Nature of droplet source Droplet heat/moisture fluxes Scaling model of source

1. A parameterization of sea spray contributions to mass and heat fluxes in hurricanes based on breaking wave properties.C. W. Fairall and J.-W. Bao, NOAA Earth System Research Laboratory, Boulder, CO 80305 Melicie Desflots and Shuyi Chen, Rosenstiel School of Marine and Atmospheric Science, U. Miami, Miami, FL 33149, USA • Nature of droplet source • Droplet heat/moisture fluxes • Scaling model of source • Simpler Parameterization

3. Production and Removal at the sea-air interface 1 2 3 4 5 1 Turbulent transport 2 Molecular diff. 3 Mean fall speed 4 Slip due to Inertia 5 Source Number(r)/m2/sec HOWEVER: At least one additional piece of information is required to characterize the soucre. *Initial ejection velocity Wej *Effective height h Rate of change=Inputs-Removal=Source-Deposition For concentration n (#/volume)

4. Example: Qn is delta-function source at height h=2m

5. Simplified Steps in the Sea Spray Chain • Droplets thrown in air: Source – Qn(r ) at h • Individual drops transfer heat/moisture to air • Cumulative effect computed by integrating over droplet spectrum: Ql’=Droplet latent heat flux Qs’=Drop sensible heat flux

6. Source function whitecap scaling:A single whitecap produces sea spray distribution Swhitecap[r]

7. Source Scaling with Forcing • Forcing = • Whitecap fraction • U3 • U*3 • P Energy going into wave breaking • P2/3 • Л(c) length of breaking waves per unit area

8. Original Droplet Equations: Wind Speed DrivenFairall/Andreas/Kepert Early 1990’s Direct sensible Direct Latent Raw Droplet Latent Raw Droplet Sensible Net fluxes emerging from top of droplet layer Alpha accounts for feedback (droplet – T/q profile interactions)

9. Fairall et al. 1994 Droplet Source Functions Fairall-Banner Physical Model: Balance of energy produced by wave breaking and lost in production of drops and bubbles. Error function describes probability drop trajectory escapes surface. P energy wave breaking σ surface tension r droplet radius η Kolmogorov microscale in the ocean f fraction of P going into droplet production Utop wind speed near breaker top Ub group speed of breaking wave Λ Unspecified length scale (or, P/ Λ volume dissipation near surface)

10. Sn Surface Source Strength for Sea Spray Droplets

11. Energy Of Wave Breaking • Wave Model • P computed from wave spectral model • Energy flux from atmosphere

12. Version 1.0: Wave parameters related to U“Typical/Equilibrium Waves” • a=.013;% Andreas • b=.50; • twave=b*u;% wave period (s) • hwave=a*u.^2;% wave significant height (m) • lwave=grav/2/pi*twave.^2;% wave length (m) • cwave=grav/2/pi*twave;% wave phase speed (m/s) • h=hwave/2;% wave top height above mean sea level • ustw=sqrt(rhoa/1e3)*usr;% ustar in the water • P=0.5*ustw.^2.*cwave;% energy breaking of waves (m/s)^3 Tuned to fit Andreas/Fairall at U=30 m/s

13. Version 2.0: Wave parameters related to U, u*Parameters fit to Couple Atmosphere-Wave Models: U Miami – Hurricane URI - Idealized • usr=1.*.057*u;% U Miami model • z0=zu./exp(kon*u./usr); • cwave=1*(10+0.16*u); • hwave=1.*(1+.25*u); • h=hwave/2; • P=4.*1.28e-5*u.^3.22;% U Miami model • P=rhoa*3.5*usr.^3.5/rhow;% URI model Tuned to fit Andreas/Fairall at U=30 m/s

15. Feedback Defined by distortions of the temperature & humidity profiles in the Droplet evaporation zone: δT δq

16. Feedback Effects • From δT & δq compute new values of droplet sensible and latent heat values: Qs and Ql • This defines feedback coefficients