Satellite-Based Ocean Surface Turbulent Fluxes - Satellite-based Applications on Climate Change - page 161

transition layer (Lykossov 2001 ). A detail discussion of the atmospheric and
oceanic boundary layer is in Kraus and Businger ( 1994 ).
In bulk aerodynamic formulation, the turbulent transfer of momentum (or
surface stress,

), sensible heat flux (SHF), and latent heat flux (LHF) at the air-sea
interface can be written as

τ

τ ¼ ρC D ðU U s Þ j jðU U s Þ

(11.1a)

¼ ρC p C H ðU U s ÞðT s T a Þ

SHF (11.1b)

LHF ¼ ρL v C E ðU U s ÞðQ s Q a Þ (11.1c)

where is air density; C p the specific heat at constant pressure; L υ the latent heat of

vaporization; C D , C H , and C E are, respectively, the bulk transfer coefficients for
momentum, sensible heat, and latent heat; U is the air velocity; and U s is ocean
surface current. Surface stress is a vector and has a magnitude of the square of the
wind difference |( U U s )| 2 in the direction of ( U U s ). |( U U s )| is the absolute
value of the difference of surface wind and ocean surface current.
The surface wind U is typically a few to tens of m s 1 and U s ~cms 1 ; hence, in
most cases the assumption ( U U s )

ρ

U is made.
With input parameters such as wind speed ( U ), the sea surface temperature ( T s ),
the air potential temperature ( T a ), the air specific humidity ( Q a ) at the reference
height, and the saturation specific humidity ( Q s ) which is determined by T s through
the Clausius-Clapeyron relation, the fluxes can be calculated with the appropriate
transfer coefficients.
Based on similarity theory, the surface fluxes in Eqs. ( 11.1a , 11.1b , 11.1c ) can
also be derived from scale analysis with scaling parameters for wind or friction
velocity ( u *), temperature ( θ *), and humidity ( q *) defined as

τ ¼ ρu 2 (11.2a)

¼ρC p u θ SHF (11.2b)

LHF ¼ρL v u q

(11.2c)

θ s (or SKT) and wind, temperature, and
humidity at a measurement or reference heights within the atmospheric surface
layer, the scaling parameters are solved through the roughness lengths z 0 and
dimensionless gradients of wind, temperature, and humidity. The dimensionless
gradients of wind, potential temperature, and humidity are functions of the stability
parameter z / L , where z is the measurement height and L is the Monin-Obukhov
length, L ¼u * 3 /

For a given surface skin temperature

~ 0.4 and B 0 is
the buoyancy, B 0 ¼ gw 0 ρ 0 , where g is the gravitational acceleration and w 0 and

κ B 0 , where κ is the von Karman constant κ

ρ 0
are the fluctuations of vertical velocity and density, and is defined as positive for
stable and negative for unstable boundary layers (see Garratt 1992 ; Chou et al.
2003 ). The transfer coefficients of momentum, heat, and moisture flux are therefore