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  • Zou, Z., J. Song, P. Li, J. Huang, J. A. Zhang, Z. Wan, and S. Li, 2019: Effects of swell waves on atmospheric boundary layer turbulence: A low wind field study. J. Geophys. Res. Oceans, 124, 56715685, https://doi.org/10.1029/2019JC015153.

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  • Zweers, N. C., V. K. Makin, J. W. de Vries, and G. Burgers, 2010: A sea drag relation for hurricane wind speeds. Geophys. Res. Lett., 37, L21811, https://doi.org/10.1029/2010GL045002.

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  • View in gallery

    Model domain and topography. The black line represents the coastline.

  • View in gallery

    Typhoon paths of the 10 numerical experiments and observations for (a) Typhoon Nida and (b) Typhoon Haima. The region selected for Cd, wind stress, latent heat flux, SST, mixed layer depth, and vertical velocity analysis is marked with a blue box for each typhoon process.

  • View in gallery

    Minimum sea level pressure of the 10 numerical experiments and observation for (a) Typhoon Nida and (b) Typhoon Haima.

  • View in gallery

    Maximum wind speed of the 10 numerical experiments and observation for (a) Typhoon Nida and (b) Typhoon Haima.

  • View in gallery

    Temporal variation of Cdn, wind stress, latent heat flux, and wind speed, averaged over the selected region (marked with a blue box in Fig. 2 for each typhoon) during Typhoons (a),(c),(e),(g) Nida and (b),(d),(f),(h) Haima.

  • View in gallery

    Temporal variation of SST and oceanic mixed layer depth, averaged over the selected region (marked with a blue box in Fig. 2 for each typhoon).

  • View in gallery

    Temporal variation in profiles of vertical velocity during Typhoon Nida averaged over the selected region (marked with a blue box in Fig. 2a).

  • View in gallery

    Temporal variation in profiles of vertical velocity during Typhoon Haima averaged over the selected region (marked with a blue box in Fig. 2b).

  • View in gallery

    Distributions of 1000 × Cdn at hour 51 (1400 UTC 20 Oct 2016) from the start of the simulation for Typhoon Haima.

  • View in gallery

    Observed and simulated wind field at 10 m height above mean sea level at hour 51 (1400 UTC 20 Oct 2016) from the start of the simulation for Typhoon Haima.

  • View in gallery

    Positions at which the value of Cdn was analyzed. The black circles denote the positions where the maximum wind speed (see Fig. 4b) occurred when the Typhoon Haima stayed over the sea area during the five simulations.

  • View in gallery

    Variation in Cdn with wind speed in the five numerical experiments. The data were collected at the positions shown in Fig. 11 during the entire simulation of Typhoon Haima.

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Effect of Drag Coefficient Parameterizations on Air–Sea Coupled Simulations: A Case Study for Typhoons Haima and Nida in 2016

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  • 1 a CAS Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China
  • | 2 b First Institute of Oceanography, and Key Laboratory of Marine Science and Numerical Modeling, Ministry of Natural Resources, Qingdao, China
  • | 3 c Laboratory for Ocean Dynamics and Climate, Pilot National Laboratory for Marine Science and Technology, Qingdao, China
  • | 4 d Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology, Qingdao, China
  • | 5 e Center for Ocean Mega-Science, Chinese Academy of Sciences, Qingdao, China
  • | 6 f University of Chinese Academy of Sciences, Beijing, China
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Abstract

Reasonable parameterization of air–sea momentum flux is important for the accuracy of ocean and atmosphere simulations, and in the numerical model, the parameterization of the air–sea momentum flux becomes a problem of parameterization of the sea surface wind stress drag coefficient (Cd). In this study, five kinds of typical Cd parameterization methods were assessed in the simulation of two typhoon cases, one of which was a supertyphoon and another was a common severe typhoon, based on an atmosphere–wave–ocean coupled model. Based on the two case studies, it was found that the typhoon path and minimum sea level pressure were not very sensitive to Cd parameterizations, though the spatial distribution of Cd and its variation with wind speed were all very different across the parameterization methods. However, Cd has a significant effect on the wind speed, and at high wind speed, the simulated maximum wind speed compared better with the observation in the experiment that adopted the Cd calculation method considering the effects of sea spray. Also, Cd plays an important role in the feedback processes between atmosphere and ocean during the typhoon process, through its effect on the air–sea heat and momentum flux, SST, ocean mixed layer depth, ocean currents, etc. The results of this study answered the question of how the Cd affects the atmosphere and ocean during the typhoon process, and to what extent they are affected, which can help to explain or even further improve the simulation results.

Denotes content that is immediately available upon publication as open access.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Junchuan Sun, sunjunchuan@fio.org.cn

Abstract

Reasonable parameterization of air–sea momentum flux is important for the accuracy of ocean and atmosphere simulations, and in the numerical model, the parameterization of the air–sea momentum flux becomes a problem of parameterization of the sea surface wind stress drag coefficient (Cd). In this study, five kinds of typical Cd parameterization methods were assessed in the simulation of two typhoon cases, one of which was a supertyphoon and another was a common severe typhoon, based on an atmosphere–wave–ocean coupled model. Based on the two case studies, it was found that the typhoon path and minimum sea level pressure were not very sensitive to Cd parameterizations, though the spatial distribution of Cd and its variation with wind speed were all very different across the parameterization methods. However, Cd has a significant effect on the wind speed, and at high wind speed, the simulated maximum wind speed compared better with the observation in the experiment that adopted the Cd calculation method considering the effects of sea spray. Also, Cd plays an important role in the feedback processes between atmosphere and ocean during the typhoon process, through its effect on the air–sea heat and momentum flux, SST, ocean mixed layer depth, ocean currents, etc. The results of this study answered the question of how the Cd affects the atmosphere and ocean during the typhoon process, and to what extent they are affected, which can help to explain or even further improve the simulation results.

