Journal of Hydrology, 100 (1988) 143 176
143
Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
[2]
TRACING OF W A T E R M O V E M E N T IN THE U N S A T U R A T E D ZONE
USING S T A B L E I S O T O P E S OF HYDROGEN A N D OXYGEN
C.J. BARNES and G.B. ALLISON
CSIRO, Division of Water Resources Research, GPO Box 1666, Canberra, A.C.T. 2601 (Australia)
CSIRO, Division of Water Resources, Private Bag 2, P.O. Glen Osmond, S.A. 5064 (Australia)
(Received December 10, 1987; accepted for publication December 12, 1987)
ABSTRACT
Barnes, C.J. and Allison, G.B., 1988. Tracing of water movement in the unsaturated zone using
stable isotopes of hydrogen and oxygen. J. Hydrol., 100: 14~176.
The development of an analytical model for movement of the stable isotopic species of water in
unsaturated soils is presented by means of a review of recent literature on the subject. The model
adequately represents experimental observations of isotope profiles during evaporation from
saturated or unsaturated soils, under both nonisothermal and nonsteady conditions. Interpretation of field isotope profiles using the model is discussed, and indications are made of areas where
further work is desirable.
INTRODUCTION
Craig and G o r d o n (1965) modelled the isotopic b e h a v i o u r of w a t e r evaporating from a free w a t e r body into the a t m o s p h e r e by a p p l y i n g F i c k ' s law of
diffusion to v a p o u r m o v e m e n t above the a i r / w a t e r interface. S u b s e q u e n t l y
t h e i r a p p r o a c h h a s been developed further, a n d extended to e v a p o r a t i o n from
s a t u r a t e d and u n s a t u r a t e d soils, u n d e r b o t h u n s t e a d y and steady-state
conditions.
U n d e r l y i n g this t h e o r e t i c a l effort was the o b s e r v a t i o n t h a t a n u m b e r of
features were c o m m o n to stable isotope profiles in the surficial layers of field
soils across a wide r a n g e of climatic conditions.
G r o u n d w a t e r r e p l e n i s h m e n t o c c u r s by b o t h indirect (or localized) r e c h a r g e
t h r o u g h streambeds, depressions, etc., a n d direct (or local) r e c h a r g e t h r o u g h
the surficial materials. It is this l a t t e r form of r e c h a r g e w h i c h often leads to a
difference in the isotopic s i g n a t u r e b e t w e e n rainfall and the u n c o n f i n e d
g r o u n d w a t e r . To o b t a i n h y d r o l o g i c i n f o r m a t i o n from the isotopic c o m p o s i t i o n
of g r o u n d w a t e r , the processes o c c u r r i n g in the u n s a t u r a t e d zone w h i c h .lead to
c h a n g e s in isotopic c o m p o s i t i o n m u s t be t a k e n into a c c o u n t .
In a seminal p a p e r Z i m m e r m a n n et al. (1967a) d e m o n s t r a t e d t h a t the
e n r i c h m e n t of d e u t e r i u m in the soil w a t e r of a s a t u r a t e d soil c o l u m n decreased
0022-1694/88/$03.50
Lc'~1988 Elsevier Science Publishers B.V.
144
NOTATION
Symbol
Unit
First use
defining eqn.
Definition
D*
D
D,*
Dv
E
f
g
h~,
N sat
R
R ....
Ro
R*
R,.~p
R~
t
w
z
m2s ~
m~s ~
m2s 1
m2s 1
ms 1
(1), (8b)
after (5), (Sa)
(7), (8b)
(8b)
(1)
(8a)
(8b)
(12)
(7)
(1)
(1)
(2)
(4)
(10)
(12)
(13)
after (5)
(1)
(6)
(3)
(7)
(7), (10)
(4)
(5)
(6)
(5)
(9)
(9)
(11)
(13)
(7)
(7)
(4)
Effective liquid diffusivity of isotopes
Molecular diffusivity of liquid water
Effective diffusivity of water vapour
Molecular diffusivity of water vapour
Evaporation rate
Liquid flow impedance factor
Vapour flow impedance factor
Relative humidity of the atmosphere
Saturated water vapour density
Isotope ratio in liquid water
Isotope ratio of feed water
Isotope ratio at z - 0
Isotope ratio of standard water
Isotope ratio of water vapour
Isotope ratio of atmospheric water vapour
Time coordinate
Filter velocity
Depth coordinate, positive downwards
Depth of evaporating front
Length scale for liquid diffusion
Length scale for vapour diffusion
Equilibrium fractionation factor
Isotope ratio "'delta-value"
Delta value of feed water
Delta wdue at z - z,.t
Delta value at z
z0
Delta wdues for 2 H / 1 H ratios
Delta values for 1~O/1~O ratios
Equilibrium enrichment
Boltzmann variable
kinetic fractionation factor
Density of liquid water
Parts per thousand
z~.t
z,
z,
~*
,~
,~....
b,.~
4,
5,,,&2,-~,~
kg m 3
s
ms ~
m
m
m
m
a 1 8 , 5 iSre ~
~.
).
~r"
p
%0
m s 1,~
kgm a
exponentially with depth, with the decay length approximately proportional to
the evaporation rate.
T h i s w o r k w a s l a t e r e x t e n d e d t o u n s a t u r a t e d s o i l s b y M u n n i c h e t al. (1980)
a n d B a r n e s a n d A l l i s o n (1983). I t w a s s h o w n t h a t b e n e a t h t h e e v a p o r a t i n g f r o n t
isotope profiles were of similar shape to those for saturated materials, and
furthermore that the lowering of slope of the oxygen-18/deuterium relationship
was due to the decreased influence of atmospheric turbulence. The theory has
been used to obtain evaporation rates in the field for systems showing steady
e v a p o r a t i o n f r o m a w a t e r t a b l e ( A l l i s o n a n d B a r n e s , 1983, 1985; F o n t e s e t al.,
1986; C h r i s t m a n n a n d S o n n t a g , 1987).
Recently, the theoretical approach has been extended to cover nonsteady
evaporation from soils, under both laboratory and field conditions (Walker et
145
al., 1988; Barnes and Walker, 1988), and the effects of temperature gradients in
the soil (Barnes and Allison, 1984).
In this paper we review the available literature on isotope studies which
have been carried out in the unsaturated zone, and identify areas requiring
further study. To this end we follow in outline a model which appears to
describe adequately the behaviour of isotopes in porous materials. We begin
with steady, isothermal evaporation from a saturated sand, proceed to unsaturated, nonisothermal conditions, and finally to nonsteady evaporation.
Effects of other processes, such as infiltration, transpiration and the presence
of salt on the isotope profiles are considered. In the light of this model,
examples of field profiles are discussed, and where possible an interpretation of
the observed features is given.
1. EVAPORATION FROM SATURATEDSOILS
Zimmermann et al. (1967a) reported isotope concentrations in pore waters as
a function of depth for a number of saturated sand columns undergoing evaporation. In contrast to the earlier work of Craig and Gordon (1965) and
others for evaporation from open water bodies, where the assumption was
generally made that the water body was more-or-less well mixed, they assumed
that the soil effectively prevented any v e r t i c a l mixing. They explained the
observed exponential isotope profile as the result of competition between
diffusive and convective fluxes; at equilibrium the two must balance. For the
existence of a steady-state concentration gradient near the surface, equality of
the diffusive and convective fluxes implies that:
D*dR/dz
=
E(R
-
Rre~)
(1)
where D* is the effective diffusivity of the isotope in the pore water and E is
the evaporation rate. Rre s is the isotope ratio of the water entering the column
from below (see Notation section for definition of symbols and notation). The
solution of this differential equation gives:
Rros + (R0 - Rres)exp( - z / z l )
R -
(2)
where:
zl =
(3)
D*/E
and D* has been assumed constant, which will be the case provided only that
the pore space is homogeneous with depth.
Because variations in stable isotope concentrations are generally small in
percentage terms, isotope concentrations are usually expressed as relative
deviations from the concentration of a standard water, usually Standard Mean
Ocean Water (SMOW)_multiplied by 1000 (i.e. "per mille", denoted by %0).
Thus, if R* is the isotope ratio of the standard, the "delta-value" is defined by:
5
=
(R/R*
-
1) × 1000(%o)
Equation (2) then becomes:
(4)
146
5 2
-20
0
(%0) rel. tO S M O W
-10
i
0
i
i
10
20
i
20
40
6G
E
r- 8(]
E
S
J
•
52
A
4-2 ( ~ 8 - 3-6
100
12C
140
160
Fig. 1. D e p t h / d e l t a value r e l a t i o n s h i p for steady-state e v a p o r a t i o n from a s a t u r a t e d sand column,
t o g e t h e r with e x p e r i m e n t a l parameters. The oxygen-18 profile is scaled onto the same curve as the
d e u t e r i u m profile.
=
(~res -~ (~0 -- ~res)
exp(
z/zl)
(5)
[Zimmermann et al. (1967a) used the molecular diffusivity D ( = D * / f ) and the
filter velocity w = ( E l f ) , in place of D* and E in eqn. (1); the factor f (a function
of water content) accounts for the reduced cross-sectional area available for
diffusion in porous media, and the increased effective path length or tortuosity.
They took tortuosity into account by using a value for D of 1.5 x 10 ~m2s 1 [cf.
2.3 x 10 9m2s ~ given by Mills (1973), for free water.]
Figure 1 compares theoretical (solid line) and observed isotope profiles for
evaporation from a saturated medium sand, reproduced from Allison et al.
