SURFACE FLUXES
249
Otherwise, the slow changes in C HN generally follow the evolution of
C DN , as expected from (29) and Fig. 5.
4.1
Bulk flux estimates
Estimating the turbulent fluxes from average atmospheric and sea
surface properties is essentially the inverse of determining transfer coefficients, and accordingly the bulk formulae are the inverse of (27):
τ = ρ C D |∆
U | ∆
U,
(41)
Q H = ρ c p C H (θ(z θ ) − SST ) |∆
U |
(42)
E = ρ C E (q(z q ) − q sat (SST )) |∆
U |
(43)
Q E = Λ E
(44)
where ∆
U =
U (z u ) −
U 0 . The mean wind,
U (z u ), potential air temperature, θ(z θ ), and specific humidity, q(z q ), may be from different heights,
z u , z θ and z q , respectively. The surface current is often, but not always,
negligible relative to the wind. A constant density, ρ ≈ 1.22kg/m 3 may
be sufficient, but a more accurate expression is
ρ =
P o
R gas θ(z θ ) (1. + .608 q(z q ))
,
(45)
where R gas = 287.04J/kg/K is the gas constant for dry air. The order
1% effects of temperature on Λ and of humidity on c p are usually ignored.
Although it is clear that a skin temperature should be used to compute
the longwave radiation (7), a definitive study has not been conducted
to determine whether a skin or bulk SST is more appropriate for (42).
At present the determining factor is to use the same temperature as
was used to compute C H , which is usually a bulk temperature, because
skin temperature is a very difficult measurement. This becomes an issue
when satellite estimates of skin SST are available. In (43), the air at the
sea surface is assumed to be saturated, with a specific humidity given
well enough by
q sat (SST ) = 0.98 ρ
−1 640380kg/m
3 e
(−5107.4K/SST ) ,
(46)
where the factor 0.98 applies only over sea-water. The saturation assumption has not been verified, but since it is used in formulating C E , it
should be applied in the inverse (43). The exact relation between evaporation and surface latent heat flux (44), depends on the fact that the
latent heat required to evaporate comes from the liquid (the ocean). In
the case of evaporation from spray this still holds unless droplets entirely
249
Otherwise, the slow changes in C HN generally follow the evolution of
C DN , as expected from (29) and Fig. 5.
4.1
Bulk flux estimates
Estimating the turbulent fluxes from average atmospheric and sea
surface properties is essentially the inverse of determining transfer coefficients, and accordingly the bulk formulae are the inverse of (27):
τ = ρ C D |∆
U | ∆
U,
(41)
Q H = ρ c p C H (θ(z θ ) − SST ) |∆
U |
(42)
E = ρ C E (q(z q ) − q sat (SST )) |∆
U |
(43)
Q E = Λ E
(44)
where ∆
U =
U (z u ) −
U 0 . The mean wind,
U (z u ), potential air temperature, θ(z θ ), and specific humidity, q(z q ), may be from different heights,
z u , z θ and z q , respectively. The surface current is often, but not always,
negligible relative to the wind. A constant density, ρ ≈ 1.22kg/m 3 may
be sufficient, but a more accurate expression is
ρ =
P o
R gas θ(z θ ) (1. + .608 q(z q ))
,
(45)
where R gas = 287.04J/kg/K is the gas constant for dry air. The order
1% effects of temperature on Λ and of humidity on c p are usually ignored.
Although it is clear that a skin temperature should be used to compute
the longwave radiation (7), a definitive study has not been conducted
to determine whether a skin or bulk SST is more appropriate for (42).
At present the determining factor is to use the same temperature as
was used to compute C H , which is usually a bulk temperature, because
skin temperature is a very difficult measurement. This becomes an issue
when satellite estimates of skin SST are available. In (43), the air at the
sea surface is assumed to be saturated, with a specific humidity given
well enough by
q sat (SST ) = 0.98 ρ
−1 640380kg/m
3 e
(−5107.4K/SST ) ,
(46)
where the factor 0.98 applies only over sea-water. The saturation assumption has not been verified, but since it is used in formulating C E , it
should be applied in the inverse (43). The exact relation between evaporation and surface latent heat flux (44), depends on the fact that the
latent heat required to evaporate comes from the liquid (the ocean). In
the case of evaporation from spray this still holds unless droplets entirely