Effect of Tropical Cyclone Wind Forcing on Improving Upper Ocean Simulation: An Idealized Study

Abstract

We examined how wind forcing affects the upper ocean response under idealized tropical cyclone (TC) conditions. In this study, we constructed three parameterized wind fields with varying spatial and temporal resolutions for TCs of different intensities and translation speeds. The simulated surface and subsurface temperatures were cooler and deeper when using the blended wind fields owing to their higher wind speeds compared to those from coarse–resolution wind fields. Additionally, TC–induced currents were significantly stronger on the right side of the TC track, with notable differences in current velocities. Similar to the increase in ocean currents, the simulated turbulent kinetic energy driven by the blended winds is significantly higher than that simulated by the coarse-resolution wind fields. These findings suggest that using high-quality wind fields to drive ocean models can enhance the accuracy of the upper ocean response to TCs. The sensitivity of the upper ocean responses to wind forcing depends on the TC’s intensity and translation speed. Stronger and slower-moving TCs induce greater vertical shear and enhanced mixing. Therefore, accurate wind stress as a surface boundary condition is crucial for numerical ocean models.

1. Introduction

Tropical cyclones (TCs) are among the most powerful natural hazards, causing significant economic and human losses in coastal regions. In recent years, track forecasts of TCs have steadily improved owing to advancements in numerical models [1,2,3]. However, forecasting their intensity has only shown modest progress and remains a challenging problem [4] owing to the limited availability of observational wind data in the inner core of TCs [2]. Enhancing our understanding of the interactions between the ocean and TCs using remote sensing observations and numerical modeling is crucial for improving typhoon forecasting accuracy [3,5].

Surface wind stress is a critical parameter for ocean, atmosphere, and surface wave models. TC winds can affect various oceanic aspects, including surface currents, boundary layer thickness, surface temperature, and heat flux [6,7]. Accurate atmospheric wind forcing is essential for numerical simulations exploring the interactions between the ocean and TCs [8].

Atmospheric wind forcing for ocean numerical models is typically obtained from climate prediction system reanalysis wind products, TC parameterized wind fields, and blended ocean winds that combine reanalysis wind products with satellite winds. To systematically assess the accuracy of reanalysis wind products for TCs, a comparison with the best track data revealed that reanalysis products significantly underestimate TC intensity [9,10,11,12]. When comparing the radial profile of the 10 m wind from QuickSCAT with reanalysis winds, it was found that reanalysis products underestimated the high wind speeds in the core area but accurately represented the moderate and low wind speeds in the outer regions of TCs [11,13,14]. The underestimation of high winds significantly affects the accuracy of simulated sea surface temperature (SST), subsurface temperature, and ocean currents in numerical ocean models [15,16,17,18]. Moreover, the precision of storm surge modeling depends on the reanalysis wind products’ ability to accurately represent TC intensity [19].

To address the underestimation of TC intensity in the reanalysis wind products, TC surface winds derived from parametric models and satellite measurements are used to drive ocean circulation and storm surge models [20,21,22]. These parametric models include the symmetric wind model (Holland model) [23] and the asymmetric wind model (Willoughby model and Ueno model) [24,25]. These models calculate surface wind fields based on the maximum wind speed (MWS), the radius of maximum wind (RMW), and the central pressure from the TC best track dataset. TC surface winds are underestimated in the outer region and overestimated in the eyewall region [24]. Blended winds, combining reanalysis winds with TC parameterized surface winds from the Holland model, are used to drive a coupled wave–circulation model to examine interactions between surface gravity waves and ocean currents during three severe weather events [26]. Additionally, blended winds based on the Holland model and satellite scatterometer QuikSCAT winds were used in numerical simulations to investigate the characteristics of TC-induced upper ocean dynamics and biochemical responses [27]. A parametric wind model called the CycWind model [28] has been developed to improve the accuracy of simulating TC surface winds. The CycWind model accounts for the first-order asymmetry of the wind field induced by the TC’s forward motion and can simulate the radial wind profile of a TC with a double eyewall. Using surface winds from the CycWind model and the Climate Forecast System Reanalysis (CFSR) [29], the near-inertial motions induced by the TC were studied with the Regional Ocean Modeling System (ROMS) [15]. These studies have shown that TC surface winds generated by parametric or atmospheric models can replicate TC intensities and structures similar to those observed.

Accurate information on a TC’s position, intensity, and structure is crucial for simulating the upper ocean responses to TCs. To quantify the effects of wind forcing on the upper ocean response to TCs, idealized TC winds with varying intensities and translation speeds are constructed. These wind fields drive a high-resolution three-dimensional (3D) circulation model (ROMS) [30,31] to simulate oceanic temperature and currents. We analyze the spatial distribution of oceanic temperature and currents to explore the impact of TC wind forcing and the contributions of TC intensity and translation speed to oceanic responses.