(1983a). Because oxygen-18 and deuterium concentrations are linearly related,
both isotope profiles have the same shape. The observed evaporation rate was
1.14 mm d ~, compared with the value calculated from the exponential rate of
decay of the profile with depth of 1.12mmd 1.
In assuming isothermal conditions, the above analysis ignores the lowering
of temperature at the surface due to latent heat effects. For sufficiently low
evaporation rates, this effect will be minimal, but at higher evaporation rates
147
(e.g. 10 mm d 1, which was the highest rate used by Zimmermann et al., 1967a)
a significant reduction in surface temperature may be expected. The magnitude
of the surface temperature depression must be less than the equivalent wet bulb
depression. However, as the temperature dependence of the self diffusion
coefficient of water is of the order of 2.5%/°C for saturated systems at steady
state, a few degrees lowering of the surface temperature will have only a small
effect on the isotope profile.
2. EVAPORATIONFROM UNSATURATED SOILS
Much has been written on the modelling of water movement in the unsaturated zone (Philip and De Vries, 1957; Taylor and Carey, 1964; Philip, 1969,
1988; Jury, 1973; Raats, 1975; J u r y and Letey, 1979; Corey and Klute, 1985).
Recently, the more traditional deterministic approach to water movement in
soils has been supplemented by a stochastic one (e.g. Jury, 1988), involving
both solute and water transport.
The heavy isotopic species of water can be considered as a solute species, but
with certain properties which make them almost model tracers for water
movement (Dincer and Davis, 1984). Their physical and chemical similarities to
bulk water remove most of the complications associated with other tracers (e.g.
adsorption), while their very small concentrations in natural waters allow
their flow equations to be linearized. Hence it is appropriate to employ the
theoretical approaches which have been developed for solute and water
movement in unsaturated systems, with equations for isotope movement
linearized with respect to the isotope concentrations. One of the advantages of
using these isotopes to obtain information about water movement is that the
relevant diffusivities vary slowly with water content, in contrast to the
extreme variation of the soil water ~'diffusivity" with this parameter, for
example. The development of the theory of stable isotope movement in unsaturated soils so far has used the deterministic approach as given, for example,
in Philip and De Vries (1957); and this is the approach followed below.
Isothermal evaporation
Experiments for unsaturated materials similar to those carried out by
Zimmermann et al. (1967a), were repeated by Allison et al. (1983a) for a variety
of materials. Similar experiments, although not at steady state, were reported
by Munnich et al. (1980). At steady state the isotope profiles were similar to
those observed by Zimmermann et al., except that the maximum in the profile
occurred a short distance below the surface. Above this maximum the isotope
concentration decreased rapidly towards the surface. Figure 2 shows two
isotope profiles which clearly demonstrate these features: Fig. 2a taken from
Allison et al. (1983a) for steady evaporation from an unsaturated column of
0.5-1mm sized aggregates of the clay mineral attapulgite; and Fig. 2b, an
unsteady arid zone dune profile reproduced from Barnes and Allison (1982).
Nonsteady profiles, both in the laboratory (Munnich et al., 1980) and in the field
148
5 2 (%0) rel. to S M O W
-lO
-2O
0
10
20
30
i
i
i
'1
1
-40
-20
-10
10
0
20
i
0
u0
(a)
-30
o'
•
-
°o o
9o
Io
oo
oo
oo
0-1
~
Io
Io
oo
OQ
2
QO
0-2
oo
oo
3
oo
QD
0 •
oo
•
0.3
E
o
oo
ce
oo
o
•
t
o
0-5
2"
°:
6
OOD
0"6
S
Fig. 2. Isotope profiles in unsaturated soils. (a) Experimental, steady-state profile similar to that
of Fig. 1; (b) field profile from an unvegetated arid zone sand dune.
as in Fig. 2b, h a v e a shape similar to steady-state ones, but different in detail
as will be seen later.
In the zone above the m a x i m u m in the isotope profile, the isotope c o n c e n t r a tion d e c r e a s e s rapidly t o w a r d s the surface. This is due to diffusion of w a t e r
v a p o u r to the soil surface from the r e g i o n in which e v a p o r a t i o n takes place,
and w h e r e the isotope m a x i m u m also lies (Barnes and Allison, 1983). The
analysis of Z i m m e r m a n n et al. is modified to t a k e into a c c o u n t this region of
w a t e r v a p o u r m o v e m e n t at the top of the profile; and also the possibility of
v a p o u r phase diffusion of isotopes below the m a x i m u m (Barnes and Allison,
1984); and the effect on the k i n e t i c f r a c t i o n a t i o n f a c t o r in the " d r y " soil l a y e r
t h r o u g h w h i c h the w a t e r v a p o u r has to diffuse.
F o l l o w i n g B a r n e s and Allison (1983), and recognizing that, at least in
m o d e r a t e l y wet soils, the zone in w h i c h significant e v a p o r a t i o n o c c u r s is
n a r r o w , the soil profile can be divided into two parts: an u p p e r one in which
w a t e r m o v e m e n t is by v a p o u r diffusion, and lower one in which liquid t r a n s p o r t
is significant. In the lower r e g i o n isotope m o v e m e n t in u n s a t u r a t e d soil was
shown to be similar to t h a t u n d e r s a t u r a t e d conditions, if a c c o u n t is made of
the d e p e n d e n c e of the effective diffusivities of isotopes on w a t e r content, b o t h
in the liquid and the v a p o u r state (see the n e x t section). The l a t t e r is i m p o r t a n t
because isotopes m a y still diffuse in the v a p o u r phase even t h o u g h t h e r e is no
149
relative humidity gradient, and no bulk movement of water vapour. This point
was overlooked in Barnes and Allison (1983) (cf. Zouari et al., 1985), but was
later recognized (Barnes and Allison, 1984). At steady state the profile in this
region is found to be exponential with respect to a modified depth function
which takes into account changes in water content, affecting both the
convective velocity and the ability of the isotopes to diffuse. Thus, beneath the
region where evaporation occurs:
(~
(~ref
((~ef
--
t~ref)
exp [ - idz/(zl + Zv)]
(6)
Zef
where z~ is defined by eqn. (3) above, and:
Zv = (~*aVD*N~at)/(Ep)
(7)
Here, ~* and a v are the equilibrium and kinetic fractionation factors, which are
discussed later in this section, see pp. 152 and 153.
The characteristic lengths, Zl and Zv, indicate the relative importance of
liquid and vapour diffusion. They are proportional to the effective diffusivities
D* and D* respectively, and inversely proportional to the evaporation rate E.
From eqn. (6) it can be seen that the effect of vapour diffusion is to increase the
effective diffusivity of the isotopes, leading to a more extensive isotope profile
than would be possible with liquid diffusion alone. [Barnes and Allison (1983)
assumed that the effective diffusivity was proportional to the water content,
and introduced a modified length scale slightly different to that implicit in the
exponential of eqn. (6)].
In dry soils, where the paths for liquid diffusion are discontinuous and
tortuous, z~ will decrease with water content, while zv will increase, so that Zv
may dominate z~. J u r y and Letey (1979) point out that vapour diffusion may be
enhanced by a ~series/parallel" type flow, where vapour diffusion pathways are
short circuited by liquid-filled pores. The result is that, as a function of water
content, the sum (Zv + zl) will vary smoothly over the entire range of water
contents, with rate of variation somewhat less than that of the water content,
except near saturation.
The effective diffusivities
In Barnes and Allison (1983), and Allison et al. (1984), it was assumed that
the cross-sectional area available for diffusion was directly proportional to
water content. The relatively good agreement with the experimental results
(the solid line in Fig. 2a) tends to suggest that this is a reasonable assumption
for the materials and water contents studied there, and that vapour diffusion
below the isotope maximum was small in these experiments.
The effective diffusivities D* and D ' a r e both functions of water content, but
will vary in quite different ways in response to changing water content. Both
diffusivities will be proportional to the respective molecular diffusivities of the
150
isotopes in liquid water and in air, multiplied by an impedance factor representing the effective cross-sectional area available for diffusion, and tortuosity
(defined as the ratio of the effective path length to the true path length). Thus
the effective diffusivities may be represented:
D*
D*-
-
fD
(8a)
gDv
(Sb)
where D and D v are the respective molecular diffusivities, and f and g represent
the effects of the porous medium in reducing the effective diffusion rates.
For steady-state or slowly varying profiles, appropriate to evaporation, the
effect of dead-end pores and relatively immobile volumes of water will be
negligible, and at saturation, the whole of the pore space will be available for
liquid diffusion. For vapour movement in a dry sand, Penman (1940) determined
experimentally a tortuosity of 0.66, but for liquid movement in soils having
more complicated structure (e.g. clay minerals) it may be much smaller, with
values as low as 0.24).1 having been found even when water-saturated (Porter
et al., 1960; Nye, 1979; Barraclough and Tinker, 1982; Johnston, 1987).
In unsaturated materials, the cross-sectional area available for diffusion in
the liquid phase will decrease in proportion to the water content (provided it
is not too low), while the tortuosity will also decrease. The factor f may then
be modelled as the product of tortuosity and the volumetric water content. This
is the approach used almost universally so far for isotope diffusion in unsaturated soils (Munnich et al., 1980; Barnes and Allison, 1983; Allison et al.,
1983a; Sonntag et al., 1985; Yousfi et al., 1985; Zouari et al., 1985; Christmann
and Sonntag, 1987). Equation (6) reduces to eqn. (21) of Barnes and Allison
(1983), only if this assumption is made, as well as assuming a constant
tortuosity. In drier soils, the continuity of liquid-filled pores may begin to break
down, with a consequent drastic reduction in the effective liquid diffusivity.
