>c</b>), respectively, but for friction velocity (m s<sup>−1</sup>). (<b>g</b>), (<b>h</b>), and (<b>i</b>) as in (<b>a</b>), (<b>b</b>), and (<b>c</b>), respectively, but for surface sensible heat flux (W m<sup>−2</sup>). (<b>j</b>), (<b>k</b>), and (<b>l</b>) as in (<b>a</b>), (<b>b</b>), and (<b>c</b>), respectively, but for surface latent heat flux (W m<sup>−2</sup>). The black vectors in (<b>a</b>–<b>c</b>) denote the 10-m horizontal wind speed.</p> "> Figure 7
<p>Azimuthal-mean tangential velocity (m s<sup>−1</sup>) in the radius–height cross-section at 54 h for (<b>a</b>) CTL and (<b>b</b>) MM5. (<b>c</b>) and (<b>d</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but for the radial velocity (m s<sup>−1</sup>). The black line in (<b>a</b>,<b>b</b>) represents the height of the maximum tangential wind speed (h<sub>vt</sub>). The black line in (<b>c</b>,<b>d</b>) represents the inflow layer depth (h<sub>vr</sub>).</p> "> Figure 8
<p>Time–radius Hovmöller diagrams of azimuthal-mean tangential wind (m s<sup>−1</sup>) at 2-km height for (<b>a</b>) CTL and (<b>b</b>) MM5 from 24 h to 72 h. (<b>c</b>) and (<b>d</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but for radial wind (m s<sup>−1</sup>) at 0.25-km height. The black line in (<b>a</b>,<b>b</b>) represents the radius of maximum tangential wind speed (RMW) at 2 km height. The green line in (<b>c</b>,<b>d</b>) represents the maximum inflow at 0.25-km height.</p> "> Figure 9
<p>Azimuthal-mean potential temperature (K) in the radius–height cross-section for (<b>a</b>) CTL and (<b>b</b>) MM5 at 54 h. The thick black line represents the RMW.</p> "> Figure 10
<p>Time–height Hovmöller diagrams of azimuthal-mean potential temperature (K) inside RMW for (<b>a</b>) CTL and (<b>b</b>) MM5. (<b>c</b>) and (<b>d</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but for warm core (K) averaged inside a radius of 1.5 degrees from the typhoon center.</p> "> Figure 11
<p>Azimuthal-mean flow (shaded color) in the radius–height cross-section of radial velocity (m s<sup>−1</sup>) for (<b>a</b>) CTL and (<b>b</b>) MM5 at 54 h. (<b>c</b>) and (<b>d</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but for tangential velocity (m s<sup>−1</sup>). (<b>e</b>) and (<b>f</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but for vertical velocity (m s<sup>−1</sup>). (<b>g</b>) and (<b>h</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but for latent heating rate (K h<sup>−1</sup>). The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.</p> "> Figure 12
<p>Radius–height cross-sections of azimuthal-mean angular momentum (AAM) (shaded color, 10<sup>6</sup> m<sup>2</sup> s<sup>−1</sup>) for (<b>a</b>) CTL and (<b>b</b>) MM5 at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.</p> "> Figure 13
<p>Radius–height cross-section of azimuthal-mean AM budget terms (shaded color, m<sup>2</sup> s<sup>−2</sup>), including (<b>a</b>) radial advection of mean AM, (<b>b</b>) radial advection of eddy AM, (<b>c</b>) vertical advection of mean AM, (<b>d</b>) vertical advection of eddy AM, (<b>e</b>) mean Coriolis force term, and (<b>f</b>) sum of all AM budget terms for CTL at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.</p> "> Figure 14
<p>As in <a href="#atmosphere-15-01140-f013" class="html-fig">Figure 13</a>, but for MM5 including (<b>a</b>) radial advection of mean AM, (<b>b</b>) radial advection of eddy AM, (<b>c</b>) vertical advection of mean AM, (<b>d</b>) vertical advection of eddy AM, (<b>e</b>) mean Coriolis force term, and (<b>f</b>) sum of all AM budget terms for CTL at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.</p> "> Figure 15
<p>Azimuthal-mean radial velocity (shaded colors, m s<sup>−1</sup>) at 54 h from the Sawyer–Eliassen (SE) solution with total forcing sources for (<b>a</b>) CTL and (<b>b</b>) MM5. (<b>c</b>) and (<b>d</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with symmetric diabatic heating only. (<b>e</b>) and (<b>f</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with asymmetric eddy momentum and heating only. (<b>g</b>) and (<b>h</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with turbulent momentum diffusion only. (<b>i</b>) and (<b>j</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with residual terms only. The wind vectors (m s<sup>−1</sup>) induced by the total forcing sources overlapped in each panel indicate the radial and vertical wind components (m s<sup>−1</sup>) with their reference vectors given at the lower right corner.</p> "> Figure 16
<p>Azimuthal-mean vertical velocity (shaded colors, m s<sup>−1</sup>) at 54 h from the Sawyer–Eliassen (SE) solution with total forcing sources for (<b>a</b>) CTL and (<b>b</b>) MM5. (<b>c</b>) and (<b>d</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with symmetric diabatic heating only. (<b>e</b>) and (<b>f</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with asymmetric eddy momentum and heating only. (<b>g</b>) and (<b>h</b>) as in (<b>a</b>) and (<b>b</b>), respectively, but with residual terms only. The wind vectors (m s<sup>−1</sup>) induced by the total forcing sources overlapped in each panel indicate the radial and vertical wind components (m s<sup>−1</sup>) with their reference vectors given at the lower right corner.</p> ">
Versions Notes

Abstract

:
The influences of surface layer (SL) physics schemes on the simulated intensity and structure of Typhoon Rai (2021) are investigated using the WRF model. Numerical experiments using different SL physics schemes—revised MM5 scheme (MM5), Eta similarity scheme (CTL), and Mellor–Yamada–Nakanishi–Niino scheme (MYNN)—are conducted. The results show that the intensity forecast of Typhoon Rai is largely influenced by SL physics schemes, while its track forecast is not significantly affected. All three experiments can successfully capture the movement of Rai, while CTL provides better intensity simulation compared to the other two experiments. The higher ratio of enthalpy exchange coefficient to drag coefficient (CK/CD) in CTL than MM5 and MYNN leads to significantly increased surface enthalpy fluxes, which are crucial for the typhoon intensification of the former. To explore the influence of SL physics on the structural evolution of the typhoon, the azimuthal-mean angular momentum (AM) budget is utilized. The results indicate that asymmetric eddy terms may also largely contribute to the AM tendencies, which are relatively more comparable in the weaker TC for MM5, compared to the stronger TC with the dominant symmetric mean terms for CTL. Furthermore, the extended Sawyer–Eliassen (SE) equation is solved to quantify the transverse circulations of the typhoon induced by different forcing sources for CTL and MM5. The SE solution indicates that the transverse circulation above and within the boundary layer is predominantly induced by diabatic heating and turbulent friction, respectively, for both CTL and MM5, while all other physical forcing terms are relatively insignificant for the induced transverse circulation for CTL, except for the large contribution from the eddy forcing in the upper-tropospheric outflow for MM5. With the stronger connective heating in the eyewall and boundary-layer radial inflow, the linear SE analysis agrees much better with the nonlinear simulation for CTL than MM5.

