Sea-spray-mediated heat flux plays an important role in air–sea heat transfer. Heat flux integrated over the droplet size spectrum can simulate well the total heat flux induced by sea spray droplets. Previously, a fast algorithm of spray flux assuming single-radius droplets (A15) was widely used, as the full-size spectrum integral is computationally expensive. Based on the Gaussian quadrature (GQ) method, a new fast algorithm (SPRAY-GQ) of sea-spray-mediated heat flux is derived. The performance of SPRAY-GQ is evaluated by comparing heat fluxes with those estimated from the widely used A15. The new algorithm shows a better agreement with the original spectrum integral. To further evaluate the numerical errors of A15 and SPRAY-GQ, the two algorithms are implemented into the coupled Climate Forecast System model version 2.0 (CFSv2.0) and WAVEWATCH III (WW3) system, and a series of 56 d simulations in summer and winter are conducted and compared. The comparisons with satellite measurements and reanalysis data show that the SPRAY-GQ algorithm could lead to more reasonable simulation than the A15 algorithm by modifying air–sea heat flux. For experiments based on SPRAY-GQ, the sea surface temperature at middle to high latitudes of both hemispheres, particularly in summer, is significantly improved compared with the experiments based on A15. The simulation of 10 m wind speed and significant wave height at middle to low latitudes of the Northern Hemisphere after the first 2 weeks is improved as well. These improvements are due to the reduced numerical errors. The computational time of SPRAY-GQ is about the same as that of A15. Therefore, the newly developed SPRAY-GQ algorithm has potential to be used for the calculation of spray-mediated heat flux in coupled models.
Sea spray droplets, ejected from oceans, include film drops, jet drops and
spume drops (Veron, 2015). The first two types of droplets are
generated from bubble bursting caused by ocean surface wave breaking, with
radius ranging from 0.5 to 50
The sea-spray-mediated heat transfer mainly occurs within the droplet
evaporation layer (DEL) near the sea surface (Andreas and Decosmo, 1999,
2002; Fairall et al., 1994). Sea spray droplets with the same temperature as the
ocean surface can lead to sensible heat flux in DEL, while water evaporated
from these droplets can further release latent heat to the atmosphere
(Andreas, 1992; Borisenkov, 1974; Bortkovskii, 1973; Wu, 1974; Monahan
and Van Patten, 1988; Ling and Kao, 1976). Part of the sea-spray-mediated
sensible heat is absorbed by droplet evaporation, which further increases
the air–sea temperature difference and thus increases the sea-spray-mediated sensible heat flux (Fairall et al., 1994; Andreas and
Decosmo, 2002). Since strong winds produce more sea spray droplets with a
larger radius, sea-spray-mediated heat fluxes increase with wind speed
(Fairall et al., 1994) and contribute to more than 10 % of the
total surface heat flux after reaching the threshold speed (
The usual bulk parameterizations in numerical models for surface fluxes only include the interfacial (turbulent) fluxes (e.g., Fairall et al., 1996) while neglecting the significant contributions of sea spray droplets in DEL (Andreas et al., 2008; Fairall et al., 1994; Smith, 1997; Emanuel, 1995). Andreas and Emanuel (2001) implemented sea-spray-mediated heat flux and momentum flux parameterizations into a simple tropical cyclone model and found that the sea-spray-mediated heat flux can significantly enhance tropical cyclone intensity. The similar enhancement of tropical cyclone intensity was also noticed in recent regional coupling systems by including sea-spray-mediated heat flux (Xu et al., 2021a; Liu et al., 2012; Garg et al., 2018; Zhao et al., 2017). In the First Institute of Oceanography Earth System Model, Bao et al. (2020) first incorporated the sea-spray-mediated heat flux in global climate simulation. Following Bao et al. (2020), Song et al. (2022) found that the sea-spray-mediated heat flux can lead to cooling at the air–sea interface and westerlies strengthening in the Southern Ocean, and it thus improves estimates of sea surface temperature (SST).
