Ocean Surface Wave Eﬀects on Development of Explosive Cyclone

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Introduction
An explosive cyclone is defined as a more intense extratropical cyclone whose central sea level pressure (SLP) drops by more than 24 hPa in a 24 hour period (Sanders & Gyakum, 1980).Explosive cyclones' surface wind speed and central SLP often reach values equivalent to a tropical cyclone and generate extreme ocean surface waves.They are one of the major causes of severe marine disasters such as coastal floods, ship accidents, and structural damage to offshore platforms.For example, early in January 2018, an explosive cyclone ran along the eastern coast of the U.S. and caused serious blizzards over the eastern U.S. In Massachusetts, high ocean waves have flooded large coastal areas.The total damage caused by this storm amounted to about $1.1 billion.The cyclone was ranked the most powerful winter storm in the history of the U.S.
Three possible mechanisms can rapidly intensify extratropical cyclones: upperlevel forcing associated with potential vorticity anomalies, instability by energy fluxes from the ocean, and massive latent heat releases (Catto, 2016).Explosive cyclones usually emerge in the vicinity of the Gulf Stream and the Kuroshio/Kuroshio Extension.The western boundary currents supply a large amount of sensible and latent heat into the atmosphere.Many studies have pointed out that a large amount of heat supply can rapidly intensify the extratropical cyclones through increasing atmospheric instability and latent heating (e.g., Kuo et al. 1991;Reed et al. 1993;Takayabu et al. 1996;Gyakum & Danielson 2000;dal Piva et al. 2011).The sensible and latent heat supply from the sea surface rapidly develops the explosive cyclone by maintaining the vertical atmospheric circulation of the updraft region (Nuss & Kamikawa, 1990).Hirata et al. (2015Hirata et al. ( , 2019) ) reported the detailed processes of the rapid development of explosive cyclones.First, the sensible and latent heat on the surface layer is advected to the middle troposphere (~600 hPa level) by an intense updraft along the bent-back front near the cyclone center.Then, the equivalent potential temperature increases and strengthens the diabatic heating due to vapor condensation.The resulting latent heat release produces positive potential vorticity in the lower troposphere and enhances the explosive cyclone development.
Ocean surface waves greatly influence the sensible and latent heat supply from the sea surface through sea surface roughness (e.g., Donelan et al. 1993;Oost et al. 2002;Powell et al. 2003;Donelan et al. 2004;Babanin and Makin 2008;Andreas et al. 2012).Drennan et al. (2003) confirmed that the sea surface rough-ness is inversely proportional to the wave age, which is the ratio of wave phase speed and wind friction velocity (  / * ,   ∶ phase speed,  * ∶ friction velocity).The young and steep waves at a short fetch roughen the sea surface and transfer a large amount of sensible and latent heat into the atmosphere.Swells (  /( * cos ) > 1,  ∶ relative angle of the wave to the surface wind) affect sea surface roughness as well (e.g., Sullivan et al., 2014;Mahrt et al., 2018).Patton et al. (2019) performed a large-eddy atmospheric simulation above moving ocean surface waves and proposed a correction formula of the friction velocity with wave age and wind-wave directional difference.The changes in the sea surface roughness may affect the mesoscale atmospheric circulation (e.g., Perrie et al., 2005;Zhang et al., 2006).Pianezze et al. (2018) implemented an atmosphere-ocean-wave coupled model to evaluate the impacts of the ocean surface waves on a tropical cyclone.They reported that the waves roughened the sea surface and enhanced the sensible and latent heat transfer into the atmosphere from the sea surface.Renault et al. (2012) reported that the heat and momentum flux parameterization depending on the sea surface wave showed the most skillful simulation for extratropical cyclones.Those studies imply that the ocean surface waves have essential roles in the explosive cyclone.However, because explosive cyclones are different from tropical cyclones in the high translation speed and the atmospheric fronts, it is still unknown how the ocean surface waves modify the development of an explosive cyclone.
The sea surface temperature (SST) is an important factor controlling sensible and latent heat supply from the sea surface.It is well known that the ocean surface waves intensify vertical mixing in the ocean boundary layer through interactions of pre-existing turbulence.The alternation in the ocean vertical mixing primarily changes the SST.Many previous studies have clarified that the wave-derived changes in SST affect the mesoscale atmosphere phenomena (e.g., Reichl et al., 2016;Wang & Sheng, 2016;Staneva et al., 2017;Pianezze et al., 2018;Wu et al., 2019).Stoney et al. (2017) introduced the non-breaking waveinduced mixing effect into a numerical ocean model.They found that the waveinduced mixing modified shear-induced entrainment and suppressed upwelling under a tropical cyclone, resulting in SST changes near the tropical cyclone trajectory and changing the cyclone intensity.Aijaz et al. (2017) introduced the wave-induced mixing effect into an atmosphere-ocean-wave coupled model and investigated the impacts on the underlying ocean of a tropical cyclone track.They detected significant cooling of the SST and deepening of the mixed layer depth under the tropical cyclone center, which weakened the intensity of the tropical cyclone.Many studies indicate that the wave-induced transformations in internal structures of the ocean boundary layer can weaken the intensity of tropical cyclones, which usually appear in a hot season (e.g., Wada et al., 2010;He & Chen, 2011;Toffoli et al., 2012;Zhang et al., 2018).Meanwhile, an explosive cyclone generally appears in a cold season, when the depth of the ocean mixed layer is much deeper than in a warm season.How the waveinduced transformations in ocean mixing can affect the mesoscale atmospheric phenomena like an explosive cyclone in a cold season in mid-latitude zones remains to be elucidated.
This study aims to clarify the effects of ocean waves on the development of explosive cyclones.An atmosphere-ocean-wave coupled model is tailored to elucidate how the atmosphere-ocean-wave interactions affect the atmospheric and oceanic turbulent boundary layers and, consequently, the development of the explosive cyclone and quantitatively evaluate the ocean wave impacts on the explosive cyclone development.This study aims to analyze one representative explosive cyclone that emerged in the Northwestern Atlantic in January 2018 and brought severe disasters in the Eastern U.S.
The paper is structured as follows.Section 2 provides basic information of the explosive cyclone and the ocean's surrounding environment.Section 3 describes and explains the implementation of an atmosphere-ocean-wave coupled model to analyze the ocean wave impacts on the development of an explosive cyclone.Section 4 overviews the simulation results with the atmosphere-ocean-wave coupled model and verifies the accuracy with in-situ observations.Section 5 demonstrates the effects of the ocean waves on the evolution of the explosive cyclone with the atmosphere-ocean-wave coupled model's sensitivity experiments.Finally, Section 6 summarizes the results and interpretations obtained from the sequential analyses.