The paper is structured as follows: Section 2 outlines the model and experimental design employed in this study. Section 3 examines the effects of wind forcing on ocean temperature and current responses. A summary of the study is presented in Section 4.

2. Materials and Methods

2.1. Ocean Circulation Model

We employed ROMS to study the impact of surface wind forcing on the ocean response to TCs. ROMS is a 3D hydrodynamic model with a free surface and terrain-following capabilities. It can solve the Reynolds-averaged Navier–Stokes equations under assumptions of hydrostatic equilibrium and Boussinesq approximations [30,31]. Various advection schemes, turbulence models, lateral boundary conditions, and surface and bottom boundary layer schemes were implemented in ROMS. The model uses a split-explicit time stepping scheme to solve the baroclinic equations for 3D and the barotropic equations for depth-integrated equations. For this study, the time interval for the baroclinic mode is 60 s, and for the barotropic mode, it is 3 s.

The ROMS model range is from 120°E to 140°E and from 5°N to 35°N (Figure 1a). It has a horizontal resolution of approximately 1/12° (~8 km). The vertical coordinate system is discretized into 32 sigma layers, with resolutions ranging from 1 to 4 m in the upper 30 m and 7 to 40 m from 30 to 200 m depth. The sigma-coordinate stretching parameters ${\theta }_s$, ${\theta }_b$, and $\mathrm{T}\mathrm{c}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}$ are set to 8, 0, and 50 m, respectively. The domain’s bathymetry is uniformly set at 5000 m without land boundaries. A selective smoothing scheme is applied to the bathymetry to preserve significant changes in depth, which can influence the stability of the sigma-coordinate pressure gradient solver.

The model is initialized in all experiments with horizontally homogeneous salinity and temperature. The density distribution primarily relies on the temperature structure. We employed identical initial temperature and salinity profiles (Figure 1b–d), derived from climatological hydrographic data at the coordinates (120°E, 20°N) in September, obtained from the World Ocean Atlas (WOA) 18 [32]. The vertical temperature and salinity profiles show a stable structure with a distinct upper mixed layer. In this study, the mixed layer depth is approximately 38.9 m, defined as the shallowest depth where the temperature decreases by 0.5 °C compared to the near-surface temperature. Initially, the ocean is calm with no currents. The atmospheric wind forcing for the ocean model was derived from idealized TC wind vectors using a parametric cyclone wind field model (refer to Section 2.2).

The momentum and buoyancy fluxes are parameterized using the Coupled Ocean–Atmosphere Response Experiment (COARE) 3.0 bulk–flux formulation [33,34]. Flux coefficients for momentum, latent heat, and sensible heat fluxes are nonlinear functions of wind speed, the atmosphere–ocean temperature gradient, and the humidity gradient. The drag coefficient ($C_d$) in the bulk formula is calculated as follows,

$$C_d\left(U_{10}\right)=(0.55+2.97\tilde{U}-1.49\tilde{U})\times {10}^3$$

(1)

where $\tilde{U}=U_{10}/U_{ref}$, $U_{10}$ is the wind speed at 10 m height, and $U_{ref}=31.5m/s$ is the reference wind speed at which the drag coefficient reaches its maximum value in the expression [35]. Additionally, vertical mixing is parameterized using the generic length scale turbulence closure scheme with the Mellor–Yamada level 2.5 scheme (MY25) [36]. The constant coefficients for MY25 are adapted from those provided in [37] by Kantha and Clayson. In an experiment involving a realistic TC, a positive feedback mechanism resulted in reduced SST cooling and consequently intensified TCs. However, in the idealized TC experiment, the wind fields remain unchanged. Thus, the air–sea radiation fluxes are constant throughout this study.

2.2. Idealized TC Wind Model

Idealized TC wind forcing is used to evaluate surface winds’ impact on enhancing the upper oceanic response simulation. The wind vectors are derived from an analytical model of wind and pressure profiles in TCs [23,38,39].

$$V_g\left(r\right)=\sqrt{\left(P_n-P_c\right)\frac{B}{{\rho }_a}{\left(\frac{R_{max}}{r}\right)}^B\exp {\left(-\frac{R_{max}}{r}\right)}^B+{\left(\frac{rf}{2}\right)}^2}-\frac{rf}{2}$$