The tortuosity may also be expected to decrease significantly for the same
reason, and zl may be effectively zero at low (nonzero) water contents.
Recent experimental evidence (Porter et al., 1960; Barraclough and Tinker,
1982; Johnston, 1987) suggests that the tortuosity also decreases approximately
linearly with water content over almost the whole range up to saturation. It
should be noted that the impedance factors used by these authors differ from
the one defined above, which must be divided by the water content for
comparison. With few exceptions (Scott and Paetzold, 1978) impedance factors
in the liquid phase have been measured for chloride, and unless anion
exclusion has been explicitly included in calculations, results may not be
directly applicable to diffusion of the stable isotopes of water.
On the other hand, vapour diffusion will play an increasingly important role
at lower water contents. The factor g may be modelled similarly to the factor
f, except that the cross-sectional area available for diffusion is now the air filled
porosity. Vapour diffusion may also be enhanced in systems with appreciable
water content by the "series/parallel" flow mechanism of Philip and De Vries
(1957). That is, small isolated pockets of water which are no longer able to
151
contribute to liquid diffusion may enhance vapour diffusion by short-circuiting
the vapour pathway, provided a concentration gradient exists. Thus, at all nonzero water contents, the effective cross-sectional area available for diffusion in
the vapour phase may be expected to be somewhat greater than would be
calculated from the air-filled porosity alone (Scotter, 1976; Scott and Paetzold,
1978). The tortuosity will also be affected by these considerations, but only to
the extent t h a t its variation across the range for which vapour movement is
important will be small, and in this case a value close to that of Penman (which
was measured for vapour diffusion) may be universally appropiate.
The sum of the characteristic lengths, zv + z~, which indicates the extent of
diffusion, will vary smoothly with water content, even though independently
t h e variation of either zv or z~ with water content may be more rapid. This
suggests t h a t diffusion of isotopes plays a major part in the formation of isotope
profiles at all water contents, ensuring the ubiquitous shape of measured
profiles. The fact that both evaporation rate and the total effective diffusivity
decrease with water content tends to restrict the range of the length scale
observed in nature.
It is clear from the above considerations that the variation of the effective
diffusivities with water content may be quite complicated, and that the models
currently used for predicting diffusivities, particularly for vapour diffusion,
have long been regarded as inadequate (e.g. J u r y and Letey, 1979). Given the
number of investigations now using stable isotope techniques to estimate
evaporation rates from isotope profiles (see below), and the fact that these
estimates are directly proportional to the effective diffusivities; direct measurements of these parameters on a range of materials seems warranted. This could
be done using steady-state techniques as suggested in Barnes and Allison
(1984), or more rapidly using the unsteady theory developed in Walker et al.
(1988) and Barnes and Walker (1988), after the fashion of Bruce and Klute
(1956) for measuring the unsaturated hydraulic conductivity of soils (cf.
Scotter, 1976).
The oxygen-18/deuterium relationship
As a surface body of water evaporates, enrichment of both oxygen-18 and
deuterium occurs, with changes in the delta-values of oxygen-18 and deuterium
closely correlated, with a slope of 4-6 in 52 51s space. Water samples
extracted from the surface layers of a soil have been found to produce slopes
in the range 2-5 (with lowest slopes generally produced by drier soils), so that
such water shows greater relative enrichments of oxygen-18 over deuterium,
when compared with meteoric waters (see Fig. 3).
Although the effective diffusivities of the isotopic species HD160 and H.~O
in liquid water differ slightly (Mills, 1973; Mills and Harris, 1976; Harris and
Woolf, 1980), both are within 1% of the self diffusion coefficient for liquid
water. Similarly, molecular diffusivities of water vapour for both H~O and
HDlSO differ by less than 0.5%, although they differ from that of normal water
152
0
~2 = 4"2 ~18
20
S
.
"=8"
=10
=20
"304
"2
()
I
2
4
6
818
8
1'0
I
12
t
14
1'6
1'8
(°//oo) rel. to S M O W
Fig. 3. Oxygen-18/deuterium r e l a t i o n s h i p s for e x p e r i m e n t a l steady-state columns of Figs. 1 a n d 2a,
e x h i b i t i n g a lower slope for t h e u n s a t u r a t e d (solid triangles) profile.
vapour by nearly 3% (see below). The decay lengths, zl and Zv, will then be
approximately the same for both isotopic species. From eqn. (6) profiles for both
isotopes will have almost identical shapes and so isotope concentrations at any
depth are expected to be approximately linearly related according to:
((~2 -- (~2res)/((~20 -- ~2res)
:
((~18 -- ~18res)/((~lS0 -- ~18res)
(9)
where the subscripts 2 and 18 refer to the heavy isotopes of hydrogen and
oxygen of mass 2 and 18 respectively. The slope of the relationship between
oxygen-18 and deuterium delta-values clearly depends only on the ratio of the
total surface enrichments of the two isotopes. If the surface isotope concentration can be predicted in terms of the concentration at depth, the slope can be
predicted. Figure 3 shows oxygen-18/deuterium relationships for the profiles
given in Figs. 1 and 2a, demonstrating the lower slope for the unsaturated
profile.
Two effects have been shown to contribute separately to the production of
an excess of heavy isotopes at a site where evaporation is proceeding (Craig
and Gordon, 1965), and are termed the equilibrium and kinetic effects, respectively.
The equilibrium effect is due to small differences in chemical potential
between the isotopic species. As a result, when liquid water is in equilibrium
with its vapour at a given temperature, the isotope ratios in the vapour phase
are less than those in the liquid phase and:
Rvap =
~*Rliq
(10)
where the parameter a* is less than, but close to, unity. The temperature
153
dependence of this parameter (the "equilibrium fractionation factor") was
studied extensively by Majoube (1971). (Note that Majoube's '~equilibrium
fractionation factor" is the inverse of what we have defined here.) In keeping
with the delta-value notation introduced earlier, the '~equilibrium enrichment"
~* is usually defined by:
r.* = (1
~*) × 1000(%o)
(11)
At 25°C, the equilibrium enrichment is 73.69/00 for deuterium, and 9.3%0ofor
oxygen-18.
The kinetic effect contributing to the isotope maximum at the evaporating
surface is due to slightly different rates of diffusion of the different isotopic
species through the atmospheric boundary layer. Merlivat (1978) has measured
these diffusivities, finding that under static conditions diffusivity ratios were
approximately temperature independent. She found that the molecular diffusivity of water vapour was 24.9 and 28.1%o greater than that of HDI~O and
H~O, respectively. Thus, while the deuterium equilibrium enrichment is about
eight times that for oxygen-18, the kinetic effect is similar in magnitude for
both species.
Combining these two effects into a Fickian model of diffusion of water
vapour away from the site of evaporation, Barnes and Allison (1983) following
Craig and Gordon (1965) obtained the expression:
~*R 0 = (l - ha)~VRres + haR a
(12)
where Ra is the isotopic ratio of atmospheric water vapour far from the surface,
and av is the kinetic fractionation factor, discussed below. Equation (12) allows
us to calculate the slope of the oxygen-18/deuterium relationship, via eqn. (5)
provided the kinetic fractionation factor a v is known.
The kinetic fractionation factor
The slope of the oxygen-18/deuterium relationship for isotope profiles in
saturated soil is found to be in the range 4-6, as for free water. This can be
predicted from eqns. (5) and (9) using typical values of the isotope ratios and
relative humidity in the atmosphere, provided that the kinetic fractionation is
about half that given by Merlivat (1978) for the molecular diffusivities in the
vapour phase. It is known (see for example Ehhalt and Knott, 1965; Eriksson,
1965; Zimmermann et al., 1967a) that the degree of kinetic fractionation is
affected by turbulence in the atmospheric boundary layer, leading to a
reduction in kinetic enrichment by 50% during evaporation from a free water
body, compared with that expected from molecular diffusion.
Allison et al. (1983a) following Brutsaert (1975), and suggested that the
lower oxygen-18/deuterium slopes observed for dry soils arose as a result of the
increased significance of laminar flow over turbulent flow during diffusion of
the isotopes to the atmosphere. In a series of experiments using varying thicknesses of dry porous material over an evaporating source of water they showed
154
24
3
'
16
8
~4
A, . /
0
0
-16
1 z~
Free water
2 •
Perforated sheet only
3 o
6ram mulch
4 •
12ram mulch
"32
-4
0
4
8
12
618 (°//00) rel. to S M O W
Fig. 4. Comparison of oxygen-18/deuterium slopes for free water and constant-feed pans covered
with different thicknesses of mulch.
that as the dominant diffusive resistance changed from atmospheric (as over a
free water body) to being due to the porous medium, the kinetic fractionation
varied from 50 to 100% of the value due to molecular diffusion. This led to a
concomitant change of slope in the oxygen-18/deuterium relationship. Figure
4, taken from Allison et al. (1983a) shows the variation in slope of the oxygen18/deuterium relationship for different thicknesses of dry porous material over
water evaporating under otherwise identical conditions. Atmospheric
resistance for these experiments was found to be equivalent to a few millimetres of soil. Using these results they were able to explain quantitatively the
results of a series of steady-state column experiments using a variety of
materials, including both detailed profile shapes and the slopes of the oxygen18/deuterium plots. These materials ranged from sand to a loam, and included
attapulgite, an aggregated material with a very high microporosity.