Overview of the Explosive Cyclone in January 2018
An explosive cyclone was generated on 03 January at the east of Florida in the Northwestern Atlantic, propagated northeastward, and rapidly developed between 18:00 UTC 03 January and 18:00 UTC 04 January when the central SLP dropped by 53 hPa from 1004 hPa to 950 hPa (NOAA 2019).The maximum deepening rate of the cyclone was 3.3 hPa/hour in the ERA-Interim reanalysis (Dee et al., 2011).Historically, there have been only two explosive cyclones with the deepening rate exceeding 3.3 hPa/hour in the Northern Hemisphere between 1979 and 2014.The track of the cyclone center and the temporal evolution of the central pressure are shown in Fig 1, according to the analysis data of Climate Forecast System Version 2 (CFSv2;Saha et al. 2014).The rapid development of the explosive cyclone occurred during 0:00 and 18:00 UTC on 04 January.The cyclone induced an intense blizzard over the East of the U.S., Canada and even in Florida, and generated storm surge along the Massachusetts Bay.The cyclone also generated extremely high waves.At the observational buoy above East Scotia Slope, 17.1 m significant wave height was observed on 05 January.
The structure of the explosive cyclone well resembled the Shapiro-Keyser model (Shapiro & Keyser, 1990).At the rapid development stage, a strong updraft occurred around the western part of the bent-back front located to the northwest of the cyclone center.Latent heating by vapor condensation intensified in the vicinity of the bent-back front and deepened the explosive cyclone development.The primary factor of the rapid development of the January 2018 explosive cyclone was the supply of sensible and latent heat from the Gulf Stream (Hirata et al., 2019).Since the sea surface states and the heat content in the ocean boundary layer are essential factors of the rapid development of the explosive cyclone, we will investigate the SST and the ocean thermal structure. .With vertical mixing under the cyclone, SST changes depend on the ocean thermal structure.The Gulf Stream axis lies around 41˚N in the vertical cross-section of water temperature.In the south of the Gulf Stream, warm water stays above the cold water; we define this temperature profile as a type-T profile.On the other hand, in the north of the Gulf Stream, the cold water exists above the warm water, i.e., the thermal inversion is found; we define this type of profile as a type-I profile.Due to the presence of the Labrador Current, the type-I profile spreads north of the Gulf Stream.The boundary between the warm and cold currents is north of 41˚N (Fig 2b).The explosive cyclone passed over regions where the thermal profiles switched from type-T to type-I.Since the SST underlying the explosive cyclone has considerable influence on the cyclone development, we investigate the impact of the variation of the thermal profiles on the cyclone development in Section 5.3.The coupled model used in this study is composed of three components: the atmosphere model, the ocean current model, and the ocean surface wave model.This atmosphere-ocean-wave (AWO) coupled model is composed of the Weather Research and Forecasting (WRF) Model (version 3.9) as the atmosphere component model (Skamarock et al. 2008), the Coastal and Regional Ocean COmmunity model (CROCO; http://www.croco-ocean.org),and the WAVEWATCH III version 6.07 (WW3; WW3DG 2019).For variable exchange among the atmosphere-ocean-wave coupled model, the OASIS3-MCT code is used in each model program.The interval of variable coupling is every 6 minutes, which is the least common multiple of the time steps of the three models used for this coupled modeling.The calculation domain of each model is common and designated by the red line, as shown in Fig 1a .The model coupling strategy is illustrated in Section 3.4.