(2)

where $V_g$ is the gradient wind at radius $r$; $P_c$ is the central pressure; $P_n$ is the surface pressure, assumed constant at 1013 hPa; $R_{max}$ is the RMW; ${\rho }_a=1.28\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ is the air density; and $f$ is the Coriolis parameter. Parameter $B$ represents the Holland pressure profile parameters, which determine the kurtosis and intensity of a TC. Holland (2008) [39] considered the TC’s pressure, intensity, latitude, and translation speed to redefine the Holland $B$ parameter,

$$\left\{\begin{array}{c}{B}_s=-4.4\times {10}^{-5}∆p^2+0.01∆p+0.03\frac{\partial p}{\partial t}-0.014\phi +0.15v_t^x+1.0\\ x=0.6\left(1-\frac{∆p}{215}\right)\\ B=1.6B_s\end{array}\right.$$

(3)

where $∆p=p_n-p_c$ is the pressure drop from a defined external pressure to the TC center, $\phi$ is latitude, and $v_t$ is the translation speed of a TC.

The axisymmetric wind field constructed by the parameterized model represents the gradient wind field above the ocean surface. The wind field used in the ocean numerical model is the 10 m wind field. Therefore, it is crucial to adjust the idealized wind fields to the standard 10 m elevation using the following formula,

$$V_{10}=K_m{V}_g$$

(4)

$$K_m=\ln \left(10/z_0\right)/\mathit{ln}\left(z_g/z_0\right)$$

(5)

where $V_{10}$ is the wind speed at 10 m height, $z_g$ is the gradient wind height $V_g(z=z_g)$. $K_m$ is a correction factor, and $z_0$ is the surface roughness.

The TC surface winds are biased toward the storm center. The parametric wind model assumes a circular wind structure that does not fully represent the actual surface wind field, necessitating corrections for the inflow angle [40,41].

$${\alpha }_{SR}\left(\theta ,r\right)={\tan }^{-1}\frac{V_b·sin{\alpha }_1}{V_b·cos{\alpha }_1+V_{10}\left(r\right)}$$

(6)

where $V_b$ is the magnitude of the surface motion vector. The angle between the vectors ${\overrightarrow{V}}_{10}\left(r\right)$ and ${\overrightarrow{V}}_b$ is defined as

$${\alpha }_1=\frac{\pi }{2}+\theta -A_1$$

(7)

where $A_1$ is the direction of the surface motion vector to the east. Overlaying the TC’s moving wind field creates an asymmetrical effect, resulting in non-uniform wind speeds on both sides of the TC’s track.

2.3. Experimental Design

Three idealized TC wind fields with varying resolutions were generated using the Holland parametric model: (1) a high-resolution TC parameterized asymmetric wind field (W1) with a temporal resolution of 1 h and a spatial resolution of 1 km; (2) a low-resolution TC parameterized asymmetric wind field (W2) with a temporal resolution of 6 h and a spatial resolution of 25 km; and (3) blended winds (W3) between W1 and W2. The W3 winds ($V_{new}$) can be calculated using Equation (8), which incorporates weighting coefficients [42],

$$V_{new}=V_1\left(1-e\right)+e{V}_2$$

(8)

where $V_1$ is the W1 winds, and $V_2$ is the W2 winds. The weight coefficient $e$ is calculated via

$$e=\frac{C^4}{1+C^4}$$

(9)

$$C=r/\left(n{R}_{max}\right)$$

(10)

where $r$ is the radial distance between the TC center and the calculation grid point. The empirical parameter $n$ is set to be 9.

The spatial resolution of the W3 winds is 8 km, consistent with the horizontal resolution of ROMS, and the temporal resolution is 1 h. Figure 2a–c depict the spatial distribution of the W1, W2, and W3 winds for Category 3–5 Typhoons (referred to as STY) at model time 72 h. The radius of the maximum winds (RMW) is calculated using a quadratic equation that best fits its relationship with the MWS [43]. The best-fitting quadratic equation is given by $R_{max}=0.0086V_{max}^2-1.96V_{max}+130.95$, where $V_{max}$ is the MWS. The MWS of the W1, W2, and W3 winds is 73, 69, and 72 m/s, respectively. The W2 winds are derived by downscaling the W1 winds. Owing to its relatively coarse spatial resolution, which approaches the RMW, a significant difference exists between the wind fields of W1 and W2 at the eyewall (Figure 2b). The wind speeds of the W2 winds in the inner core area of TCs are significantly underestimated. As a result, the W2 winds cannot accurately replicate the TC intensities and structures, showing performance similar to the CFSR wind field in realistic TC cases. The W1 winds represent the TC surface wind field observed by multiple satellites, whereas the W3 winds integrate satellite winds with CFSR winds.

The upper ocean response to TCs is influenced by factors such as the TC intensity, size, and translation speed [44,45,46,47,48]. To investigate the impact of TC intensities and translation speeds on wind forcing effects on the upper ocean, we performed six sensitivity experiments (

Table 1. List of cases and associated parameters related to TC for sensitivity experiments.