1. Introduction

The tropical cyclone (TC) is one of the most powerful and destructive weather phenomena on Earth and causes heavy losses to people and property. Accurately forecasting the TC’s track and intensity is crucial for mitigating its impacts on lives and property. Although there have been remarkable advances in forecasting TC track, improving TC intensity forecasts remains a challenge [1,2,3,4].
Numerical model prediction depends on many factors, in which physical processes play an important role. Many studies have shown that the influences of the planetary boundary layer (PBL), cloud-microphysics, and cumulus parameterization on typhoon track and intensity are larger than the other physical parameterizations [5,6,7]. While numerous studies have demonstrated the significant influence of surface fluxes on TC development and intensity [8,9,10,11], and have explored the effects of PBL parameterization schemes on TC simulations [12,13,14], relatively few studies have discussed the impact of surface layer (SL) physics schemes on the track and intensity of TC.
At the base of the atmospheric boundary layer is the SL, which is the thinnest layer of the lowest atmosphere by an order of several tens of meters. SL physics schemes represent the physical processes occurring in the lowest part of the atmosphere, particularly the interactions between the surface and the upper boundary layer of the atmosphere. These schemes play a crucial role in accurately simulating weather and climate by determining the exchange of momentum, heat, and moisture between the SL and upper boundary layer [15]. The primary circulation of various weathers in the SL has a major impact on the movement and equilibrium of heat, moisture, and momentum. Tastula et al. [16] reported that the SL physics scheme is necessary to maintain the accuracy of numerical weather forecasting systems. Sensible and latent heat fluxes at the surface are crucial for the formation, development, and maintenance of TCs [17,18,19,20].
Surface exchange coefficients for enthalpy (CK) and momentum (CD) are used to quantify the transfer rates between the surface and the upper boundary layer. Many studies were made to estimate CK and CD from in situ observations, for example, French et al. [21] and Jarosz et al. [22] stated that the exchange coefficient for momentum increased and then declined with surface wind speed. Zhang et al. [23] illustrated that the average CK from observations was about (1.16 ± 0.07) × 10−3. Additionally, Donelan et al. [24] conducted laboratory studies indicating that CD increased from around 1.5 × 10−3 to approximately 3.0 × 10−3 for 10-m wind speeds between 5 and 30 m s−1, and remained constant for wind speeds exceeding 30 m s−1. Haus et al. [25] suggested that, at the same 10-m wind speed, the ratio CK/CD varies between 0.5 and 2. Liu et al. [26] and Smith [27] indicated that the exchange coefficients of heat and moisture are nearly independent of 10-m wind speed over 25 m s−1.
The predicted intensity and structure of TCs are sensitive to CK and CD, which are defined within SL physics schemes. Coronel et al. [28] indicated that increasing the surface drag reduces low-level tangential velocity and induces a stronger inflow near the surface and toward the center of the typhoon. Ming and Zhang [29] conducted numerical studies using various formulations of CK and CD and indicated that the structure of typhoons is significantly influenced by the ratio of exchange coefficient. Wang and Miao [30] conducted sensitivity tests for SL physics schemes and reported that different SL physics schemes have an impact on the precipitation characteristics and circulation of sea breezes over Hainan Island. Shin and Hong [31] noted that SL parameterization can influence the PBL’s physical process by calculating the surface fluxes, wind speed, and potential temperature—all of which have impacts on TC development. Ma et al. [32] indicated that SL physics schemes slightly impacted TC tracks but strongly affected TC intensity as well as the dynamic and thermal structures of the PBL.
Observation evidence indicates that typhoon intensification is closely related to higher axisymmetrization and more intense inner-core convection associated with many typhoons over the WNP [33]. During axisymmetrization, TC intensification can be contributed to by both symmetric flow (mean) and asymmetric (eddy) flow. By using the analyses of the absolute angular momentum budget, Zhang et al. [34] quantified the contributions of mean flow and eddy motions to typhoon intensity. This azimuthal-mean budget analysis helps identify the contributions of different physical processes to the evolution of developing TCs [35]. For understanding of the typhoon intensification associated with developing TCs, the Sawyer–Eliassen (SE) equation in pseudo-height coordinates has been applied to investigate the responses of a primary mean vortex to different forcing sources [36]. The use of the pseudo-height coordinates can simplify the nonlinear radial pressure gradient for the SE modeling [37,38]. A more general form of the SE equation in height coordinates has also been constructed to explore the spinup of the tropospheric vortex [39,40,41,42,43,44,45]. Ji and Qiao [44] found that the unbalanced-dynamics solution from the extended SE equation captures the peak inflow in the boundary layer of the simulation better than both the balanced-dynamics SE solution [43] and pseudo-balanced-dynamics SE solution [42]. Nguyen and Huang [45] also applied the extended SE equation to explain the intensification sensitivities of a simulated supertyphoon in response to differently configured forcing sources.
Typhoon Rai was a powerful and destructive TC that hit Southeast Asia in December 2021. According to the Japan Meteorological Agency (JMA), Rai originated as a tropical depression at 1800 UTC on December 11 and initially moved westward. It later intensified into a tropical storm intensity at 0600 UTC on 13 December and strengthened to a typhoon intensity at 1800 UTC on 14 December. At 0600 UTC on 16 December, Rai reached its first peak intensity with maximum sustained winds of 105 kt and a central pressure of 915 hPa over the Philippine island of Siargao, and then made its first landfall. After crossing several islands in the central Philippines, Rai entered the South China Sea. Over the South China Sea, Rai reached its second peak intensity at 1800 UTC on 18 December before weakening to a tropical depression strength. The typhoon eventually dissipated over mainland areas on 22 December. Typhoon Rai brought extreme rains, strong winds, and storm surges, and caused extensive flooding, landslides, and destruction of infrastructure in the Philippines. The storm resulted in over 400 deaths, with many more injured and missing, and caused over $1.02 billion USD in damages. The significant impact of Rai highlights a need for improved forecasting of typhoon track and intensity.
The Weather Research and Forecasting (WRF) model is a mesoscale numerical weather prediction (NWP) system designed for both atmospheric research and operational forecasting. It is currently used operationally by the National Centers for Environmental Prediction (NCEP) and other national meteorological centers, as well as in real-time forecasting by laboratories, universities, and companies. The WRF model has been employed in numerous studies to simulate the track and intensity of TCs. In the WRF model, there are three popular SL parameterizations: the revised MM5 scheme (MM5), Eta similarity scheme (MO), and Mellor–Yamada–Nakanishi–Niino scheme (MYNN). These SL physics schemes are all developed under the Monin–Obukhov theory and employ different approaches to express the stability function. In MM5, the surface exchange coefficients for momentum, heat, and moisture are calculated using stability functions, which are similar to [46,47]. The MO scheme includes the parametrization of a viscous sublayer, which Janjic [48] explicitly parameterizes over water surfaces. The MYNN surface layer determines the surface layer length scale based on Monin–Obukhov theory.
Many PBL parameterizations have set fixed SL physics schemes, therefore there have been relatively few studies that discussed the separated SL impacts from the PBL physics schemes. Therefore, this study employs the same PBL parameterization, while using three different SL physics schemes (MM5, MO, and MYNN) to investigate their effects on the intensity and structure of Typhoon Rai (2021). Section 2 introduces the WRF configuration and sensitivity experiments for SL physics schemes conducted in this study. Simulated results from the sensitivity experiments are presented and compared with observations in Section 3. Section 4 analyzes the characteristics of the SL and PBL for each experiment. Section 5 explores dynamic aspects, including analyses of angular momentum (AM) budget, and the Sawyer–Eliassen (SE) solution, to examine the structural evolution of the typhoon influenced by different SL physics schemes. The linear SE solution can help quantify the contributions of different forcing sources to the transverse circulation of the nonlinear TC for different vortex spinups. Finally, conclusions are presented in Section 6.