Denotes content that is immediately available upon publication as open access.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Junchuan Sun, sunjunchuan@fio.org.cn

1. Introduction

Air–sea momentum flux is an important process at the air–sea interface. Generally, the momentum flux from the air includes the direct flux to waves and the direct flux to currents (via surface viscous stress), while the flux into currents includes the flux from waves (via wave dissipation) and the direct flux from the wind (Fan et al. 2010; Wu et al. 2019). The momentum flux from the air (wind stress) is usually calculated by the bulk formula (Liu et al. 2012), as presented in Eq. (1):
τ=ρU*2=ρCdU102,
where τ is wind stress, ρ is the air density, U* is the friction velocity, U10 is the wind speed at the height of 10 m, and Cd is the wind stress drag coefficient, which has a dependence on the surface stability and roughness length prescribed by Monin–Obukhov similarity theory (Fairall et al. 1996; Grachev et al. 1998, 2011):
Cd1/2=Cdn1/2[1Cdn1/2kΨ];Cdn=κ2[ln(10z0)]2,
where Ψ is the function representing the stability, n refers to neutral stability, and under neutral atmospheric conditions Ψ equals 0; κ which is von Kármán’s constant equals 0.4, and z0 is the sea surface roughness. Then the parameterization of the air–sea momentum flux (wind stress) becomes a problem of the parameterization of Cd or z0 (when Ψ equals 0). More details about Eq. (2) can also be found in Fairall et al. (2003).

Reasonable parameterization of the wind stress is of great importance for the accurate predictions of oceanic and atmospheric processes. Rossby and Montgomery (1935) determined Cd to be a constant of 0.0013 using observations made in Germany. However, Deacon and Webb (1962) found that Cd is dependent on wind speed when analyzing the observed data. Later observations also found that Cd is not only related to wind speed but also to the state of the sea surface waves (Donelan 1990; Drennan et al. 2003; Johnson et al. 1998; Kitaigorodskii and Volkov 1965; Larsén et al. 2003; Toba et al. 1990).

The work mentioned above was carried out under low and medium wind speeds, and the Cd increases when the wind speed increases. However, Alamaro (2001), and Alamaro et al. (2002) showed that the Cd decreases with increasing wind speed when the wind speed is greater than 25 m s−1. Powell et al. (2003) also found that Cd decreased with increasing wind speed when the wind speed reached a certain value (>33 m s−1) after analyzing the wind profiles measured by the global positioning system sondes under typhoon conditions, whereas in the study by Donelan et al. (2004), Cd reached a saturation value (approximately 0.0025) at a high wind speed (>33 m s−1) and no longer increased with increasing wind speed. Recently, Curcic and Haus (2020) updated the saturation value of Cd to 0.0026 at a moderate wind speed of >25 m s−1. The value of Cd was also affected by the water depth, as the Cd near the shore is different from that in the deep sea (Gao et al. 2009; Zachry et al. 2013; Zhao et al. 2015).

For the parameterization of sea surface roughness, Charnock (1955) suggested the famous Charnock relation:
gz0U*2=α,
where g is the gravitational constant, α is the Charnock parameter, which was assumed to initially be constant, and each Charnock constant corresponds to a formula for calculating z0 or Cdn, which is linearly dependent on wind speed (Charnock 1958; Wu 1980). However, it has been recognized that α should be a parameter related to the sea state.

Many scholars have given different Charnock parameters based on laboratory experiments or observational data, some of which are related to the wave age (Donelan 1990; Drennan et al. 2005; Oost et al. 2002; Stewart 1974; Toba et al. 1990), some are dependent on the wave steepness (Guan and Xie 2004; Taylor and Yelland 2001), and some studies also considered the effects of sea spray when calculating the sea surface roughness (Liu et al. 2012). Despite many years of studies, the accuracy of the parameterization methods of Cd still cannot be guaranteed, and the uncertainty of this coefficient is roughly a factor of 2 when it is calculated by different methods under the same wind conditions (Oost et al. 2002). So how does the Cd affects the atmosphere and ocean during the typhoon process? To what extent can the results be affected when adopting different parameterization methods of Cd in the simulation? It is necessary to study the sensitivity of the simulation results to these parameterization methods.

Studies have investigated the effect of Cd parameterizations on the simulation results. These studies show that the parameterization methods of Cd or z0 can affect some of the simulation results (Feng et al. 2016; Moon et al. 2008; Pineau-Guillou et al. 2018). However, these studies mainly used the atmosphere, ocean, or wave model alone (Li et al. 2016; Moon et al. 2008; Thomsen et al. 2014) or the atmosphere–wave (Doyle 2002; Pineau-Guillou et al. 2018; Varlas et al. 2018) and ocean–wave partially coupled model (Drews 2013; Feng et al. 2016; Kim et al. 2015; Staneva et al. 2017), which were unable to determine the feedbacks between the atmosphere and ocean caused by the different parameterizations of Cd or z0.

Full atmosphere–wave–ocean coupling has been established in recent years and has been used to study ocean–wave interactions under tropical conditions (Smith et al. 2013), the wave state in the Caspian Sea (Bruneau and Toumi 2016), and the outbreak of extreme cold air over the Adriatic Sea (Ricchi et al. 2016). However, the studies mentioned above adopted only one type of Cd and were unable to discuss the sensitivity of the simulation results to the air–sea momentum flux parameterizations. Guan et al. (2012) studied the effect of surface roughness parameterization methods on the simulated typhoon path and intensity based on a full atmosphere–wave–ocean coupled model, but the ocean responses were not discussed. Therefore, it is necessary to use the state-of-the-art atmosphere–wave–ocean coupled model to investigate the effects of Cd on the simulation results of the atmosphere and ocean simultaneously.

