An Improved Sea Spray-Induced Heat Flux Algorithm and Its Application in the Case Study of Typhoon Mangkhut (2018)

Abstract

The prediction of tropical cyclone (TC) intensity has been a lasting challenge. Numerical models often underestimate the intensity of strong TCs. Accurately describing the air–sea heat flux is essential for improving the simulation of TCs. It is widely accepted that sea spray has a nonnegligible effect on the heat transfer between the atmosphere and the ocean. However, the commonly used sea spray-induced heat flux algorithms have poor applicability under high wind speeds, and it is difficult to apply these algorithms to models to forecast TCs. In this study, we proposed an improved sea spray-induced heat flux algorithm based on the FASTEX dataset. This improved algorithm performs much better under high wind speed conditions than the commonly used algorithms and can be used in a coupled numerical model. The addition of sea spray-induced heat fluxes noticeably enhances the total air–sea heat fluxes and allows more energy to be transferred from the ocean to the lower atmosphere. In the simulation of TCs, the addition of sea spray-induced heat fluxes significantly improves the simulation of TC intensity and makes the low-pressure structure and wind field structure more fully developed in the horizontal direction.

1. Introduction

Tropical cyclones (TCs) are one of the most severe weather systems that cause very large losses of life and property in coastal regions [1]. Accurate forecasting of tropical cyclone (TC) track and intensity are of great significance. The forecasting of TC track has greatly improved in the past few decades due to the progress in the numerical forecasting models; however, the prediction of TC intensity still remains a long-term challenge [2,3]. The uncertainties induced by air–sea interaction and the complexities of the microphysical process inside TCs are two important difficulties that affect the TC intensity prediction [4].

As the primary energy source for TCs, the ocean plays an important role in the generation and development of TCs, and accurate descriptions of the energy exchange between the ocean and the atmosphere are crucial for forecasting TC intensity [5,6]. TCs gain energy from the sea surface in the forms of latent heat flux and sensible heat flux [7].

The role of heat transfer between the ocean and the atmosphere in the development of TCs has been revealed by many studies [7,8,9]. From both observations and numerical simulations, Emanual [10] proposed that heat transfer from the ocean is the primary factor for the development and maintenance of TCs; based on this, Rotunno and Emanual [11] elaborated that wind-induced surface heat exchange (WISHE) leads to the enhancement of the potential temperature in the atmospheric boundary layer. After heat acquired from the sea surface is redistributed by cumulus convection, the circulation of the TC enhances, which further increases the heat transfer and intensification of the TC. The abovementioned role of surface heat flux in TC intensification is consistent with the observations that TCs are more likely to intensify when passing through high surface heat flux areas but always decay after landing [8].

The air–sea heat flux is essential to the intensification of TCs, and the accurate description of the air–sea surface heat flux in numerical modeling systems is of great significance for improving the forecasting of TCs. $H_{L,int}$ and $H_{S,int}$ can be calculated from the bulk flux algorithm based on the parameterizations of $C_q$ and $C_h$ (or $z_0$, $z_t$, and $z_q$) in numerical models [12]. $C_q$ and $C_h$ are the exchange coefficients for latent and sensible heat flux, respectively. $z_0$, $z_t$, and $z_q$ are the roughness for momentum, sensible heat, and water vapor, respectively, which are often estimated from parameterization schemes in numerical models [13]. According to the existing methods, the parameterization schemes of heat flux can be roughly divided into the following categories: (1) Based on the observations in low and moderate wind conditions, the latent heat flux exchange coefficient $C_q$ and the sensible heat flux exchange coefficient $C_h$ are treated as constants [14,15,16]. (2) By fitting observations directly to dimensionless parameters, such as the roughness Reynolds number $R_r$, the water vapor roughness $z_q$, and the sensible heat roughness $z_t$ can be denoted as a function of dimensionless parameters [12,17,18]. (3) The ratio between $z_t$ or $z_q$ and $z_0$ is described as a function of the roughness Reynolds number $R_r$: $z_{t,q}/z_0=f\left(R_r\right)$ [19,20]. Under high wind speed conditions induced by TCs, a significant amount of sea spray has been observed in the marine boundary layer due to wave breaking [21]. It is widely accepted that sea spray has a nonnegligible effect on the heat transfer between the atmosphere and the ocean [22,23]; however, the above heat flux parameterization schemes do not take into account the effect of sea spray on the heat flux. The mechanism of how sea spray affects heat flux has been thoroughly investigated, and the general consensus is that the sea spray’s re-entry process enhances heat transfer [24]. After being blown into the air from the warm ocean surface, the temperature of the spray droplets is higher than that of the surrounding air, and the spray droplets release sensible heat to the surrounding air while cooling. At the same time, due to the humidity difference between the droplets and the surrounding air, the droplets release latent heat while evaporating, and then return to the ocean; therefore, the surface heat flux is enhanced when the sea spray is generated [25]. Theoretical analysis and observations show that spray-induced heat flux can account for at least 10% of the total heat flux when $U_{10}$ reaches 12 m/s [26]. Using a fully coupled modeling system, the impacts of sea spray on the wave conditions and the lower atmosphere were examined by Shpund et al. [27]; their results showed that areas with stronger winds have larger sea spray-induced heat flux, and the presence of sea spray can induce moistening of the near-surface air, an effect on the stability profile, and an increase in wind speed. Therefore, the total air–sea latent and sensible fluxes ($H_{L,T}$ and $H_{S,T}$) can be expressed as:

$$H_{L,\mathrm{T}}=H_{L,int}+H_{L,sp}$$

(1)

$$H_{S,T}=H_{S,int}+H_{S,sp}$$

(2)

where $H_{L,int}$ and $H_{S,int}$ represent the exchanging latent and sensible heat flux at the air–sea interface, and $H_{L,sp}$ and $H_{s,sp}$ represent the sea spray-induced latent and sensible heat fluxes, respectively.

To quantitatively assess the impact of sea spray on the sensible and latent heat fluxes, Andreas et al. [28] proposed a parameterization algorithm based on the sea spray generation function developed by Andreas et al. [22]. This algorithm calculates the heat fluxes of different radii of spray droplets separately and then integrates the droplet radii to obtain the total heat flux. Afterward, Andreas et al. [13,25,26] made several improvements to this scheme and obtained a fast algorithm; we call it the AN15 algorithm in this paper. The algorithm is presented in Section 3.1.