3-1. Model Fundamental Configuration
The WRF model is the atmospheric component of the coupled model.The governing equations are the flux-form Euler equations written with a terrainfollowing hydrostatic-pressure vertical coordinate.WRF provides various options of physical parameterizations for representing clouds, radiation, turbulence, microphysics, surface layer, etc.The microphysics scheme used was WRF Single-moment 6-class scheme (Hong & Lim, 2006) to predict the mixing ratio of six water categories: cloud, water vapor, cloud ice, graupel, snow, and rain.The Betts-Miller-Janjic scheme (Janjic, 1994) was used for the cumulus parameterization.The longwave radiation scheme was the Rapid Radiative Transfer Model (RRTM;Mlawer et al. 1997), and the shortwave radiation scheme was a simple downward integration scheme (Dudhia, 1989).The turbulence scheme for the planetary boundary layer was the Mellor-Yamada-Nakanishi-Niino (MYNN) 2.5 level scheme (Nakanishi and Niino 2009).For the surface layer, a revised MM5 Monin-Obukhov scheme was used (Jiménez et al., 2012).The surface sensible and latent heat flux is calculated with COARE (Coupled Ocean-Atmosphere Response Experiment; Fairall et al., 2003) version 3.0 parameterization.The horizontal grid resolution is 0.08˚in both latitude and longitude with 326 × 501 points.It covers the region of 24~50˚N and 85~45˚W.The vertical grid is 60 stretched levels with an enhanced resolution close to the ground.The time-step of WRF is 30 s.The spin-up run is performed from 00:00 UTC 22 December 2017 to 00:00 UTC 01 January 2018 with the initial condition of CFSv2.The WRF experiments were forced at the lateral boundary conditions of 6-hourly CFSv2.
The CROCO model was used for the ocean component.This model is a variant of ROMS (Regional Ocean Modeling System), originally developed by UCLA (University of California, Los Angeles).The model configuration is based on incompressible hydrostatic equations with the Boussinesq hypothesis.The model grid system consists of a horizontal Cartesian coordinate and a vertical terrainfollowing coordinate.The domain covers the same area as the WRF domain with the horizontal resolution of 1/18˚in both latitude and longitude with 729 × 597 points.The temporal discretization used was a third-order time-splitting scheme with baroclinic and barotropic time steps of 360 s and 9 s, respectively.The bathymetry was built from the ETOPO2v2 with a two arc-minute global.The vertical levels were divided into 45 layers with an enhanced resolution near the upper ocean surface.The highest layer thickness was about 2 m.The minimum depth is set as 20 m.The initial and boundary conditions are constructed from GOFS (Global Ocean Forecasting System) 3.1 analysis output (available online at https://www.hycom.org/dataserver/gofs-3pt1/analysis)developed by the NRL (Naval Research Laboratory) in the U.S. with two days interval.
For the ocean surface wave component, the WW3 model was used.Propagating free surface waves in water with limited depth and currents are generally described with amplitude and phase.WW3 solves the spectral action density balance equation with random phases for selected wavenumber-direction spectra.The third-order scheme by Tolman ( 2002) was used to calculate the wave propagation.The nonlinear wave-wave interactions were modeled with the Discrete Interaction Approximation (DIA, Hasselmann, et al. 1985).The wind-wave interaction is modeled and parameterized following Ardhuin et al. (2010).The bottom friction source term based on the SHOWEX experiments was used by Ardhuin et al. (2003), and the depth-induced wave breaking was modeled with the way of Battjes & Janssen (1978).The WW3 simulation domain corresponds to the domains of WRF and CROCO: Northwestern Atlantic of 24~50˚N and 85~45˚W with a spatial resolution of 0.075˚.The global time step was 360 s, and the source term time step was 10 s.The spectral discretization of WW3 was 36 divisions for the direction (every 10˚) and 35 for the frequency.The surface wind and sea-ice content derived from 6-hourly CFSv2 forced the wave model.The spin-up run was computed for two weeks until 00:00 UTC 01 January 2018.The lateral boundary conditions for the domain were the wave model in the whole Atlantic.The wave model was computed with meridional 0.25å nd zonal 0.2˚resolutions from 01 to 10 January 2018.The spin-up run for the parent domain was computed for the previous December 2017.