2. Model Configuration and Numerical Experiments

2.1. Model Configuration

This study uses version 4.5.1 of the WRF model [15] to simulate Typhoon Rai. Two-way interactive triple-nested domains are utilized with horizontal resolutions of 18 km (320 × 491 grid points), 6 km (271 × 310 grid points), and 2 km (382 × 445 grid points), respectively (refer to Figure 1). The outermost domain is fixed, while the two inner domains are moving along with the simulated typhoon center. There are 51 vertical layers with a model top at 20 hPa. The simulation period for Rai is from 0000 UTC on 14 December to 0000 UTC on 18 December for a total of 96 h, which covers nearly the entire lifecycle of Rai from its initial stages to its landfall in the Philippines. Initial and boundary conditions are obtained from the National Centers for Environmental Prediction’s Final (FNL) dataset with a spatial resolution of 0.25° × 0.25°.
The track and intensity of Typhoon Rai are determined using the best track data provided by JMA, which includes 6-hourly typhoon center locations and 10-min averaged maximum wind speed (Vmax). To validate the simulation results, the Joint Typhoon Warning Center (JTWC) best track data is also referenced, which includes 1-min averaged maximum wind speed. Additionally, average hourly accumulated precipitation data from the Global Satellite Mapping of Precipitation (GSMaP) is used. These data are derived from a multi-satellite precipitation product and can be accessed at https://sharaku.eorc.jaxa.jp/GSMaP accessed on 20 September 2024.

2.2. Sensitivity Experiments

To investigate how surface layer (SL) physics schemes influence the intensity and structure of Typhoon Rai, three different schemes are compared: MO [48,49,50], MM5 [51], and MYNN [52,53], referred to as CTL, MM5, and MYNN experiments, respectively. The details of these three schemes are given in Appendix A. The other model physics schemes for the simulation experiments include the Kain–Fritsch cumulus parameterization [54,55], applied only to the outermost domain, the Lin microphysical scheme [56], the MYNN PBL scheme [52,57], the Noah Land Surface Model [58], the Dudhia shortwave radiation scheme [59], and the Rapid Radiative Transfer Model for GCMs (RRTM) longwave radiation scheme [60] over all three domains. Note that, among PBL parameterizations, the MYNN PBL scheme is unique in its compatibility with all three SL physics schemes (MO, MM5, and MYNN). A summary of the physics schemes for the simulation experiments is listed in Table 1.

3. Simulation Results

3.1. Simulated Track and Intensity

Figure 2 shows the simulated track and intensity of Typhoon Rai from three sensitivity experiments using the different SL physics schemes above; the best tracks from JMA and JTWC for Typhoon Rai are also included for comparison. According to the best track, Typhoon Rai initially moved west–northwestward before making landfall in the Philippines (Figure 2a). The simulated tracks are rather straight for all three experiments and compare well with the best track, but with slightly northward deviations on the last day of the forecast. The simulated track errors are primarily caused by the difference in forecasted translation speeds, with a slightly slower movement than that observed. The reasons for errors in the forecast of translation speed can include various factors, such as inaccuracies in the initial conditions, limitations on representativeness of the model physics, and the complexity of the typhoon’s interaction with the surrounding environment. Specifically, uncertainties in the surface layer physics schemes and their impacts on typhoon motion can contribute to some forecast errors. As a result, all three simulations show that the simulated typhoon translations are slightly slower than the best track.
The intensity of Vmax for CTL closely matches that from JMA in the first 54 h, with a slight overestimation thereafter (Figure 2b). CTL reaches its peak intensity at 60 h with a maximum wind speed of 60 m s−1, slightly stronger than the best track intensity from JMA. MM5 effectively captures the intensification rate observed by JMA in the last two days and reaches a peak intensity of approximately 54 m s−1 at 54 h, consistent with JMA. MYNN, on the other hand, exhibits a slightly weaker intensity than MM5, which reaches a maximum intensity of 48 m s−1 at 54 h. Clearly, both MM5 and MYNN simulate relatively weaker intensities than CTL. Besides, Table 2 indicates that CTL exhibits a better simulated intensity than the other two experiments (MM5 and MYNN), evidenced by higher correlation coefficients, smaller bias, and smaller root mean square error for simulated intensity in 24–54 h when compared to the best track intensity from JMA. This suggests that the intensity forecast of the typhoon is notably influenced by SL physics schemes, while the track forecast is not significantly affected.

3.2. Simulated Precipitation

Figure 3 shows the simulated 12-hourly accumulated rainfall from the three experiments in three different periods: before landfall (48–60 h), at landfall (60–72 h), and after landfall (72–84 h) in the Philippines. Rainfall observations for verification are obtained from the multi-satellite precipitation product from JAXA (GSMaP) during corresponding simulation times. Note that all three experiments simulate the landfall times somewhat later than indicated by JMA. Consequently, there is a lag in the rainfall area between observations and simulations. The major rainfall in the three experiments exhibits relatively similar areas, with the primary concentration south of the typhoon center. Generally, the rainfall for GSMaP and simulations are quite comparable in terms of both pattern and intensity. However, CTL shows slightly better agreement with GSMaP than the other two experiments, particularly during and after the typhoon making landfall in the Philippines. Indeed, the simulated precipitation from MM5 and MYNN is lower (higher) than that observed by GSMaP, particularly south of the typhoon center at 48 h (60 h). The results suggest that precipitation is less sensitive to SL parameterizations for Typhoon Rai (2021) in this study, despite the timing difference in simulating the landfall compared to the observations.

4. Characteristics of Surface Layer and Planetary Boundary Layer

4.1. Characteristics of Surface Layer

The intensity of TCs is correlated with the ratio of the exchange coefficient (CK/CD), as suggested by several earlier studies [29,61,62]. The exchange coefficients CK and CD are calculated by different methods for the three different SL physics schemes, as shown in Appendix A. Figure 4 shows the ratio of the exchange coefficient (CK/CD) as a function of the 10-m wind speed for the three experiments. When the wind speed is below 25 m s−1, the ratio CK/CD gradually decreases with increasing wind speed for all the three experiments, in which MM5 and MYNN show a larger rate of decrease compared to CTL. However, when the wind speed exceeds 25 m s−1, the ratios CK/CD of all the three experiments remain unchanged, which is consistent with [27]. MYNN and MM5 exhibit a similar ratio CK/CD, whereas CTL maintains a significantly higher ratio CK/CD when wind speeds are larger than 25 m s−1. A higher ratio CK/CD indicates stronger typhoon intensity, as for CTL.
The friction velocity u * represents the shear stress exerted by the wind on the surface and is closely related to the surface drag coefficient and the 10-m wind speed. Figure 5a shows the time evolution of averaged friction velocity for the three experiments from 24 to 72 h, including both the intensification and subsequent weakening phases of the typhoon. Throughout the forecast period, it is evident that the friction velocity of CTL consistently exceeds that of the other two experiments, corresponding to its higher Vmax. The friction velocity values for MM5 and MYNN exhibit slight differences, which contributes to the slight differences in Vmax observed between these two experiments, as shown in Figure 2b. This relationship highlights the significant influence of friction velocity on the simulated wind speeds across different model configurations.
Figure 5b,c shows the time evolutions of surface sensible heat flux and surface latent heat flux around the typhoon center for the three experiments. The time evolutions of sensible heat flux (Figure 5c) are nearly consistent with that of the latent heat flux (Figure 5c) with significantly smaller magnitudes. All three experiments reach their peak values for surface fluxes (both latent and sensible heat flux) at 54 h, just before the typhoon made landfall in the Philippines. CTL shows significantly stronger surface fluxes compared to MM5 and MYNN. The difference in surface fluxes of latent heat and sensible heat corresponds to the different magnitudes of ratio CK/CD in the three experiments (Figure 4), indicating different levels of efficiency in transferring momentum from the atmosphere to the ocean surface.
Figure 6 shows the variables related to SL physics, such as surface wind speed, friction velocity, and surface sensible and latent heat fluxes, at 54 h, when the typhoon reaches its peak intensity. Compared to MM5 and MYNN, CTL exhibits significantly stronger and more symmetric surface wind speeds with a well-defined eyewall structure (Figure 6a–c). In MM5, the distribution of surface wind is similar to MYNN, but the wind on the eastern semicircle is slightly stronger in MM5 compared to MYNN. As noted earlier, stronger typhoon intensity is associated with higher surface friction velocity, which leads to increased vertical mixing. Accordingly, CTL shows notably higher friction velocity due to its stronger wind speeds (Figure 6d). The distribution of friction velocity in CTL is rather symmetric, while it is mainly concentrated in the eastern semicircle of the typhoon for MM5 and MYNN (Figure 6e,f). It is evident that the friction velocity is highly influenced by different SL physics schemes.
The distribution of surface fluxes (Figure 6g–l) correlates closely with the distributions of surface wind and friction velocity. The higher surface fluxes mainly concentrate in the eyewall region, where surface wind speed is stronger (Figure 6a–c). The substantially higher ratio CK/CD in CTL results in significantly higher surface fluxes of both sensible heat and latent heat compared to the other two experiments (Figure 3). This higher ratio CK/CD induces greater sensible and latent heat fluxes. This implies that CTL has more energy supply for typhoon intensification. In general, the influence of SL physics schemes on the typhoon intensity and structure is evident through exchange coefficients, friction velocity, and surface fluxes. CTL shows the highest values in these parameters, followed by MM5, with MYNN displaying the lowest values. This highlights how different SL physics schemes impact the energy exchange processes in TC development and intensification.