Since the parameterization of sea-spray-mediated heat flux derived from observations requires full-size spectral integral and thus is computationally expensive for large-scale models (Table 1, details in Sect. 4.2; Andreas, 1989, 1990, 1992; Andreas et al., 2015), a simplified algorithm based on a single radius of sea spray droplets (Andreas et al., 2015, 2008) is widely used in atmosphere–ocean coupling systems (Xu et al., 2021a; Liu et al., 2012; Garg et al., 2018; Zhao et al., 2017; Song et al., 2022; Bao et al., 2020) and is apt to produce numerical errors. To reduce these numerical errors induced by the single radius of sea spray droplets, we develop a new fast algorithm of sea-spray-mediated heat flux based on the Gaussian quadrature (GQ) method, a fast and accurate way to calculate spectral integral. The GQ method has been successfully used for the estimation of domain-averaged radiative flux profiles (Li and Barker, 2018). The performance of the GQ-based fast algorithm of the sea-spray-mediated heat flux is evaluated and compared with the simplified algorithm for single radius of Andreas et al. (2015), referred to as A15 hereafter. The results are first compared with the original parameterization using full-size spectral integral (A92, hereafter). Then, the parameterizations with different algorithms are implemented in a global coupled atmosphere–ocean–wave system (Shi et al., 2022), and the results are compared with global satellite measurements and reanalysis data.
The run time of the coupled Climate Forecast System model version 2.0 (CFSv2.0) and WAVEWATCH III (WW3) system's global experiments for 7 d forecast with different parameterizations.
The rest of the paper is structured as follows: observation and reanalysis data for comparisons are introduced in Sect. 2, the derivation of the GQ-based fast algorithm and the global coupling system are described in Sect. 3, the performance of the new fast algorithm is evaluated in Sect. 4, and finally, a summary and discussion are given in Sect. 5.
The fifth-generation European Centre for Medium-range Weather Forecasts
(ECMWF) Reanalysis (ERA5; Hersbach et al., 2020) 10 m wind speed
(WSP10), 2 m air temperature (T02), 2 m dew point temperature, surface
pressure, and significant wave height (SWH) with a spatial resolution of
0.5
The effects of sea spray droplets on sensible and latent heat fluxes
(
The radius-specific sea-spray-mediated sensible
(
Since the calculation of
To derive the general approximate values of
The distribution of occurrence frequency in percentage for
GQ radius nodes:
A coupled system based on Climate Forecast System model version 2.0
(CFSv2.0) and WAVEWATCH III (WW3) is employed to evaluate and compare the
effects of sea-spray-mediated heat flux parameterized by A15 and SPRAY-GQ.
The CFSv2.0-WW3 has three components, the Global Forecast System (GFS;
The CFSv2.0 is mainly applied for intraseasonal and seasonal prediction
(e.g., Saha et al., 2014). The atmosphere component GFS uses a
spectral triangular truncation of 382 waves (T382) in the horizontal,
equivalent to a grid resolution of nearly 35 km, and 64 sigma–pressure
hybrid layers in the vertical. The MOM4 is integrated on a nominal
0.5
In the coupling system, the WW3 obtains 10 m wind and ocean surface current from CFSv2.0 and then provides wave parameters to CFSv2.0. Several wave-mediated processes, including upper ocean mixing modified by Stokes drift-related processes, air–sea fluxes modified by surface current and Stokes drift, and momentum roughness length, are considered. Details of this system are referred to in Shi et al. (2022).
A series of numerical experiments is conducted to evaluate the effects of the two fast algorithms (A15 and SPRAY-GQ) of sea-spray-mediated heat flux on ocean, atmosphere and waves in two 56 d periods, from 3 January to 28 February 2017 and from 3 August to 28 September 2018 for boreal winter and boreal summer, respectively. For each period, two sensitivity experiments are carried out. The first is the SPRAY-A15 experiment in which A15 is used with two-way full coupling. The second is the SPRAY-GQ experiment in which SPRAY-GQ fast algorithm is used instead of A15. In addition, we also carry out another 7 d experiment using A92 (SPRAY-A92) to test the run time.