3-2. Atmosphere-Wave Interaction
In this study, we configure the coupled model so that the surface roughness and the friction velocity in the atmospheric model are dependent on the surface ocean wave parameters.Here, a part of the boundary layer model of the WRF relevant to this study will be outlined.
The friction velocity  * is an important parameter that represents the surface stress: where   is the surface stress, and   is the air density.The surface aerodynamic roughness length  0 is a vital parameter that exchanges surface information to the atmosphere in a coupled model.The  0 is parameterized as: where  is the kinematic viscosity,  is the gravitational acceleration, and  is the Charnock coefficient, equal to 0.0185 without wave coupling.This relation is also called a Charnock relationship.The Charnock coefficient  is a function of ocean wave parameters in this model (discussed later).Though  * and  0 are not independent,  * is calculated first in the model integration procedure.The  * is calculated as: where   (= 0.4) is von-Karman constant,  () is the wind speed at the height  in the atmospheric model,  is the Monin-Obukhov length, and   is the stability function of momentum.The  0 in Eq.( 2) is computed at the previous iteration in the model with  * in Eq.( 1).The time step of the atmospheric model is much shorter than the wave model.Therefore, the atmospheric model well incorporates the status of the ocean waves.The  * is also associated with the heat flux from the surface.The sensible heat flux   and the latent heat flux   are defined as where   is the specific heat under constant pressure (=1004 J/Kkg),   is the latent heat of evaporation,  is the potential temperature, and  is the specific humidity.The subscript  (lower case) indicates a value at the surface.  is the sensible heat transfer coefficient, and   is the latent heat transfer coefficient, and they are affected by the wave conditions through  * .
The wave information is passed to the atmosphere via the Charnock coefficient : where   is the wave-induced stress defined as: where   is the water density,  is the wave frequency,  is the wave direction, and  in is the input source term.The  in is calculated with the method ST4 option of the WW3 in this study (cf. Ardhuin et al. 2010).
In addition to the wave-induced stress, misalignment of the direction of wave and wind is taken into account.
where  age is the wave age defined by ,  is the relative angle of the wave to the surface wind, and  is a constant parameter equal to 0.007.Patton et al. (2019) reported that replacing the original  * with  *  in the WRF model leads to an improved vertical wind profile above the sea.
Although previous studies have investigated the influences of wave coupling on the atmosphere, how wave coupling affects the explosive cyclone and the turbulent boundary layer is still unclear.Note that the current study does not consider the impacts of sea spray to clarify the influence of the ocean waves themselves on explosive cyclone development.

3-3. Wave-induced Mixing
Our experiment examined how wave-induced mixing affects the ocean field with an explosive cyclone.It is expected that grown waves by the explosive cyclone should enhance the ocean vertical mixing and transform the ocean thermal structure.We applied the non-breaking wave-induced ocean mixing effects into the coupled model.The wave-induced mixing was introduced into the turbulent momentum governing equations in the CROCO model.In this study, the CROCO adopted the GLS (generic length scale) approach, which is a kind of turbulence second-order closure scheme to parameterize turbulent momentum flux.In this research model, the Mellor-Yamada level 2.5 (MY25) scheme is assigned (Mellor & Yamada, 1982).The wave-current interaction that we focus on is the turbulence effects on the internal ocean by surface waves.
In the ocean model, a new term of the non-breaking wave-induced mixing  wave was appended to the existing shear production  in the turbulent momentum governing equations, as suggested by Babanin (2011).The original shear production term  is defined as where (, , ) is the current velocity, ( ′ ,  ′ ,  ′ ) is the turbulent velocity, and   is the eddy viscosity.The overbar represents the Reynolds-averaged value.
The modified shear production term  +  wave is used in the coupled model's GLS scheme.According to Ghantous and Babanin (2014a), the new term  wave is defined as where (= 0.0014) is an empirical constant following Babanin (2017),  is the wavenumber,  is the peak angular frequency,   is the significant wave height, and  is the water depth.This formulation was derived from laboratory experiments and numerical simulations.The method assumes that the turbulence dissipation by the non-breaking waves should be equal to the turbulence production rate (Huang & Qiao, 2010).The method also assumes that all energy dissipated by non-breaking waves goes into turbulence production.With the new term  wave , the wave-induced mixing effect was appended to the eddy viscosity   .In high-grown waves under the explosive cyclone, the ocean mixing is expected to be enhanced, and the boundary layer behaviors transform.

4-1. Reproducibility of fully coupled simulation
The reproducibility of the wind speed and SLP in the AWO experiment was significantly improved compared to the AO experiment.The marine buoy data in the Northwestern Atlantic were analyzed to verify the numerical simulations' accuracy (AWO and AO); eight buoy observations were selected for comparison.
The observation data was collected by the National Data Buoy Center (NDBC; https://www.ndbc.noaa.gov/)and the Environment and Climate Change Canada (http://www.meds-sdmm.dfo-mpo.gc.ca/isdm-gdsi/index-eng.html).The locations of these buoys are shown in Fig 7 .These buoys were selected because of their proximity to the trajectory of the explosive cyclone, as well as their availability during the cyclone emergence.The simulation comparisons with the observations were carried out at hourly intervals to match the numerical simulation output intervals.The data was subsampled into hourly intervals when the observation intervals were 10 minutes.The   time-series of the observation and the AWO experiment results at the LaHave Bank location (42.5˚N, 64.02˚W; 1300 m depth) are illustrated in Fig 8 .Overall, the simulation well reproduced the observed   .The bias and the correlation coefficient during the nine days are -0.8 m and 0.86, respectively.The biases at the other locations are within 0.8 m, and the correlation coefficients are over 0.85.Consequently, the wave simulation showed excellent agreement with the observations.The surface wind speed and the SLP were analyzed for all eight locations.The Taylor diagrams describe the skills of each model for the observations, as illustrated in Fig 9 .The surface wind speed simulation results were fitted to the anemometer height of each location with the Monin-Obukhov similarity theory.The surface wind speed analysis illustrated that the simulations well reproduced the observations, and the AWO performance was superior to the AO.The correlation coefficient at every point during the nine days was over 0.95.The reproducibility for the SLP of both simulations was also considerably high; hence the AWO performance was higher than the AO.This is because the changes of the heat and momentum exchanges on the air-sea interface, induced by the ocean surface waves, affected the free atmosphere.This consequence indicates that ocean surface waves play a significant role in developing the explosive cyclone.The detailed mechanism is discussed in the next section.

