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the boundary layer and into the bulk surface water. This is dis-
solution of CO
2
.
Exhalation and dissolution (or inhalation) is illustrated in the
figure 4.
Rate Equations for the Exchange of CO
2
between Air
and Sea Water
From the three basic assumptions underlying our physiochemi-
cal model, and application of Ficks
’
law, we can write:
F = A. k (CiC
O2
– C
CO2
) = A
.
k (p
CO2
.
C
*
CO2
– C
CO2
)
(5)
The equation contains the following parameters:
F is exchange rate or flux, inhalation or exhalation
A is diffusion area
k is mass transfer coefficient
C
i
CO2
is concentration of dissolved CO2 at the air/sea inter-
face
C
*
CO2
is solubility of CO2 at sea surface temperature and sa-
linity, for a partial pressure of CO
2
= 1, i.e. carbon dioxide is
the only gas present.
C
CO2
is concentration of dissolved CO2 in the bulk surface
layer
P
CO2
is the partial pressure of CO
2
in air.
Elementary film theory allows us to write the flux equation also
in a slightly different notation:
F = A ( D/
∂
)
∆
CO2
(6)
Here
D is diffusivity of dissolved CO
2
∂
is thickness of the boundary layer
∆
CO2
is the concentration gradient of dissolved CO
2
across
the boundary layer, also referred to as the driving force for
diffusion
In differential notation:
dF = k.
∆
CO2
.
dA (7)
Then, in order to find the net flux of CO
2
exchange we can
“simply” integrate over the total global sea surface:
F =
∫
k.
∆
CO2
.
dA
(8)
The flux values will be positive in cold waters where dissolution
occurs. In warm waters the driving force will be negative, lead-
ing to negative flux values and exhalation of CO
2
.
The Conveyor Belt Model of Sea Surface Circulation
The ocean is breathing in carbon dioxide in cold regions and
breathing out in warm areas. Cold and warm oceans are con-
nected by complex circulation patterns, which are described by
a first approximation model called the Conveyor Belt Model.
Some of the features of this model follow below.
Enormous amounts of warm surface water is streaming to-
wards the cold polar areas. The Golf Stream along the Norwegian
West Coast is one example. In Arctic and Antarctic this warm
water cools down and fills up with carbon dioxide from air. Sea
water density differences make the surface water sink, eventu-
ally forming new deep water.
The deep water moves slowly along the sea bottom, and will
finally resurface again around equator, after a journey believed
to have lasted more than one thousand years!
The Conveyor Belt Model is a very crude description, but
useful for our discussion later on. The model is illustrated in
Fig.5.
Discussion
We have previously discussed the seasonal variations of CO
2
levels in air. If we for now disregard these variations between
summer and winter, what are the other factors that decide the
concentration of CO
2
in the atmosphere?
Direct and reliable measurements of carbon dioxide in air as
seen in Fig.1, started around 1960. Most researchers neverthe-
less assume 280 ppm as the stable level before mankind started
extensive burning of fossil fuels at the beginning of the twenti-
eth century. If this is true, then dissolution and exhalation must
have been equal, and flux integration over the total sea surface
must have been zero:
Fig.1.
Seasonal cycling of CO
2
levels in air. Ref: Data
from measurements in air near Hawaii.
Fig.2.
Model for interaction of CO
2
with Sea
Water (illustration).
Fig.3.
Solubility of CO
2
at the Air/
Sea Interface.