#	Experiments		MWS (m/s)	TSP (m/s)	RMW (km)
1	TS	W1	20.3	5	66
		W2	17.5
		W3	20.0
2	TY	W1	36.7	5	35
		W2	34.0
		W3	36.0
3	STY (T5)	W1	73.0	5	25
		W2	69.0
		W3	72.0
4	T3	W1	72.1	3	25
		W2	67.5
		W3	72.0
5	T10	W1	75.3	10	25
		W2	70.8
		W3	75.0

). Figure 2d shows the parametric wind profiles of the W1 winds with varying intensities. The effects of idealized TC winds, including W1, W2, and W3, were examined in each of these sensitivity experiments. The temperature and current responses simulated using the W1 winds serve as the reference baseline experiment. In this study, we investigated the impact of accurate wind forcing on upper ocean parameters by comparing simulations using the W2 and W3 winds. Experiments 1–3 involved idealized TC winds with varying intensities, encompassing Tropical Storms (TS), Category 1–2 Typhoons (referred to as TY), and STY. Experiments 3–5 were designed to explore how wind forcing influences the upper ocean response to TCs with different translation speeds, including slow- (T3), medium- (T5), and fast-moving (T10) TCs.

2.4. Evaluation Metrics

In this study, two statistical criteria are chosen to assess the performance of the wind forcing: the root mean square error ($RMSE$) and the correlation coefficient ($R^2$), calculated as

$$RMSE=\sqrt{\frac{1}{N}{\sum }_{i=1}^N{(X_i-Y_i)}^2}$$

(11)

$$R^2=\frac{{\sum }_{i=1}^N(X_i-{\overline{\mathrm{X}}}_i)(Y_i-{\overline{\mathrm{Y}}}_i)}{\sqrt{{\sum }_{i=1}^N{(X_i-{\overline{\mathrm{X}}}_i)}^2}\sqrt{{\sum }_{i=1}^N{(Y_i-{\overline{\mathrm{Y}}}_i)}^2}}$$

(12)

where $X$ is the evaluated data, $Y$ is the reference data, $N$ is the number of total matchups, and ${\overline{\mathrm{X}}}_i$ and ${\overline{\mathrm{Y}}}_i$ are the means of the evaluated data and the reference data, respectively.

Additionally, we use skill scores ($SS$) to quantify the performance of the different experiments. ${SS}_r$ and ${SS}_c$ are given by

$${SS}_r\left(e\right)=1-\frac{RMSE\left(e\right)}{RMSE\left(b\right)}$$

(13)

$${\mathrm{S}\mathrm{S}}_c\left(e\right)=\frac{R^2\left(e\right)}{R^2\left(b\right)}-1$$

(14)

where $b$ is the numerical experiment using the W2 winds, and $e$ is the numerical experiment forced by the W3 winds. ${SS}_r>0$ indicates an improved simulation when $RMSD\left(e\right)<RMSD\left(b\right)$. ${SS}_c>0$ indicates better model performance when $R^2\left(e\right)>R^2\left(b\right)$.

3. Results and Discussion

3.1. The Impact of Wind Forcing on Temperature Responses

The horizontal distributions of SST cooling, ocean currents, and turbulent kinetic energy (TKE) were simulated using idealized TC wind fields and ROMS. The results are depicted in Figure 3. As the TC moved northward, significant SST cooling occurred on both sides of the TC track (Figure 3a–c). The size and magnitude of the large patches of the SST cooling wake on the right rear of the TC correlate positively with the TC intensity. The simulated maximum SST cooling forced by the W1 winds is −0.84 °C, −1.51 °C, and −2.67 °C for TS, TY, and STY, respectively. Figure 3a–c illustrate that the SST cooling on the right side of the TC track is significantly more pronounced compared to the left side. This rightward bias can be attributed to two main factors. First, the asymmetry of wind stress caused by the TC’s translation speed can introduce greater mechanical energy into the ocean on the right side of the TC track (in the Northern Hemisphere). Second, there is potential for enhanced mixing owing to resonance between the winds and the inertial currents on the same side of the storm, further intensifying SST cooling. The ocean currents (Figure 3d–f) and TKE (Figure 3g–i) also display a pronounced rightward bias. The maximum current velocities are 0.87, 1.44, and 2.03 m/s in the TS, TY, and STY experiments, respectively. Figure 3g–i illustrate that TKE increases with the wind stress applied to the ocean. The TKE levels are influenced by the magnitude of the surface wind speeds, rather than the wind direction. The simulated vertical distributions of the subsurface temperature differences, ocean currents, and TKE using the W1 wind fields and ROMS are shown in Figure 4. The upper ocean subsurface temperature and current responses to an idealized TC exhibit a rightward bias, which is consistent with the surface temperature responses. Figure 4a–c show a maximum decrease of 0.89 °C, 2.80 °C, and 2.93 °C within 2RMW in the experiments of TS, TY, and STY, respectively. After the TC passed, the maximum current velocities and TKE are 0.64, 1.57, and 1.81 m/s and 0.21, 1.24, and 1.64 ${\mathrm{m}}^2/{\mathrm{s}}^2$ for TS, TY, and STY, respectively (Figure 4d–i). This characteristic aligns with the rightward bias of the TC surface wind field, indicating that the mixing and entrainment caused by strong winds are the primary factors contributing to the reduction in ocean temperature, and the increase in current velocity and TKE.