Through the AN15 fast algorithm, Andreas et al. [13] calculated that the interfacial and spray-induced heat fluxes depend on a 10 m wind speed in the range of $0 \mathrm{m}/\mathrm{s}\le U_{10}\le 40 \mathrm{m}/\mathrm{s}$ and found that spray-induced heat fluxes exceeded the interfacial heat fluxes in both sensible and latent heat fluxes when $U_{10}$ reaches approximately 25 m/s. With the increase in $U_{10}$, the proportion of the spray-induced heat fluxes in the total heat fluxes increases (see Figure 9 in [12] for more details). Andreas et al. suggested that this improved fast algorithm can be applied to high wind speed environments, such as hurricane-strength winds, where sea spray will play a dominant role in the heat fluxes. In theory, a heat flux calculated considering the sea spray is closer to the real heat flux, and a more reasonable heat flux may simulate a more reasonable tropical cyclone intensity. However, Andreas did not test the effect of this algorithm with a $U_{10}$ of greater than 40 m/s, and they also did not apply the AN15 algorithm to the numerical model. To test the applicability of this algorithm under high wind speeds, we applied the AN15 algorithm to the Coupled Ocean–Atmosphere–Wave–Sediment Transport model (COAWST) [29] and tried to simulate the super typhoon Mangkhut (2018). However, the model was unsustainable and blew up because the heat flux simulated by AN15 is much larger than normal and caused the WRF to explode. A detailed explanation is in Section 3.1.

In this paper, we find the shortcomings of the existing sea spray-induced heat flux algorithm, and we propose an improved, fast sea spray heat flux algorithm that can be used to simulate a super typhoon. The specific changes are expanded upon in detail below. Then, we explore the effect of sea spray heat flux on TCs. In the COAWST system, we propose the inclusion of the sea spray-induced heat flux in the surface layer parameterization scheme of the WRF-ARW 4.2.2. The significant wave height proposed by the wave model SWAN transports to the WRF model. The air–sea heat flux calculated by the surface layer parameterization scheme transports to the boundary layer parameterization schemes and then affects the whole system. Under high wind speeds, such as a storm surge or TC, the effect of the sea spray on the heat flux cannot be neglected; the use of the new sea spray-induced heat provides a more realistic simulation of the air–sea interaction processes. To the best of our knowledge, this present work is the first study to use the COAWST model to investigate the impact of sea spray heat flux on the super typhoon Mangkhut ($U_{10}>70 \mathrm{m}/\mathrm{s}$).

The remainder of this paper is organized as follows: In Section 2, we introduce the observational data used to improve the AN15 algorithm and describe the COAWST model. In Section 3, based on more than 2000 sets of observational data, we propose an improved sea spray-induced heat flux algorithm applicable for high wind speed conditions and compare the results of the improved and the old algorithms. An overview of super typhoon Mangkhut and the experimental design are given in Section 4. In Section 5, we apply the improved, fast algorithm to the coupled model and analyze the effect of sea spray heat flux on the super tropical cyclone. A summary and conclusions are provided in Section 6.

2. Data and Model Descriptions

2.1. FASTEX Dataset

In this paper, the Fronts and Atlantic Storm-Track Experiment (FASTEX) [30] dataset is used to test the effect of the improved algorithm in low to moderate wind conditions. The FASTEX dataset contains numerous observations of air–sea interface fluxes and contributes greatly to the research on air–sea exchanges [31]. This dataset includes reliable measurements of the sensible heat flux, latent heat flux, wind speed, sea surface temperature, air temperature, humidity, and significant wave height. The above data are necessary to propose and improve the AN15 algorithm [13]. The data used in our research include 2435 sets of eddy-covariance measurements of heat fluxes. It is noted that the wind speeds only reach up to 30 m/s.

The purpose of the FASTEX is to collect data related to atmospheric frontal waves that have an impact on Europe. The FASTEX obtained many measurements of the air–sea interaction processes and ocean surface from four ships placed in the Atlantic, 15–18 buoys, and five aircraft during January and February 1997 [32]. The FASTEX data came from four main sources: the ETL motion-corrected flux package, the ship’s Athena system, the ETL mean measurement systems, and the TSK wave-height recorder [33]. The air–sea flux data and other mean values are produced by the first three systems, and the final system produces the wave data. It is worth mentioning that the flux data used in this paper were calculated by the direct eddy correlation [34].

2.2. Model Description and Configuration

The air–sea heat flux has an important impact on the evolution and intensification of TCs. A single atmospheric model cannot simulate the process of air–sea interaction. Therefore, we used the COAWST model to explore the effect of the heat flux on the super typhoon Mangkhut. The model was developed and maintained by Warner et al. [29] and includes an independent atmospheric model, ocean model, wave model, and sediment transport model. This coupled model relies on the model coupling toolkit (MCT) to exchange variables between the different models [35]. The COAWST model is an open source code, which can be used for different model configurations and explores many natural phenomena, such as the effect of sea spray on the air–sea interaction, flash floods, and dynamics of TCs [36,37,38,39]. In our experiments, the atmospheric model and the wave model are activated to provide variables for calculating the sea spray-induced heat flux. The interval time between the WRF and SWAN is 1800 s. It is worth mentioning that, compared with the JTWC, the simulated intensity calculated by the fully coupled model is worse than that without adding ROMS. The current numerical models tend to underestimate the intensity of super TCs, and the addition of ROMS exacerbates the problem. Other studies also found that adding ocean circulation models will make the TC intensity weaker in the western North Pacific [40,41]. TCs cause upwelling and bring a cold deviation of the sea surface temperature (SST), which causes the simulated intensity to be weaker. The impacts of the SST or circulation on TCs are beyond the scope of this paper, so we did not activate ROMS to improve the experimental efficiency.

2.2.1. Atmospheric Model

The Weather Research and Forecasting (WRF-ARW 4.2.2) model is the atmospheric component employed in the COAWST modeling system. This model is configured as a nonhydrostatic, 3D fully compressible atmospheric model with various physical parameterization schemes. The boundary and initial conditions used in this paper are obtained from the NCEP Final Operational Global Analysis and Forecast data available at 0.25° × 0.25° resolution and six-hour intervals. Three two-way nested grids, shown in Figure 1, were used in the present research. The three grids are d01, d02, and d03 in order from outside to inside. The horizontal resolution of d01 is 27 km, and its integration time step is 90 s. Grid d02 has a horizontal resolution of 9 km, and its integration time step is 30 s. The horizontal resolution of d03 is 3 km, and its integration time is 10 s. It should be noted that d03 moves along the TC vortex, and its position is calculated every 15 min. In this study, the microphysics scheme comes from Purdue Lin [42]. Both shortwave and longwave radiation are resolved by the Rapid Radiative Transfer Model for Global Circulation Models (RRTMG) [43]. The planetary boundary is based on the Mellor-Yamada Nakanishi and Niino (MYNN) level 2.5 [44]. The MYNN is set to the surface layer model [45], the land surface model is unified Noah, and the Kain–Fritsch cumulus parameterization [46] is applied only in d01 and d02.