4.2. Characteristics of Planetary Boundary Layer

In the following sections, we will discuss further the characteristics related to the boundary layer and typhoon dynamics by comparing two representative experiments with strong and weak intensity, the CTL and MM5 experiments.
Figure 7 shows the azimuthal-mean tangential velocity and radial velocity below 2.5-km height in the radius–height cross-section for CTL and MM5 at 54 h. The tangential velocity for CTL is generally stronger than that for MM5 (Figure 7a,b), consistent with the simulated typhoon intensity. For CTL, the maximum tangential velocity exceeds 70 m s−1 at a radius of 0.3 degree from the typhoon center, whereas for MM5 it reaches about 50 m s−1 at a radius of 0.5 degree. Similarly, the radial velocity in the boundary layer is notably stronger and develops more deeply for CTL compared to MM5 (Figure 7c,d). This result is consistent with findings by [63], which highlights the influence of surface exchange coefficients on the vertical structure of wind velocities above the SL.
The boundary-layer height is a critical parameter that regulates the vertical distribution of turbulent fluxes and determines where turbulent mixing becomes negligible. The kinematic boundary-layer height in this study is defined as the height of maximum tangential wind speed (hvt) and the inflow layer depth (hvr), which is defined as the height where the inflow reduces to 10% of its peak value, following [64]. The boundary-layer height for CTL is almost consistently higher than that for MM5 for both, defined by hvt or hvr. The difference in hvr (Figure 7c,d) between CTL and MM5 is slightly greater than that observed in hvt (Figure 7a,b). Moreover, all the experiments can capture the decrease of hvr and hvt with decreasing radius inside the eyewall, consistent with [65]. These results underscore the relationship between boundary-layer heights and surface flux parameterization.
Figure 8 presents the Hovmöller plot of azimuthal-mean tangential wind velocity at 2-km height and radial wind velocity at 250-m height from 24 to 72 h for CTL and MM5. Over time, the outer vortex circulation expands more noticeably for CTL compared to MM5 (e.g., see the contours of 40 m s−1). Throughout the simulation period, both tangential and radial velocities in CTL are consistently stronger than those in MM5. Indeed, in the first 6 h (24–30 h), Rai is a moderate TC with maximum tangential velocity reaching 35 m s−1 and radial inflow intensity reaching 8 m s−1 in CTL, whereas in MM5 both are only 30 m s−1 and 8 m s−1, respectively. In the next 24 h, the intensity is doubled, and the simulated typhoons reach peak intensity (peaking at 60 h for CTL and 54 h for MM5) with maximum tangential velocity exceeding 60 m s−1 and radial velocity exceeding 20 m s−1 for CTL, while for MM5 they only reach 45 m s−1 and 14 m s−1, respectively. The radius of maximum tangential wind speed (RMW) contracts inward as the typhoon intensity increases, with CTL starting contraction at 46 h and MM5 beginning at 50 h, illustrating the difference in intensity evolution between the two experiments.
Potential temperature plays a crucial role in determining atmospheric stability, indicating an unstable atmosphere when the potential temperature decreases with height. Unstable conditions (or weaker stability) promote upward vertical motions, which tend to intensify TCs. Potential temperature for both experiments generally increases with height but decreases outward with radius, as shown in Figure 9, except for near the lowest eyewall. The vertical gradient of potential temperature for CTL is considerably smaller (i.e., the slope is deeper) than MM5, supporting the stronger eyewall development in the former with weaker stability. Specifically, within the eye of the typhoon, CTL exhibits a maximum potential temperature of approximately 318 K at 2-km height, whereas MM5 shows a slightly lower value of about 314 K. This peak in potential temperature within the eyewall emphasizes the presence of a warm core structure, which is essential for TC development and intensification.
Since higher potential temperatures are concentrated inside the inner vortex core in Figure 9, Figure 10a,b shows the Hovmöller plots of averaged potential temperature inside the RMW for CTL and MM5 from 24 to 72 h, respectively. Over time, potential temperature increases rapidly for CTL, reaching its peak at 60 h, consistent with the peak intensity shown in Figure 2b. In contrast, the potential temperature for MM5 remains relatively lower and increases only slightly over time.
The warm core structure of a TC is characterized by two key parameters: warm core strength and warm core height. Warm core strength is defined by the maximum potential temperature anomaly, while warm core height is defined by the height of the maximum potential temperature anomaly. According to the hydrostatic balance, a lower MSLP corresponds to a larger warm core [66]. The strength and height of the warm core are thus closely correlated with the intensity of the typhoon. Figure 10c,d shows the time evolution of the warm core or potential temperature anomaly averaged within a radius of 1.5 degrees from the typhoon center. Warm core herein is defined as the difference between the potential temperature at a local grid and the mean potential temperature within a radius of 350 km from the typhoon center. The warm core becomes warmer over time for both experiments, with CTL consistently exhibiting a warmer warm core compared to MM5. During 54 to 60 h, the warm core height of CTL ranges from about 14 to 16 km, whereas for MM5 it ranges from 8 to 10 km, and the warm core strength of CTL is up to 9 K, much warmer than MM5. This result is consistent with the simulated Vmax for both experiments, indicating that the strength and height of the warm core are consistent with the intensity of the simulated typhoon.

5. Dynamic Analyses

5.1. Azimuthal-Mean Typhoon Structure

The differences in the TC development to different SL impacts are further illustrated by their mean dynamic structures. Figure 11 shows the azimuthal-mean radial, tangential, and vertical wind components, as well as the associated latent heating rate at the radius–height cross-section at 54 h for CTL and MM5. The transverse circulations for both experiments exhibit similar typical patterns, but the associated wind components are considerably stronger for CTL. The low-level inflow and upper-level outflow in the inner vortex for CTL are much stronger than MM5 (Figure 11a,b) and are associated with stronger tangential wind speed that develops more highly and widely (Figure 11c,d). The strong inward flow decelerates rapidly near the eyewall and then rises with strong updrafts for CTL, while the updraft in the eyewall is much weaker for MM5, associated with the much weaker near-surface inflow. Stronger upward motions are induced in the inner eyewall for both experiments (Figure 11e,f). The latent heating is always confined below about 13-km height close to the lower flank of the upper-level outflow layer (Figure 11g,h). With much stronger upward motions in the eyewall, the latent heating at a maximum rate of over 32 K h−1 for CTL is also significantly larger than MM5 (a maximum rate of about 25 K h−1). RMW for CTL remains smaller throughout the troposphere compared to MM5, expanding outward with height. These characteristics of the dynamic features are typical of intense typhoons for CTL, in contrast to those of MM5, with a much less consolidated eyewall.