The objective of this study is to investigate how the Cd affects the atmosphere and ocean during the typhoon process, and to what extent they are affected, which can help to explain or even further improve the simulation results. Using the atmosphere–wave–ocean coupled model, Typhoons Nida and Haima, which occurred in 2016, were simulated in several numerical experiments, in which a total of five kinds of typical Cd parameterization methods were assessed. To the best of our knowledge, this work is the first study that adopted the fully coupled ocean–atmosphere–wave model over the South China Sea to investigate the effect of Cd parameterizations on the TC track, intensity, and air–sea feedbacks. Moreover, the characteristics of Cd calculated by different methods during the simulation were also discussed. The rest of the paper is organized as follows. A description of the coupled model, model setup, and design of the numerical experiments are provided in section 2. In section 3, analysis on the effect of Cd on the simulation results are presented. A discussion on the results is provided in section 4, and the main findings are summarized in section 5.

2. Materials and methods

The effect of the air–sea momentum flux parameterization methods on the simulation results of the atmosphere and ocean was studied based on the atmosphere–wave–ocean coupled model, and a total of five kinds of air–sea momentum flux parameterization methods were used in the design of the numerical experiments. The atmosphere–wave–ocean coupled model, the design of the experiments and the typhoon processes that were simulated in this study will be introduced in this section.

a. Atmosphere–wave–ocean coupled model

The atmosphere–wave–ocean coupled model used in this study is the Coupled Ocean–Atmosphere–Wave Sediment Transport (COAWST) (version 3.1) model system, which was developed by Warner et al. (2008, 2010). The COAWST model system comprises four components (ocean, atmosphere, wave, and sediment transport components), and in this study, only the atmosphere model, the wave model, and the ocean model components were used.

1) Atmosphere model

The Advanced Weather Research and Forecasting (WRF; Skamarock et al. 2005) Model, version 3.6, was adopted as the atmospheric component in COAWST. The WRF Model is a nonhydrostatic, quasi-compressible atmospheric model that uses an Arakawa-C horizontal grid and a sigma-pressure vertical coordinate grid. In this study, the model domain (Fig. 1) ranges from 15°S to 45°N in latitude and from 99° to 135°E in longitude, with a horizontal resolution of 1/12° × 1/12° and 31 sigma levels in the vertical direction. The lateral open boundaries and initial conditions are derived from NCEP Final Operational Global Analysis data (FNL) with a 0.25° × 0.25° resolution and 6-h interval.

Fig. 1.
Fig. 1.

Model domain and topography. The black line represents the coastline.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Physical parameterization methods for subgrid-scale processes, including planetary boundary layer, surface layer, longwave and shortwave radiation, and so on that were adopted in this study are listed in Table 1. Notably, the Eta similarity scheme for surface layer is adopted to allow for increased bottom roughness of the atmosphere over the ocean. Correspondingly, the Mellor–Yamada–Janjić scheme (MYJ) is selected for the planetary boundary layer scheme.

Table 1.

Physical parameterizations used in the WRF Model.

Table 1.

2) Wave model

The Simulating Waves Nearshore (SWAN) model was adopted as the wave component in the COAWST model. SWAN is a third-generation spectral wave model designed for shallow water areas (Booij et al. 1999). In this study, the grid of SWAN is the same as that of WRF. The bathymetry of the SWAN model is from the ETOPO1 dataset, which is provided by the National Geophysical Data Center (NGDC). The wave spectrum was resolved between 0.042 and 0.42 Hz in frequency and from 0° to 360° in angle at angular increments of 15°. For the boundary condition, the JONSWAP spectrum (Hasselmann et al. 1973) is used, and the initial condition is zero.

3) Ocean model

The Regional Ocean Modeling System (ROMS) model was adopted as the ocean component in the COAWST model. ROMS is a free-surface, three-dimensional, terrain-following, primitive equation ocean model (Haidvogel et al. 2000), which has been widely used for a diverse range of applications (Marchesiello et al. 2003; Yang et al. 2018). In this study, ROMS uses the same horizontal grid and bathymetry as SWAN, with 30 s-coordinate layers in the vertical. The vertical coordinate transformation equation is 2, and the stretching function is 4. The vertical s-coordinate parameters are set as follows: theta_s = 7.0, theta_b = 0.4 (theta_s and theta_b are the surface and bottom control parameters in the vertical stretching function), and tcline = 10 m (width of the surface or bottom boundary layer in which a higher vertical resolution is required during stretching). The initial condition and lateral open boundaries are obtained from the hindcast simulation described in Sun et al. (2019). For the lateral boundary conditions used in the ROMS, the Chapman boundary condition (Chapman 1985) is used for free surface. The Flather boundary condition (Flather 1976) is adopted for the 2D momentum. The radiation and nudging boundary conditions (Marchesiello et al. 2001) are selected for the 3D momentum and tracers. In this study, the tide influence is not considered in the ROMS model.

b. Experiments

To study the effect of air–sea momentum flux parameterization methods on the simulation results of the atmosphere and ocean, several numerical experiments were designed based on the atmosphere–wave–ocean coupled model. Each experiment adopted one kind of air–sea momentum flux parameterization method. In the COAWST model system, there are three schemes available to allow for the exchange of wave data to WRF for use in the Eta similarity scheme for surface layer, which allows for an increased bottom roughness of the atmosphere over the ocean, including the methods of Taylor and Yelland (2001), Drennan et al. (2005), and Oost et al. (2002). For the method of Taylor and Yelland (2001), the sea surface roughness was calculated by the wave height and wave steepness, for the method of Drennan et al. (2005), the sea surface roughness was predicted by the wave height and wave age, and for the method of Oost et al. (2002), wavelength and wave age were used to calculate the sea surface roughness. In this study, we added the parameterization method of Liu et al. (2012), which not only considers the effect of the wave age but also the sea spray on the sea surface roughness.

