Chemistry Reference
In-Depth Information
where
Pr
is the Prandtl number of heat in the water,
Sc
is the Schmidt
number of the gas in the water, and
n
is a model-dependent exponent.
Traditional turbulence-diffusion models (based on the boundary layer
adjoining a solid wall) imply that
n
= 2/3, but a value
n
= 1/2 is appropriate
for a boundary layer adjoining a free surface (Jähne and Haussecker 1998).
The appropriate value of n depends on the wind stress and the surfactant
loading of the surface. Soloviev and Schluessel (1994) have described a
procedure for estimating gas transfer velocities from measurements of heat
transport, assuming that transport is adequately described by the classical
(Danckwerts) surface renewal model. The key relationship can be written
in the form:
h
n
K
M
Pr
Sc
K
(3)
g
where M is a non-dimensional number, related to the distribution of surface
temperature. A similar equation can be written for any surface renewal
model but the value of M is model dependent.
A major difficulty with applying large footprint measurements of the
cool skin, is the question of homogeneity. The models described above re-
quire an assumption of horizontally homogenous distribution of heat flux
and sub-surface turbulence within the footprint. Such an assumption is
highly dubious, for example patches of relatively intense turbulence may
be expected near breaking waves (Rapp and Melville 1990, Woolf 1995).
The detrimental effect on our simple model can be understood from the
following thought experiment: Consider turbulent exchange to be en-
hanced by a factor
N
over a fraction 1/
N
of the sea surface. For large N, we
find that the air-sea exchange of a gas will be doubled, but the spatially av-
eraged cool skin effect is barely altered.
In summary, large footprint measurements permit an estimate of gas
transfer velocities, but these estimates are sensitive to model assumptions.
Furthermore, large footprint measurements give no direct information on
the characteristics of surface renewal. Also, the method is extremely sensi-
tive to drift in the calibration of either the surface or the bulk temperature
measurement.
2.2 Imagery and “surface thermometry”
In cool skin conditions, an eddy bringing sub-surface water to the surface
will create a “warm anomaly” on the sea surface. Temperature fluctuations
on the sea surface will be highly sensitive to the character of surface re-
newal. The turbulence-diffusion paradigm implies that the vertical scale of
eddies diminishes asymptotically to molecular scales close to the surface,