Munnich and co-workers (Munnich et al., 1980; Sonntag et al., 1985) reported
on a number of experiments for unsteady evaporation using materials of
different grain sizes, including medium and coarse sands. They reported that
155
although oxygen-18/deuterium slopes for the finer materials were adequately
predicted by the above theory, coarser material resulted in slopes which were
closer to those expected for evaporation through a fully turbulent boundary
layer, even though the drying front had proceeded relatively further down the
column. This effect was attributed to penetration of atmospheric turbulence
into the soil for the coarser materials (Farrell et al., 1966) but the precise
mechanism is not yet fully understood. They also investigated the effect of
varying relative humidities on the oxygen-18/deuterium slope, and reported
results which were at variance with theoretical predictions, for which they
were unable to offer an explanation. Saxena (1987) looked at the effects of grain
size on oxygen-18 concentrations in lysimeter leachate, and found that the
courser materials showed greater enrichment of leachate. This would appear to
support the conclusion that these materials provide opportunity for turbulent
penetration of the soil, with the resulting advection of the water vapour
causing enhanced evaporation from the soil.
Klotz et al. (1987) investigated oxygen-18/deuterium slopes for columns of
medium sand of different lengths which were subjected to constant or periodic
rates of infiltration of water for long periods of time, and different rates. The
leachate draining from the bottom of the columns showed considerable isotopic
enrichment, with low slopes for the ~2-~1s plots. Their results were explained
using the unsaturated zone theory discussed above.
Nonisothermal effects
The impetus for the development of the above theory came from a desire to
understand isotope profiles measured in the field. However, this theory does
not take into account the sometimes appreciable temperature gradients which
are found in real soils. The effect of temperature gradients on the water fluxes
is generally small, except if the temperature gradient is very large, as may
occur in the upper 100-300mm of soil, or if the soil is very dry. In these cases
temperature induced vapour movement may dominate the water flux, and must
be properly accounted for. The work of Philip and De Vries (1957) (see also
Sophocleous, 1979) indicates a number o f mechanisms by which thermal
gradients might cause water movement in either the vapour or the liquid phase,
and suggest an approach to model such movement. Because water movement
in the unsaturated zone under a thermal gradient often involves a change of
state, it is likely t h a t isotope fractionation may occur, leading to changes in the
profiles described above.
Figure 5, reproduced from Dincer et al. (1974) shows the effect of annual and
diurnal surface temperature fluctuations on the temperature profiles within
dune sands in the Saudi Arabian arid zone. Diurnal temperature gradients of
up to 200°C m 1 in the upper 100 mm are evident, while for the deeper annual
temperature cycle, gradients are more modest (up to 5°Cm 1 in the top few
metres). Measurable variations in temperature may persist below 10 m for the
156
(a)
Sand temperature (°C)
15
20
25
30
J
1
i
i
OF
G
B 22 sop
13 Oct
C
1972
o 28 o o t
E
2,
F
G
H
I
25Dec
22 Jan
5Mar
5 May
H
E
%,
~q
35
I D
A
\~
\\/\
,972
\\/
ov
\~
~ \
[\
1973
(b)
20
r~
0"1!
30
40
50
60
i
J
i
i
\ (
=\ [
~1
/
/
/
A
B
0600 hr
0715 hr
D
1020 hr
70
7
1,OOhr
0"3
Dry- moist sand interface
Fig. 5. Annual (a) and diurnal (b) temperature variations in the surface layers of an arid zone dune.
annual temp er a t ur e cycle in dune sands, whereas diurnal effects rarely
p en etr ate below 300 ram.
Sonntag et al. (1980) reported on a computer model which was used to
describe moisture and isotope movement in an arid zone dune, allowing both
evaporation and infiltration. The model appeared to be similar to the box model
used by Craig and Gordon (1965), but few details were provided.
In adapting Philip and De Vries' (1957) model Barnes and Allison (1984)
assumed t h a t water movement was so small that latent and sensible heat effects
were negligible, so t h a t the t em pe r at ur e distribution could be t aken as givenl
and heat tr an s por t was not coupled with the mass t ransport of water. Since
many of the parameters involved in t h e equations for isotope movement are
t e m p e r a t u r e dependent (including diffusivities, vapour pressure, and equilibrium fractionation factors), the resulting analysis was considerably more
157
5 0 (%0)
-4O
-20
i
i
0
rel. to S M O W
20
,
i
40
I
i
I
40
fl
f
i
oo,°
.,'
i!
]
i
o..
. . . . . . . . .
:
80
Non isothermal
.--120
E
E
Isothermal
Temp. profile
5
E
16E
= 10 "8 ms "1
ha = 0"2
T
= T~+(To-T~Iexp(-Z/ZT)
TO = 4 0 ° C
20C
T~ =
20°C
Z T = 0"05 m
5~ = -100 %o
240
res_
8 D -- 00//00
280
I
1()
20
Temperature
3'0
(°C)
40
Fig. 6. A comparison of theoretically predicted isothermal and non-isothermal isotope profiles.
complicated than t h a t for the isothermal version given above, even for steadystate conditions. The only new feature to come from their analysis was the
theoretical prediction that isotope profiles may show a secondary minimum
below the surficial maximum, but the effect for the conditions they modelled
was small (see Fig. 6). Allison et al. (1983a) had earlier compared isothermal
and nonisothermal steady-state isotope profiles experimentally, but no data
were obtained in the region where the secondary minimum may be expected.
For comparable rates of evaporation, the isotope profiles showed similar
features, although the evaporating front for the isothermal profile was more
than twice as deep as for the nonisothermal one.
Water vapour fluxes, driven by temperature gradients of the size measured
by Dincer et al. (1974), can be calculated through Fick's law by assuming
representative values for the temperature-dependent effective diffusivities.
158
Thus, if a relatively dry sand has a 30% air filled porosity and a vapour
tortuosity factor of 0.66, for a mean soil temperature of 35°C, temperature driven vapour fluxes will be of the order of 0.2 and 0.005 mm d 1for the
diurnal and annually induced temperature gradients of 200 and 5°C m 1 respectively. Equivalent evaporation rates are obtained for evaporation from sand at
the same temperature, when the evaporating front is 0.075 and 3.0 m, respectively, beneath the soil surface. Thus, for dry soils, diurnal temperature
gradients may be expected to perturb the upper part of the profile, whereas only
extremely dry profiles such as those measured by Fontes et al. (1986) and
Christmann and Sonntag (1987) will be appreciably affected by the deeper
annual temperature cycle. In the case of these latter profiles, neglect of temperature induced vapour movement may have biased the calculated estimates
of evaporation rate.
Figure 5 shows that strong diurnal cooling of the soil surface may occur. For
very dry soils, this may lead to atmospheric water vapour being condensed and
subsequently re-evaporated. Rose (1968) found possible evidence for such a
mechanism by measuring water contents, but this process has not been investigated using isotopes.
Nonsteady evaporation
In the field it is the exception rather than the rule for evaporation to be
constant with time. After a soil profile has been wet up by infiltration from a
rainfall event, for example, typically it will drain fairly rapidly to "field
capacity" and then more slowly. Evaporation will at first be relatively
constant, while water is freely available at the surface. Subsequently, when
soil physical factors become limiting, the evaporation rate will decrease, with
cumulative evaporation increasing as the square root of time. Munnich et al.
(1980) suggested that the evaporation rate changes only slowly after a period
of time, and that isotope profiles may be interpreted as "quasi steady-state"
profiles, with an exponential decay reflecting the current evaporation rate.
However, Allison et al. (1983b) applied a simplified model of evaporation
(Heller, 1968) to isotope movement through a dry surface layer. They showed
that the inherent time dependence of the evaporation rate resulted in isotope
profiles having a complimentary error function form. That is, the decay in
isotopic concentrations with depth is much more rapid than the exponential
rate suggested by Munnich et al.
Subsequently, Walker et al. (1988) and Barnes and Walker (1988) have
extended the steady-state model to nonsteady evaporation from a soil with
initially uniform water content, and attempted to apply the results to interpret
experimental data.
Isotope movement under unsteady conditions can be modelled using considerations of mass balance, by equating the time rate of change of total isotope
concentration with the divergence of the isotope flux at each point in the
medium. The isotope flux is then assumed to be equal to the sum of a diffusive
159
(a)
-30
1
°juD
2
3
V
==
0
~-4~
v~
o•
•
"$
tA
V~
v
¢,, - 5 0
¢,0
•
l
-60
0-4
I
Q ~Q v
I
~ •
eAv•
V
i
(b)
I
V
I
•
vv., . •
0.3
It:
g.
E
E 0-2
o
t&
17 &
0.1
I
0-0001
i
[0
0-0 02
/~ (mm s -1/2)
I
l
0.0004
Fig. 7. W a t e r c o n t e n t a n d d e u t e r i u m isotope profiles for e x p e r i m e n t a l c o l u m n s e v a p o r a t i n g u n d e r
i d e n t i c a l c o n d i t i o n s , for different l e n g t h s of time: 1, t = 250 h; 2, t = 100 h; 3, t = 50 h.
part proportional to the concentration gradient, and a convective part proportional to the liquid phase water velocity (Barnes and Allison, 1984). For nonisothermal systems, a further equation involving heat transport must be added
also (see e.g. Philip and De Vries, 1957; Sophocleous, 1979).
Because of the complicated dependence of the diffusivities and other
parameters on water content and on temperature, analytic solutions of the
general equations for unsteady and nonisothermal isotope movement are not
possible. Attempts at numerical solution of these equations which have been
carried out by the authors have been complicated by the peaked nature of the
isotope profiles, which require careful handling in order to avoid numerical
instabilities in the solution.