Based on the daily global WSP10, T02, 2 m dew point temperature, surface
pressure and SWH of ERA5, the daily global OISST, and the ESA monthly global
salinity,
Scatterplots of
To test the robustness of the results, we also use WSP10, T02 and SPH of the OAFlux
dataset to estimate
The same as Fig. 3, but WSP10, 2 m air temperature and 2 m specific humidity of OAFlux are used.
In addition, since it is common to derive SWH from empirical equations
(e.g., Andreas et al., 2008, 2015; Andreas and Decosmo,
2002; Andreas, 1992), we also use SWH generated by empirical equations of
WSP10 (Andreas, 1992) instead of ERA5 SWH to estimate
The same as Fig. 4, but SWH is derived by WSP10 instead of ERA5 SWH.
To compare the computational time of different parameterizations in the large-scale modeling system, the run time of the fully coupled experiments for 7 d forecast is given in Table 1 as an example. It is shown that the run time is about the same for SPRAY-GQ and SPRAY-A15. Both experiments run about 17 times faster than SPRAY-A92.
To illustrate the numerical errors of the two fast algorithms discussed in
the context of the coupled system, comparisons are made for simulated SSTs,
WSP10s and SWHs against OISST and ERA5 reanalysis. The results in the
first 3 d are excluded in the comparison, since the wave influences
are weak at the beginning of the simulations. Overall, the WSP10s of
simulations are generally in the range of 0–25 m s
The 53 d average SST (
The 53 d average differences of total heat flux
In the austral summer, compared with OISST, large SST biases (
To understand the effects of sea spray droplets on SST, we calculate the
total heat flux
(TH
The same as Fig. 6, but for August–September 2018 in
0–360
The same as Fig. 7, but for August–September 2018.
In the Southern Ocean, although direct differences of
The 53 d average WSP10 (m s
The same as Fig. 10, but for August–September 2018.
In the boreal summer, large SST biases (
Compared with experiment SPRAY-A15, significant differences of WSP10 in
SPRAY-GQ occur at middle to low latitudes of the NH (0–360
The ME of WSP10 (SPRAY-A15 minus ERA5) is 0.28 and 0.47 m s
The simulated SWHs changes are closely related to the changes of WSP10s (Shi et al., 2022). Therefore, the differences of SWHs (Figs. 12 and 13) are consistent with those of WSP10s (Figs. 10 and 11), with overestimated (underestimated) WSP10s corresponding to overestimated (underestimated) SWHs compared with ERA5. The SWHs in SPRAY-GQ are significantly different from those in SPRAY-A15 (Figs. 12b and 13b). In winter (summer), the SWH RMSE averages for SPRAY-A15 and SPRAY-GQ are 1.31 m (0.98 m) and 1.23 m (0.87 m), and after the first 2 weeks the RMSE and MAE in SPRAY-GQ are significantly lower than those in SPRAY-A15 at 95 % confidence level in both winter (Fig. 12c) and summer (Fig. 13c).
The 53 d average SWH (m) differences between SPRAY-A15
and ERA5 (
The same as Fig. 12, but for August–September 2018.
The direct and indirect effects of sea spray droplets on heat fluxes can
influence estimates of WSP10 and then SWH. The changes of WSP10s are related
to the direct effects
(
Based on a GQ method, we develop a new fast algorithm based on Andreas's (1989, 1990, 1992) full-size microphysical parameterization (A92) for sea-spray-mediated heat fluxes. Using global satellite measurements and reanalysis data, we found that the difference between SPRAY-GQ and A92 is significantly smaller than that between A15 and A92 (Andreas et al., 2015). To evaluate the numerical error of the SPRAY-GQ/A15 fast algorithm, we implement them in the two-way coupled CFSv2.0-WW3 system. A series of 56 d simulations from 3 January to 28 February 2017 and from 3 August to 28 September 2018 are conducted. The results are compared against satellite measurements and ERA5 reanalysis. The comparison shows that the sea-spray-mediated heat flux in SPRAY-GQ can reasonably modulate total heat flux compared with SPRAY-A15 and significantly reduce the SST biases in the Southern Ocean (middle to high latitudes of the NH) for the austral (boreal) summer and WSP10 and SWH after the first 2 weeks at middle to low latitudes of the NH for both boreal winter and summer. Overall, our fast algorithm based on GQ is applicable to sea-spray-mediated heat flux parameterization in coupled models.
