Accelerated estimation of sea-spray-mediated heat flux using Gaussian quadrature: case studies with a coupled CFSv2.0-WW3 system

Abstract

Abstract. 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.

Improvement of Global Forecast of Tropical Cyclone Intensity by Spray Heat Flux and Surface Roughness

“…For the corresponding wave‐induced processes, the system contains the wave‐modified momentum roughness length, a number of Stokes drift related mixing processes, the effect of Stokes drift on the relative velocity of fluxes, as well as the spray heat flux. Full details of the coupling system can be found in Shi and Xu (2023) and Shi et al. (2022).…”

“…The total heat flux generated by spray droplets can be accurately reproduced by integrating the heat flux spectrums over the full droplet radii (Andreas, 1989, 1990, 1992). In CFSv2.0‐WW3, a spray heat flux parameterization based on GQ method (SPRAY‐GQ; Shi & Xu, 2023) is applied to rapidly calculate the integral of spectrums for spray sensible and latent heat fluxes ( Q S ( r 0 ) and Q L ( r 0 )) over the initial radius ( r 0 ): $$$\int \nolimits_{2\mu \mathrm{m}}^{500\mu \mathrm{m}}{Q}_{S}\left({r}_{0}\right)d{r}_{0}\approx \frac{498}{2}\sum\limits _{i=1}^{3}{\omega }_{i}{Q}_{S}\left({r}_{Si}\right),$$$ $$$\int \nolimits_{2\mu \mathrm{m}}^{500\mu \mathrm{m}}{Q}_{L}\left({r}_{0}\right)d{r}_{0}\approx \frac{498}{2}\sum\limits _{i=1}^{3}{\omega }_{i}{Q}_{L}\left({r}_{Li}\right),$$$ $$${r}_{S1}=459.056,{\,r}_{S2}=294.185,{\,r}_{S3}=166.771,$$$ $$${r}_{L1}=443.914,{r}_{L2}=251.0498,$$$ …”

“…The total heat flux generated by spray droplets can be accurately reproduced by integrating the heat flux spectrums over the full droplet radii (Andreas, 1989(Andreas, , 1990(Andreas, , 1992. In CFSv2.0-WW3, a spray heat flux parameterization based on GQ method (SPRAY-GQ; Shi & Xu, 2023) is applied to rapidly calculate the integral of spectrums for spray sensible and latent heat fluxes (Q S (r 0 ) and Q L (r 0 )) over the initial radius (r 0 ): here ω 1 = ω 3 = 0.556 and ω 2 = 0.889 are GQ weights respectively for three nodes. r S1 (r L1 ), r S2 (r L2 ) and r S3 (r L3 ) are the radii in micrometers corresponding to GQ nodes.…”

“…What is the relative contribution of spray heat flux and modified surface roughness to TC‐intensity change? To unravel these questions, we implement a new surface roughness parameterization and a Gaussian Quadrature (GQ)‐based accelerated parameterization of spray heat flux into the global coupled ocean‐atmosphere‐wave system (Shi & Xu, 2023; Shi et al., 2022). Several sensitivity experiments are carried out.…”