Finally, 10 numerical experiments were designed to investigate the effect of the air–sea momentum flux parameterization methods on the simulation during the typhoon process. Relevant details of the 10 experiments are listed in Table 2, where z0 is the sea surface roughness, u* is the friction velocity, g is the gravitational constant, Hs is the significant wave height, Cp and Lp is the phase speed and wavelength of the spectral peak, β* is defined as Cp/u*, and ω is calculated by the following equation:
ω=min(1,acr/κu*),
in which acr is the critical terminal fall velocity of spray droplets and was estimated as 0.64 m s−1, and κ = 0.4 is the von Kármán constant.
Table 2.

Design of experiments.

Table 2.

In the WRF–ROMS and WRF experiments, the default method of calculating the sea surface roughness was used, which does not explicitly consider the wave effect. Experiment WRF–ROMS means the typhoon would be simulated by the coupled WRF and ROMS model. In WRF–ROMS–SWAN experiments 1 to 4, the typhoon would be simulated by the atmosphere–wave–ocean coupled model with the different air–sea momentum flux parameterization methods mentioned above, while In WRF–SWAN experiments 1 to 4, the typhoon would be simulated by the atmosphere–wave coupled model.

In this study, the momentum flux into the ocean currents was set as equal to the flux from the air during the simulation; that is, the wind stress of the ocean model and the bottom stress of the atmosphere model were consistent in the parameterizations. The wave model was forced by the wind speed from the atmosphere model, and the wave results were adopted in the calculation of the sea surface roughness in WRF–ROMS–SWAN experiments 1 to 4 and WRF–SWAN experiments 1 to 4. For the coupled simulations, the sea surface temperature (SST) in the WRF Model was updated from ROMS model, while for the SST data used in WRF stand-alone, they were derived from the 9 km microwave and infrared optimally interpolated (MW_IR OI) sea surface temperature daily products (http://data.remss.com/SST/daily_v04.0/mw_ir/), which was interpolated to the WRF grid with 6-h interval.

c. Typhoon cases

Typhoons Nida and Haima, which occurred in 2016 were chosen as the study cases and were simulated in the 10 numerical experiments listed in Table 2. Typhoon Nida formed on 30 July over the sea area east of Philippines, and made landfall over Guangzhou City, China, on 2 August. While for Typhoon Haima, it formed over the sea area southeast of Philippines on 15 October, reaching category 5 on the Saffir–Simpson hurricane wind scale during the typhoon life, and made landfall over Shanwei City, China, on 21 October. For the two selected typhoon cases, one was a super typhoon (Haima), and the other one was a common severe typhoon (Nida), which can help to make a more comprehensive analysis about the Cd effect on the atmosphere and ocean. The information on the typhoon path and strength was obtained from the Joint Typhoon Warning Center (JTWC) best track dataset of the tropical cyclones in the western North Pacific.

During the simulations of different experiments, the models were initialized at 1200 UTC 31 July 2016 for Typhoon Nida and at 1200 UTC 18 October 2016 for Typhoon Haima. All of these models were run for 3 days. For the coupled model, the time interval for the data to be transferred between different models was specified as the same value of 600 s.

3. Results

a. Typhoon path

The simulated typhoon paths from the 10 numerical experiments and the observed paths are shown in Fig. 2. It can be seen that the typhoon paths of the 10 experiments agreed well with the observations for both the two typhoon cases during the simulation periods, and the simulated typhoon paths were very close to each other, which means that the typhoon path is not very sensitive to the sea surface roughness parameterization methods. Besides, the simulated start and end positions of the typhoon were also very similar in the 10 experiments for both typhoon cases. This may indicate that, the translation speed of the typhoon is also not sensitive to the sea surface roughness parameterization.

Fig. 2.
Fig. 2.

Typhoon paths of the 10 numerical experiments and observations for (a) Typhoon Nida and (b) Typhoon Haima. The region selected for Cd, wind stress, latent heat flux, SST, mixed layer depth, and vertical velocity analysis is marked with a blue box for each typhoon process.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

b. Typhoon intensity and strength

The simulated minimum sea level pressure and maximum wind speed were also compared with the observations, and the results are shown in Figs. 3 and 4 . Figure 3 shows that, the simulated typhoon intensities were weaker in the atmosphere–ocean and atmosphere–wave–ocean coupled model than that in the atmosphere alone or atmosphere–wave coupled model (Fig. 3). This is because the variation of SST was considered in the atmosphere–ocean and atmosphere–wave–ocean coupled model. As the typhoon passed by, significant cold wake could occur along the typhoon path (Mrvaljevic et al. 2013), and such cold wake can have a negative feedback on typhoon intensification. Take the typhoon process of Haima as an example, at hour 38 of the simulation, the typhoon enters the South China Sea (Fig. 2b), then the difference of the simulated minimum sea level pressure among the 10 experiments became more significant (Fig. 3b), and the results of experiments considering the variation of SST agreed better with the observation, while the other experiments underestimate the rising of the sea level pressure. As for the Typhoon Nida, the simulation results also showed that the typhoon intensity can be greatly affected by the cold wake (Fig. 3a), though the improvement of the simulated minimum sea level pressure through atmosphere–ocean coupling were not as obvious as that for the Typhoon Haima. But, overall, it can be indicated that, considering the variation of SST through atmosphere–ocean coupling was more reasonable in the physical mechanism and can probably improve the simulation results. So, in the following analysis, we focused on the simulation results of the experiments including atmosphere–ocean coupling.

