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

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## Abstract

**:**

## 1. Introduction

## 2. Data and Model Descriptions

#### 2.1. FASTEX Dataset

#### 2.2. Model Description and Configuration

#### 2.2.1. Atmospheric Model

#### 2.2.2. Wave Model

## 3. An Improved Algorithm YJ22 and Its Application

#### 3.1. The Process of Proposing AN15 and Its Problems

^{2}, and ${H}_{S,sp}$ exceeds 2500 W/m

^{2}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/m

^{2}, and the magnitude of the sensible heat flux is several hundred W/m

^{2}. 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

#### 3.3. Application of the YJ22 in the COAWST Model

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

#### 4.2. Experiments Design

## 5. Results and Discussion

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

#### 5.1.1. TC Track

#### 5.1.2. TC Intensity

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

#### 5.3. Heat Flux Analysis of TC

^{2}and 317.74 W/m

^{2}, respectively; the total air–sea heat flux simulated by Experiment 1 is 572.18 W/m

^{2}. 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

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Model domains in the simulation of TC Mangkhut. the outermost box is d01, d02 is the white box, and the red box represents d03. The blue box represents the domain of SWAN.

**Figure 2.**(

**a**) Values of the interfacial and spray-induced latent and sensible fluxes calculated by the AN15 algorithm for a range of ${U}_{10}$ under the typical tropical cyclone environment; (

**b**) the whitecap coverage ${W}_{F94}$ as a function of the 10 m wind speed ${U}_{10}$. The dotted line represents the whitecap coverage equal to 1.

**Figure 3.**The comparison of ${W}_{H18}$ and ${W}_{F94}$ with 10 m wind speed ${U}_{10}$. The black line represents ${W}_{H18}$, and the blue line represents ${W}_{F94}$.

**Figure 4.**Comparison of the performance of the original and modified algorithms in the simulation of air–sea latent heat flux: (

**a**) reflects the difference between the measurements and the modeled heat flux, including the sea spray-induced heat flux calculated by the AN15 algorithm; (

**b**) also reflects the difference between the measurements and modeled results, but, here, the sea spray-induced heat fluxes are calculated by the modified algorithm. The independent variable is the 10 m, neutral-stability wind speed ${U}_{N10}$. The difference between this and ${U}_{10}$ is notable. The ordinate represents the difference between the measurements and the modeled values. The black solid line represents the modeled values, which are equal to the observations. The red lines represent the least-squares fit to all data. The smaller the slope of the red line is, the better the effect on the model.

**Figure 5.**Comparison of the performance of the original and modified algorithms in the simulation of air–sea sensible heat flux. Other settings are the same as in Figure 4. (

**a**) reflects the difference between the measurements and the modeled heat flux, including the sea spray-induced heat flux calculated by the AN15 algorithm; (

**b**) also reflects the difference between the measurements and modeled results, but, here, the sea spray-induced heat fluxes are calculated by the modified algorithm.

**Figure 6.**Comparison of the new and the original wind functions ${V}_{L}$ and ${V}_{S}$. The black curve represents the wind functions ${V}_{L}$ and ${V}_{S}$ in AN15. The yellow circles represent the values of new wind functions calculated by the modified scheme with the measurements in the FASTEX. The red curve represents the new wind functions, which are fitted with a cubic polynomial based on the yellow circles. (

**a**,

**c**) reflect the wind functions ${V}_{L}$ and ${V}_{S}$ under low to moderate wind speed conditions; (

**b**,

**d**) reflect the wind functions ${V}_{L}$ and ${V}_{S}$ under low to high wind speed conditions. (

**a**,

**c**) are parts of (

**b**,

**d**), and the rectangular boxes in (

**b**,

**d**) represent the extent of (

**a**,

**c**).

**Figure 7.**Comparison of ${W}_{H18}$ and ${W}_{F94}$ with a 10 m wind speed ${U}_{10}$. The black line represents ${W}_{H18}$, and the blue line represents ${W}_{F94}$. The TC environment is the same as that in Figure 2.

**Figure 9.**The TC tracks (

**a**) and track errors (

**b**) simulated by different experiments. The squares represent the central location of the TC at 0000 UTC.

**Figure 10.**Along-track(

**a**) MSLP and (

**b**) VMAX from five numerical experiments and the JTWC best track data.

**Figure 11.**The spatial distribution of the 10 m wind speed (m/s) as simulated by the five experiments. The colors represent the wind speed values, and the arrows represent the wind direction.

**Figure 12.**Hovmöller diagrams of the SLP as simulated by the five experiments (

**a**–

**e**). The abscissa is the radial distance from the center of the TC, and the ordinate is the simulation time.

**Figure 13.**Hovmöller diagrams of the azimuthally averaged winds (expressed by colors) and radial winds (expressed by lines) simulated by the five experiments (

**a**–

**e**). The abscissa is the radial distance from the center of the TC, and the ordinate is the simulation time.

**Figure 14.**Hovmöller diagrams of the azimuthally averaged latent heat flux ${H}_{L,T}$ simulated by the five experiments (

**a**–

**e**). The abscissa is the radial distance from the center of the TC, and the ordinate is the simulation time.

**Figure 15.**Hovmöller diagrams of the azimuthally averaged sensible heat flux ${H}_{S,T}$ simulated by the five experiments (

**a**–

**e**). The abscissa is the radial distance from the center of the TC, and the ordinate is the simulation time.

**Figure 16.**Average heat flux within 150 km of the TC center: (

**a**) represents the air–sea latent heat flux, (

**b**) represents the air–sea sensible heat flux, (

**c**) represents the total air–sea heat flux, and (

**d**) represents the total sea spray-induced heat fluxes. The abscissa represents the simulation time.

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 |

**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 |

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**MDPI and ACS Style**

Lan, Y.; Leng, H.; Sun, D.; Song, J.; Cao, X.
An Improved Sea Spray-Induced Heat Flux Algorithm and Its Application in the Case Study of Typhoon Mangkhut (2018). *J. Mar. Sci. Eng.* **2022**, *10*, 1329.
https://doi.org/10.3390/jmse10091329

**AMA Style**

Lan Y, Leng H, Sun D, Song J, Cao X.
An Improved Sea Spray-Induced Heat Flux Algorithm and Its Application in the Case Study of Typhoon Mangkhut (2018). *Journal of Marine Science and Engineering*. 2022; 10(9):1329.
https://doi.org/10.3390/jmse10091329

**Chicago/Turabian Style**

Lan, Yunjie, Hongze Leng, Difu Sun, Junqiang Song, and Xiaoqun Cao.
2022. "An Improved Sea Spray-Induced Heat Flux Algorithm and Its Application in the Case Study of Typhoon Mangkhut (2018)" *Journal of Marine Science and Engineering* 10, no. 9: 1329.
https://doi.org/10.3390/jmse10091329