Discussions
The wave coupling made notable changes in the explosive cyclone development and the underlying ocean.This section explains the detailed changes and clarifies the mechanisms derived by the wave coupling.

5-1. Wave-driven Changes in Explosive Cyclone Development
The wave coupling to the atmosphere-ocean coupled model moderately deepened the central SLP of the explosive cyclone.The lowest central SLP in the AWO experiment was deeper by 2 hPa than the AO experiment at 4:00 UTC on 05 January (Fig 1b).Fig 10a shows that the total amount of sensible and latent heat flux from the sea surface significantly increased around the cyclone center in the AWO compared to the AO during the rapid cyclone development (12:00 UTC on 04 January).HF total is defined as the area-averaging of sensible and latent heat flux in the square area bounding with 82˚W-60˚W and 25˚N-45˚N.This HF total stands for an amount of heat that the explosive cyclone obtained from the ocean.The HF total in the AWO experiment exceeded that in the AO during the cyclone advent (Fig 11a).On the other hand,  10 under the cyclone declined in the AWO experiment compared to the AO (Fig 11b).This decline is caused by the increase in the sea surface friction derived from the wave coupling.The mechanisms of how the surface heat flux increased and the wind speed decreased will be discussed in detail in Section 5.2.
The SST changed significantly with the wave coupling, as shown in Fig 10b .The SST south of the Gulf Stream cooled down, while the SST north of the Gulf Stream warmed up.This division can be attributed to the vertical temperature profile in the internal ocean.The SST warmed up in the north of the Gulf Stream with the temperature inversion (type-I profile), while the SST cooled down in the south of the Gulf Stream with the typical temperature profile (type-T).The wave mixing effect intensified the vertical mixing in the ocean mixed layer (details in Section 5.3).
The SST cooling south of the Gulf Stream decreases the heat supply from ocean to atmosphere, while the SST warming north of the Gulf Stream does the opposite.Since the total heat amount HF total from ocean to atmosphere consequently increased in the AWO experiment against the AO, the SST cooling effect on HF total was insignificant compared to the other wave-induced effects.The factors affecting the enhanced HF total are the wave-intensified roughness and consequent enhancement in the heat transfer coefficient, and will be discussed in Section 5. 2The atmospheric thermal parameter changed significantly with the amplified surface sensible and latent heat supply.To evaluate the effects of the enhanced heat supply from the ocean with the waveinduced interactions in the AWO experiment, the equivalent potential temperature   vertical profile around the cyclone center was investigated.Fig 12 illustrates the time evolution of vertical profiles of   in AWO experiment and   difference between AWO and AO around the cyclone center from the sea surface to 600 hPa level.The averaging area is defined as a 5 ∘ × 5 ∘ square whose center coincides with the cyclone center.During the rapid development of the explosive cyclone between 0:00 and 18:00 UTC on 04 January (Fig 1a) in the AWO experiment,   in the low troposphere around the cyclone center was warmed by ample sensible and latent heat supply from the sea surface, and the convectively unstable condition was strengthened (Fig 12a).Fig 12b shows that   in the AWO experiment was much higher than that in the AO not only near the surface but also over the middle troposphere (~600 hPa level).An intense updraft occurred in front of the warm front and circulated counterclockwise around the cyclone center.The   warming spread vertically because the intense updraft near the bent-back front lifted high   air on the surface.Consequently, the thermal condition in the middle troposphere around the cyclone center became convectively unstable.The convective instability stimulates the vapor condensation and latent heat release in the explosive cyclone.During the rapid development, the precipitation around the cyclone center (same 5 ∘ × 5 ∘ square as the   calculation) in the AWO experiment was also amplified compared to the AO ( In summary, the wave-coupling effects in the fully coupled experiment strengthened convectively unstable conditions near the surface with larger heat supply from the sea surface to the atmosphere, strengthened precipitation and latent heating around the center, and finally, intensified the explosive cyclone development.The wave-coupling effects should play an important role in the explosive cyclone development since they helped the numerical simulation reproduce the explosive cyclone more precisely, as mentioned in Section 4.