Fig. 3.
Fig. 3.

Minimum sea level pressure of the 10 numerical experiments and observation for (a) Typhoon Nida and (b) Typhoon Haima.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Fig. 4.
Fig. 4.

Maximum wind speed of the 10 numerical experiments and observation for (a) Typhoon Nida and (b) Typhoon Haima.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

For the convenience of further analyzing the performances of different experiments, we define the following expression:
ΔP=1010Pc.
Here, Pc is the central minimum sea level pressure, and ΔP is the difference between the peripheral pressure (assumed as 1010 hPa) and minimum sea level pressure, representing the intensity of the typhoon. Then the mean relative difference of the simulated ΔP was calculated according to Eq. (6):
MRD=i=1n(maximinimini)/n×100%.

Here, MRD means the mean relative difference, and maxi (mini) represents the simulated maximum (minimum) value of ΔP or maximum wind speed between the experiments of WRF–ROMS and WRF–ROMS–SWAN 1–4 at time i. The results show that the MRD of the simulated ∆P were 7.5% and 6.7% for Typhoons Nida and Haima, respectively. This low value of MRD of the simulated ∆P means that the effect of the sea surface roughness parameterization on the simulated central minimum sea level pressure may not be significant.

Figure 4 shows that the main trends in the maximum wind speed during the two typhoon processes were successfully simulated by the numerical experiments. The MRD of the simulated maximum wind speed were also calculated according to Eq. (6), and the results show that the MRD of the simulated maximum wind speed were 13.3% and 19.5% for Typhoons Nida and Haima, respectively, obviously larger than the MRD of the simulated ΔP, indicating that the sea surface roughness parameterization method can significantly affect the simulated maximum wind speed. Figure 4 also shows that, at high wind speed, the simulated maximum wind speed was better in the experiment that adopted the Cd calculation method considering the effect of sea spray (experiment WRF–ROMS–SWAN 4), and this phenomenon was especially significant during Typhoon Haima (Fig. 4b). This phenomenon is supposed to be associated with the momentum and heat fluxes, and the explanations in detail are provided in the following section.

c. Feedback processes between atmosphere and ocean

As mentioned above, SST is a critical factor for typhoon intensity, and the study of Warner et al. (2010) also indicated that the minimum sea level pressure is extremely sensitive to sea surface temperature during hurricane process. In fact, SST affects the sea level pressure mainly through its effect on the heat flux, because the typhoon gains energy from the ocean mainly from the latent heat (Malkus and Riehl 1960). So, in this section, we analyzed the effect of the Cd on the momentum and latent heat fluxes, oceanic mixed layer depth and also the ocean vertical velocity which are all associated with the change of SST. The regions selected for analysis were marked with a blue box for each typhoon process (Fig. 2). The area of the blue box generally corresponds to the area where the typhoon reached its peak intensity. In this section, Cdn which is directly determined by z0 was used to indicate the variation of Cd, because the main differences between the experiments are the calculation methods of z0.

The temporal variation of Cdn, wind stress, latent heat flux and wind speed, averaged over the selected region during the two typhoon processes are shown in Fig. 5. It can be seen that the latent heat flux (Figs. 5e,f) corresponded well with the wind stress (Figs. 5c,d), and not with the wind speed (Figs. 5g,h). But in fact, the latent heat fluxes are directly dependent on surface wind speed and the sea–air humidity difference (Liu et al. 1979). One possible explanation for this result is that the wind stress parameterization can affect both the wind speed and sea–air humidity difference in the atmosphere–ocean coupled simulations, thus the simulation results showed that the greater the wind stress, the more latent heat flux from the ocean to the atmosphere, thus contributes to the increase of typhoon intensity. But from another point of view, the greater the wind stress, the more kinetic energy dissipate from the atmosphere to the ocean, thus weakens typhoon intensity, because the wind stress of the ocean corresponds to the bottom stress of the atmosphere. These are two opposite feedbacks for the wind stress (momentum flux) to affect the typhoon intensity. The relative importance of these two feedback functions is difficult to be determined, and may be different during different typhoon processes.

Fig. 5.
Fig. 5.

Temporal variation of Cdn, wind stress, latent heat flux, and wind speed, averaged over the selected region (marked with a blue box in Fig. 2 for each typhoon) during Typhoons (a),(c),(e),(g) Nida and (b),(d),(f),(h) Haima.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

For example, from Figs. 3a, 5c, and 5e we can find that, when Typhoon Nida passed the selected area (in Fig. 2a), the wind stress in experiment WRF–SWAN–ROMS3 was larger than other experiments, more latent heat was gained by the atmosphere, and the minimum sea level pressure was lower than other experiments. While when Typhoon Haima passed the selected area (in Fig. 2b), the minimum sea level pressure in experiment WRF–ROMS–SWAN3 was higher than other experiments (see Fig. 3b), though its latent heat flux was the largest among the experiments (see Figs. 5d,f), a possible reason may be the higher wind stress dissipated more kinetic energy from the atmosphere in experiment WRF–ROMS–SWAN3.

