A Sea-Spray Thermodynamic Parameterization Including Feedback

C. W. Fairall *, J-W. Bao, and J. WilczakNOAA Environmental Technology Laboratory (ETL)

Boulder, CO

1. Background

2. Source strength

3. Feedback

4. Sensitivities

5. Model tests

Original Droplet EquationsFairall/Andreas circa 1990

H c C U T Ts a pa H o a' ( )

H L C U q T ql a e E s o a' ( ( ) )

Q c F T Ts w pw v o a' ( )

Q L Fl w e E'

F r S r drv n 4 3 3 / ( )

F r S r drEf

rn 4 3

33

/ ( )

Sn Surface Source Strength for Sea Spray Droplets

Droplet Source Functions

43

94

1 23

4 3

rS r

fl r

erfU h V S lope

nf

u

( )P r

exp [ ( ) ] * [ (( ) /

)] //

S f U S rn no ( ) ( ) f U W Ub( ) . . 3 8 1 0 6 3 4

P energy wave breaking σ surface tensionr droplet radiusη Kolmogorov microscale f fraction of P going into droplet productionVf=droplet mean fall velocity

Fairall et al. 1994

Fairall, Banner, Asher Physical Model

Feedback

Partitioning of Droplet Contribution:Stages of cooling/evaporation

• Simplification: consider large droplets that are ejected, cool to wet bulb temperature and re-enter ocean with negligible change in mass

• Stages:– Cool from To to Tair = Qs– Cool from Tair to Twet = Ql_a– Evaporation while at Twet = Ql_b

• Total droplet enthapy transfer Qse=Qs+Ql_a• Enthalpy Bowen ratio = Qs/Ql_a=(To-Ta)/(Ta-Twet)• Qs=Qse*bowen/(1+bowen)

Feedback Characterization δTa

H L C U q T q T Tl a e E s o s d d [ ( ) ( )]

H L C U T T Ts a e E o a a [ ( )]

Q c F T Tse w pw v o w ( ) Q L G U h T q T T q T Tlb w e o s a a s d d ( ) ( )[ ( ) ( )]

T T feed T T feed sa d a w

1 1

1* ( ) * ( )

feed QQ H Q H feed tune

l

l s se s

( ) / _

Effect on the fluxes:

Turbulent Fluxes Above the Droplet Evaporation Layer

H H Q Q H L C U q Q Ql to t l la lb l e E a la l_ ' '

H H Q H Q H c C U T Q H Qs to t s s s lb s p H f s s l_ ' '

Direct Transfer Coefficients Assumed in Parameterization

10 15 20 25 30 35 40 45 50 55 60

1

1.5

2

2.5

3

3.5

4

x 10-3

U10 (m/s)

Cd, C

k

Ratio of Transfer Coefficients With Droplet Enthalpy Flux

10 15 20 25 30 35 40 45 50 55 600.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

U10 (m/s)

Cd/C

kFeedtune=0.3, 1.0, 3.0

source=1.0

source=0.1

Feedback Sensitivity:Source Strength=0.3

Model Tests (Bao and Ginis)

• IVAN, ISABEL– GFDL operational– GFDL new zo, zt– WRF

• PLANS– HWRF at high resolution – matrix of tune values– Explicit droplet model (Kepert/ Fairall) in HWRF– Coordinate with Penn State LES work

Simulation with GFDL Operational Model: Isabel

But:Simulations with New Cd and Ce/Ch

New Cd Ce/Ch Old Cd Ce/Ch