To evaluate the impact of wind forcing on upper ocean simulation, we compared the thermodynamic parameters simulated by the W3 winds with those driven by the W2 winds in the numerical ocean model. Given the resolution differences in TC winds, the MWS of the W3 winds is consistently higher than that of the W2 winds throughout the entire life cycle. Figure 5 depicts the horizontal distributions of the simulated SST cooling difference across different intensities. The results show that SST cooling induced by the W3 winds is notably stronger, particularly in a radius of 2RMW. The simulated maximum SST cooling differences between the W1 and W2 winds are 0.11 °C, 0.24 °C, and 0.33 °C in the TS, TY, and STY experiments, respectively (Figure 5a–c). For the W3 winds, the corresponding SST cooling differences are 0.05 °C, 0.06 °C, and 0.10 °C (Figure 5d–f). Additionally, there is hysteresis in the SST response to TCs, with maximum cooling observed at the right rear of the TC (Figure 4). The overall $R^2$ values for simulated SST cooling between W1 and W2 winds are 0.969, 0.972, and 0.958, with RMSE values of 0.049 °C, 0.120 °C, and 0.416 °C in the experiments of TS, TY, and STY, respectively (

Table 2. Root mean square errors ($RMSE$), correlation coefficients ($R^2$), and skill scores (${SS}_r$ and ${SS}_c$) for SST cooling simulated using the W2 and W3 winds in the TS, TY, and STY experiments.

Experiments	W2 Winds		W3 Winds		${\mathit{S}\mathit{S}}_{\mathit{r}}$	${\mathit{S}\mathit{S}}_{\mathit{c}}$
	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$
TS	0.049	0.969	0.020	0.992	0.592	0.024
TY	0.120	0.972	0.039	0.994	0.675	0.023
STY	0.416	0.958	0.089	0.998	0.786	0.042

). For the simulated SST cooling using the W3 winds, the corresponding $R^2$ values are 0.992, 0.994, and 0.998, with RMSE values of 0.020 °C, 0.039 °C, and 0.089 °C in the TS, TY, and STY experiments, respectively. The skill scores for simulated SST cooling quantify the performance in these experiments with varying intensities of TCs. Across all experiments, simulations using the W3 winds outperform those using the W2 winds. Particularly in STY cases, the sensitivity of the wind forcing effects on the upper ocean response is more pronounced.

All three idealized TC wind fields with varying intensities induced cooling of the ocean surface and subsurface temperatures. The magnitude and depth of cooling varied with the intensity of the TCs. The maximum decreases in the mixed layer temperature forced by the W2 winds are 1.04 °C, 1.51 °C, and 4.81 °C in the TS, TY, and STY experiments, respectively. Corresponding changes in the mixed layer temperature driven by the W3 winds were slightly higher, at 1.15 °C, 2.87 °C, and 3.81 °C. Figure 6 illustrates the vertical distributions of the simulated temperature differences in the east–west direction across different intensities. The simulated maximum temperature changes between W1 and W2 winds are 0.35 °C, 0.71 °C, and 1.06 °C in the TS, TY, and STY experiments, respectively (Figure 6a–c). For the W3 winds, the corresponding differences in temperature cooling are 0.15 °C, 0.28 °C, and 0.82 °C (Figure 6d–f). Similar to the variations in SST cooling, the changes in subsurface temperature influenced by the wind stress are more pronounced in the STY experiment. Compared to the temperature simulated by the W2 winds, the vertical temperature cooling simulated by the W3 winds is more pronounced in 2RMW. This difference is likely attributable to the higher surface wind speeds generated by W3, which enhance mixing in the mixed layer, intensifying the cooling effect from upwelling more significantly than the warming effect caused by mixing.