Generally, the lower minimum sea level pressure corresponds to higher maximum wind speed during the typhoon process (Atkinson and Holliday 1977), but when comparing the minimum sea level pressure and maximum speed between different experiments, we can find that such relationship may be affected by the difference of Cd. For example, during the first 20 simulation hours of Typhoon Haima, the maximum wind speed in experiment WRF–ROMS–SWAN4 was significantly larger than that in other experiments (Fig. 4b), though the corresponding minimum sea level pressure was not the lowest (Fig. 3b). This is due to the smaller Cd in experiment WRF–ROMS–SWAN4, which might be caused by the effect of sea spray at high wind speeds. As shown in Fig. 5b, there was a significant decrease of the Cd [smaller Cdn indicates smaller Cd according to Eq. (2)] in experiment WRF–ROMS–SWAN4, when Typhoon Haima passed by the analysis area, causing lower wind stress (Fig. 5d) compared with other experiments. The parameterization method of sea surface roughness in experiment WRF–ROMS–SWAN4 achieved better maximum wind speed at high wind speed among the coupled experiments, especially during Typhoon Haima.

The simulation results of the oceanic responses including the temporal variation of SST and oceanic mixed layer depth (at which the temperature was lower by 0.5°C than SST), averaged over the selected region for the two typhoon processes, are shown in Fig. 6; also, the temporal variation in profiles of area averaged vertical velocity are provided in Figs. 7 and 8 for Typhoons Nida and Haima, respectively. The results show that, when the typhoon passed by the selected area, stronger wind stress corresponded to more SST decrease, deeper mixed layer depth, and larger vertical velocity, during both the two typhoon processes. This implied that these oceanic responses may be determined mainly by the wind stress (momentum flux). This phenomenon was not difficult to understand, because stronger wind stress (momentum flux) induce stronger ocean buoyance flux, turbulent mixing, thus makes more SST decrease and deeper mixed layer depth. Besides, as Figs. 7 and 8 show, stronger wind stress could induce stronger near inertial current, and also stronger upwelling that take more cold water to cool the mixed layer.

Fig. 6.
Fig. 6.

Temporal variation of SST and oceanic mixed layer depth, averaged over the selected region (marked with a blue box in Fig. 2 for each typhoon).

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Fig. 7.
Fig. 7.

Temporal variation in profiles of vertical velocity during Typhoon Nida averaged over the selected region (marked with a blue box in Fig. 2a).

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Fig. 8.
Fig. 8.

Temporal variation in profiles of vertical velocity during Typhoon Haima averaged over the selected region (marked with a blue box in Fig. 2b).

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Then, from the analysis above, we can conclude that the feedbacks between the atmosphere and ocean during typhoon process can greatly influence the typhoon intensity and ocean response, and Cd can affect these feedbacks significantly through its effect on the air–sea momentum and heat flux, SST, ocean mixed layer depth, ocean currents, etc. So the accurate calculation of the Cd was very important in the numerical simulations.

d. Horizontal distribution of Cd and wind field

As indicated by the study of Lee and Chen (2012), the horizontal distribution of Cd may affect the structure of the wind field. Also, according to Table 2, in experiment WRF–ROMS, the z0 is determined by the wind speed; then the spatial distribution of Cd is similar to that of the wind speed, while for experiments WRF–ROMS–SWAN 1 to 4, the spatial distribution of Cd is also affected by the wave field. Then the spatial distributions of Cd between the experiments of WRF–ROMS and WRF–ROMS–SWAN 1 to 4 were supposed to be very different. So the character of the horizontal distribution of Cd and its effect on the wind structure were investigated in this section. Same as section 3c, we used Cdn to indicate the horizontal distribution character of Cd.

To validate the simulated wind field, we searched the Advanced Scatterometer (ASCAT) satellite dataset which are produced by Remote Sensing Systems and sponsored by the NASA Ocean Vector Winds Science Team (Ricciardulli and Wentz 2016), and found that the wind field contains a complete structure of Typhoon Haima which was observed at about 1400 UTC 20 October 2016 in our study area. So the horizontal distribution of the simulated Cdn and wind field were analyzed at this time, and were provided in Figs. 9 and 10 . It can be seen from Fig. 9 that the spatial distributions of Cd in the different experiments were very different, and the value of Cdn around the typhoon center is significantly larger in experiment WRF–ROMS–SWAN3 than that in other experiments, but the corresponding wind speed is significantly lower than the observation (Fig. 10), indicating the sea surface roughness parameterization method in WRF–ROMS–SWAN3 may not be a good choice. Figure 10 also shows that the wind speed in experiment WRF–ROMS–SWAN4 is also less than the observation, though the maximum wind speed in experiment WRF–ROMS–SWAN4 was better than other experiments at high wind speed (Fig. 3). This means the applicability of the sea surface roughness parameterization method in WRF–ROMS–SWAN4 is still limited.

Fig. 9.
Fig. 9.

Distributions of 1000 × Cdn at hour 51 (1400 UTC 20 Oct 2016) from the start of the simulation for Typhoon Haima.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Fig. 10.
Fig. 10.

Observed and simulated wind field at 10 m height above mean sea level at hour 51 (1400 UTC 20 Oct 2016) from the start of the simulation for Typhoon Haima.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

e. Wind stress drag coefficients

The difference in the simulation results between experiments WRF–ROMS and WRF–ROMS–SWAN 1 to 4 was mainly caused by the different sea surface roughness (or wind stress drag coefficient) parameterization methods. Therefore, this section focuses on the characteristics of Cdn calculated by different parameterization methods. As Typhoon Haima is a super typhoon, so the simulation results of this typhoon process were adopted for analysis. The value of Cdn was collected at the positions where the maximum wind speed (that was provided in Fig. 4) occurred when the typhoon stayed over the sea area during the five numerical simulations, and these positions are shown in Fig. 11, which can ensure that the Cdn under the maximum wind speed can be analyzed.

Fig. 11.
Fig. 11.