5.2. AAM Budget Analysis

To explore the structural evolution of the typhoon influenced by surface layer physics schemes, this study utilizes the azimuthal-mean AM (AAM) budget in cylindrical coordinates. The governing equation for the AAM budget is as follows [35]. Figure 12 presents the AAM in the radius–height cross-section for CTL and MM5 at 54 h. In both experiments, the mean AM decreases inward and upward with the TC center. Contours of AM slope outward with height in the upper outflow layer, a characteristic observed in intense hurricanes over the ocean [34]. At this time, the AM outside of the RMW is stronger, with a higher developed same contour in the middle troposphere in CTL compared to MM5. The upper-level outflow extends deeper and is more robust outside the radius of 0.5 degrees for CTL than for MM5. Furthermore, CTL exhibits more intense low-level inflow with deeper penetration of stronger AM. Overall, the deep inflow outside the RMW observed in CTL effectively transports larger AM inward toward the inner core, contributing to its stronger intensity compared to MM5.
Figure 13 shows the AAM budget terms for CTL at 54 h. Radial mean AM advection gives a positive contribution in the low-level inflow region while producing a larger negative AM tendency in the eyewall (Figure 13a), while vertical mean AM advection tends to offset radial mean AM advection in the low-level inflow, upper-level outflow, and eyewall regions (Figure 13c). The contribution of radial eddy AM advection is mainly negative in the eyewall at 5–16-km height, while it shows a mixed contribution, both positive and negative, outside the eyewall and in the upper outflow layers (Figure 13b). The contributions of vertical eddy AM advection are mainly positive in the eyewall at 2–10-km height and negative in the upper outflow layers (Figure 13d). The Coriolis term contributes positive and large negative AM in response to the strong low-level inflow and upper-level outflow, respectively (Figure 13e). The sum of all the AM budget terms shows a positive AM tendency generated in the boundary layer near the eyewall region and a negative AM tendency in the eyewall from 3–14-km height (Figure 13f).
Similar to Figure 13, Figure 14 shows the AAM budget terms, but for MM5 at 54 h. Overall, the patterns of the AAM budget terms are quite similar between MM5 and CTL, although with different magnitudes. The sum of all AAM budget terms (Figure 14f) for MM5 shows a positive AM tendency in the eyewall below 10-km height, primarily driven by positive contributions from vertical mean and eddy AM advection (Figure 14c,d). Above 10 km height in the eyewall, there is a negative AM tendency, mainly due to radial and vertical eddy AM advection (Figure 14b,d). Contributions from radial mean AM advection (Figure 14a) and the Coriolis term (Figure 14e) are relatively smaller at this time compared to the other terms. It is evident that the AM tendency for MM5 is somewhat weaker than that for CTL (Figure 13f and Figure 14f). Note that the contributions of eddy terms to AM tendency are significant for both experiments. In general, the weaker TC for MM5 exhibits a much less vertical consolidation of the AM budget terms, unlike the strong TC for CTL, where the intense eyewall can present a much higher vertical extent of the AM transport.

5.3. Analysis with the Solution of the Extended Sawyer–Eliassen Equation

In this section, we solve the extended SE equation to explore the contributions of different forcing terms to the transverse circulation of the primary vortex. Detailed formulations and methods for solving the SE equation can be found in [45]. The forcing sources involved in the unbalanced vortex include mean diabatic heating, asymmetric eddy momentum and heating, turbulent momentum and heat diffusion, as well as the unbalanced dynamics of the radial wind tendency equation (departing from gradient–wind balance, U ˙ ), the non-hydrostatic equation (departing from hydrostatic balance, W ˙ ), and the residue from the tangential velocity tendency equation ( V ˙ ). The numerical domain used for solving the SE equation is 0–3 degrees in the radial with a resolution of 0.025 degrees and the original 51 vertical levels of the vertical coordinate of the WRF model.
Figure 15 shows the radial velocity induced by the SE solution with total forcing sources and constituents (diabatic heating, asymmetric eddy momentum and heating, turbulent momentum diffusion, and the residual terms) at 54 h for CTL and MM5. The SE solution (Figure 15a,b) gives consistent radial velocity, comparing well with the nonlinear simulations (Figure 11a,b), except for the underestimated upper-level outflow near 16-km height and the radial inflow in the boundary layer. The diabatic heating notably induces radial outflow at the upper levels and radial inflow in the boundary layer below 2-km height for both experiments (Figure 15c,d). In CTL, the contribution of eddy terms (asymmetric eddy momentum and heating) to induced radial velocity is relatively smaller, except for above 10 km (Figure 15e), to coincide with their significant impact on the azimuthal-mean AM tendency (see Figure 13b,d). In contrast, for MM5, eddy terms significantly contribute to the more intense radial velocity, especially above 10 km (Figure 15f), corresponding to their larger impacts on AM tendency (Figure 14b,d). Turbulent momentum diffusion induces radial inflow below 1-km height and radial outflow above (Figure 15g,h). The residual terms ( U ˙ , V ˙ , and W ˙ ) contribute to the induced radial velocity mainly in the upper levels above 12 km and in the boundary layer (Figure 15i,j). In summary, for CTL, radial velocity is primarily induced by diabatic heating to generate the upper-level outflow and by turbulent momentum diffusion to produce boundary layer inflow, consistent with previous research [42,44]. However, the upper-level outflow is mainly produced by the eddy terms for MM5.
Similar to Figure 15, Figure 16 shows the vertical velocity induced by the SE solution with total forcing sources and constituents. The SE solution with total forcing sources (Figure 16a,b) also effectively captures the vertical motions from the nonlinear simulation (Figure 11e,f). For both experiments, the vertical updrafts are mainly induced by diabatic heating for both in the eyewall and outside the eyewall (Figure 16c,d). The eddy terms induce small vertical updrafts in the upper eyewall from 12–18-km height for CTL (Figure 16e), whereas they induce strong vertical updrafts in this region for MM5 (Figure 16f). The contribution of the residual terms to vertical velocity is mainly above 10-km height, but it is insignificant for both experiments (Figure 16g,h). Therefore, the eddy terms significantly contribute to the induced transverse circulation above 10-km height for MM5 compared to CTL.