To investigate the effects of spray-mediated heat flux on simulations, two
56 d experiments without sea spray effect (CTRL) in boreal winter and
summer are conducted, respectively, and the differences of simulated SST,
WSP10, SWH, T02 and SPH between SPRAY-GQ and CTRL are compared in Figs. S17–S21 in the Supplement. The introduction of sea spray cannot
significantly reduce the global overall errors of simulations, but it leads
to regional improvements (blue in Figs. S17e and f–S21e and f). For example,
compared with CTRL in January–February 2017, SST MAE of SPRAY-GQ in the southeast of
Australia decreases (Fig. S17e) because of warmer SST (Fig. S17c) related
to reduced wind (Fig. S18c). The reduced wind here also leads to lower SWH
(Fig. S19c) and thus reduced SWH overestimation (Fig. S19e). Meanwhile,
SPRAY-GQ reduces MAE of T02 and SPH (Figs. S20e and S21e) by increasing
temperature and moisture (Figs. S20c and S21c). The reduced errors are related
to the relatively large WSP10s over the areas (Figs. S2 and S3), since the
effects of sea spray become important at wind speeds larger than 10 m s
In addition to the variables aforementioned, the changes of simulated cloud fraction were also compared. However, the effects of sea-spray-mediated heat flux on cloud fraction are non-significant for the 2-month simulation, so the results are not shown. Besides this, the lack of other processes related to sea spray may be one of the reasons why the global overall error cannot be reduced effectively. For example, for simulated WSP10 and SWH in SPRAY-GQ, the significant overestimations in the SH still exist especially in August–September 2018 (Figs. S18 and S19 in the Supplement). As Andreas (2004) indicated, sea spray droplets also influence the surface momentum flux by injecting more momentum into the ocean from the atmosphere, which might further decrease the surface wind speed. We will consider this process in a future study.
Sea-spray-mediated heat fluxes are related to the sea spray generation
function (SSGF). Based on a number of laboratory and field observations,
varieties of SSGF were derived (e.g., Koga, 1981; Monahan et al., 1982;
Troitskaya et al., 2018; Andreas, 1992, 1998, 2002; Fairall et al., 1994;
Veron, 2015), whereas their differences can reach six orders of magnitude
(Andreas, 1998). There is currently no consensus on the most suitable
choice. In this study, we use SSGF of Fairall et al. (1994),
recommended by Andreas (2002), to get a mean bias of 3.70 and
0.095 W m
When wind speed is larger than 10 m s
Based on the cloud microphysical parameterization of Pruppacher and Klett (1978), Andreas (1989, 1990, 1992) proposed a parameterization of sea-spray-related heat fluxes for droplets with different radius, from formation
at sea surface to equilibrium with environment; that is,
The total sea spray fluxes are obtained by integrating
In Eq. (A8), the
Andreas (2003) and Andreas et al. (2008, 2015) developed a fast
algorithm to approximate
Here,
GQ is a method to approximate the definite integral of a function
For a function
The sea spray code can be found at
The supplement related to this article is available online at:
FX and RS designed the experiments and RS carried them out. RS developed the code of coupling parametrizations and produced the figures. RS prepared the paper with contributions from all co-authors. FX contributed to review and editing.
The contact author has declared that neither of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors are grateful to Jiangnan Li for help with the GQ codes. We also thank the two anonymous reviewers and the handling editor for their constructive comments.
This research has been supported by the National Key Research and Development Program of China (grant nos. 2020YFA0607900 and 2021YFC3101601) and the National Natural Science Foundation of China (grant no. 42176019).
This paper was edited by Qiang Wang and reviewed by two anonymous referees.