2.2.2. Wave Model

Simulating Waves Nearshore (SWAN) [47] is employed as the wave model component in the COAWST model. In the two-way coupled WRF-SWAN run, SWAN provides the variables needed in the calculation of the sea spray-induced heat flux, such as the sea surface temperature and the significant wave height every 1800 s. Then, SWAN exchanges these variables to the WRF with the coupler MCT to simulate the sea spray-induced heat flux. The 10 m fields from the WRF are the forcing fields of the SWAN model. In this study, the data derived from the WaveWatch III model are selected as the boundary condition data. The horizontal resolution of SWAN is approximately 9 km, and the integration time step is 60 s. The domain of SWAN, in the simulation of Mangkhut, is shown as the blue box in Figure 1. In order to make the simulation of initial waves more accurate, we chose the method of “hot start”. The simulation times of the WRF and SWAN are the same.

3. An Improved Algorithm YJ22 and Its Application

3.1. The Process of Proposing AN15 and Its Problems

The sea spray heat flux scheme proposed by Andreas et al. is one of the most widely used sea spray heat flux schemes [26]. This paper uses the latest version of this scheme, revised in 2015, the AN15 algorithm [13], which can be expressed as:

$$H_{L,sp}={\rho }_w{L}_v\left\{1-\left[{\frac{r\left({\tau }_{f,50}\right)}{50\mu m}}^3\right]\right\}{V}_L\left(u_{*}\right)$$

(3)

$$H_{S,sp}={\rho }_w{C}_w\left(T_s-T_{eq,100}\right)V_S\left(u_{*}\right)$$

(4)

In Equation (3), ${\rho }_w$ is the density of seawater, $L_v$ is the latent heat of vaporization, ${\tau }_{f,50}$ is the residence time of droplets in the air with a 50 μm initial radius, and $r\left({\tau }_{f,50}\right)$ is the radius of the droplets when they fall back into the sea. In Equation (4), $C_w$ is the specific heat, $T_s$ is the sea surface temperature, and $T_{eq,100}$ is the equilibrium temperature of the droplets with an initial radius of 100 μm. $V_L$ and $V_S$ are the wind functions of the bulk friction velocity $u_{*}$. Andreas et al. [13] fitted them as:

$$V_S=3.92\times {10}^{-8}, 0\le u_{*}\le 0.1480$$

(5)

$$V_S=5.02\times {10}^{-6}{u}_{*}^{2.54}, 0.1480\le u_{*}$$

(6)

$$V_L=1.76\times {10}^{-9}, 0\le u_{*}\le 0.1358$$

(7)

$$V_L=2.08\times {10}^{-6}{u}_{*}^{2.39}, 0.1358\le u_{*}$$

(8)

In these equations, $V_L$, $V_S$, and $u_{*}$ are all in units of m/s.

To determine why the AN15 scheme cannot be applied to super tropical cyclones, we need to review the process of its proposal. According to the microphysical model, Andreas et al. [28] estimated the spray-induced latent and sensible flux related to all droplets of the radius $r_0$ as:

$$Q_L\left(r_0\right)={\rho }_w{L}_v\left\{1-{\left[\frac{r\left({\tau }_f\right)}{r_0}\right]}^3\right\}\left(\frac{4\pi r^3}{3}\frac{dF}{d{r}_0}\right)$$

(9)

$$Q_S\left(r_0\right)={\rho }_w{C}_w\left(T_s-T_{eq}\right)\left[1-\exp \left(-{\tau }_f/{\tau }_T\right)\right]\left(\frac{4\pi r^3}{3}\frac{dF}{d{r}_0}\right)$$

(10)

In Equation (9), $r\left({\tau }_f\right)$ represents the radius when the droplets fall back into the sea surface. In Equation (10), $\left(T_s-T_{eq,100}\right)\left[1-\exp \left(-{\tau }_f/{\tau }_T\right)\right]$ represents the difference between the initial temperature of a droplet and the temperature when it falls back into the sea. This temperature difference is closely related to the sensible heat exchange of a droplet with a radius $r_0$. $T_S$ is the sea surface temperature, which also denotes the initial temperature of a droplet with the radius $r_0$. $T_{eq}$ represents the equilibrium temperature of the droplet, ${\tau }_f$ represents the time-scale of a droplet’s residence in air, and ${\tau }_T$ is the e-folding time that estimates the rate of the exponential temperature change (for more details, please refer to [13,48,49]).

The sea spray generation function is denoted as $dF/d{r}_0$ [22], which provides the number of sea spray droplets produced per second, per square meter of the sea surface, per micrometer increment in the droplet radius [50]. The volume flux of droplets with initial radius $r_0$ is represented as $\left(4\pi r_0^3/3\right)dF/d{r}_0$.

To obtain the total sea spray heat fluxes, Andreas et al. integrated Equations (9) and (10) over the droplet radii and obtained Equations (11) and (12). The upper and lower radius limits of this integration are determined according to the experiments of Fairall et al. [51].

$$\overline{Q_L}={{\displaystyle \int }}_{1.6\mu m}^{500\mu m}{Q}_L\left(r_0\right)d{r}_0$$

(11)

$$\overline{Q_S}={{\displaystyle \int }}_{1.6\mu m}^{500\mu m}{Q}_s\left(r_0\right)d{r}_0$$

(12)

Although the calculations of $\overline{Q_L}$ and $\overline{Q_S}$ are based on the microphysical model [28], there are some uncertainties and approximations in this process, and the sea spray generation function is one of the largest uncertainties. Therefore, $\overline{Q_L}$ and $\overline{Q_S}$ cannot be used as the final spray-induced heat flux. Andreas and DeCosmo [26,52,53,54] hypothesized that the actual spray-induced latent and sensible heat fluxes are:

$$H_{L,sp}=\alpha \overline{Q_L}$$

(13)

$$H_{S,sp}=\beta \overline{Q_S}-\left(\alpha -\gamma \right)\overline{Q_L}$$

(14)

where $\alpha$, $\beta$, and $\gamma$ are assumed to be small, positive tuning coefficients estimated from the data. The aim of these coefficients is to minimize the impact of uncertainties and approximations on the AN15 scheme.

Because the calculations in Equations (11) and (12) are too intensive for numerical models, Andreas et al. proposed a fast algorithm suitable for numerical models. According to the observation data of the HEXOS and FASTEX, Andreas et al. found that droplets with radii of 50 and 100 μm are extremely instructive when calculating spray-induced heat flux (see Figure 2 in [54]). Then, they found that the microphysical behavior of 50 μm droplets might be a good indicator of $H_{L,sp}$, and the behavior of 100 μm droplets might be a good indicator of $H_{S,sp}$. For these calculations, the water temperature is 20 °C, the air temperature is 18 °C, the RH is 90%, the barometric pressure is 1000 mb, and the surface salinity is 34 psu. Under this hypothesis, they proposed the fast algorithm AN15, as shown in Equations (3) and (4). The wind functions $V_S$ and $V_L$ are shown in Equations (5)–(8).