6. Conclusions

In this study, the WRF model is utilized to explore how the intensity and structure of Typhoon Rai (2021) are influenced by surface layer physics schemes, namely the revised MM5 scheme (MM5), Eta similarity scheme (CTL), and Mellor–Yamada–Nakanishi–Niino scheme (MYNN). These schemes are developed under the Monin–Obukhov theory and employ different approaches to express the stability function. The simulation results indicate that Rai has a smaller track forecast sensitivity to use of different surface layer physics schemes but a greater intensity forecast sensitivity. For the simulated results of track and intensity, the simulation using the Eta similarity scheme (CTL) provides better intensity simulation compared to the other two schemes.
CTL consistently maintains a significantly higher ratio CK/CD compared to MM5 and MYNN, indicating that a higher CK/CD ratio correlates with stronger typhoon intensity. The higher ratio CK/CD in CTL results in significantly higher surface fluxes of heat and moisture, leading to greater sensible and latent heat fluxes, which provide more energy supply for typhoon intensification. Overall, the influence of SL physics schemes on typhoon intensity and structure is evident through exchange coefficients, friction velocity, and surface fluxes. CTL exhibits the highest values in these physical quantities, followed by MM5, while MYNN shows the lowest values. This underscores how different SL physics schemes impact the dynamics of energy exchange crucial for TC development and intensification.
The typhoon structures are significantly influenced by SL physics schemes. In the CTL experiment, tangential velocity and radial inflow in the boundary layer are generally stronger compared to the other two experiments, which corresponds to the simulated stronger typhoon intensity. This finding is consistent with [63], emphasizing how surface flux parameterization influences the vertical structure of wind velocities above the SL. Additionally, CTL also exhibits a warmer and higher warm core than MM5. This result correlates well with the simulated intensity in both experiments, indicating that the strength and height of the warm core are consistent with the intensity of the simulated typhoon.
To explore the structural evolution of the typhoon influenced by SL physics schemes, this study utilizes the AAM budget. Overall, the patterns of the AAM budget terms are somewhat similar between MM5 and CTL, albeit with different magnitudes. It is evident that the AM tendency for MM5 is somewhat weaker than that for CTL. Generally, the weaker TC for MM5 shows a much less vertical consolidation of the AM budget terms, in contrast to the stronger TC for CTL, where the intense eyewall exhibits a much higher vertical extent of the AM transport. The asymmetric eddy terms may also largely contribute to the AM tendencies, which are relatively more comparable in the weaker TC for MM5, compared to the stronger TC with the dominant symmetric mean terms for CTL.
The extended SE equation, as used in [45], is solved to investigate the induced transverse circulation of the primary vortex for CTL and MM5. The forcing sources used for the extended SE equation include mean diabatic heating, asymmetric eddy transport, turbulent diffusion, and the forcing terms associated with the unbalanced dynamics for the radial wind equation and hydrostatic equation, as well as the residue from the tangential velocity tendency equation. The results show that the solution of the extended SE equation agrees well with the nonlinear simulation for both experiments, except for the underestimated upper-level outflow near 16-km height and the boundary-layer inflow. The transverse circulation both above and within the boundary layer for CTL is predominantly induced by diabatic heating and turbulent friction, respectively, with negligible contributions from other forcing terms. However, the eddy terms also significantly contribute to the induced transverse circulation at upper levels above 10-km height for MM5. Moreover, the contributions of eddy terms from MM5 to the transverse circulation are coincident with their significant impact on the AM tendency. With the stronger connective heating in the eyewall and boundary-layer radial inflow, the SE analysis for CTL agrees better with the nonlinear simulation than MM5. The SL physics, based on Eta Similarity scheme, has improved the simulation of Typhoon Rai, and should be further illustrated for more typhoon cases.
This study examines the effects of three different SL physics schemes (MM5, MO, and MYNN) on the intensity and structure of Typhoon Rai (2021). The results presented in this study have offered scientific insights into the responses of the TC evolution to different SL physics. However, the impact of these schemes may vary significantly across different typhoons over different oceans. Future research will focus on assessing the impacts of these schemes on the simulated tracks and intensities of various TCs for a broader view.

Author Contributions

Conceptualization, C.-Y.H.; Methodology, C.-Y.H. and T.-H.H.; Software, Formal analysis, and Data curation, T.-H.H. and T.-C.N.; Writing—original draft preparation, T.-H.H. and T.-C.N.; Writing—review and editing, C.-Y.H., T.-H.H. and T.-C.N.; Project administration, C.-Y.H. All authors have read and agreed to the published version of the manuscript.

Funding

This study was supported by the National Science and Technology Council (NSTC) (grant no. NSTC 113-2111-M-008-003) in Taiwan.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The FNL data were obtained from the website of the NCEP and the best track data are obtained from the JMA and JTWC, and the model forecasts are available from the workstation of the typhoon laboratory at the Department of Atmospheric Sciences, National Central University (NCU) from 140.115.35.103.

Acknowledgments

The authors would like to thank J.-S. Hong at the Central Weather Administration (CWA) and K.-S. Chung at the National Central University (NCU) for valuable comments on the research work for the manuscript. This study was supported by the National Science and Technology Council (NSTC) in Taiwan. Computation was supported by the National Center for High-Performance Computing (NCHC) in Taiwan.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Appendix A.1. Surface Layer Parameterization

The SL physics scheme includes the transfer of heat, moisture, and momentum from the surface to the PBL above. A general framework of surface fluxes of momentum ( τ ), heat (HFX), and moisture (QFX) is given by
τ = ρ C D U 2
H F X = ρ c p C H U θ g − θ
Q F X = ρ C Q U q v g − q v
where ρ is air density, C D ,   C H , and C Q are exchange coefficients for momentum, heat, and moisture, respectively, c ρ is the specific heat capacity, and U is wind speed in the lowest model level. θ and θ g are potential temperature at the lowest model level and at the ground, respectively, while q v and q v g are water vapor mixing ratio at the lowest model level and at the ground, respectively. The main differences between the three SL schemes (MO, MM5, and MYNN) are in the exchange coefficients C D ,   C H , and C Q , which are related to the roughness length for momentum, heat, and moisture.
The air–sea enthalpy flux H is defined as the sum of its energy
H = ρ C K U k * − k
where C K is the enthalpy exchange coefficient, calculated from C H and C Q , k* is the saturation-specific enthalpy at the surface and k is the specific enthalpy at the ground.

Appendix A.2. MO Scheme

The MO scheme [50], based on similarity theory [49], is often referred to as the MYJ or Eta scheme. This scheme consists of parameterizations of a viscous sub-layer. Over land, the effects of sub-layer are addressed through variable roughness heights for temperature and humidity, as proposed by [67]. Over water, the sub-layer is explicitly parameterized following [48].
The exchange coefficients of the MO scheme [68] are given by
C D = k 2 ln z + z o m z o m − ψ m z + z o m L + ψ m z o m L 2
C H = k 2 R ln z + z o m z o m − ψ m z + z o m L + ψ m z o m L ln z + z o m z 0 t − ψ h z + z o m L + ψ h z 0 t L  
C Q = C H
where ψ m is the similarity function for momentum, ψ h is the similarity function for heat, k is the Von Kármán constant (0.4), L is Obukhov length, R is the bulk Richardson number, z is reference height of the lowest model level, z o m is roughness length for momentum, and z o t is roughness length for heat and moisture. Detailed descriptions of similarity functions ψ m and ψ h can be found in reference [68].

Appendix A.3. MM5 Scheme

The MM5 scheme employs stability functions consistent with [46,47,69] to determine surface exchange coefficients for heat, moisture, and momentum. To enhance surface fluxes of heat and moisture, it uses a convective velocity approach based on [70]. The current version of this scheme does not include a thermal roughness length parameterization. Over water, roughness length is related to friction velocity through a Charnock relation.
The exchange coefficients of the MM5 scheme [51] are given by
C D = k 2 ln z + z 0 z 0 − ψ m z + z 0 L + ψ m z 0 L 2
C H = k 2 ln z + z 0 z 0 − ψ m z + z 0 L + ψ m z 0 L   ln z + z 0 z 0 − ψ h z + z 0 L + ψ h z 0 L
C Q = k 2 ln z + z 0 z 0 − ψ m z + z 0 L + ψ m z 0 L   ln ρ c P k z u * C s + z z l − ψ h z L + ψ h z l L
where z o is momentum roughness length, z l = 0.01 m refers to the value over land, ρ is the density in the surface layer, u * is the friction velocity, c ρ is the specific heat capacity at constant pressure, c s is the specific heat capacity at constant pressure. Detailed descriptions of similarity functions ψ m and ψ h can be found in reference [51].