Positions at which the value of Cdn was analyzed. The black circles denote the positions where the maximum wind speed (see Fig. 4b) occurred when the Typhoon Haima stayed over the sea area during the five simulations.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

Figure 12 provides the variation in Cdn with the wind speed in the five numerical experiments. As the sea surface roughness parameterization methods in experiment WRF–ROMS did not consider the wave effect (Table 2), the Cdn was affected by only the wind speed, so the value of Cdn is determined when the wind speed is given. When the wave effect was considered in calculating the sea surface roughness in experiments WRF–ROMS–SWAN 1 to 4, the value of Cdn can be different for a given wind speed, as shown in Fig. 12, because the wave state may be different under the same wind speed.

Fig. 12.
Fig. 12.

Variation in Cdn with wind speed in the five numerical experiments. The data were collected at the positions shown in Fig. 11 during the entire simulation of Typhoon Haima.

Citation: Journal of Atmospheric and Oceanic Technology 38, 5; 10.1175/JTECH-D-20-0133.1

The trends in Cdn with wind speed were very different for the five numerical experiments. In experiment WRF–ROMS, Cdn varies linearly with wind speed, and the value of Cdn increase when the wind speed increases. In experiment WRF–ROMS–SWAN4, the value of Cdn increases when the wind speed increases at the beginning but decreases as the wind speed continues to grow after the wind speed exceeds a critical value. In experiment WRF–ROMS–SWAN3, the value of Cdn increases with the increase in wind speed, but it becomes constant when it reaches a certain level for a given wave state. Generally, the value of Cdn in experiment WRF–ROMS–SWAN3 is larger than that in other experiments.

4. Discussion

The effects of the sea surface roughness parameterization methods on simulations have been studied for many years. Unlike previous studies, this study adopted the atmosphere–wave–ocean coupled model on typhoon simulations, which can simultaneously address the effects of the sea surface roughness parameterization methods on both atmospheric and oceanic processes; thus, the feedbacks between the atmosphere and ocean models, which were caused by the effect of sea surface roughness methods, can be simulated. In this study, it was found that Cd plays an important role in the feedback processes between atmosphere and ocean during the typhoon process, through its effect on the typhoon intensity, air–sea heat flux, SST, ocean mixed layer depth, ocean currents, etc. This phenomenon may be difficult to simulate with the ocean or atmosphere model alone.

And for the two selected typhoon cases, Typhoons Haima and Nida had a maximum wind speed of 74.6 and 41.2 m s−1, respectively, which allows for a more comprehensive analysis about the Cd effect on the atmosphere and ocean. This is especially important for investigating the impact of sea spray on the typhoon intensity, because the impact of sea spray was shown to be more significant at high wind conditions in this study. This is different from the study of Prakash et al. (2019), which concludes that the effect of sea spray on the simulation of wind intensity of TC Vardah (the maximum wind speed of which was 36.1 m s−1) is only marginal.

Among the numerical experiments, the spatial distribution of Cd and the variation in Cd with wind speed are all very different for the five kinds of sea surface roughness parameterization methods, but the simulated typhoon path and minimum sea level pressure were very close for different experiments, which means that the simulation results of the typhoon path and minimum sea level pressure were not sensitive to the sea surface roughness parameterization methods. As shown in the studies by Doyle (2002), Guan et al. (2012), and Li et al. (2016), typhoon tracks were negligibly sensitive to the sea surface roughness parameterization method. For the minimum sea level pressure, it was also found to not be appreciably affected by the parameterization method of Cd (Moon et al. 2007). Thomsen et al. (2014) even suggested that the wind speed–dependent parameterization of Cd is sufficient for an atmosphere–ocean coupled model and that it is not necessary to consider the wave effect when calculating Cd. However, based on the results of our numerical experiments, the kind of sea surface roughness parameterization method can still affect the simulation results, such as the wind speed, latent heat and momentum fluxes, and some oceanic processes.

This study shows that the change in the maximum wind speed was significant for different experiments, although the minimum sea level pressure was very close to each other. Moon et al. (2007) found a similar phenomenon when adopting a new Cd based on an atmosphere model alone. This was confirmed again in the study by Green and Zhang (2013), which showed that Cd affected the relationship between the minimum sea level pressure and maximum 10-m wind speed using the WRF Model. Based on the atmosphere–wave model, Wu et al. (2016) also found that the near-surface wind speed was reduced when the swell influence was considered in the wind stress calculation, which again confirmed that the simulated wind speed is sensitive to the wind stress parameterization.

In terms of the wind stress parameterization impact on the oceanic processes, Figs. 68 show that the simulated SST, mixed layer depth, and vertical currents were obviously affected by the sea surface roughness parameterization method. This confirmed the results of previous studies. For example, Wu et al. (2019) showed that introducing sea state in the calculation of momentum and energy fluxes can change the divergence (convergence) of the wind stress and thus can modify the ocean upwelling frequency by >10%. Staneva et al. (2017) also found that when the circulation model adopted sea-state-dependent fluxes, the simulations and observations agreed better. Based on the ocean–wave coupled model, Feng et al. (2016) found that the change in the storm surge ranged from −0.82 to 0.48 m during Typhoon Usagi, when the wave effect on the sea surface wind stress was considered, which is very important for storm surge prediction.

In this study, when comparing the distributions and variations of Cd between different experiments, Cdn was used instead of Cd. This is because the main differences between the experiments are the calculation methods of z0, and Cdn is directly determined by z0. This ignored the effect of stability on Cd as indicated in Eq. (2). In fact, the atmospheric stability is one of the factors that cannot be neglected when calculating the air–sea momentum flux. For example, Rastigejev et al. (2011) and Andreas et al. (2015) included stratification effects on their marine atmospheric boundary layer models, and Shabani et al. (2014) also took the stability condition into account when calculating the drag coefficients based on the field data over surf zone. As indicated by Kara et al. (2005), the stratification of the marine atmospheric boundary layer can affect the Cd significantly, especially at low to moderate wind speeds. But the very high wind speed occurred at limited area in the typhoon wind field. So, from this point of view, we think the effect of stratification on the simulation results of typhoon cannot be neglected. This is worth studying further. Moreover, as shown by Grachev and Fairall (2001), upward momentum transfer occurs at light winds and swell conditions, but this can only occur below the wind speed of about 2 m s−1. The area of the typhoon eye may satisfy this condition, but such area is limited, and the upward momentum is not large enough to affect the typhoon intensity significantly. We therefore think such upward momentum may not play an important role in the typhoon simulation. But such effect also needs to be quantified by further simulation experiments in a future study.