According to the observation data of the HEXOS and FASTEX, Andreas found that droplets with radii of 50 and 100 $\mu m$ are extremely instructive when calculating spray-induced heat flux. Under this hypothesis, Andreas et al. [54] proposed the fast algorithm AN15, as shown in Equations (7) and (8). The wind functions $V_S$ and $V_L$ are shown in Equations (9)–(12).

Andreas proposed that sea spray plays a dominant role in air–sea heat exchange [13]. Therefore, we tried to extrapolate the AN15 algorithm to typhoon-strength winds and apply it to the simulation of the super typhoon Mangkhut ($U_{10}>70 \mathrm{m}/\mathrm{s}$). When we directly applied AN15 to simulate Mangkhut, however, the model computed enormous spray-induced heat fluxes and crashed. Therefore, the AN15 scheme is not applicable for high wind speed conditions.

Figure 2a presents the values of the interfacial and spray-induced latent and sensible fluxes calculated by the AN15 algorithm under typical TC conditions: the 10 m air temperature ($T_{10}$) is 26 °C, and the sea surface temperature and salinity are 28 °C and 34 psu, respectively. The relative humidity is 90%, and the sea level pressure is 950 hPa. As shown in Figure 2a, both the interfacial fluxes ($H_{L, int}$ and $H_{S,int}$) and spray-induced fluxes ($H_{L,sp}$ and $H_{S,sp}$) increase with $U_{10}$. The spray-induced fluxes increase faster than the interfacial fluxes, especially under high wind speeds ($U_{10}>30 \mathrm{m}/\mathrm{s}$). It is worth noting that $H_{L,sp}$ reaches a staggering value of 11,000 W/m², and $H_{S,sp}$ exceeds 2500 W/m² when $U_{10}=80 \mathrm{m}/\mathrm{s}$. These two values significantly exceed the normal magnitude of the air–sea heat flux. In general, the values of latent heat flux do not exceed 2000 W/m², and the magnitude of the sensible heat flux is several hundred W/m². Therefore, we concluded that the heat flux calculated by AN15 is obviously larger than the true value when $U_{10}>40 \mathrm{m}/\mathrm{s}$. The AN15 scheme will significantly overestimate the magnitude of the heat flux when $U_{10}>50 \mathrm{m}/\mathrm{s}$. However, $U_{10}>50 \mathrm{m}/\mathrm{s}$ is very common for typhoon conditions. Hence, the applicability of AN15 under high wind speeds is defective.

3.2. An Improved Sea Spray-Induced Heat Flux Algorithm YJ22

To apply the AN15 scheme to high wind speed environments, such as typhoons, we have improved the applicability of this scheme at high wind speeds and proposed the improved sea spray-induced heat flux algorithm YJ22.

After analysis, we found that the problem of the AN15 scheme under high wind speeds is due to the sea spray generation function $dF/d{r}_0$. Andreas et al. adopted the function from Fairall et al. [51]:

$$\frac{dF}{d{r}_0}=W\left(U_{10}\right)f_n\left(r_0\right)$$

(15)

where $W\left(U_{10}\right)$ is the whitecap coverage, which is expressed as a decimal, and $f_n\left(r_0\right)$ is the droplet source spectrum per square meter of the whitecap. The form of the whitecap coverage given by Fairall et al. [51](abbreviated as $W_{F94}$) is:

$$W_{F94}=3.84\times {10}^{-6}{U}_{10}^{3.41},$$

(16)

Since the proposal of the $W_{F94}$ is mainly based on observations at low and moderate wind speeds, its applicability at high wind speeds is defective. Figure 2b shows the relationship between $W_{F94}$ and $U_{10}$, and $W_{F94}$ monotonically increases with $U_{10}$. The physical meaning of the whitecap coverage is the ratio of the whitecap area to the sea surface area; therefore, the upper limit of the whitecap coverage is one. However, Figure 2b shows that $W_{F94}$ exceeds one when $U_{10}$ exceeds 40 m/s. $W_{F94}$ even exceeds 10 when $U_{10}$ reaches 80 m/s. This unreasonable whitecap coverage results in unreasonable heat fluxes under high wind speeds.

To solve the applicability of the AN15 scheme under high wind speeds, the natural method is to choose a more reasonable whitecap coverage parameterization scheme to replace the $W_{F94}$ scheme. However, due to the difficulty in obtaining whitecap coverage data under high wind speeds, the applicability of most current $W$ parameterization schemes under high wind speeds is doubtful [55]. To replace the $W_{F94}$ scheme, a new whitecap parameterization scheme suitable for high wind speed conditions is needed. Based on recent satellite observations under wind speeds, Hwang et al. [56] proposed a new $W$ parameterization scheme (abbreviated as $W_{H18}$):

$$W_{H18}=\left\{\begin{array}{lll}0,& & U_{10}\le 3.30 m/s\\ 0.30{\left(0.01U_{10}{\left(-0.0160U_{10}^2+0.967U_{10}+8.058\right)}^{0.5}-0.11\right)}^3,& & 3.30<U_{10}\le 9.97 m/s\\ 7\times {10}^{-7}{U}_{10}^{2.5}{\left(-0.0160U_{10}^2+0.967U_{10}+8.058\right)}^{1.25},& & 9.97<U_{10}\le 35.00 m/s\\ 0.003U_{10}^{1.25},& & U_{10}>35.00 m/s\end{array}\right.$$

(17)

Hwang analyzed the performance of $W_{H18}$ under high wind speed and found that the $W_{H18}$ scheme can still obtain relatively reasonable whitecap coverage, even in extreme wind conditions of 100 m/s. Figure 3 shows the comparison of $W_{H18}$ and $W_{F94}$ with the 10 m wind speed. The $W_{H18}$ scheme can also generate reasonable whitecap coverage under high wind speeds ($U_{10}>40 \mathrm{m}/\mathrm{s}$). Therefore, we replaced $W_{F94}$ in the AN15 scheme with $W_{H18}$ to improve the applicability of the AN15 scheme under high wind speeds. We used the FASTEX dataset to verify the modification and proposed an improved algorithm.

The ideal situation is that the modified scheme will generate values that better fit the observed data than the values calculated by the original AN15 scheme. By comparing the difference between the observations and modeled values computed from Equations (9)–(14) with two different $W$ parameterization schemes, Figure 4 and Figure 5 reflect the performance of the AN15 and modified algorithm under low to moderate wind conditions. The abscissa represents the 10 m, neutral-stability wind speed $U_{N10}$, and the ordinate represents the difference between the measurements and the modeled values. It is easy to understand that the smaller the difference is, the better the effect on the model. The black solid line represents the modeled values equal to the observations; the value of the black solid line is equal to 0, which means the difference between the modeled values and the observations is 0. The red lines represent the least-squares fit to all the data at a 95% confidence level. Comparing Figure 4a,b, we can see that the values simulated by the modified scheme are closer to the real values, especially between $U_{N10}$ from 15 to 25 m/s. The black dotted line represents a $U_{N10}$ equal to 15 m/s. The modified algorithm significantly improves the simulation in the area to the right of the dotted line. The slope of the fitted line in (b) is also closer to 0 than in (a). Meanwhile, the modified algorithm also improves the simulation of sensible heat flux (shown in Figure 5a,b).