Appendix A.4. MYNN Scheme

The MYNN Eddy Diffusivity–Mass Flux (EDMF) scheme was outlined in [52] and further detailed by [53]. The convective velocity follows [70,71]. Over land, the scalar roughness length is determined by [72,73,74,75]. Over water, roughness length is taken as a time-varying quantity followed by [72,76,77,78].
The exchange coefficients of the MYNN scheme [79] are given by
C D = k 2 ln z 1 + z 0 z 0 − ψ m z 1 + z 0 L + ψ m z 0 L 2
C H = k 2 ln z 1 + z 0 z 0 − ψ m z 1 + z 0 L + ψ m z 0 L   ln z 1 + z 0 z t − ψ h z 1 + z 0 L + ψ h z t L
C Q = k 2 ln z 1 + z 0 z 0 − ψ m z 1 + z 0 L + ψ m z 0 L   ln z 1 + z 0 z q − ψ h z 1 + z 0 L + ψ h z q L
where z 1 is the height of the first model half-level, z o is momentum roughness length, z t is roughness length for heat, and z q is roughness length for moisture. Detailed descriptions of similarity functions ψ m and ψ h can be found in reference [79]. In the case of most model configurations, z t = z q , leading to C H = C Q   = C K .

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Figure 1. The WRF model domains for Rai at the initial time. The outermost box (d01) denotes the outermost domain, while the red and blue boxes (d02 and d03, respectively) denote the two inner moving domains. The dashed black line (JMA) with cycles at intervals of 24 h indicates the best track from JMA from 0000 UTC 14 December to 0000 UTC 18 December 2021.
Figure 1. The WRF model domains for Rai at the initial time. The outermost box (d01) denotes the outermost domain, while the red and blue boxes (d02 and d03, respectively) denote the two inner moving domains. The dashed black line (JMA) with cycles at intervals of 24 h indicates the best track from JMA from 0000 UTC 14 December to 0000 UTC 18 December 2021.
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Figure 2. (a) Tracks of Typhoon Rai, including the best track data from JTWC (dashed black line) and JMA (solid black line), as well as simulated tracks for CTL (red line), MM5 (blue line), and MYNN (green line), during the period from 0000 UTC 14 December to 0000 UTC 18 December 2021. Circle symbols in (a) indicate the time every 24 h. (b) as in (a), but for the 10-m maximum wind speed (Vmax, m s−1).
Figure 2. (a) Tracks of Typhoon Rai, including the best track data from JTWC (dashed black line) and JMA (solid black line), as well as simulated tracks for CTL (red line), MM5 (blue line), and MYNN (green line), during the period from 0000 UTC 14 December to 0000 UTC 18 December 2021. Circle symbols in (a) indicate the time every 24 h. (b) as in (a), but for the 10-m maximum wind speed (Vmax, m s−1).
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Figure 3. 12-h accumulated precipitation (mm) during 48–60 h from (a) multi-satellite precipitation product GSMaP, (b) CTL, (c) MM5, and (d) MYNN. (e), (f), (g), and (h) as in (a), (b), (c), and (d), respectively, but during 60–72 h. (i), (j), (k), and (l) as in (a), (b), (c), and (d), respectively, but during 72–84 h.
Figure 3. 12-h accumulated precipitation (mm) during 48–60 h from (a) multi-satellite precipitation product GSMaP, (b) CTL, (c) MM5, and (d) MYNN. (e), (f), (g), and (h) as in (a), (b), (c), and (d), respectively, but during 60–72 h. (i), (j), (k), and (l) as in (a), (b), (c), and (d), respectively, but during 72–84 h.
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Figure 4. Simulated ratio of enthalpy exchange coefficient to drag coefficient (CK/CD) as a function of 10-m wind speed for CTL (red line), MM5 (blue line), and MYNN (green line) at 54 h.
Figure 4. Simulated ratio of enthalpy exchange coefficient to drag coefficient (CK/CD) as a function of 10-m wind speed for CTL (red line), MM5 (blue line), and MYNN (green line) at 54 h.
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Figure 5. Time evolutions of (a) friction velocity (m s−1), (b) surface sensible heat flux (W m−2), and (c) surface latent heat flux (W m−2) for CTL (red line), MM5 (blue line), and MYNN (green line), averaged within the area of 300 × 300 km around the typhoon center from 24 h to 72 h.
Figure 5. Time evolutions of (a) friction velocity (m s−1), (b) surface sensible heat flux (W m−2), and (c) surface latent heat flux (W m−2) for CTL (red line), MM5 (blue line), and MYNN (green line), averaged within the area of 300 × 300 km around the typhoon center from 24 h to 72 h.
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Figure 6. Horizontal distribution of 10-m wind speed (shaded color, m s−1) for (a) CTL, (b) MM5, and (c) MYNN at 54 h. (d), (e), and (f) as in (a), (b), and (c), respectively, but for friction velocity (m s−1). (g), (h), and (i) as in (a), (b), and (c), respectively, but for surface sensible heat flux (W m−2). (j), (k), and (l) as in (a), (b), and (c), respectively, but for surface latent heat flux (W m−2). The black vectors in (a–c) denote the 10-m horizontal wind speed.
Figure 6. Horizontal distribution of 10-m wind speed (shaded color, m s−1) for (a) CTL, (b) MM5, and (c) MYNN at 54 h. (d), (e), and (f) as in (a), (b), and (c), respectively, but for friction velocity (m s−1). (g), (h), and (i) as in (a), (b), and (c), respectively, but for surface sensible heat flux (W m−2). (j), (k), and (l) as in (a), (b), and (c), respectively, but for surface latent heat flux (W m−2). The black vectors in (a–c) denote the 10-m horizontal wind speed.
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Figure 7. Azimuthal-mean tangential velocity (m s−1) in the radius–height cross-section at 54 h for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but for the radial velocity (m s−1). The black line in (a,b) represents the height of the maximum tangential wind speed (hvt). The black line in (c,d) represents the inflow layer depth (hvr).
Figure 7. Azimuthal-mean tangential velocity (m s−1) in the radius–height cross-section at 54 h for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but for the radial velocity (m s−1). The black line in (a,b) represents the height of the maximum tangential wind speed (hvt). The black line in (c,d) represents the inflow layer depth (hvr).
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Figure 8. Time–radius Hovmöller diagrams of azimuthal-mean tangential wind (m s−1) at 2-km height for (a) CTL and (b) MM5 from 24 h to 72 h. (c) and (d) as in (a) and (b), respectively, but for radial wind (m s−1) at 0.25-km height. The black line in (a,b) represents the radius of maximum tangential wind speed (RMW) at 2 km height. The green line in (c,d) represents the maximum inflow at 0.25-km height.
Figure 8. Time–radius Hovmöller diagrams of azimuthal-mean tangential wind (m s−1) at 2-km height for (a) CTL and (b) MM5 from 24 h to 72 h. (c) and (d) as in (a) and (b), respectively, but for radial wind (m s−1) at 0.25-km height. The black line in (a,b) represents the radius of maximum tangential wind speed (RMW) at 2 km height. The green line in (c,d) represents the maximum inflow at 0.25-km height.
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Figure 9. Azimuthal-mean potential temperature (K) in the radius–height cross-section for (a) CTL and (b) MM5 at 54 h. The thick black line represents the RMW.
Figure 9. Azimuthal-mean potential temperature (K) in the radius–height cross-section for (a) CTL and (b) MM5 at 54 h. The thick black line represents the RMW.
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Figure 10. Time–height Hovmöller diagrams of azimuthal-mean potential temperature (K) inside RMW for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but for warm core (K) averaged inside a radius of 1.5 degrees from the typhoon center.
Figure 10. Time–height Hovmöller diagrams of azimuthal-mean potential temperature (K) inside RMW for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but for warm core (K) averaged inside a radius of 1.5 degrees from the typhoon center.