5-2. Effect of Atmosphere-Wave Coupling
The generation of the ocean surface wave modifies the surface roughness and changes the atmosphere and the internal ocean through air-sea interactions.Comparing the A and AW experiments clarifies how the wave directly changed the atmosphere and resulted in the intensification of the explosive cyclone.Fig 14 displays the relationships  0 and   with  10 at 0:00 on 05 January in the same wind bin (3 m/s).In the wave coupling (AW) experiment,  0 defined by equation ( 2) was affected by ocean waves via the wave-affected friction velocity  *  (equation ( 8)) and the Charnock coefficient  (equation ( 6)).Without the wave coupling, friction velocity was calculated with equation (3), and the Charnock coefficient is  = 0.0185.The sensible heat transfer coefficient   is derived from equation (4), The latent heat transfer coefficient   is usually equal to   .The AW experiment generally shows larger  0 and   than those in the A experiment (Fig 14).This intensified  0 leads to an increase in the surface friction in all wind speed conditions.The enhanced surface friction brought weaker surface wind speed.As shown in Fig 15b, the surface wind speed around the cyclone center decreased dominantly in the AW experiment.The decrease of the surface wind speed is reasonable compared with the previous research for the case of a tropical cyclone (Pianezze et al., 2018).Therefore, the roughened sea surface in the AW experiment weakened the surface wind speed.
Despite the surface wind speed reduction, the surface heat transfer coefficient   was larger in intermediate and high wind speeds ( 10 > 4 m/s) for the AW experiment than the A experiment (Fig 14b).Since the wind speed is usually over 10 m/s under the explosive cyclone,   in the AW experiment generally overwhelmed   in the A experiment.The surface heat flux HF total from the ocean to the atmosphere is proportional to  10 and   .Although the increase in   competed with the decrease in  10 due to the enhanced  0 , the consequent HF total was generally larger in the AW experiment than the A experiment at 12:00 on 04 January (Fig 15a).This tendency was maintained entirely during the explosive cyclone advent, which corresponds to the comparison between the AWO and AO, as shown in Fig 11a .HF total increased in the cyclone center's southern area and declined slightly in the eastern area of the cyclone center.The total amount of HF total consequently was augmented during the cyclone advent in the AW experiment compared to the A experiment (not shown). 10 generally decreased when the wave coupling was active at 12:00 UTC on 04 January (Fig 15b).Although several areas had stronger  10 in the AW experiment compared to the A experiment,  10 weakened in most areas with the enhanced  0 in the AW experiment.The area-average wind speed under the explosive cyclone decreased in the AW experiment, corresponding to the comparison between the AWO and AW experiments (Fig 11a).The same explanation applies when comparing the AWO and AO experiments, as demonstrated in Section 5.1.The   alternation enhanced the sea surface sensible and latent heat transfer into the lower atmosphere in the AWO experiment.The sensible and latent heat flux amplification from the sea surface generated convectively unstable conditions in the surface atmospheric layer.This effect should mainly intensify the explosive cyclone development in the fully coupled model. .The WO simulated warmer water temperature in the upper mixed layer and cooler temperature at the bottom of the mixed layer.In terms of the   , the WO produced much higher values in the mixed layer at Point-P after the EC passed over the location (Fig 17d).The increased magnitudes in   are 0.5  2 / at most.The vertical mixing intensified as the wave height grew at Point-P when and after the explosive cyclone passed over the point.Therefore, the experiment revealed wave-induced mixing  wave enhanced vertical mixing and deepened the MLD over a broad area.The enhanced mixing impacted the modeled SST significantly, but with differing effects for the thermal profile types; warming and cooling of upper mixed layer temperatures for the type-I and type-T profiles, respectively.The deepening in MLD due to the wave-induced vertical mixing is consistent with the previous study on a tropical cyclone in the Gulf of Mexico (Aijaz et al., 2017;Pianezze et al., 2018).Jenkins et al. (2012) reported corresponding results that the wave-induced mixing enhances vertical mixing and cools SST down under an extratropical cyclone in the north of the U.K.
To summarize, the wave-induced ocean mixing enhanced the vertical mixing under the explosive cyclone, and the SST changes were affected by the deeplocated water temperature due to enhanced vertical mixing in the mixed layer.
With the effect of the non-breaking wave-induced mixing, the SST south of the Gulf Stream was cooled down with the type-T temperature profile; the SST north of the Gulf Stream was warmed up with the type-I temperature profile.Note that this ocean-wave coupling does not change the Gulf Stream axis in the short duration investigated during the cyclone advent in this study.The non-breaking wave-induced mixing enhanced the vertical mixing, transformed the ocean mixed layer's vertical structure, but the resultant SST change was not as dominant on the development of the explosive cyclone compared to the enhancement in the sensible and latent heat supply by the ocean surface wave.

