Bulk Parameterizations for Wind Stress and Heat Fluxes (Chou 1993; Chou et al. 2003) Outlines: Eddy correlation (covariance) method Eddy correlation (covariance) method Surface layer (or Monin-Obukhov) similarity theory Surface layer (or Monin-Obukhov) similarity theory Bulk aerodynamic fomulations Bulk aerodynamic fomulations

Definition of parameters for bulk flux model: Z -- Reference height for wind, temperature, and humidity (can be different for different variables) Z -- Reference height for wind, temperature, and humidity (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 (salinity, cool skin effect) Qs – Sea surface saturation specific humidity (salinity, cool skin effect) Q -- Surface air specific humidity at Z Q -- 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 heat Cp -- Isobaric specific heat Lv -- Latent heat of vaporation Lv -- Latent heat of vaporation C D, C H, C E – Bulk transfer coefficients for momentum, sensible and latent heat fluxes C D, C H, C E – Bulk transfer coefficients for momentum, sensible and latent heat fluxes L -- Monin-Obukhov length { =  v u * 2 /( g k  v * ) } L -- Monin-Obukhov length { =  v u * 2 /( g k  v * ) } k -- von Karmen constant ( =0.4) k -- von Karmen constant ( =0.4)  --  kinematic viscosity of air  --  kinematic viscosity of air

Eddy Correlation (Covariance) Method Wind stress  = -  w ’ u ’ > (1a) Sensible heat flux F SH =  C P  w ’ T ’ > (1b) Latent heat flux F LH =  L V  w ’ q ’ > (1c) Where Vertical wind: w = + w’ Wind speed : u = + u’ Temperature: T = + T’ Humidity: q = + q’

Surface Layer (Monin – Obukhov) Similarity Theory Profile Scaling Parameters: Wind: u *  =  1/2   ----   =  u * 2 (2a) Temp. :  * = – F SH  C P u * ) ----  F SH = –  Cp u *  * (2b) humidity: q * = – F LH  (  Lv u * )  F LH = –  Lv u * q * (2c) M-O length : L =  V u * 2  (g k  V* ) ----  L ~ u( ∂ u/ ∂ z)  M-O length : L =  V u * 2  (g k  V* ) ----  L ~ u( ∂ u/ ∂ z)  Z/L = 0, = 0, neutral atm sfc layer (mechanical turbulence dominant) Z/L < 0, unstable atm sfc layer (convective turbulence dominant) Z/L > 0, > 0, stable atm sfc layer (mechanical turbulence suppressed)

Nondimensional Gradients of Wind, Potential Temperature, and Humidiy: (k Z/u * )(∂u/∂Z) =  u (Z/L) (3a) (k Z/u * )(∂u/∂Z) =  u (Z/L) (3a) (k Z/  * )(∂  /∂Z) =  T (Z/L) (3b) (k Z/  * )(∂  /∂Z) =  T (Z/L) (3b) (k Z/q * )(∂q/∂Z) =  q (Z/L) (3c) (k Z/q * )(∂q/∂Z) =  q (Z/L) (3c) Z/L = 0, neutral,  u =  T =  q = 1 Z/L < 0, unstable,  u = (1 – 16 Z/L) ,  T =  q = (1 – 16 Z/L )   T =  q = (1 – 16 Z/L )  Z/L > 0, stable,  u =  T =  q = Z/L von Karman constant: k = 0.40

Vertical Profiles of Wind, Potential Temperature, Humidity (U – Us)/u * = [ln(Z/Z o ) –  u (Z/L)]/k (4a) (  –  s )/  * = [ln(Z/Z oT ) –  T (Z/L)]/k (4b) (Q – Qs)/q * = [ln(Z/Z o q ) –  q (Z/L)]/k (4c)  =∫(1 –  ) d ln(Z/L), L =  v u * 2 /(g k  v* )   Eq.(4) obtained by adding 1 and subtracting 1 on right hand side of Eq.(3), dividing Z on Eq.(3), then integrating Eq.(3) from lower boundary (Z o, Z oT, and Z o q ) to height Z.

Stability Functions:  =∫(1 –  ) d ln(Z/L) Z/L = 0, neutral,  u =  T =  q = 0 Z/L > 0, stable,  u =  T =  q =  7 Z/L Z/L < 0, unstable,  u = 2 ln [ (1 + x)/2] + ln[ (1 + x 2 )/2] – 2 tan -1 x +  /2  T =  q = 2 ln[(1 +y)/2] x =  u -1 y =  T -1 =  q -1

Bulk Aerodynamic Formulations: Wind stress  =  C D (U – Us) 2 (5a) Sensible heat flux F SH =  C P C H (U – Us) (  s –  ) (5b) Latent heat flux F LH =  L V C E (U – Us) (Qs – Q) (5c) *Input parameters: U(Z),  s, , Qs, Q(Z), and Z * C D = k 2 /[ln(Z/Z O ) –  u (Z/L)] 2 (6a) C H = C D 1/2 k/[ln(Z/Z OT ) –  T (Z/L)] (6b) C E = C D 1/2 k/[ln(Z/Z Oq ) –  q (Z/L)] (6c) * Eq. (6) obtained by combining Eqs. (2), (4), & (5). Us = 0.55 u * (~0)

ASTEX: Atlantic Stratocumulus Transition Experiment COARE: Coupled Ocean-Atmosphere Response Experiment FASTEX: Fronts and Atlantic Storm Track Experiment JASMINE: Joint Air-Sea Monsoon Interaction Experiment KWAJEX: Kwajalein Experiment NAURU99: Nauru ’99 Experiment SCOPE: San Clemente Ocean Probing Experiment TIWE: Tropical Instability Wave Experiment PACSF99: Pan-American Climate Study in eastern Pacific during 1999 MOORINGS: Buoy service in the North Pacific

1913-hourly fluxes calculated from ship data using GSSTF2 bulk flux model vs observed (a) wind stresses determined by ID method, (b) latent and (c) sensible heat fluxes determined by covariance method of 10 field experiments. C: COARE F: FASTEX X: other experiments

Conclusions: GSSTF2 bulk flux model for turbulent fluxes validated well by comparing hourly turbulent fluxes computed from research ship data with those of 10 field experiments conducted by the NOAA/ETL scientists over tropical and northern midlatitude oceans during (Chou et al. 2003) GSSTF2 bulk flux model for turbulent fluxes validated well by comparing hourly turbulent fluxes computed from research ship data with those of 10 field experiments conducted by the NOAA/ETL scientists over tropical and northern midlatitude oceans during (Chou et al. 2003) GSSTF2 bulk flux model for latent heat flux validated well by comparing hourly latent heat fluxes computed from research ship data with those of 12 field experiments conducted by NOAA/ETL and French scientists over tropical and northern midlatitude oceans during (Curry et al. 2004) GSSTF2 bulk flux model for latent heat flux validated well by comparing hourly latent heat fluxes computed from research ship data with those of 12 field experiments conducted by NOAA/ETL and French scientists over tropical and northern midlatitude oceans during (Curry et al. 2004)