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Figure 11. Azimuthal-mean flow (shaded color) in the radius–height cross-section of radial velocity (m s−1) for (a) CTL and (b) MM5 at 54 h. (c) and (d) as in (a) and (b), respectively, but for tangential velocity (m s−1). (e) and (f) as in (a) and (b), respectively, but for vertical velocity (m s−1). (g) and (h) as in (a) and (b), respectively, but for latent heating rate (K h−1). The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
Figure 11. Azimuthal-mean flow (shaded color) in the radius–height cross-section of radial velocity (m s−1) for (a) CTL and (b) MM5 at 54 h. (c) and (d) as in (a) and (b), respectively, but for tangential velocity (m s−1). (e) and (f) as in (a) and (b), respectively, but for vertical velocity (m s−1). (g) and (h) as in (a) and (b), respectively, but for latent heating rate (K h−1). The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
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Figure 12. Radius–height cross-sections of azimuthal-mean angular momentum (AAM) (shaded color, 106 m2 s−1) for (a) CTL and (b) MM5 at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
Figure 12. Radius–height cross-sections of azimuthal-mean angular momentum (AAM) (shaded color, 106 m2 s−1) for (a) CTL and (b) MM5 at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
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Figure 13. Radius–height cross-section of azimuthal-mean AM budget terms (shaded color, m2 s−2), including (a) radial advection of mean AM, (b) radial advection of eddy AM, (c) vertical advection of mean AM, (d) vertical advection of eddy AM, (e) mean Coriolis force term, and (f) sum of all AM budget terms for CTL at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
Figure 13. Radius–height cross-section of azimuthal-mean AM budget terms (shaded color, m2 s−2), including (a) radial advection of mean AM, (b) radial advection of eddy AM, (c) vertical advection of mean AM, (d) vertical advection of eddy AM, (e) mean Coriolis force term, and (f) sum of all AM budget terms for CTL at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
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Figure 14. As in Figure 13, but for MM5 including (a) radial advection of mean AM, (b) radial advection of eddy AM, (c) vertical advection of mean AM, (d) vertical advection of eddy AM, (e) mean Coriolis force term, and (f) sum of all AM budget terms for CTL at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
Figure 14. As in Figure 13, but for MM5 including (a) radial advection of mean AM, (b) radial advection of eddy AM, (c) vertical advection of mean AM, (d) vertical advection of eddy AM, (e) mean Coriolis force term, and (f) sum of all AM budget terms for CTL at 54 h. The green line represents the RMW. The reference vector in the lower right corner represents the radial and vertical wind components.
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Figure 15. Azimuthal-mean radial velocity (shaded colors, m s−1) at 54 h from the Sawyer–Eliassen (SE) solution with total forcing sources for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but with symmetric diabatic heating only. (e) and (f) as in (a) and (b), respectively, but with asymmetric eddy momentum and heating only. (g) and (h) as in (a) and (b), respectively, but with turbulent momentum diffusion only. (i) and (j) as in (a) and (b), respectively, but with residual terms only. The wind vectors (m s−1) induced by the total forcing sources overlapped in each panel indicate the radial and vertical wind components (m s−1) with their reference vectors given at the lower right corner.
Figure 15. Azimuthal-mean radial velocity (shaded colors, m s−1) at 54 h from the Sawyer–Eliassen (SE) solution with total forcing sources for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but with symmetric diabatic heating only. (e) and (f) as in (a) and (b), respectively, but with asymmetric eddy momentum and heating only. (g) and (h) as in (a) and (b), respectively, but with turbulent momentum diffusion only. (i) and (j) as in (a) and (b), respectively, but with residual terms only. The wind vectors (m s−1) induced by the total forcing sources overlapped in each panel indicate the radial and vertical wind components (m s−1) with their reference vectors given at the lower right corner.
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Figure 16. Azimuthal-mean vertical velocity (shaded colors, m s−1) at 54 h from the Sawyer–Eliassen (SE) solution with total forcing sources for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but with symmetric diabatic heating only. (e) and (f) as in (a) and (b), respectively, but with asymmetric eddy momentum and heating only. (g) and (h) as in (a) and (b), respectively, but with residual terms only. The wind vectors (m s−1) induced by the total forcing sources overlapped in each panel indicate the radial and vertical wind components (m s−1) with their reference vectors given at the lower right corner.
Figure 16. Azimuthal-mean vertical velocity (shaded colors, m s−1) at 54 h from the Sawyer–Eliassen (SE) solution with total forcing sources for (a) CTL and (b) MM5. (c) and (d) as in (a) and (b), respectively, but with symmetric diabatic heating only. (e) and (f) as in (a) and (b), respectively, but with asymmetric eddy momentum and heating only. (g) and (h) as in (a) and (b), respectively, but with residual terms only. The wind vectors (m s−1) induced by the total forcing sources overlapped in each panel indicate the radial and vertical wind components (m s−1) with their reference vectors given at the lower right corner.
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Table 1. The physics schemes used for the three experiments.
Table 1. The physics schemes used for the three experiments.
Physics SchemesSchemes
CTLMM5MYNN
Surface layer physics schemeMOMM5MYNN
Microphysics parameterization schemeLin
Cumulus parameterization schemeKain–Fritsch
Planetary Boundary-Layer parameterizationsMYNN
Shortwave schemeDudhia
Longwave schemeRRTM
Table 2. Assessment statistics of simulated maximum 10-m wind speed for Typhoon Rai from 0000 UTC 15 December (24 h) to 0600 UTC 16 December (54 h) by comparing to JMA. (R: correlation coefficient; BIAS: bias; and RMSE: root mean square error).
Table 2. Assessment statistics of simulated maximum 10-m wind speed for Typhoon Rai from 0000 UTC 15 December (24 h) to 0600 UTC 16 December (54 h) by comparing to JMA. (R: correlation coefficient; BIAS: bias; and RMSE: root mean square error).
ExperimentsRBIAS (m s−1)RMSE (m s−1)
CTL0.995−0.4120.849
MM50.930−4.2705.378
MYNN0.932−5.3595.745
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Hoang, T.-H.; Huang, C.-Y.; Nguyen, T.-C. Effects of Surface Layer Physics Schemes on the Simulated Intensity and Structure of Typhoon Rai (2021). Atmosphere 2024, 15, 1140. https://doi.org/10.3390/atmos15091140

AMA Style

Hoang T-H, Huang C-Y, Nguyen T-C. Effects of Surface Layer Physics Schemes on the Simulated Intensity and Structure of Typhoon Rai (2021). Atmosphere. 2024; 15(9):1140. https://doi.org/10.3390/atmos15091140

Chicago/Turabian Style

Hoang, Thi-Huyen, Ching-Yuang Huang, and Thi-Chinh Nguyen. 2024. "Effects of Surface Layer Physics Schemes on the Simulated Intensity and Structure of Typhoon Rai (2021)" Atmosphere 15, no. 9: 1140. https://doi.org/10.3390/atmos15091140

APA Style

Hoang, T. -H., Huang, C. -Y., & Nguyen, T. -C. (2024). Effects of Surface Layer Physics Schemes on the Simulated Intensity and Structure of Typhoon Rai (2021). Atmosphere, 15(9), 1140. https://doi.org/10.3390/atmos15091140

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