3.2. The Impact of Wind Forcing on Current Responses

The strong wind stress from TCs induces an upper ocean current response, which typically exhibits a rightward (leftward) bias in the Northern (Southern) Hemisphere owing to enhanced wind–current resonance [49,50,51,52]. Horizontal distributions of simulated near-surface currents vary with TC intensities, as shown in Figure 7. Ocean currents induced by TC winds increase significantly on the right side of the TC track, especially in STY cases. The maximum differences in ocean currents simulated using W1 and W2 winds are 0.26, 0.38, and 0.54 m/s in the TS, TY, and STY experiments, respectively (Figure 7a–c). The maximum differences in simulated currents using W3 winds compared to W1 winds are 0.14, 0.17, and 0.25 m/s in the TS, TY, and STY experiments, respectively (Figure 7d–f).

Table 3. $RMSE$, $R^2,$ and ${SS}_r$ and ${SS}_c$ for surface current simulated using the W2 and W3 winds in the TS, TY, and STY experiments.

Experiments	W2 Winds		W3 Winds		${\mathit{S}\mathit{S}}_{\mathit{r}}$	${\mathit{S}\mathit{S}}_{\mathit{c}}$
	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$
TS	0.466	0.921	0.194	0.953	0.584	0.035
TY	0.570	0.892	0.225	0.984	0.605	0.103
STY	1.183	0.832	0.347	0.994	0.707	0.195

presents the $RMSE$, $R^2$, ${SS}_r,$ and ${SS}_c$ values for surface currents simulated using W2 and W3 winds. Across all cases, numerical experiments with W3 winds demonstrate superior accuracy. As discussed earlier, the ocean currents simulated with W3 winds significantly outperform those with W2 winds.

The vertical distribution of simulated ocean current differences with varying intensities is depicted in Figure 8. Similar to the increases in ocean surface currents, the ocean mixed layer current intensifies significantly on the right side of the TC track, particularly in the STY cases. The maximum differences in ocean currents simulated using W1 and W2 winds are 0.40, 0.74, and 1.13 m/s for the TS, TY, and STY experiments, respectively (Figure 8a–c). Similarly, the maximum differences in simulated currents using W3 winds compared to W1 winds are 0.20, 0.51, and 0.78 m/s for the TS, TY, and STY experiments, respectively (Figure 8d–f). Owing to the higher wind speeds in W3 compared to W2, the increased velocity results in stronger ocean currents. This enhancement is particularly notable in 2RMW on the right side of the TC track (Figure 8). Among the different storm types, STY shows the most pronounced differences in wind forcing affecting the upper ocean currents, whereas TS exhibits the weakest impact of wind forcing.

3.3. The Impact of TC Translation Speed on Oceanic Responses

The primary impact on the upper ocean during the TC passage is SST cooling. Significant asymmetry in SST is observed, with the greatest cooling typically occurring to the right of the TC track. Near-surface cooling results mainly from entrainment mixing. The oceanic response to TCs is influenced by both their translation speed and intensity. Figure 9 illustrates the horizontal distributions of simulated SST cooling differences across varying translation speeds. For T3, an increase in wind speed leads to a more pronounced SST cooling, with the largest difference of approximately 0.87 °C observed on the right side of the TC track at a distance of 2RMW (Figure 9a). The simulated maximum SST cooling changes between W1 and W2 winds are 0.33 °C and 0.17 °C in the experiments of T5 and T10, respectively (Figure 9b,c). For the W3 winds, the corresponding SST cooling differences are 0.29 °C, 0.10 °C and 0.08 °C (Figure 9d–f). In contrast, T10 shows minimal SST cooling differences on the right side of the track, attributed to reduced vertical mixing or lesser upwelling. Among these sensitivity experiments with varying translation speeds, simulations using W3 winds demonstrate the most favorable results (

Table 4. $RMSE$, $R^2,$ and ${SS}_r$ and ${SS}_c$ for the simulated SST cooling using W2 and W3 winds in STY experiments with varying translation speeds of T3, T5, and T10.

Experiments	W2 Winds		W3 Winds		${\mathit{S}\mathit{S}}_{\mathit{r}}$	${\mathit{S}\mathit{S}}_{\mathit{c}}$
	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$
T3	0.562	0.936	0.104	0.983	0.815	0.050
T5	0.416	0.958	0.089	0.998	0.786	0.042
T10	0.082	0.970	0.037	0.998	0.548	0.029

). The overall $R^2$ values of the simulated SST cooling between the W1 and W2 winds are 0.936, 0.958, and 0.970, with $RMSE$ values of 0.562 °C, 0.416 °C, and 0.082 °C in the experiments of T3, T5, and T10, respectively. For the simulated SST cooling using the W3 winds, the corresponding $R^2$ values are 0.983, 0.998, and 0.998, with $RMSE$ values of 0.104 °C, 0.089 °C, and 0.037 °C in the T3, T5, and T10 experiments, respectively. The T3 experiment exhibits poorer performance, highlighting that variations in wind forcing have a more significant impact on T3.