160
It has been found that, under isothermal conditions and assuming certain
simple boundary and initial conditions, water content profiles at different
points in space and time are functions of a single variable involving both space
and time. This observation has allowed fairly simple theoretical and experimental investigation of the assumptions underlying the theory of water
movement in unsaturated soils (Bruce and Klute, 1956; Philip, 1969; Scotter,
1976). It is necessary to assume that the effect of gravity is absent (as for
horizontal absorption or desorption) or is relatively small compared to the
other terms, so that it may be neglected. This has found to be a good approximation for moderately dry soils. Walker et al. (1988) and Barnes (1988) have shown
that under similar conditions, the isotope profile is also a function of this
variable only.
The transformation necessary to achieve this one-dimensional solution is
the so-called "Boltzmann" similarity transformation (Boltzmann, 1894), where
substitution of the variable:
is found to reduce diffusion-type equations in time and space [Philip, 1969, eqn.
(31)] to an equation in one dimension provided that boundary and initial
conditions are of a compatible form. The necessary initial condition for the
water content and isotope concentrations is that the profiles should be uniform
with depth. Compatible boundary conditions, such as constant concentrations,
or flux decreasing with the square root of time, are also necessary. These
conditions, while apparently quite restrictive, often correspond reasonably
well to natural systems, such as just after drainage has effectively stopped
following a recharge event.
Figure 7, taken from Barnes (1988) shows water content and isotope profiles
taken from a series of three experimental columns evaporating under identical
conditions, but for different lengths of time. The water content and isotope
profiles are seen to collapse approximately onto single curves, as functions of
the variable X, i.e. the profiles at different times are approximately "similar" in
shape. Similarity is not obeyed initially as a profile dries out, because the
kinetic fractionation varies as a function of time as the "bone dry layer"
increases in thickness. After a short time, however, the kinetic fractionation
approaches the value for laminar diffusion, and the isotope profile approaches
similarity.
Two questions important for the interpretation of field data arise. Firstly, for
a given instantaneous evaporation rate, what difference is there between a
steady-state profile (evaporating from a water table at constant depth), and an
unsteady one which is drying out from the surface? In other words, if an
estimate of evaporation rate was made from the latter type of isotope profile by
assuming that it was in steady state, how significant would the error be? The
second question concerns the time taken for the isotope profile to develop. For
a given evaporation rate (i.e. depth to the isotope maximum) does one form of
profile develop more quickly than the other?
161
~2
0
-40
i
i
(%0)
0
,
rel. to SMOW
,
40
i
i
80
i
\\
20
/'f/
~-. 40
E
E
6O
r
~
Steady
~m~
Unsteady
80
100
Fig. 8. Comparison of steady-state and unsteady deuterium profiles for the same instantaneous
evaporation rate, for a hypothetical soil.
As a partial answer to the first question, Barnes and Walker (1988)
considered evaporation from a soil with physical properties such that the water
content profile was always a step function. They showed that for a given
evaporation rate for this soil, the absolute differences between the profiles at
any depth were small, although the unsteady profile has a reduced isotope
maximum, so t h a t estimates of evaporation rates made by fitting an exponential form to the unsteady profile would give a good estimate of evaporation in
this case (see Fig. 8). It is not clear how well this observation applies to soils
with more realistic water content distributions. It should be noted t h a t in both
steady and unsteady cases under isothermal conditions, evaporation rates will
be identical for identical depths of the evaporating front. The second question
is dealt with under the discussion of field profiles.
162
3. INFLUENCE OF SALTAND VEGETATION ON ISOTOPE PROFILES
Effect ofsalt
Soluble salts are known to have an effect on the rate of evaporation of
brines. For instance, Harbeck (1955) cites evidence that a 1% change in
solution density due to soluble salts produces approximately a 1% change in
the evaporation rate. He also recognized that the effect depended on the
mixture of salts present. The main effect of the salts is to reduce the chemical
activity of water, so that the vapour pressure deficit which drives evaporation
is reduced (Salhotra et al., 1985). A secondary effect will be a raising of the
surface temperature relative to t h a t of a comparable fresh water system.
Gonfiantini (1965) and Lloyd (1966) measured the isotopic composition of
evaporating pans of brine, and showed that the resulting isotopic enrichment
was reduced at high salinities compared to evaporation from fresh water pans.
This was ascribed to the above mentioned effect of salinity on the effective
relative humidity. Sofer and Gat (1972, 1975), Stewart and Friedman (1975) and
Gat (1979), showed that dissolved salt usually reduced the equilibrium fractionation, with the degree of reduction dependent on the particular salt.
Because the kinetic fractionation factor reflects the conditions of the atmospheric boundary layer, such as the degree of turbulence and the diffusive
resistance away from the surface, this factor is not affected directly by salinity.
However, since the effect of kinetic fractionation is proportional to the
effective relative humidity, according to eqn. (11), very saline surface solutions
will reduce the kinetic fractionation.
When a saline solution evaporates from a porous material, movement of salt
occurs in the liquid phase only, and evaporation will result in high salt concentrations near the evaporating front, even for quite small initial concentrations in the evaporating water body. As a result of diffusion in the liquid phase,
a salt concentration gradient will develop (Allison and Barnes, 1985; Ullman,
1985).
Under conditions of near saturation in solutes, care must be taken in
estimating evaporation rates from the depth of the isotope maximum because
of the reduction of the saturated vapour pressure at the evaporating front. A
further complication may arise if a salt crust develops, thus modifying
tortuosity and porosity. An experimental difficulty is caused by gypsum which
is usually present in evaporitic environments, as most of the techniques
developed for extracting water from sediments will also remove a part of the
water of crystallization of gypsum. This may be quite different isotopically
from t h a t of the pore water and a technique such as centrifugation with a
nonmiscible heavy liquid must be used for obtaining the pore water.
Recently, Walker and Dighton (1988) have studied the simultaneous
movement of water, salt and isotopes during evaporation. They were able to
show that even at very low soil water potentials, liquid movement was significant, and also to show how salt gradients can modify the isotopic composition
of soil water.
163
Effects of vegetation
Several authors have found an effect of vegetation on the isotope profiles in
the underlying soil. Zimmermann et al. (1967a) reported that isotope profiles
beneath grass were relatively less enriched than nearby profiles under bare
ground. Similar observations were reported by Bath et al. (1982a,b) for different
sites corresponding to different land usage on the English chalk, and have also
been observed by us beneath arid zone dunes.
The observations of Zimmermann et al. prompted them to carry out
experiments to determine whether plant roots were capable of producing fractionation, but under the saturated conditions of their experiments, no fractionation was found. Subsequently Allison et al. (1983b) confirmed this result
for unsaturated conditions, even for very dry soils. FSrstel (1982) also reported
no fractionation in oxygen isotopes between water obtained from twigs taken
from plants and soil water in field experiments.
Zimmermann et al. (1967a) concluded t h a t in their case the main effect of the
grass cover was the reduction in soil evaporation, leading to a less enriched
profile beneath the vegetation. In contrast, Bath et al. (1982a,b) concluded that
the differences they observed were due to selective infiltration rather than
evaporation, presumably due to preferential transpiration of the isotopically
heavier rainfall events of summer.
Barnes and Allison (1983) considered theoretically the effect on the shape of
the isotope profile of water removal from the soil by the non-fractionating
process of transpiration. Because transpiration both removes some enriched
water and causes a water flux at depth which is greater than the evaporative
flux at the soil surface, the isotope profile at depth may be expected to decay
more quickly than would be expected in the absence of transpiration. On the
other hand, partial shading of the soil surface a n d / o r lower soil water contents
which may be expected under vegetation will act to reduce the soil evaporation
rate, as observed by Zimmermann et al., and may ultimately lead to deeper
isotope profiles, given sufficient time for their development. Christmann (1986)
also discusses the effect of transpiration on the isotope maximum using a
simple mathematical model, and shows t h a t transpiration may be expected to
reduce the maximum isotope concentration in the soil. Rodhe (1987) and
Saxena (1987) also include some discussion on the effects of vegetation.
The total isotopic enrichment in the unsaturated zone under vegetation will
thus depend on the relative effects of deeper profiles due to lower evaporation
rates on the one hand, and lower water contents and the effect of the transpiration stream on the other. The mean time between rainfall events will also
influence the mean isotopic concentration of recharge as the rate of isotopic
enrichment will decrease with time (i.e. with the evaporation rate); this seems
to be the dominant effect for the observations of Zimmermann et al. In the arid
zone, the effect of lower soil moisture under vegetation would appear to be
dominant leading to less total enrichment of isotopes in the surface layers, and
consequently less enrichment of deep percolation, under vegetation. The
164
selective infiltration mechanism of Bath et al. (1982a) may also be important in
arid zone infiltration because of the observed tendency of heavier rainfalls to
be isotopically light.
4. FIELD APPLICATIONS
The use of unsaturated stable isotopes profiles in field investigations has
become widespread in recent years (see, e.g., the contributions to IAEATECDOC-357, 1985). Initially investigations were aimed at examination of
isotopic modifications to water which infiltrated through the unsaturated zone
to the water table (Gat and Tsur, 1967; Zimmermann et al., 1967a). More
recently, investigations have been aimed at using stable isotopes to determine
the distributed groundwater recharge rate (Dincer et al., 1974; Saxena and
Dressie, 1983; Saxena, 1987; Vachier et al., 1987), and recharge mechanisms
(Bath et al., 1982a,b; Fontes, 1983; Issar et al., 1985; Darling and Bath, 1988;
Darling et al., 1987); and also to obtain evaporation rates from groundwater
discharge zones (Allison and Barnes, 1983; 1985; Fontes, 1983; Sontag et al.,
1985; Yousfi et al., 1985; Christmann, 1986; Fontes et al., 1986; Christmann and
Sonntag, 1987) and the upper layers of arid zone soils (Barnes and Allison, 1982;
Zouari et al., 1985).