Summary and Conclusions
This study revealed that the ocean surface waves play a substantial role in intensifying the sensible and latent heat supply from the sea surface and reinforcing the ocean vertical mixing with thermal structure transformation.The integrated effect of these changes intensified the explosive cyclone development.These conclusions were proposed by a coupled atmosphere-ocean-wave model for the explosive cyclone which emerged in the Northwestern Atlantic in January 2018.These wave effects successfully improved the reproducibility of the explosive cyclone in numerical simulations.
We have shown that the ocean waves enhanced the surface sensible and latent heat supply, and strengthened convective instability and precipitation.In other words, the ocean surface waves significantly affected the mesoscale atmospheric phenomenon through sea surface thermodynamics changes.The ocean surface wave's effect on the explosive cyclone was illustrated in Fig 18 .The featured explosive cyclone, generated to the east of Miami, propagated northward along the US east coast with the central SLP deepening.The central SLP reached the lowest value near Massachusetts Bay.The sensible and latent heat supply from the sea surface to the atmosphere increased in the entire region where the cyclone passed.Nevertheless, the oceanic responses were distinct depending on the region due to the internal thermal structure; while the SST south of the Gulf Stream cooled down, the SST north of the Gulf Stream warmed up.Through various sensitivity experiments, the following underlying physical processes were clarified.
The physical processes of the wave impact on the explosive cyclone development are summarized in the schematic diagrams in Fig 19 .The coupling process of atmosphere and wave enhanced the sensible and latent heat supply from the sea surface over the entire Northwestern Atlantic and intensified the cyclone development.As the equivalent potential temperature   increased, convective instability was strengthened in the surface-atmosphere layer.The convective instability prevailed up to the middle troposphere and amplified precipitation accompanying latent heating near the bent-back front.Consequently, the increase in latent heating produced positive potential vorticity and deepened the SLP of the explosive cyclone center.Additionally, the surface wind speed declined since the sea surface friction increased due to the enhanced drag coefficient   .It is reasonable that the enhanced sensible and latent heat supply associated with the atmosphere-wave-ocean interaction was the most significant factor in intensifying the explosive cyclone's development, corresponding with the previous studies.On the other hand, the ocean and wave coupled processes differed between the north and south regions of the Gulf Stream.The nonbreaking wave-induced mixing cooled down the SST south of the Gulf Stream, while the SST warmed up in regions when the cyclone passed over the Gulf Stream because of the temperature inversion layer (type-I).This result agrees with previous studies reporting that the SST response to the developing explosive cyclone is sensitive to vertical mixing.Despite the reduction of SST in the south of the Gulf Stream, the resultant surface sensible and latent heat supply into the atmosphere was enhanced because the wave impact enhancing the transfer coefficients of heat flux overwhelmed the impact of the SST reduction.We succeeded in improving the reproducibility of the explosive cyclone in numerical simulations by the explicit calculation of wave-induced effects.
The work conducted here is the first step to resolving the surface wave effects on explosive cyclones, and there are still unresolved phenomena in this research area.For example, when the ocean wave's phase speed is faster than the surface wind speed, the swell generates the upward momentum flux and distorts the wind vertical profile (e.g., Sullivan et al., 2008;Hanley and Belcher 2008).The boundary layer parameterizations used in the atmospheric model usually assume the logarithmic wind profile, but the swell-induced turbulent momentum should invalidate the assumption.Moreover, the sea spray is also another key in this research area.Including the sea spray could bring some improvement in the atmospheric simulation.These aspects should be studied in future works.
This study showed that ocean waves can significantly affect the mesoscale atmospheric circulation through momentum and heat supplies from the sea surface.
The waves also exhibited great potential in transforming the thermal structures in the marine boundary layer through enhanced vertical mixing.This study concludes that the wave-induced interactions should be considered to improve numerical weather and ocean predictions in mid-latitude regions.

Introduction
This supporting information includes an ocean model configuration in this study.It explains how the non-breaking wave-induced mixing is calculated in the ocean model.

Text S1. Ocean Model Configuration
The governing equations of the ocean model of CROCO are the same as the ones proposed by Uchiyama, McWilliams, & Shchepetkin (2010)  To solve the turbulent momentum flux in the governing equations, GLS (generic length scale) approach to parameterizing them is provided in the CROCO code.The wave-current interaction that we focus on is the turbulence effects on the internal ocean by surface waves.
The generic length scale (GLS) approach is a kind of turbulence second-order closure scheme.The approach solves two quantities on turbulence: turbulence kinetic energy  1 and generic parameter, which will be defined later.The  1 (per unit mass) is defined as In the CROCO model, several GLS approaches are provided.In the model of this research, the Mellor-Yamada level 2.5 (MY25) scheme is assigned.In the MY25 scheme, two equations on turbulent quantities are solved explicitly.The generic parameter in this scheme is  1 , where  is the turbulent length scale.

Fig 2
Fig 2 displays the SST horizontal distribution and vertical cross-section of water temperature just before the explosive cyclone genesis.The explosive cyclone was generated in the warm area south of the Gulf Stream, and it propagated northward across the Gulf Stream (Fig 2a).With vertical mixing under the cyclone, SST changes depend on the ocean thermal structure.The Gulf Stream axis lies around 41˚N in the vertical cross-section of water temperature.In the south of the Gulf Stream, warm water stays above the cold water; we define this temperature profile as a type-T profile.On the other hand, in the north of the Gulf Stream, the cold water exists above the warm water, i.e., the thermal inversion is found; we define this type of profile as a type-I profile.Due to the presence of the Labrador Current, the type-I profile spreads north of the Gulf Stream.The boundary between the warm and cold currents is north of41˚N (Fig 2b).The explosive cyclone passed over regions where the thermal profiles switched from type-T to type-I.Since the SST underlying the explosive cyclone has considerable influence on the cyclone development, we investigate the impact of the variation of the thermal profiles on the cyclone development in Section 5.3.