Through the above analysis, the value calculated by the modified algorithm is closer to the real observations than AN15, especially in the region where the $U_{N10}$ is greater than 15 m/s. This result supports our hypothesis that the original whitecap coverage parameterization scheme affects the applicability of the AN15 scheme under high wind speeds. However, the calculations used in Figure 4 and Figure 5 are too complex for the numerical models (Equations (9)–(14)). To solve this problem, we imitated AN15 and proposed an improved, fast spray-flux algorithm that is suitable for high wind speed environments. Andreas et al. found that droplets with radii of 50 and 100 μm have good guiding significance in the calculation of $H_{L,sp}$ and $H_{s,sp}$; therefore, they proposed the wind functions $V_L$ and $V_S$ to avoid integration.

To apply the improved AN15 scheme to TC forecasting, we proposed the new wind functions $V_L$ and $V_S$ based on the FASTEX dataset. According to Hwang’s $W_{H18}$ scheme, we divide the wind speed range into two parts: (i) $0<U_{10}\le 35$ m/s is the medium and low wind speed range; (ii) $U_{10}>35$ m/s is the high wind speed range. The wind range of the FASTEX is from 0 to 30 m/s, therefore, we were able to use these measurements to fit the wind functions under medium and low wind speed environments. The transformation of $U_{10}$ and $u_{*}$ uses the function proposed by Andreas et al. [57].

First, we applied the $W_{H18}$ to the AN15 scheme and calculated the modified wind functions $V_L$ and $V_S$, using the measurements in the FASTEX. During this wind range, we also divided wind functions into three subsections, according to the subsection of $W_{H18}$. After many experiments, cubic polynomial fitting provides the best fitting result. Figure 6a,c represent the comparison of the new and original wind functions $V_L$ and $V_S$ from low to moderate wind speeds, respectively. The values of the new wind functions are smaller than the original values. The specific fitting results are shown in Equations (18) and (19).

However, due to a lack of observations in the high wind speed range, ($U_{10}>35 \mathrm{m}/\mathrm{s}, \mathrm{which} \mathrm{is} \mathrm{equal} \mathrm{to} u_{*}>1.7987 \mathrm{m}/\mathrm{s}$), we take another approach to calculating wind functions under high wind speeds. As shown in Equations (9) and (10), Andreas incorporates all uncertainties in the spray-induced algorithm, which of course includes whitecap coverage, into the wind functions. Therefore, we removed the original whitecap coverage $W_{F94}$ from the original wind functions, multiplied it by the new whitecap coverage $W_{H18}$, and then obtained the new wind functions under high wind speeds. Figure 6b,d reflects the comparison of new wind functions and the original functions. It is easy to find that the magnitudes of new wind functions are much smaller than the original ones. The complete, new wind functions $V_L$ and $V_S$ are shown below.

$$V_L=\left\{\begin{array}{ll}0,& 0\le u_{*}\le 0.1067 m/s\\ 1.571\times {10}^{-7}{u}_{*}^3+1.479\times {10}^{-7}{u}_{*}^2-4.421\times {10}^{-8}{u}_{*}+2.89\times {10}^{-9},& 0.1067<u_{*}\le 0.3508 m/s\\ -2.546\times {10}^{-8}{u}_{*}^3+1.567\times {10}^{-7}{u}_{*}^2-2.709\times {10}^{-8}{u}_{*}+3.761\times {10}^{-9},& 0.3508<U_{10}\le 1.7987 m/s\\ 1.865\times {10}^{-9}{u}_{*}^3-2.566\times {10}^{-8}{u}_{*}^2+1.534\times {10}^{-7}& u_{*}+1.021\times {10}^{-7},u_{*}>1.7987 m/s\end{array}\right.$$

(18)

$$V_S=\left\{\begin{array}{ll}0,& 0\le u_{*}\le 0.1067 m/s\\ 5.366\times {10}^{-6}{u}_{*}^3+1.799\times {10}^{-6}{u}_{*}^2-7.048\times {10}^{-7}{u}_{*}+4.92\times {10}^{-8},& 0.1067<u_{*}\le 0.3508 m/s\\ -3.453\times {10}^{-7}{u}_{*}^3+3.678\times {10}^{-6}{u}_{*}^2-8.405\times {10}^{-7}{u}_{*}+1.142\times {10}^{-7},& 0.3508<U_{10}\le 1.7987 m/s\\ 4.661\times {10}^{-8}{u}_{*}^3-6.744\times {10}^{-7}{u}_{*}^2+4.748\times {10}^{-6}& u_{*}+1.432\times {10}^{-6},u_{*}>1.7987 m/s\end{array}\right.$$

(19)

By replacing the unreasonable whitecap coverage in AN15 with $W_{H18}$, we have improved the applicability of this algorithm at moderate to high wind speeds. To avoid a complex integration process and apply this algorithm to numerical models to forecast TCs, we fitted a set of new wind functions $V_L$ and $V_S$ with the measurements of the FASTEX dataset and then obtained a new, fast heat flux algorithm that includes sea spray transfer, which is suitable for high wind speeds (Equations (3), (4), (18), and (19)). We named this algorithm YJ22. The performance of the YJ22 scheme under the typical TC environment (same as Figure 2a) is shown in Figure 7. Compared with Figure 2a, the YJ22 scheme performs much better than the AN15 scheme and obtains reasonable $H_{s,sp}$ and $H_{L,sp}$ under high wind speeds; therefore, we can try to apply the YJ22 scheme to the numerical model to simulate a TC.

3.3. Application of the YJ22 in the COAWST Model

To study the effect of sea spray-induced heat flux on TCs, we implemented the YJ22 algorithm in the COAWST model. Because the simulation of a TC mainly occurs in the WRF model, we decided to implement the YJ22 algorithm into the surface layer of the WRF. Warner et al. [29] reserved an interface for variable exchange with the wave model in the MYNN surface layer module, and we will insert the YJ22 in this module. The sea spray-induced heat flux calculated by the surface layer module will transfer to the boundary layer schemes, which will affect the whole system.