Groundwater recharge rates and mechanisms
For areas where there is a marked seasonal temperature cycle (e.g. those
with cool to temperate climates), the isotope concentrations of rainfall are
seasonally '~tagged" because of the temperature dependence of isotope concentrations of precipitation (Dansgaard, 1964; see also the reviews on isotope
concentrations in precipitation in White, 1983; Rodhe, 1987; Saxena, 1987).
Thus recharge waters from successive seasons can be identified in deep unsaturated profiles where piston flow is the dominant mechanism of water
movement, although diffusive attenuation of the signal is to be expected.
Measurements of recharge rates in the unsaturated zone have been made by
successive observations of isotope profiles, or by observing the displacement
between successive seasonal inputs (Eichler, 1965, as quoted in Zimmermann et
al., 1967a; Thoma et al., 1979; Bath et al., 1982a,b; Saxena and Dressie, 1983;
Saxena, 1987; see also Zimmermann et al., 1967b). Figure 9 is reproduced from
Saxena (1987) and shows more or less cyclic variations in oxygen-18 concentrations in soil moisture, which Saxena identified with annual recharge aliquots.
By observing the displacement following one year's infiltration, an estimate of
that year's recharge can be obtained by integrating the water content profile
over that interval.
For this method to be useful, it is necessary that the isotopic signature of
rainfall changes over the year, that there is significant recharge during both
summer and winter periods, and that measurements are made beneath the root
zone. The first of these requirements may make the technique unsuitable for
165
518 I,Yoo)
-14
0
0-6
1.2
rel. to SMOW
-12
i
i
-10
i
i
1_
2°
1"8
E
~
2.4
e-
B
3-0
3-6
4.2
4-8
Fig. 9. Oxygen-18 profile of soil moisture at a field site in Sweden. The letters correspond to
identified peaks in summer and winter precipitation; the recharge rate is about 260 mm yr-1.
areas with e q u a t o r i a l or m a r i t i m e climates w h e r e t h e r e is little d i f f e r e n t i a t i o n
b e t w e e n seasons, w h e r e a s the second excludes arid and semiarid climates
w h e r e rainfall is v e r y variable, and no r a i n m a y fall for long periods. The
t e c h n i q u e appears to be most successful w h e n r e c h a r g e is h i g h (20(~
300 mm yr 1 or more). An a d d i t i o n a l a d v a n t a g e in such areas is t h a t the r o o t
zone is u s u a l l y shallow, and sampling can be c a r r i e d out n e a r the surface. If the
r e c h a r g e r a t e is low, or the d e p t h of roots is large, the size of the isotope
peaks will be r e d u c e d by diffusion. A l t e r n a t i v e l y , if a r e c o r d of the isotopic
c o n c e n t r a t i o n of p r e c i p i t a t i o n is kept, it m a y be possible to identify the passage
of w a t e r from p a r t i c u l a r events t h r o u g h the soil profile (Dincer et al., 1974).
This m e t h o d would be suitable for arid zones, e x c e p t t h a t the m e t e o r o l o g i c a l
s t a t i o n s c o l l e c t i n g isotope samples in these regions are r e l a t i v e l y sparse, and
rainfall v a r i a b i l i t y and climatic difficulties g e n e r a t e special sampling problems
in these areas.
A l t h o u g h m u c h has been said a b o u t the r e l a t i v e merits of the piston flow
model (e.g. Z i m m e r m a n n et al., 1967a; S h a r m a and Hughes, 1985) it is clear t h a t
it will r e m a i n a good model d u r i n g u n s a t u r a t e d flow conditions. M a c r o p o r e
166
flow can only occur under saturated conditions, and for pores which are
directly connected to the surface. For distributed recharge, bypass flow
through macropores will only occur when the rainfall intensity exceeds the
saturated hydraulic conductivity of the soil matrix.
If significant flow does occur through macropores and cracks, the soil matrix
which is sampled may be bypassed, and thus will not reflect the true recharge
rate. Bath et al. (1982a,b), and Darling and Bath (1988) have used stable
isotopes in this way to compare flow mechanisms in the English chalk. In order
to explain tritium and solute profiles, as well as the stable isotope data, they
were forced to consider a model involving a continuum of pore sizes. They
observed similar isotope profiles at significantly different sites, with the
profiles tending towards uniformity after a certain depth. The depth at which
uniformity was obtained varied with the recharge rate, and this uniformity was
attributed by them to effects of dispersion. For high recharge rates seasonal
cyclicity was preserved for several metres, whereas for lower rates (less than
200 mm yr-1) the cyclicity was damped.
Fontes (1983) also summarizes a number of experimental field investigations
into flow mechanisms in the unsaturated zone using a variety of tracers,
including stable isotopes. Lysimeter studies on a number of different soils, with
either n a t u r a l rainfall or irrigation, showed only partial piston flow, and
evidence of quite complicated interactions between water in large and small
pores within the soil matrix.
Stable isotope work involving investigations into pathways for infiltration
has been mostly semiquantitative, with little use made of the considerable body
of literature available on macropore flow; see e.g. White (1985) and references
therein. Stable isotopes are ideal tracers for both field and laboratory investigations of this kind, and closer cooperation between those using stable
isotopes on the one hand, and those attempting to derive quantitative models
of water movement in complex porous media on the other, would appear to offer
scope for a more detailed examination of the processes involved. A model of
isotope movement involving both evaporation and infiltration is necessary,
and it is essential that heterogeneity be realistically accounted for (e.g. Jury,
1988) if field observations are to be accurately interpreted.
Allison (1987) has recently reviewed methods of estimating groundwater
recharge in arid and semi-arid regions, including the use of stable isotopes. In
these regions, distributed recharge through the unsaturated zone is thought to
be strongly biased towards the heavier rainfall events, with little or no deep
percolation from the more numerous smaller events. The critical size of the
events which will produce significant recharge will depend on the effect of
capillary rise of soil water to the surface, i.e. on the grain size (Dincer et al.,
1974). Allison et al. (1983b) (see Fig. 10) observed that for four dunes in the
Australian arid zone, having different mean annual rainfall, the enrichment of
the deep soil water of the unsaturated zone relative to the local Meteoric Water
Line appeared to be related to an independent estimate of the recharge rate. A
very simple model of recharge through the dune suggested that this enrichment
167
Oo
a
1 / ~
(ram-V,)
Fig. ]0. Correlation between displacement of deep unsaturated zone water from the Meteoric Water
Line, and independent estimates of recharge for four dune sites in South Australia.
should be proportional to the inverse of the square root of the recharge rate,
and this was found to be consistent with the data. The approach is somewhat
empirical, and has not been corroborated with other data so far.
Estimation of evaporation rate
Strictly, the steady-state theory applies only to isotope profiles which have
reached steady-state so that the evaporation rate is constant; dry soils will
generally exhibit a decreasing evaporation rate. On the other hand, soils which
have been recently wetted will show an approximately constant rate of evaporation while the flow of water to the surface is not limited by soil physical
properties (i.e. during the so-called '~first stage" of evaporation). If this first
stage is sufficiently long compared with the characteristic time for development of the isotope profile, the theory may be satisfactorily applied.
Allison and Barnes (1983, 1985) used the theory of section 2 above to estimate
evaporation from near-saturated and unsaturated isotope profiles of a '~dry"
salt lake in Australia (see Fig. 11), and showed that the use of stable isotope
profiles compared favourably with a similar technique using soft water
chloride concentrations (see also Ullman, 1985). They proposed three separate
estimates of the evaporation rate.
The first method involves determination of the exponential decay length in
the profile beneath the isotope maximum. Knowledge of this parameter enables
an estimate of E to be made provided tortuosity, and hence the effective
diffusivity, can be estimated. Although this parameter seems well behaved for
the experimental systems, for fine-grained sedimentary systems the value for
the tortuosity is not w~n known. It could be measured experimentally, but thi~
was not done by Allison and Barnes, and is the major source of uncertainty in
168
(a)
(b)
6 D (°/0o) rel. to SMOW
0/
"4
~-
0
t
"... "'...
.... "...
600
800
i
_
~..1~I
4
t
'
(c)
Chloride (°/'oo)
e v
T'
8
i
0"4
0"6 120
160
=
'I
200
i
,s~
i
~i/I~'I.'~~
I
I
Sample
depth
interval
Fig. 11. Comparison of isotope and chloride profiles obtained from L. Frome in S. Australia. The
solid line is a "best fit" for estimation of the evaporation rate; the isotope profile gives an estimate
of 120 + / - 15mmyr 1, whereas the chloride profile gives l l 0 m m y r 2, with much greater
uncertainty.
their estimate of the evaporation rate. This method has the advantage of
relying on a number of data points, providing a degree of statistical robustness
to the estimate. Allison and Barnes were fortunate that the time since the last
filling of the lake was longer than the characteristic time for development of
the isotope profile.
The second method uses the isotope profile to give the depth of the evaporating front. This depth, together with a value for the effective diffusivity for the
upper part of the profile, enables the flux of vapour (the rate of evaporation)
through this part of the profile to be calculated. Again the effective diffusivity
through this region must be estimated, but in this case the effect of changing
water content and particle size is likely to be of much less significance, and the
main difficulty is in obtaining the depth of the maximum to sufficient accuracy.