One deficiency of the coupled model used in this study is that the momentum budget between the atmosphere, wave, and ocean models was not conserved. During the simulation, the wind stress of the ocean model was equal to the bottom stress of the atmosphere model, neglecting the momentum transferred to the waves. The study of Fan et al. (2010) suggested that it is better to consider the effect of the surface waves when estimating the momentum flux into currents from the atmosphere under typhoon conditions. However, according to Fan et al. (2010), the difference between the flux from the wind and the flux to the currents is only obvious for high wind speed and young wave field conditions. In our study, the spatial area of very high wind speeds appeared only in the vicinity where the maximum wind speed occurred, and the waves cannot be exposed to very high winds for a long time; thus, this deficiency of the coupled model cannot greatly affect the main conclusion of this study.

5. Conclusions

The atmosphere–wave–ocean coupled model (COAWST) was used to study the effect of air–sea momentum flux parameterization methods on the simulation results. The atmospheric and oceanic processes during Typhoons Nida and Haima were simulated by 10 numerical experiments, in which a total of five kinds of typical Cd parameterization methods were assessed. By comparing with the observation, we found that considering the variation of the SST in the atmosphere–ocean coupled model can improve the simulation results of the minimum central sea level pressure, compared with the uncoupled simulations. The simulation results also showed that the spatial distribution of Cd and the variation in Cd with wind speed are all very different for different numerical experiments, but the simulated typhoon path and sea level minimum pressure were very similar to each other. Therefore, it can be concluded that the typhoon path and sea level pressure were not sensitive to the parameterization of air–sea momentum flux.

Both the results of the simulated horizontal wind field and the maximum wind speed in different experiments showed that the sea surface roughness parameterization method can significantly affect the simulated wind speed. And by comparing with the observation, it was indicated that, at high wind speed, the simulated maximum wind speed was better in the experiment which adopted the Cd calculation method considering the effect of sea spray, because the Cd decrease significantly with the increase of the wind speed at high wind speed, but there are also alternative possible mechanisms that can achieve similar results (Donelan 2018; Troitskaya et al. 2019; Zweers et al. 2010). And in this study, none of the experiments can compare well with the observation both at low and high wind speeds, so a combination of them may be a choice in the practice, and this will be investigated in the future study.

The advantage of using the atmosphere–wave–ocean coupled model is that the atmospheric and oceanic processes can be simulated simultaneously; thus, the interaction between the atmosphere and ocean and the effect of the waves on such interaction can be simulated. For example, when more momentum flux from the atmosphere was transported to ocean, more kinetic energy was dissipated from the atmosphere to the ocean, thus weakens typhoon intensity, and more latent heat flux from the ocean to the atmosphere that contributes to the increase of typhoon intensity, which are two opposite feedbacks for the typhoon intensity. The results of the coupled model showed that, during the simulation of this study, Cd plays an important role in such feedback processes through air–sea heat and momentum flux, SST, ocean mixed layer depth, ocean currents, etc.

The results of this study answered the question of how the Cd affects the atmosphere and ocean during the typhoon process, and to what extent they are affected, which can help explain or further improve the simulation results, especially for the atmosphere–ocean coupled model. However, further study and verification of the sea surface roughness parameterization method should be based on observation. Additionally, more simultaneous observations of air–sea momentum flux and its related parameters are recommended to improve the accuracy of the air–sea momentum flux parameterization method (Babanin et al. 2018; Zhao et al. 2015; Zou et al. 2017, 2019).

In this study, we analyzed the effect of Cd on the area averaged air–sea heat flux, SST, ocean mixed layer depth, etc., but in fact, Cd may also affect the symmetric or asymmetric structures of these processes (Lee and Chen 2012). So further studies may focus on the Cd effect on the structure of the atmosphere and ocean boundary layer. Besides, this study examined the effect of Cd on typhoon simulation with two typhoon cases, which cannot fully justify the conclusions of this study, because the ocean states, the presence of mesoscale eddies (Wang et al. 2018), the shape of the coastline, and the water depth can all affect the simulation results. So more typhoon cases that occurred in more different areas are supposed to be studied in the future.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grants 41776016, 41606040), NSFC–Shandong Joint Fund (Grant U1806227), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDA19060202), and the National Key Research and Development Program of China (Grants 2016YFC1401500, 2017YFA0604102). This work was also supported by the High Performance Computing Center, IOCAS. The authors thank the COAWST Development Group for their modeling support.

Data availability statement

All the simulation data of this study are available from the Marine Science Data Center of Institute of Oceanology, Chinese Academy of Sciences at http://159.226.158.89:38817/thredds/catalog/fengCatalog.html. The information on the typhoon path and strength can be obtained from Joint Typhoon Warning Center (JTWC) best track dataset at https://www.metoc.navy.mil/jtwc/jtwc.html?western-pacific. The Advanced Scatterometer (ASCAT) satellite dataset is C-2015 ASCAT data, which are produced by Remote Sensing Systems and sponsored by the NASA Ocean Vector Winds Science Team. Data are available at www.remss.com.

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