Bulk Parameterizations for Wind SBulk Parameterizations for Wind Stress and Heat Fluxes tress and Heat Fluxes (Chou 1993; Cho(Chou 1993; Cho

u et al. 2003)u et al. 2003)

Outlines:Outlines:

Eddy correlation (covariance) methodEddy correlation (covariance) method Surface layer (or Monin-Obukhov) similariSurface layer (or Monin-Obukhov) similari

ty theoryty theory Bulk aerodynamic fomulationsBulk aerodynamic fomulations

Definition of parameters for bulk flux modelDefinition of parameters for bulk flux model :: Z -- Reference height for wind, temperature, and humidity Z -- Reference height for wind, temperature, and humidity

(can be different for different variables) (can be different for different variables) U -- Surface wind speed at Z U -- Surface wind speed at Z s -- Sea surface temperature (SST) s -- Sea surface temperature (SST) Qs – Sea surface saturation specific humidity Qs – Sea surface saturation specific humidity (salinity, cool s(salinity, cool s

kin effect) kin effect) Q -- Surface air specific humidity at ZQ -- Surface air specific humidity at Z -- Surface air potential temperature at Z-- Surface air potential temperature at Z -- Air density-- Air density Cp -- Isobaric specific heatCp -- Isobaric specific heat Lv -- Latent heat of vaporationLv -- Latent heat of vaporation CCDD, C, CHH, C, CEE – Bulk transfer coefficients for momentum, sens – Bulk transfer coefficients for momentum, sens

ible and latent heat fluxes ible and latent heat fluxes L -- Monin-Obukhov length { = L -- Monin-Obukhov length { = vv uu**

22/(/(gg kk vv**) } ) } kk -- von Karmen constant ( =0.4)-- von Karmen constant ( =0.4) ----kinematic viscosity of airkinematic viscosity of air

Eddy Correlation (Covariance) MethodEddy Correlation (Covariance) Method

Wind stress Wind stress = = -- ww’’uu’’> (1a)> (1a)

Sensible heat flux FSensible heat flux FSHSH = = C CP P ww’’TT’’> > (1b)(1b)

Latent heat flux FLatent heat flux FLHLH = = L LV V ww’’qq’’> > (1c)(1c)

Where Where

Vertical wind: w = <w> + w’Vertical wind: w = <w> + w’

Wind speed : u = <u> + u’Wind speed : u = <u> + u’

Temperature: T = <T> + T’Temperature: T = <T> + T’

Humidity: q = <q> + q’Humidity: q = <q> + q’

Surface Layer (Monin –Obukhov) Similarity Theory Surface Layer (Monin –Obukhov) Similarity Theory

Profile Scaling Parameters:Profile Scaling Parameters:

Wind: uWind: u**= = 1/21/2 ---- ---- == uu**22

(2a) (2a)

Temp. : Temp. : ** = – F = – FSH SH C CPP u u**)) ---- ---- F FSHSH == – – Cp Cp uu* * ** (2b) (2b)

humidity: qhumidity: q** == – F – FLHLH (( Lv Lv uu**)) ----- ----- F FLHLH == – – Lv Lv uu**qq* * (2c)(2c)

M-O lengthM-O length:: L = L = VVuu**22(g k (g k V*V*)) ---- ---- L L ~ u(~ u(∂∂u/u/∂∂z)z)<w’ <w’ VV

’’>>

Z/L = 0Z/L = 0, , <w’ <w’ VV’’>> = 0, = 0, neutralneutral atm sfc layer (mechanical turbulence domi atm sfc layer (mechanical turbulence domi

nant) nant)

Z/L < 0Z/L < 0, , <w’ <w’ VV’’>> < 0, < 0, unstable unstable atm sfc layer (convective turbulence domiatm sfc layer (convective turbulence domi

nant)nant)

Z/L > 0Z/L > 0, , <w’ <w’ VV’’>> > 0, > 0, stablestable atm sfc layer (mechanical turbulence suppres atm sfc layer (mechanical turbulence suppres

sed) sed)

Nondimensional Gradients of Wind, Potential TeNondimensional Gradients of Wind, Potential Temperature, and Humidiymperature, and Humidiy::

(k Z/u(k Z/u**)(∂u/∂Z) = )(∂u/∂Z) = uu(Z/L) (3a) (Z/L) (3a) (k Z/ (k Z/ **)(∂ )(∂ /∂Z) = /∂Z) = TT(Z/L) (3b) (Z/L) (3b) (k Z/q(k Z/q**)(∂q/∂Z) = )(∂q/∂Z) = qq(Z/L) (3c) (Z/L) (3c)

Z/L = 0Z/L = 0, , neutralneutral, , uu= = TT= = qq = 1 = 1

Z/L < 0Z/L < 0, , unstableunstable, , u u= (1 – 16 Z/L)= (1 – 16 Z/L) , ,

TT= = qq= (1 – 16 Z/L )= (1 – 16 Z/L )

Z/L > 0,Z/L > 0, stablestable, , uu= = TT= = qq = 1 + 7 Z/L = 1 + 7 Z/L von Karman constant: k = 0.40 von Karman constant: k = 0.40

Vertical Profiles of Wind, Potential Temperature, HVertical Profiles of Wind, Potential Temperature, Humidityumidity

(U – Us)/u(U – Us)/u** = [ln(Z/Z = [ln(Z/Zoo) – ) – uu(Z/L)]/k (4a)(Z/L)]/k (4a)(( – – ss)/)/** = [ln(Z/Z = [ln(Z/ZoToT) – ) – TT(Z/L)]/k (Z/L)]/k (4b) (4b)(Q – Qs)/q(Q – Qs)/q** = [ln(Z/Z = [ln(Z/Zooqq) – ) – qq(Z/L)]/k (4c)(Z/L)]/k (4c)

=∫(1 –=∫(1 –) d ln(Z/L), L = ) d ln(Z/L), L = vv u u**22/(g k /(g k v*v*) )

Eq.(4) obtained by adding 1 and subtracting 1 oEq.(4) obtained by adding 1 and subtracting 1 on right hand side of Eq.(3), dividing Z on Eq.(3),n right hand side of Eq.(3), dividing Z on Eq.(3), then integrating Eq.(3) from lower boundary then integrating Eq.(3) from lower boundary ((ZZoo, , ZZoToT, and , and ZZooqq) to height Z.) to height Z.