Differences between the depth of the maximum and the effective depth of
evaporation are thought to be small. This method is likely to be relatively
sensitive to temperature gradients in this part of the profile. A third method
which involves the isotope profile in the region above the maximum is not
generally practical, because low water contents and the narrowness of this
region make sampling impractical. In common with other profile techniques,
169
all three methods suffer from the disadvantage of being point estimates of the
evaporation rate, and are subject to the natural spatial heterogeneity of the
area for which the estimate is required.
Fontes et al. (1986), and Christmann and Sonntag (1987), report estimates of
evaporation for very dry sands in the Sahara. The water content and isotope
profiles were assumed to result from a process of capillary rise from a relatively
deep water table, followed by evaporation from depths of more than I m below
the surface. The very low evaporation rates reported (as low as a few mm per
year) imply a time for development of these profiles of up to a few centuries, so
that this technique can only be used in this way for extremely arid areas where
rainfall does not penetrate the soil effectively. Changes in evaporation rates
due to changes in sand thickness etc. over time periods of the order of decades
would be averaged. However, effects of temperature gradients were not taken
into account in these studies, and may be important (see below).
Time for profile development, and effect of infiltration
The characteristic time for development of an isotope profile:
= D*/E 2
(14)
can be derived for steady-state evaporation from a saturated (Zimmermann et
al., 1967a) or unsaturated soil in the absence of vapour diffusion (Barnes and
Allison, 1983). Since the length scales zv and zl are proportional to the
reciprocal of the evaporation rate, halving the evaporation rate will have the
effect of doubling the length scales, but quadrupling the time taken to reach
steady state. Bearing this in mind, Allison et al. (1984) suggested that the shape
of the isotope profile would reflect mean atmospheric and soil conditions over
a period related to the evaporation rate. For extremely low evaporation rates
(e.g. Fontes et al., 1986) this may involve millennia, whereas profiles with
evaporation rates of 10mmd -1 will be affected by conditions for only the
previous day or so. The implication is that the steady-state theory cannot be
used when conditions are not reasonably constant over the equilibration
period; in particular, infiltration of rainfall in this period will invalidate the
approach (Fontes et al., 1986).
The observation that water extracted from very dry soils could have oxygen18/deuterium slopes considerably less than the values ~ 6 typical of evaporation from free water bodies (Dincer et al., 1974), gave rise to the expectation
that such low slopes could be transferred to groundwater bodies by infiltration
through the unsaturated zone. Laboratory experiments by Klotz et al. (1987)
have shown this to be so under conditions of more or less constant recharge.
However, arid zone recharge is erratic, with most recharge thought to come
from very infrequent large events. This infrequency of recharge implies that in
general the surface soil will be very dry before a recharge event. Even though
the prior soil water is considerably enriched in heavy isotopes within these
layers, infiltrating water will so compress the isotope profile that diffusive
170
mixing occurs, and it is not usually possible to use the enriched surficial soil
waters as markers of water movement (Sonntag et al., 1985). This results in
recharge which is somewhat enriched relative to rainfall, but which does not
preserve the original low slopes. Isotope concentrations with slopes near 8, but
somewhat displaced from the Meteoric Water Line, can be obtained for water
from deep in the unsaturated zone (Allison et al., 1983b).
Fontes et al. (1986) following Allison et al. (1984) showed that if the region
of vapour movement was considered alone, a second characteristic time may be
derived, which in their case was considerably shorter than that necessary for
steady state to apply to the whole profile. For unsteady evaporation from a dry
soil, the work of Walker et al. (1988) and Barnes and Walker (1988) implies t h a t
this estimate may be seen to apply to the isotope profile as a whole. In a drying
profile with cumulative evaporation increasing as the square root of time, the
evaporating front descends at a rate proportional to (time)- ~'~.Water content
and isotope profiles are functions of the reduced variable ~ ( = zt '=). Thus, the
location of the evaporating front (or the isotope maximum) at any time gives
an estimate of the time scale necessary for profile development to that point,
namely:
~*
=
z2of/D~
(15)
Since the evaporation rate is inversely proportional to Zef, this time scale, like
the steady state one above, has a 1/E2 dependence on the evaporation rate.
Barnes and Walker (1988) showed that for the hypothetical soil they
considered, the characteristic time for the profile development was from one to
two orders of magnitude greater for the steady-state profile than for the
unsteady profile, the difference being greater for drier soils. The implication of
this is that following a recharge event, as a soil profile dries out, the isotope
profile will develop relatively rapidly, and if a water table is present the isotope
profile will approach the steady-state form as more and more of the evaporation
loss is replenished from the water table.
E x a m i n a t i o n of arid zone profiles
A feature of the isotope profiles, particularly in the arid zone, is their
remarkable uniformity with depth below the surface 2-4m which is often
observed (see Fig. 12a; Bath et al., 1982a,b), compared with the detail observed
in the upper few metres of the same profiles. Occasionally profiles show very
smooth, but exceptionally large excursions in isotope concentration at depth
(Fig. 12b). Given the extremely low water contents of the arid zone sites, the
hydrodynamic dispersion mechanism of Bath et al., (1982a,b, 1987) does not
seem adequate to account for these profiles. Another feature which has often
been observed is an apparent secondary minimum in the isotope profiles at a
depth of 1-2 m (see Fig. 12; Bath et al., 1982a; Allison and Hughes, 1983).
Although Barnes and Allison (1984) were able to demonstrate that, at least
under steady-state conditions, secondary minima could result from soil tern-
171
(a)
6 2 (%0) rel. to SMOW
-~oo
i
~
-80
,
-60
,
-4o
i
-2o
i
(b)
eg
o
20
40
i
,
J
-
-
10
(~2 (%0) rel. to SMOW
v
-80
~05
o
-60
-40
-20
0
20
o!
12
a
16
20
o
Og
o.1
10
Fig. 12. Deep unsaturated arid zone dune profiles of water content and deuterium. Both deuterium
profiles show secondary minima at 1 2m: (a) is relatively smooth at depth, whereas (b) shows
marked variation with depth to 10m.
perature gradients, the magnitude of the effect was considerably smaller than
that typically observed in the field. Allison et al. (1984) and Darling and Bath
(1988) decided that this explanation was unlikely for their profiles, and
concluded that infiltration of isotopically light precipitation was the most
likely explanation.
In order to investigate further the origin of the secondary minimum, Barnes
(unpublished data) has examined the effect of the annual temperature cycle on
isotope profiles taken from an arid zone dune at three monthly intervals. A
secondary minimum, initially present, was seen to persist throughout a
complete temperature cycle, with some attenuation. Although temperature
172
gradients were seen to persist to below 10 m depth, calculations indicate that
they are insufficient to cause significant water movement, even at the very low
water contents (less than 0.5% ) recorded.
At these sites the secondary minima appear to be a result ofisotopically light
recharge events of intermediate size. Precipitation from such events partially
penetrates the unsaturated zone, and then is removed slowly by evaporation
and/or transpiration. Only occasionally will events of this type penetrate
below the top metre or two, producing the observed secondary minima. Deep
penetration is only possible for infrequent rainfall events of relatively large
size (the magnitude will depend on the grain size, according to Dincer et al.,
(1974) which will result in water movement through the entire profile, and
produce uniform isotope profiles at depth.
5. CONCLUSIONS
The past two decades has seen considerable progress in the use of oxygen-18
and deuterium for tracing water movement in the unsaturated zone. The stable
isotopic species of water have been used to investigate the processes of infiltration, evaporation and mixing, and to make quantitative estimates of groundwater recharge and evaporation rates.
A principal advantage of using stable isotopic tracers to determine water
movement is the limited variability of the effective diffusivities with varying
water content, compared to the marked variation of the soil water ~'diffusivity", for example. Without some effort devoted to understanding the actual
variation of the diffusivities for different water contents and materials, the
stable isotope technique will remain a rather blunt tool, failing to achieve the
precision potentially available, not only for estimating evaporation rates, but
also for determining soil physical mechanisms operating during evaporation,
for example.
Temperature effects on soil water profiles and fluxes can be significant, but
appear to have little effect on isotope profiles. Further experimental clarification of the interaction of the isotope profiles with temperature gradients is
required in order to obtain greater precision in interpreting unsaturated zone
profiles; in particular, this is necessary for accurate estimation of evaporation
rates.
This review has summarised the development of a model of isotope
movement in soils, accounting for unsaturated, nonisothermal and unsteady
flow in both liquid and gas phase. Experimental evidence for the validity of
each part of the model in isolation has been obtained, sufficient to give a degree
of confidence in the model as a whole, but verification of the combined model
(e.g. unsteady, nonisothermal evaporation) is difficult because of the lack of
analytical solutions of the full model. An efficient numerical model, capable of
handling all the above features simultaneously, would greatly reduce the
experimental effort needed to complete our understanding of the development
of isotope profiles under natural conditions, but is not currently available.
173
REFERENCES
Allison, G.B., 1987. A review of some of the physical, chemical and isotopic techniques available
for estimating groundwater recharge. Proc. NATO Workshop Estimation Nat. Recharge of
Groundwater, Antalya, Turkey.
Allison, G.B. and Barnes, C.J., 1983. Estimation of evaporation from non-vegetated surfaces using
natural deuterium. Nature, 301:143 145.