The proposed YJ22 algorithm is based on AN15, and many functions in our scheme come from modified functions in the AN15 scheme. The readers can obtain the AN15 scheme at http://www.nwra.com/resumes/andreas/software.php (accessed on 15 February 2022) [13]. Compared with the AN15 algorithm, there are two main improvements in our scheme: (i) The YJ22 takes into account the effect of the significant high wave. (ii) We replaced the whitecap coverage $W_{F94}$ in AN15 with the reasonable whitecap coverage $W_{H18}$ and proposed new wind functions suitable for low to high wind conditions. Then, based on the MYNN surface layer module, we have made the YJ22 algorithm a pluggable module. The detailed embedding process is shown in Figure 8. If you add “define SPRAY_FLUX” to the header file, you can integrate the sea spray-induced heat flux calculated by the YJ22 algorithm into the model.

Input variables needed by the YJ22 algorithm include: wind speeds $U_z$ at the height $Z$, air temperature $T_z$, relative humidity $R{H}_z$, sea surface temperature SST, sea level pressure SLP, significant wave height $H$, and salinity $S$. Output variables provided by YJ22 include: the spray-induced latent heat flux $H_{L,sp}$, the spray-induced sensible heat flux $H_{S,sp}$, the air–sea interfacial latent heat flux $H_{L,int}$, and the air–sea interfacial sensible heat flux $H_{L,int}$. The main process of calculating the air–sea heat flux by the YJ22 algorithm is shown in Algorithm 1. The original functions of FIND_USTAR, NU, MAIN_FLUX, and SPRAY_FLUX can all be found at http://www.nwra.com/resumes/andreas/software.php. The realization of YJ22 is generally divided into three steps: Step 1 is to use the input variables and call the subroutines FIND_USTAR and NU to calculate some necessary physical quantities, such as the friction speed $u_{*}$, the Monin–Obukhov length $L$, and the lamination stabilities ${\mathsf{\Psi }}_m$ and ${\mathsf{\Psi }}_h$. These quantities are required later. Step 2 is to call the subroutine MAIN_FLUX to calculate the $H_{L,int}$ and $H_{S,int}$. Step 3 is to call the subroutine to calculate the $H_{L,sp}$ and $H_{S,sp}$.

Algorithm 1. The process of calculating the air–sea heat flux by the YJ22 algorithm.

Known: height $Z$, wind speed $U_z$, air temperature $T_z$, relative humidity $R{H}_z$, sea surface temperature SST, sea level pressure SLP, significant wave height $H$, salinity S

Required: $H_{L,sp}$, $H_{S,sp}$, $H_{L,int}$, $H_{S,int}$

Step 1: $u_{*}$ ← FIND_USTAR($U_z, Z$) and $L, {\mathsf{\Psi }}_m, {\mathsf{\Psi }}_h$ ← NU$\left(T_z, U_z, Z, u_{*}\right)$

Step 2: $H_{S,int}, H_{L,int}$ ← MAIN_FLUX$\left(Z, U_z, T_z, R{H}_z, SST, SLP, H_s, S\right)$ Step 3: $H_{S,sp}, H_{L,sp}$ ← SPRAY_FLUX$\left(Z, U_z, T_z, R{H}_z, SST, SLP, H_s, S\right)$

4. Case Introduction and Experimental Design

4.1. An Overview of Super Typhoon Mangkhut

From Figure 2a, we find that the magnitude of the sea spray-induced heat flux calculated by the AN15 algorithm is still reasonable when the wind speed is approximately 40 m/s. Prakash et al. [58] applied AN15 to the COAWST model for simulating the weak TC Vardah (its maximum sustained wind speed was weaker than 40 m/s); however, we tested that if the wind speed were any higher, the model would crash. In other words, the AN15 algorithm is not suitable for high wind speeds. To reflect the performance of the YJ22 algorithm under high wind speeds, we specifically selected the super typhoon Mangkhut (the maximum sustained wind speed reached 80 m/s).

Mangkhut is the 22nd named tropical cyclone in the northwest Pacific Ocean in 2018, which formed as a tropical depression on 7 September and intensified rapidly. On 11 September, Mangkhut was upgraded to a super typhoon and continued to move westward. Mangkhut was one of the strongest typhoons ever recorded and caused very large losses of life and property in China and the Philippines. Because of the severe impact and damage, Mangkhut was removed from the TC naming list. Due to the severe wind speeds, super typhoon Mangkhut is suitable for testing the performance of YJ22 and exploring the influence of spray-induced heat flux on TCs under high wind speeds.

4.2. Experiments Design

Through experiments, we successfully applied the YJ22 algorithm to the COAWST model and simulated super typhoon Mangkhut. During this process, we explored: (i) the effects of sea spray on heat flux under high wind speeds and (ii) the effects of sea spray-induced heat flux on the track, intensity, and development of TCs. To better investigate the effects of sea spray-induced heat flux on TC development, we added coefficients to the heat flux calculation formula:

$$H_{L,T}=H_{L,int}+a{H}_{L,sp}$$

(20)

$$H_{S,T}=H_{S,int}+b{H}_{S,sp}$$

(21)

We set up five numerical experiments to achieve the above goals, and the details of the five experiments are shown in

Table 1. Numerical experimental design in detail.

EXP ID	EXP Name	a	b
1	L0_S0	0	0
2	L1_S0	1	0
3	L0_S1	0	1
4	L1_S1	1	1
5	L2_S2	2	2

. Experiment 1 is the control run. In this numerical experiment, only the interfacial heat fluxes are used in the coupled model, and we do not consider the sea spray-induced heat fluxes. Experiment 2 indicates that only the influence of the spray-induced latent heat fluxes $H_{L,sp}$ on the TC is examined, and the influence of the spray-induced sensible heat fluxes $H_{S,sp}$ is not considered in the model. Experiment 3 is the exact opposite of Experiment 2. Experiment 4 takes both the $H_{L,sp}$ and $H_{S,sp}$ into account, and, in theory, this experimental result should be the most similar to the real situation. To better explore the overall effect of sea spray-induced heat fluxes on TCs, Experiment 5 doubles both the $H_{L,sp}$ and $H_{S,sp}$.

The comparison between Experiments 1 and 4 is the focus of our study. By comparing the simulation results of these two experiments, we analyze whether the addition of sea spray-induced heat fluxes can improve the TC simulation. In addition, by comparing Experiments 1 through 3, the effects of the $H_{L,sp}$ and $H_{S,sp}$ on TC simulation can be investigated; by comparing the results of Experiments 1, 4, and 5, the overall effects of sea spray-induced heat fluxes can be clearly understood.

We simulated super typhoon Mangkhut from 0000 UTC 10 September to 0000 UTC 15 September. Because Mangkhut gradually intensified to its peak during this period, we were better able to explore the effect of sea spray-induced heat fluxes on TC development. Other settings for the model have been described in detail in Section 2.2.