Stability Functions:Stability Functions: =∫(1 –=∫(1 –) d ln(Z/L)) d ln(Z/L)

Z/L = 0, neutral, Z/L = 0, neutral, uu= = TT= = qq= 0= 0

Z/L > 0, stable, Z/L > 0, stable, uu= = TT= = qq= = 7 Z/L7 Z/L

Z/L < 0, unstable,Z/L < 0, unstable,uu= 2 ln [ (1 + x)/2] + ln[ (1 + x= 2 ln [ (1 + x)/2] + ln[ (1 + x22)/2] – 2 tan)/2] – 2 tan-1-1x +x +/2/2

TT= = qq= 2 ln[(1 +y)/2]= 2 ln[(1 +y)/2]

x = x = uu-1 -1

y = y = T T-1 -1 = = qq

-1 -1

Bulk Aerodynamic Formulations:Bulk Aerodynamic Formulations: Wind stressWind stress = = C CDD (U–Us) (U–Us)2 2 (5a)(5a)

Sensible heat fluxSensible heat flux F FSHSH = = C CPP C CHH (U–Us) ( (U–Us) (s–s–) ) (5b)(5b)

Latent heat fluxLatent heat flux F FLHLH = = L LVV C CEE (U–Us) (Qs–Q) (U–Us) (Qs–Q) (5c)(5c)

*Input parameters: U(Z), *Input parameters: U(Z), s, s, , Qs, Q(Z), and Z, Qs, Q(Z), and Z

* C* CDD = k = k22/[ln(Z/Z/[ln(Z/ZOO) – ) – uu(Z/L)](Z/L)]2 2 (6a)(6a)

CCHH = C = CDD1/21/2 k/[ln(Z/Z k/[ln(Z/ZOTOT) – ) – TT(Z/L)] (6b)(Z/L)] (6b)

CCEE = C = CDD1/21/2 k/[ln(Z/Z k/[ln(Z/ZOqOq) – ) – qq(Z/L)] (6c)(Z/L)] (6c)

* Eq. (6) obtained by combining Eqs. (2), (4), & (5).* Eq. (6) obtained by combining Eqs. (2), (4), & (5).

Us = 0.55 uUs = 0.55 u* * (~0)(~0)

ASTEXASTEX: Atlantic Stratocumulus Transition Experiment : Atlantic Stratocumulus Transition Experiment COARECOARE: Coupled Ocean-Atmosphere Response Experiment : Coupled Ocean-Atmosphere Response Experiment FASTEXFASTEX: Fronts and Atlantic Storm Track Experiment : Fronts and Atlantic Storm Track Experiment JASMINEJASMINE: Joint Air-Sea Monsoon Interaction Experiment : Joint Air-Sea Monsoon Interaction Experiment KWAJEXKWAJEX: Kwajalein Experiment : Kwajalein Experiment NAURU99NAURU99: Nauru ’99 Experiment: Nauru ’99 Experiment SCOPESCOPE: San Clemente Ocean Probing Experiment : San Clemente Ocean Probing Experiment TIWETIWE: Tropical Instability Wave Experiment : Tropical Instability Wave Experiment PACSF99PACSF99: Pan-American Climate Study in eastern Pacific during 1999: Pan-American Climate Study in eastern Pacific during 1999 MOORINGSMOORINGS: Buoy service in the North Pacific : Buoy service in the North Pacific

1913-hourly fluxes 1913-hourly fluxes calculated from shicalculated from ship data using GSSTFp data using GSSTF2 bulk flux model v2 bulk flux model vs observed (a) wind s observed (a) wind stresses determinestresses determined by ID method, (b) d by ID method, (b) latent and (c) sensilatent and (c) sensible heat fluxes deteble heat fluxes determined by covariarmined by covariance method of 10 fince method of 10 field experiments.eld experiments.

C: COARE F: FASTEX X: other experime

nts

Conclusions:Conclusions: GSSTF2 bulk flux model for GSSTF2 bulk flux model for turbulent fluxesturbulent fluxes vali vali

dated well by comparing hourly turbulent fluxes dated well by comparing hourly turbulent fluxes computed from research ship data with those of computed from research ship data with those of 10 field experiments conducted by the NOAA/ET10 field experiments conducted by the NOAA/ETL scientists over tropical and northern midlatitudL scientists over tropical and northern midlatitude oceans during 1991-1999 (Chou et al. 2003)e oceans during 1991-1999 (Chou et al. 2003)

GSSTF2 bulk flux model for GSSTF2 bulk flux model for latent heat fluxlatent heat flux valid validated well by comparing hourly latent heat fluxes ated well by comparing hourly latent heat fluxes computed from research ship data with those of computed from research ship data with those of 12 field experiments conducted by NOAA/ETL an12 field experiments conducted by NOAA/ETL and French scientists over tropical and northern mid French scientists over tropical and northern midlatitude oceans during 1991-1999 (Curry et al. 20dlatitude oceans during 1991-1999 (Curry et al. 2004) 04)