Indeed, a qualitative understanding of the ocean’s response to TCs can be derived from dimensionless numbers calculated based on the TC parameters. The dimensionless storm speed is determined by the ratio of the local inertial period to the TC residence time [50],

$$S=\frac{\pi U_{TSP}}{4f{R}_{max}}$$

(15)

where $U_{TSP}$ is the translation speed, $R_{max}$ is the RMW, and $f$ is the Coriolis parameter.

When the dimensionless storm speed reaches a value of 1, the rotation of wind stress on the right side of the TC roughly matches the inertial rotation rate. Under this condition, the ocean’s response to the TC is expected to exhibit asymmetry relative to the storm path and feature significant inertial motions [50]. For STY, translation speeds are assumed to be 3 m/s (T3), 5 m/s (T5), and 10 m/s (T10), resulting in corresponding dimensionless storm velocities of 0.94, 1.57, and 3.14 m/s, respectively. These values indicate the presence of wind–current resonance on the right side of the TC track for all STY experiments with varying translation speeds. Thus, the dimensionless storm speed provides a rough estimate of the wind–current resonance coupling effect, but it may not fully distinguish the response characteristics among the three TCs with different translation speeds.

The asymmetric distribution of near-inertial surface currents leads to asymmetric vertical mixing, with stronger mixing occurring on the right side of the TC track. Figure 10 depicts the vertical distributions of the simulated temperature differences in the east–west direction across varying translation speeds. The simulated maximum temperature decreases between the W1 and W2 winds are 1.35 °C, 1.06 °C, and 0.33 °C in the experiments T3, T5, and T10, respectively (Figure 10a–c). For the W3 winds, the corresponding temperature cooling differences are 0.42 °C, 0.82 °C, and 0.16 °C (Figure 10d–f). In T3, there is a noticeable increase in the cooling of the mixed layer temperatures, highlighting a more pronounced variation in the impact of wind forcing. The increased vertical mixing observed in T3, which persists over an extended duration, is attributed to intensified vertical shear in the currents. This increased mixing transports colder water to the ocean surface, resulting in an asymmetric distribution of a cold wake. Consequently, the slower translation speed of a TC leads to a larger magnitude of the cold wake because more cold waters from deeper ocean layers are entrained to the surface, owing to longer residence times.

For T10, the penetration depth of the inertial currents is the smallest. In contrast, for T3, the inertial currents penetrate to the greatest depth, with the greatest differences observed on the right side, at the surface and subsurface levels. This is attributed to the extended residence time caused by slower translation speeds, which allows the rotation rate of wind stress on the right side of the storm to closely align with the frequency of the Coriolis force. As a result, wind–current resonance coupling is more effective in T3. Figure 11 shows the horizontal distributions of the simulated surface current differences across varying translation speeds. When comparing the ocean surface currents simulated by W2 winds, which have lower temporal and spatial resolution, with those simulated by W3 winds with higher wind speeds, significant differences are observed. The maximum differences between the W1 and W2 winds in the ocean surface current response are 0.80, 0.54, and 0.37 m/s for T3, T5, and T10, respectively (Figure 11a–c). Similarly, the maximum differences between the W1 and W3 winds in the ocean surface current response are 0.51, 0.25, and 0.21 m/s in the T3, T5, and T10 experiments, respectively (Figure 11d–f). The reduction in surface current magnitude correlates positively with the TC translation speed, while enhancement correlates negatively. The wind forcing changes the direction of the surface current to some extent but has a more significant impact on its magnitude. Changes in the surface current magnitude were observed across all sensitivity experiments, indicating that wind forcing influences surface current responses. The RMSE values of the simulated surface currents between the W1 and W2 winds are 1.445, 1.183, and 0.892 m/s in the T3, T5, and T10 experiments, respectively, while those between the W1 and W3 winds are 0.404, 0.347, and 0.343 m/s, respectively. Thus, stronger winds lead to greater increases in surface currents. Particularly in T3, the influence of wind forcing on the upper ocean response is more pronounced.

To further explore the impact of wind forcing on upper ocean currents, the vertical distributions of the simulated differences in ocean currents in the east–west direction across varying translation speeds are analyzed (Figure 12). The maximum differences in ocean currents simulated using the W1 and W2 winds are 1.20, 1.13, and 0.68 m/s in the experiments of T3, T5, and T10, respectively (Figure 12a–c). The maximum differences in simulated currents using the W3 winds compared to the W1 winds are 0.89, 0.78, and 0.57 m/s in the experiments T3, T5, and T10, respectively (Figure 12d–f). The magnitude of difference in the ocean currents is greatest for T3 and weakest for T10 when simulated using the W2 and W3 winds. Furthermore, turbulent mixing induced by wind stress predominantly influences the sea surface current, transferring momentum downward. Slower translation speeds of TCs contribute to greater changes in horizontal oceanic advection at depth.