5. Results and Discussion

5.1. Effect of Spray-Induced Heat Fluxes on TC Track and Intensity

5.1.1. TC Track

The model-simulated tracks and track errors generated by different numerical experiments are shown in Figure 9. It is easy to find that the TC tracks simulated by different experiments are basically consistent with the JTWC’s best track data, especially in the simulation of the first 72 h. The differences in the TC tracks and track errors between the five experiments are very small, which indicates that the sea spray-induced heat flux has little effect on the TC track simulation. Other studies also found that the air–sea heat flux has little effect on the TC track [4,59] because the influence of large-scale circulation on TC tracks is much greater than that of a small-scale air–sea flux. However, the intensity and structure of the TCs simulated by different experiments are different, which leads to a slight difference in the interaction between TCs and large-scale circulation. This slight difference leads to small differences in the simulated tracks. As the simulation times increase, due to the cumulative effect of the numerical simulations, there have been significant differences in the TC intensities and structures in different experiments. The interactions of TCs with large-scale circulation also show differences; this is why the track errors after 72 h are obviously different.

5.1.2. TC Intensity

We chose the minimum sea level pressure (MSLP) and the maximum sustained wind speed (VMAX) to assess the intensity of TCs because these two variables are the most used indicators. Figure 10 shows the changes in the MSLP and VMAX during the whole simulation of the super typhoon Mangkhut. The comparisons of the MSLP and VMAX between the five experiments and the JTWC data are plotted in Figure 10a,b, respectively. First, we compare the results of Experiment 1 (L0_S0) and Experiment 4 (L1_S1) to explore the effect of sea spray-induced heat fluxes on TCs. The red line represents the simulation of Experiment 1. The MSLP simulated by Experiment 1 enhances slowly, and the simulated minimum pressure is only 940.2 hPa, which is much higher than the JTWC data. Compared with Experiment 1, it is obvious that the MSLP obtained from Experiment 4 is closer to the JTWC’s best track data, and the simulated minimum is optimized to 912.9 hPa. This result proves that the sea spray-induced heat fluxes may significantly improve the simulation of TC intensity. After considering the sea spray-induced heat flux, the TC intensification speed is significantly increased, and the MSLP that a TC can reach is also lower. By comparing the results of Experiments 1, 4, and 5, we found that sea spray-induced heat fluxes can significantly change the intensification speed and maximum intensity of a TC. The greater the magnification of the sea spray-induced heat fluxes is, the faster the TC intensifies and the stronger the TC maximum intensity is. By comparing the results of Experiments 1–3, it can be found that the influence of $H_{L,sp}$ on the TC intensity is dominant in sea spray-induced heat fluxes. The intensification speed and maximum intensity simulated by Experiment 2 are obviously improved compared with the results of Experiment 1. However, the difference between the results of Experiments 1 and 3 is not obvious, which indicates that there is little effect of $H_{S,sp}$ on the TC intensity. Figure 10b shows the change trend of the VMAX, and the effects of sea spray-induced heat fluxes on the TC intensity shown in Figure 10b are consistent with those in Figure 10a.

To quantitatively analyze the influence of sea spray-induced heat fluxes on TC intensity,

Table 2. Root mean square error (RMSE) and model skill (S) for the MSLP and VMAX from 5 experiments.

Exp ID	Exp Name	MSLP		VMAX
		RMSE	S	RMSE	S
1	L0_S0	37.09	0.24	18.67	0.19
2	L1_S0	25.08	0.53	12.74	0.46
3	L0_S1	34.98	0.27	17.88	0.21
4	L1_S1	19.38	0.69	9.37	0.67
5	L2_S2	16.29	0.80	7.27	0.79

lists the root mean square error (RMSE) and model skill (S) of the intensity of the typhoon Mangkhut simulated by five experiments.

$$\mathrm{RMSE}=\sqrt{\frac{1}{N}{\displaystyle \sum }_{i=1}^N{\left(y_i-x_i\right)}^2}$$

(22)

$$\mathrm{S}=1-\frac{{\sum }_{i=1}^N{\left|y_i-x_i\right|}^2}{{\sum }_{i=1}^N\left({\left|y_i-\overline{x}\right|}^2+{\left|x_i-\overline{x}\right|}^2\right)}$$

(23)

where $x_i$ and $y_i$ are the JTWC’s best track data and model-simulated values, respectively.

The RMSE and S quantitatively confirm our above points: (i) The sea spray-induced heat fluxes were able to significantly improve the simulation of TC intensity; (ii) the spray-induced latent heat flux $H_{L,sp}$ is more important than the spray-induced sensible heat flux $H_{S,sp}$ in the simulation of TC intensity. The comparison between the results of Experiments 2 and 3 shows that only considering the $H_{L,sp}$ can significantly change the simulation of TC intensity, but only considering the $H_{S,sp}$ has little effect on the simulation. It is worth mentioning that the result of Experiment 5 is better than that of Experiment 4. The reason for this result is that the numerical model cannot accurately simulate the dynamics of a TC and the wind field error in the driving model, which leads to a weak wind field in the model simulation [3,60,61,62]. This phenomenon is common in the simulation of super TCs [62]. Experiment 5 doubled the values of sea spray-induced heat fluxes, which significantly enhanced the energy that a TC extracts from the ocean. Therefore, Experiment 5 simulated a stronger wind field than the other experiments (shown in Figure 11), which allowed the TC to reach a stronger intensity. However, there are no measurements or reasonable physical supports to indicate that taking the coefficients of sea spray-induced heat fluxes as two in the YJ22 algorithm can better simulate the TC intensity. In this experimental design, the aim of Experiment 5 is only to better explore the influence of sea spray-induced heat fluxes on TCs.

5.2. Effects of Sea Spray-Induced Heat Flux on the Evolution of TCs

To analyze the effect of sea spray-induced heat flux on the evolution of a TC, we plotted the Hovmöller diagrams of azimuthally averaged sea level pressure (SLP) and a 10 m wind $U_{10}$, shown in Figure 12 and Figure 13, respectively. The abscissa is the radial distance from the center of the TC, and the ordinate is the simulation time. Since the structure of the TC is not obvious in the first 24 h, we selected the simulations from 24 to 120 h for analysis.

Figure 12 clearly shows the intensification and horizontal evolution of the sea level pressure of the TC, and the evolutions of the low central pressure simulated by the five experiments are consistent with the MSLP shown in Figure 10a. Changes in the heat fluxes can significantly affect the distribution and evolution of the low central pressure, which is consistent with previous studies [41]. The faster the TC intensifies, the faster the low central pressure develops in the horizontal direction. By comparing the results of Experiments 1, 4, and 5, we can conclude that the addition of sea spray-induced heat fluxes could make the low central pressure of the TC develop more fully and influence the farther range. By comparing Experiments 2 and 3, we find that the $H_{S,sp}$ has little effect on the evolution of the TC’s low-pressure structure. However, the $H_{L,sp}$ plays a significant role in promoting the development of the TC’s low-pressure structure. In other words, the sea spray-induced heat fluxes can make TCs develop faster and more fully.