Fig 1 .
Fig 1. (top) Topography and bathymetry (m; shaded) and the trajectory (yellow dots) of the cyclone center designated by the local minimum of the sea level pressure (SLP) in CFSv2.The red line designates the calculation domain.(bottom) Time-series of the central minimal SLP [hPa] of the cyclone for the AWO (red) and the AO (blue) simulations.

Fig 2 .
Fig 2. (a) Horizontal distribution of SST (shaded; ℃) and surface current velocity (vector; m/s) at 0:00 UTC on 03 January in GOFSv3.1.(b) Vertical cross-section of water temperature (℃) across the black line in (a) at 0:00 UTC on 03 January.3 Data, or a descriptive heading about data Fig 3. Schematic diagram of the coupled model and exchanged variables.4 Results of Fully Coupled Simulation The evolution of the explosive cyclone was successfully reproduced in the fully coupled simulation (AWO).From 0:00 UTC on 04 January, the cyclone's central SLP dropped from 994 hPa to 947 hPa (-47 hPa) in 24 hours and reached 942 hPa at 4:00 UTC on 05 January (bottom figure in Fig 1).Although the decrease in the cyclone central pressure in the AWO experiment was slightly greater than that in the CFSv2 data, the experiment successfully reproduced the timing of the rapid intensification of the explosive cyclone.The reproduced trajectory was well traced to the CFSv2 data (Fig 4), meaning that the wave coupling does not significantly shift the cyclone's trajectory.

Fig 7 .
Fig 7. Geographical locations of the eight observation buoys in the Northwestern Atlantic.

Fig 8 .
Fig 8. Time-series of   [m] at the LaHave Bank buoy location.The red line represents the AWO experiment, while the black dots represent the observation.

Fig 9 .
Fig 9. Taylor diagrams for the observed parameters: (a) the surface wind speed [m/s] and (b) SLP [hPa] with the AWO (red dots) and AO (blue dots) experiments.The data is normalized by the standard deviation of the buoy observation data.
Fig 13).As Hirata et al. (2015) demonstrated, the enhanced unstable condition intensifies the release of latent heat around the bent-back front.The consequent latent heat produces positive potential vorticity and intensifies the rapid development of the explosive cyclone.The intense condensation of vapor led to intense precipitation and decreased   .After the rapid development of the cyclone, the reduction of   in the AWO was larger than the AO due to more precipitation (Fig 12b).

Fig 13 .
Fig 13.Time-series of precipitation [mm/h] around the cyclone center for the

Fig 14 .
Fig 14.Relationships (a)  0 [mm] and (b)   with  10 [m/s] at 0:00 UTC on 05 January.The error bars represent the standard deviations.The lines represent the A (orange) and the AW (green) experiments.

Fig 18 .
Fig 18.Schematic illustration of the ocean surface wave impacts accompanied by the explosive cyclone in this region.

Fig 19 .
Fig 19.Schematic diagram explains how the ocean waves affect the explosive cyclone development through wave-derived interactions with the atmosphere and the ocean.
Patton et al. (2019)constructed an atmospheric large-eddy simulation model followingSullivan et al. (2014)and investigated the relationships among atmospheric turbulence, wave propagating direction, and wave age.They found that the wave direction and wave age significantly influence the wind vertical profile and turbulence because the swell generates wave-induced turbulence in the atmospheric boundary layer.They suggested modifying the friction velocity  *  with the wave direction and age as

Table 1 .
Setups of the six sensitivity experiments.CFSv2 is provided as the off-line external forcing.

Table 2 .
Coupled variables among the elemental models and their detailed explanations.The first column is the sender of the variables, and the second column is the receiver.
that incorporates wavecurrent interactions.The modified governing equations of the ocean model with Reynoldswhere ( () ,  () ,  () ) is the Stokes drift, A % ,  ' ,  , B is the vortex force,  " is the Bernoulli head,  is unpreserved force,  & is an unpreserved force by the wave,  is eddy viscosity, and  * is eddy diffusivity for the scalar value  (in the model, potential temperature and salinity are solved).* is the unpreserved force for the scalar value  .The Einstein summation convention is used in these equations.These equations are closed by parameterizing the vertical momentum flux and turbulent tracer fluxes as:where the eddy viscosity  -and eddy diffusivity  ..The Stoks velocity is defined for a monochromatic wave field by  ≡ ( () ,  () ) =  1  2 ℎ (ℎ +  +  O) ℎ 2( + ℎ)  ,(7) () = − 2 • U ( () ,  () )where ℎ(, ) is the ocean's depth;  is the sea level;  O is the quasi-static sea-level by the surface wave and air-pressure;  is the wave amplitude;  is its wave number vector;  2 is a horizontal differential operator.The horizontal and vertical vortex force and Bernoulli head are defined by A % ,  ' B = − \ ×   [( \ •  2 × ) + ] −  () +  :  −  1  &5;; ) ,(15)where  9 ,  1 , and  : are constant coefficients,  &5;; is the wall proximity function, and  8 = 2.44 is the Schmidt number for  1 . and  represent production by shear and