Figure 13 depicts the horizontal distribution of simulated TKE for W2 and W3 winds compared to W1 winds, across all five sensitivity experiments. The maximum differences in TKE simulated using the W1 and W2 winds are 0.07, 0.14, 0.41, 0.48, and 0.22 ${\mathrm{m}}^2/{\mathrm{s}}^2$ in the experiments of TS with the translation speed of 5 m/s, TY with the translation speed of 5 m/s, STY with the translation speed of 5 m/s, STY with the translation speed of 3 m/s, and STY with the translation speed of 10 m/s, respectively (Figure 13(a1–e1)). The maximum differences in simulated TKE using the W3 winds compared to the W1 winds are 0.04, 0.10, 0.27, 0.33, and 0.16 ${\mathrm{m}}^2/{\mathrm{s}}^2$, respectively (Figure 13(a2–e2)). The TKE response variations align with the ocean surface currents. A stronger and slower TC increases the vertical shear of the currents, leading to significant TKE changes. The exchange of latent heat flux owing to TKE enhances vertical mixing, promoting the dispersion of horizontal momentum away from the surface.

4. Conclusions

This study investigates the impact of various wind forcings on the simulated thermodynamic and dynamic parameters of the upper ocean during TC passage. Three distinct ocean surface wind fields, each with different spatial resolutions, are generated using a TC parametric asymmetric model. Sensitivity numerical experiments are conducted using ROMS to simulate the temperatures and current velocities at the ocean surface and subsurface.

Analyses of the model results from six experiments indicate that, under these idealized TC conditions, atmospheric wind forcing significantly impacts the numerical simulation of upper oceanic responses. The spatial resolution of the TC winds causes the MWS of the W3 wind field to be significantly higher than that of the W2 wind field. When the W3 winds drive ROMS, the simulated SST cooling increases substantially in 2RMW. Compared to the reference baseline experiment with W1 winds, the simulated maximum subsurface temperature changes for W2 winds were 0.35 °C, 0.71 °C, and 1.06 °C in the TS, TY, and STY experiments, respectively. For W3 winds, the corresponding temperature cooling differences were 0.15 °C, 0.28 °C, and 0.82 °C. Consistent with the variations in temperature responses, TC-induced currents show significant enhancement, with a notable increase in current velocities observed on the right side of the cyclone. Notably, the maximum difference in ocean current velocities in the mixed layer can reach up to approximately 0.29 m/s. Variations in the TKE response align with the ocean surface currents. The maximum horizontal difference in TKE between the W1 and W2 winds was 0.48 ${\mathrm{m}}^2/{\mathrm{s}}^2$ in the experiments of STY with a translation speed of 3 m/s. For the W3 winds, the corresponding TKE difference was 0.33 ${\mathrm{m}}^2/{\mathrm{s}}^2$.

Moreover, the accuracy of the numerical simulations of the upper ocean parameters is linked to the TC intensity and translation speeds. The impact of idealized TC wind forcing on the accuracy of simulating oceanic responses is particularly significant for stronger and slower-moving TCs, which are characterized by increased vertical shear and enhanced vertical mixing. Therefore, improving the accuracy of the TC wind structure and intensity in numerical simulations is crucial for better understanding the interaction processes between TCs and the ocean.

In these idealized experiments, the W1 winds represent surface wind fields from satellite observations, while the W2 winds correspond to CFSR wind fields. Consequently, the W3 winds combine the satellite and CFSR wind fields. This study objectively quantifies the impact of W3 winds relative to W2 on improving upper ocean responses. The W3 winds significantly enhance the accuracy of numerical simulations of upper ocean dynamics and thermodynamic parameters, particularly for strong and slow-moving TCs. Typically, atmospheric wind forcing from reanalysis wind products is used in realistic experiments. However, the TC intensity and symmetric structure in these products often differ significantly from satellite observations, leading to inaccurately simulated upper ocean parameters [9,10,11,12]. Advances in remote sensing technology have enabled ocean satellites to observe the ocean with high temporal and spatial resolution. Multi-temporal observations from active and passive microwave sensors, such as synthetic aperture radars, radiometers, and scatterometers, can effectively collect comprehensive information on ocean surface wind fields. Therefore, it is crucial to improve the accuracy of atmospheric wind forcing used in ocean modeling by incorporating satellite-measured TC surface wind fields. This enhancement is essential for better understanding TC dynamics and air–sea interaction mechanisms under extreme weather conditions, as well as for improving the accuracy of TC predictions.