682
ERIKSSON AND BOLIN
Introducing a characteristic vertical distribution of water vapor given
by
G=Ge%
(8)
we obtain in such a steady state
R = R, exp [—(a — 1)aZ]
(9)
implying a balance between the advection of water vapor upwards and
removal by precipitation. With a characteristic value of A= (4 km)",
we would expect a change of R by approximately 90 °/), and 10 °/y) over
4 km for deuterium and 140, respectively (assuming an ambient tem-
perature of about +10°C).
CASE 2: Vertical transfer of water vapor by turbulence
(pw = 0).
Assuming for simplicity that A is a constant, we derive the equation
aR
1 dq dR
—,
az’ =~
“qaz
dz
(a-1)
(10)
Wenote that this equation is independent of A.
Adopting the vertical moisture distribution given by Eq. 8, we
obtain the following expression for the vertical variation of the isotopic
composition of the water vapor:
R = R, exp [-(¢Va — 1)aZ]
(11)
The plus sign in Eq. 11 corresponds to the case in which a convergence
of the turbulent transfer upwards balances the removal by precipitation, whereas the minus sign implies a corresponding balance between
convergence of a downward transfer by turbulence and removal by precipitation. The vertical distribution of the convergence has been prescribed by the assumptions of a constant value of A and the vertical
moisture distribution (Eq. 8). The general character of the result
does not change for other reasonable assumptions in this respect.
In the cases of deuterium and ‘40, only the plus sign is of interest
Since the ocean surface is the source for the turbulent transfer. Comparing the results of these cases with Eq. 9, we find a vertical de-
crease that is only one-half of what was obtained in the advective case.
This is of course an expression of the fact that mixing, in addition to
bringing about an upward transfer, also tends to decrease the vertical
gradient of the isotopic composition brought about by fractionation. We
can also qualitatively get an idea about the effect of isotopic exchange
between falling droplets and the environment. Large droplets (diameter
>0.2 cm) equilibrate slowly and fall rapidly; therefore the theory above
is applicable. Small droplets, however, adjust to the environment rapidly, and, in the limit of an infinitely rapid adjustment, there is no net
effect of the fractionation. Thus no vertical gradient in the isotopic