189, 2H, AND °*H IN NATURAL WATERS
= [ow aR + (pw)(qR)] =—aRP
681
(3)
where R is the concentration of the isotope considered in grams per
gram of H,O and a is the fractionation coefficient for condensation or
evaporation.
For the following approximate treatment, we shall introduce an
eddy exchange coefficient A defined by
WF
dq
(ow)'q’ =-A az
and
a
d(qaR)_—,._:
(ow)’(qR)’ =—A a7 = A
d(qR)
aR
(4)
In the last part of Eq. 4, we have for simplicity introduced one further
approximation in replacing qR by qR, thus assuming that there is no
correlation between the isotopic composition and the humidity content
of an air parcel. This approximation is somewhat questionable in view
of the likeliness that the descending and comparatively dry air has experienced more condensation and therefore might have fewer heavy
isotopes (see Ref. 3), Assuming similarly RP = RP, our two basic
transfer equations become
and
aq {—_.
a lawaR
aah)
A —7-| =~
==
oRP
(5)
Let us consider two Special cases.
CASE 1: Vertical advection (A = 0).
From the two equations given
1 a(gwq) _(a—-1)P
_
-@ -Dase az = awa
SIE
rol|
as Eq. 5, we derive
6)
This relation is equivalent to Rayleigh’s distillation formula
6R_
6q
Zr@-vs
(7)
CGC