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

. 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


Introduction
Figure S1 is the scatter plot of  vs 10-m wind speed.
Figure S2&S3 are the WSP10 of SPRAY-GQ in Jan-Feb, 2017 andAug-Sep, 2018.Figure S4 is the global 53-day averaged SST differences between SPRAY-A15 and OISST, and the differences between SPRAY-GQ and SPRAY-A15 in Jan-Feb, 2017.
Figure S5 is the mean error of SPRAY-A15 and SPRAY-GQ in Jan-Feb, 2017 andAug-Sep, 2018.Figure S6 is the global 53-day averaged SST differences between SPRAY-A15 and OISST, and the differences between SPRAY-GQ and SPRAY-A15 in Aug-Sep, 2018.
Figure S7&S8 are the global 53-day averaged WSP10 differences between SPRAY-A15 and ERA5, and the differences between SPRAY-GQ and SPRAY-A15 in Jan-Feb, 2017 andAug-Sep, 2018.Figure S9-S12 are the average WSP10/SWH differences between SPRAY-A15/SPRAY-GQ and satellite data, differences between SPRAY-A15/SPRAY-GQ and ERA5, and differences between ERA5 and satellite data in Jan-Feb, 2017 andAug-Sep, 2018.Figure S13&S14 are the global 53-day averaged SWH differences between SPRAY-A15 and ERA5, and the differences between SPRAY-GQ and SPRAY-A15 in Jan-Feb, 2017 and Aug-Sep, 2018.

Figure
FigureS15&S16are the 53-day average wind and SLP of SPRAY-A15 and SPRAY-GQ, and their differences inJan-Feb, 2017 and Aug-Sep, 2018.