680
ERIKSSON AND BOLIN
VARIATIONS OF ISOTOPIC COMPOSITION
It is useful to consider a few idealized cases to obtain an insight
into how the different physical processes interplay with each other.
For a more detailed treatment, see Ref. 2.
The fractionation that occurs when water vapor condenses in an
air parcel that moves upward and is cooled by an adiabatic expansion
has been discussed thoroughly by Dansgaard.' Wedistinguish between
the reversible moist adiabatic process in which all condensed water
vapor remains in the air as cloud droplets and the pseudo-adiabatic
process in which all condensed water falls out as precipitation. The
latter process usually best describes reality since the water contentgf
a cloud in the form of small droplets in suspension seldom is very
great (the mixing ratio is usually less than 0.5 x 107%). In a precipitating cloud, droplets from above fall through any given air parcel and
are in exchange with the environments; the speed of the exchange de-
pends on the fall velocity and thus onthe size of the droplets.’ This fall
and exchange is approximately what takes place in an individual con-
vection cell. Since they are involved in the large-scale vertical trans-
fer of moisture, such convection cells represent the turbulent eddies
that are responsible for part of this transfer. In addition, advection by
the mean meridional circulation cell takes place.
To
clarify
some simple aspects of this vertical transfer, we
neglect horizontal transfer and consider a steady state. We also assume a pseudo-adiabatic condensation process and neglect for a moment the exchange between the droplets and their environments after
they have formed and fallen through the atmosphere.
A bar denotes a time average, and a prime denotes a departure
from this average; for example,
q=q+q’
(1)
The maintenance of a constant vertical distribution of water vapor
implies
dire
a =
az [ow q + (ow)’q’] =—P
(2)
where Z = vertical distance
p = air density
w = vertical velocity
P = rate of condensation per unit volume and unit time
Equation 2 expresses a balance between vertical advection, vertical
turbulent transfer, and condensation (equals precipitation). Similarly,
we obtain for any isotope considered