Zhao et al. used numerical simulation experiments to find that the addition of sea spray can improve the simulation of TC wind fields [63]; however, they did not explore this issue in detail and did not analyze the effects of the $H_{L,sp}$ and $H_{S,sp}$. Figure 13 shows the development of the azimuthally averaged tangential winds and radial winds at a 10 m height in the radial direction. Both the tangential and radial wind speeds in the TC center are extremely low, and the wind speeds peak in the range of 50–100 km from the TC center, which is the active area of the TC. Then, the wind speed gradually decreases as it moves further away from the TC center. This distribution feature has also been demonstrated in other studies [4,64]. The comparison between Experiment 1 and Experiment 4 shows that the addition of sea spray-induced heat fluxes can greatly enhance the intensity of both the tangential and radial winds at the bottom of a TC and make the range further affected by high wind speeds. In addition, it will also make the radial wind field develop more fully, which will bring a stronger convergence effect. By comparing the results of Experiments 2 and 3, we find that adding the $H_{S,sp}$ alone has little effect on the evolution of the TC wind field; however, adding the $H_{L,sp}$ alone will greatly promote the development of the wind field. It is worth noting that the wind field simulated by Experiment 4 is stronger than that simulated by Experiment 2, which means that based on adding the $H_{L,sp}$, adding the $H_{S,sp}$ can promote the development of the TC wind field. This may be because the wind speeds in Experiment 4 are high; therefore, the effect of the $H_{S,sp}$ will become more obvious than that in Experiment 3.

5.3. Heat Flux Analysis of TC

We have proven that sea spray-induced heat fluxes play an important role in TC intensity and evolution. In this subsection, we explore the proportion of sea spray-induced heat fluxes in total heat fluxes in the TC environment and analyze the reasons for the differences in different experiments.

To achieve our purpose, the azimuthally averaged total latent and sensible heat fluxes ($H_{L,T}$ and $H_{S,T}$) simulated by the five experiments are shown in Figure 14 and Figure 15, respectively. As seen from Figure 14 and Figure 15, the $H_{L,T}$ is generally stronger than the $H_{S,T}$ and is the main approach of heat transfer during a TC’s evolution, which is consistent with other studies [58,65]. Therefore, the latent heat flux plays a greater role in simulating the TC intensity and structure, which is consistent with our previous conclusion. In Figure 14 and Figure 15, the distribution of the total heat fluxes is similar to that of the wind field shown in Figure 13. Both heat fluxes are weak near the TC center because the low wind speeds in the TC’s eye restrict the air–sea heat transfer. The total air–sea heat transfer is also the most active with the highest wind speed in the range of 50–100 km from the TC’s center. Then, the $H_{L,T}$ and $H_{S,T}$ decrease with increasing distance from the TC’s center. The heat transport in Figure 13 and Figure 14 corresponds to the wind field evolution in Figure 13. The TC simulated by the experiment with stronger heat transfer can obtain more energy from the ocean; therefore, the corresponding wind field can develop more fully and more strongly.

Figure 16a,b reflect the evolution of the average total latent and sensible heat fluxes ($H_{L,T}$ and $H_{S,T}$) within 150 km from the TC’s center as simulated by different experiments with the simulation time. It can be seen that the $H_{L,T}$ and $H_{S,T}$ calculated by the different experiments are quite different. In the same experiment, the heat transfer by the latent heat is more than three to five times the sensible heat, which also indicates that the latent heat flux is the main form of the air–sea heat exchange under high wind speeds. Figure 16c reflects the trend of the total air–sea heat fluxes simulated by different experiments. The order of total heat fluxes from strong to weak is Experiment 5, Experiment 4, Experiment 2, Experiment 3, and Experiment 1, which is consistent with the order of TC intensities in Figure 10. The stronger heat fluxes produce a stronger TC intensity, confirming the conclusion that the air–sea heat transfer has a significant effect on TC intensity. The evolutions of the total average sea spray-induced heat flux are shown in Figure 16d. From Figure 16d, we found that in Experiment 4, the sea spray-induced heat fluxes within 150 km of the TC’s center account for approximately 30% of the total air–sea heat fluxes. However, it is worth noting that, at the simulation time of 96 h, the total air–sea heat flux and the total sea spray-induced heat flux simulated by Experiment 4 are 941.54 W/m² and 317.74 W/m², respectively; the total air–sea heat flux simulated by Experiment 1 is 572.18 W/m². Thus, we find that $572.18+317.74=889.82<941.54$. This means that because of the addition of sea spray-induced heat fluxes, the TC can obtain more energy from the ocean, which can generate a stronger wind field and, in turn, promotes the transport of air–sea heat fluxes. This positive feedback can improve the simulation of TC intensity, which significantly improves the problem that the numerical models tend to underestimate the intensities of strong TCs.

6. Summary and Conclusions

Sea spray-induced heat fluxes become significant under high wind speeds, such as in TC environments. Applying the sea spray-induced heat flux to a numerical model can improve the simulation of TCs, in theory. However, the commonly used sea spray-induced heat-transfer algorithm AN15 is not suitable for high wind speed conditions. To solve this problem and apply spray-induced heat fluxes to the coupled model to improve the simulation of TCs, we performed a series of theoretical analyses and experiments. The key results and conclusions are given as follows:

1. We modified the unreasonable whitecap coverage and wind functions $V_L$ and $V_S$ in AN15 and proposed the improved, fast spray-induced heat flux algorithm YJ22 based on the FASTEX dataset. This algorithm can calculate reasonable sea spray-induced heat fluxes under high wind speeds and has been applied in the coupled numerical model COAWST to explore the effect of sea spray-induced heat fluxes on the super typhoon Mangkhut.

2. The sea spray-induced heat fluxes have little effect on the TC track simulation. The TC track is more dependent on large-scale circulation than on small-scale air–sea heat fluxes.

3. Sea spray-induced heat fluxes can significantly improve the simulation of TC intensity. Compared with Experiment 1, which only considers the interfacial heat fluxes, Experiment 4 can simulate the MSLP and UMAX closer to the JTWC’s best track data.

4. The influence of sea spray-induced heat fluxes on the TC structure is significant. The addition of sea spray will make the low-pressure structure and wind field structure of a TC more fully developed in the horizontal direction.

5. The addition of sea spray-induced heat fluxes obviously enhanced the total air–sea heat fluxes. After adding sea spray-induced heat fluxes, more energy is transferred from the ocean to the lower atmosphere. This process reduces the central low pressure while enhancing the 10 m wind field, making the bottom convergent airflow stronger.

In our future work, we will continue to improve the performance of the YJ22 scheme in combination with the impact of the sea surface roughness on TCs and apply this scheme to the simulation of more TC cases to verify our conclusions.