Allison, G.B. and Barnes, C.J., 1985. Estimation of evaporation from the normally "dry" Lake
Frome in South Australia. J. Hydrol., 78:229 242.
Allison, G.B. and Hughes. M.W., 1983. The use of n a t u r a l tracers as indicators of soil-water
movement in a temperate semi-arid region. J. Hydrol., 60:157 173.
Allison, G.B., Barnes, C.J. and Hughes, M.W., 1983a. The distribution of deuterium and oxygen-18
in dry soils: II. Experimental. J. Hydrol., 64:377 397.
Allison, G.B,, Barnes, C.J., Hughes, M.W. and Leaney, F.W.J., 1983b. The effect of climate and
vegetation on oxygen-18 and deuterium profiles in soils. Proc. 1983 Int. Symp. Iso. Hydrol. Water
Resour. Dev., IAEA, Vienna, No. IAEA-SM-270/20.
Allison, G.B,, Barnes, C.J. and Hughes, M.W., 1984. Towards an understanding of stable isotope
profiles in field soils. RIZA Symp. Isot. Unsat. Zone, Munich.
Barnes, C.J., 1988. An analysis of evaporation from dry soils using oxygen-18 and deuterium. J.
Hydrol. (in prep.).
Barnes, C.J. and Allison, G.B., 1982. Interpretation of stable isotope profiles in arid zone dunes.
Hydrol. Water Resour. Symp., IEA, Melbourne, pp. 9~101.
Barnes, C.J. and Allison, G.B., 1983. The distribution of deuterium and oxygen-18 in dry soils: I.
Theory. J. Hydrol., 60:141 156.
Barnes, C.J. and Allison, G.B., 1984. The distribution of deuterium and oxygen-18 in dry soils: III.
Theory for non-isothermal water movement. J. Hydrol., 74:119 135.
Barnes, C.J. and Walker, G.B., 1988. Stable isotope profiles during unsteady evaporation from a dry
soil. J. Hydrol. (submitted).
Barraclough, P.B. and Tinker, P.B., 1982, The determination of ionic diffusion coefficients in field
soils. II. Diffusion of bromide ions in undisturbed field cores. J. Soil Sci., 33:13 24.
Bath, A.H., Darling, W.G. and Brunsdon, A.P., 1982a. The stable isotope composition of infiltration
moisture in the u n s a t u r a t e d zone of English chalk. In: H.L. Schmidt, H. FSrstel and K.
Heinzinger (Editors), Stable Isotopes. Elsevier, Amsterdam, pp. 161 166.
Bath, A.H., Darling, W.G. and Brunsdon, A.P., 1982b. 150/160 and ='H/1H in rainfall and in the
u n s a t u r a t e d zone water of Chalk aquifers: a contribution to studies of recharge mechanisms.
Inst. Geol. Sci., Stable Isot. Tech. Rep. No. 20, Hydrologeol. Unity Rep. WD/ST/82/9.
Boltzmann, L., 1894. Zur Integration der Diffusionsgleichung bei variabeln Diffusionscoefficienten.
Ann. Phys., 53: 959-964.
Bruce, R.R. and Klute, A., 1956. The measurement of soil moisture diffusivity. Soil Sci. Soc. Am.,
Proc., 20:458 462.
Brutsaert, W., 1975. A theory for local evaporation (or heat transfer) from rough and smooth
surfaces at ground level. Water Resour. Res., 11:543 550.
Christmann, D., 1986. Grundwasser-Verdunstung aus unbewachsenen Boden ostsaharischer
Senken a n h a n d von Deuterium und Sauerstoff-18 in der Bodenfeuchte. Ph.D. Thesis, RuprechtKarls-Universit~it, Heidelberg, l l 2 p p .
Christmann, D. and Sonntag, C., 1987. Groundwater evaporation from East-Saharian depressions
by means of deuterium and oxygen-18 in soil moisture. Proc. Int. Symp. Use Isot. Tech. Water
Resour. Dev., Vienna, Pap. IAEA-SM-299/037.
Corey~ A.T. and Klute, A., 1985~ Application of the potential concept to soil water equilibrium and
transport. Soil Sci. Soc. Am., J., 49:3 11.
Craig, H. and Gordon, L.L, 1965. Deuterium and oxygen-18 variations in the ocean and marine
atmosphere. Proc. Conf. Stable Isot. Oceanogr. Stud. Paleotemp., Lab. Geol. Nucl., Pisa, pp.
9 130.
Dansgaard, W., 1964. Stable isotopes in precipitation. Tellus, 16: 43~467.
174
Darling, W.G. and Bath, A.H., 1988. A stable isotope study of recharge processes in the English
chalk. J. Hydrol., 101: 31-46.
Darling, W.G., Edmunds, W.M., Kinniburgh, D.G. and Kotoub, S., 1987. Sources of recharge to the
basal Nubian sandstone aquifer, B u t a n a region, Sudan. Proc. Int. Symp. Use Isot. Tech. Water
Resour. Dev., Vienna, Pap. IAEA-SM-299/117.
Dincer, T. and Davis, G.H., 1984. Application of environmental isotope tracers to modelling in
Hydrology. J. Hydrol., 68: 9~113.
Dincer, T., Al-Mugrin, A. and Zimmermann, U., 1974. Study of the infiltration and recharge
through the sand dunes in arid zones with special reference to the stable isotopes and thermonuclear tritium. J. Hydrol., 23:79 109.
Ehhalt, D. and Knott, K., 1965. Kinetische Isotopentrennung bei der Verdampfung von Wasser.
Tellus, 7: 389-397.
Eichler, R., 1965. Deuterium/isotopengeochemie des Grunstund Oberfl/ichenwassers. Geol.
Rundsch., 55:144 159.
Erickson, E., 1965. Deuterium and oxygen-18 in precipitation and other Natural Waters: Some
theoretical considerations. Tellus, 17:498 512.
Farrell, D.A., Greacen, E.L. and Gurr, C.G., 1966. Vapour transfer in soil due to air turbulence. Soil
Sci., 102:305 313.
Fontes, J.-Ch., 1983. Examples of isotope studies of the unsaturated zone. Rep. Inst. Geol. Sci., 82:
60 70.
Fontes, J.-Ch., Yousfi, M, and Allison, G.B., 1986. Estimation of the long term, diffuse groundwater
discharge in the N o r t h e r n S a h a r a using stable isotope profiles in soil water. J. Hydrol., 86:
315 327.
FSrstel, H., 1982. ~s0/l~0-ratio of water in plants and their environment (results from Fed. Rep.
Germany). In: H.L. Schmidt, H. FSrstel and K. Heinzinger (Editors). Stable Isotopes. Elsevier,
Amsterdam, pp. 503 516.
Gat, J.R., 1979. Isotope hydrology of very saline lakes. In: A. Nissenbaum (Editor), Hypersaline
Brines and Evaporitic Environments. Proceedings of the Bathsheba Seminar on Saline Lakes
and Natural Brines. (Developments in Sedimentology, 28.) Elsevier, Amsterdam, pp. 1 7.
Gat, J.R. and Tsur, Y., 1967. Modification of the isotopic composition of rainwater by the processes
which occur before groundwater recharge. Proc. Symp. Isotop. Hydrol., IAEA, Vienna. pp.
49 60.
Gonfiantini, R., 1965. Effetti isotopici nell' evaporazioni di acqua salare. Att. Soc. Tosc. Sci. Nat.,
Ser. A72, 550.
Harbeck, G.E., 1955. Studies of evaporation: The effect of salinity on evaporation. U.S. Geol. Surv.
Pap., 272 A, 1~6.
Harris, K.A. and Woolf, L.A., 1980. Pressure and temperature dependence of the self diffusion
coefficient of water and oxygen-18 water. J. Chem. Soc. Faraday Trans. I, 76:377 385.
Heller, J.P., 1968. The drying through the top surface of a vertical porous column. Soil Sci. Soc.
Am., Proc., 32: 778~786.
Issar, A.S., Gat, J.R., Karnieli, A., Nativ, R. and Mazor, E., 1985. Groundwater formation under
desert conditions. Proc. Stable Radioact. Isot. Study. U n s a t u r a t e d Soil Zone, IAEA, Vienna,
IAEA-TECDOC-357.
Johnston, C.D., 1987. Water and solute movement in deeply weathered lateritic soil profiles near
Collie, Western Australia. M. Sc. Thesis, Dept. Soil Sci. Plant Nutr., Fac. Agric., University of
Western Australia, 143 pp.
Jury, W.A., 1973. Simultaneous transport of heat and moisture through a medium sand. Ph.D.
Thesis, University of Wisconsin, Madison, Wisc.. 191 pp.
Jury, W.A., 1988. Solute transport and dispersion. In: W.L. Steffen, O.T. Denmead and I. White
(Editors), Flow and Transport in the Natural Environment: Advances and Applications.
Springer, Berlin (in press).
Jury, W.A. and Letey, J., 1979. Water movement in soil: Reconciliation of theory and experiment.
Soil Sci. Soc. Am., Proc., 43:823 827.
Klotz, D., Malowzewski, P., Moser, H. and Stichler, W., 1987. The change of ~H and 1~O contents
175
of water seeping through sand columns under different experimental conditions. Int. Symp. Use
Isot. Tech. Water Resour. Dev., IAEA, Vienna, Poster Pap. IAEA-SM-299/45P.
Lloyd, R.M., 1966. Oxygen isotope enrichment of sea water by evaporation. Geochim. Cosmochim.
Acta, 30:801 814.
Majoube, M., 1971. F r a c t i o n n e m e n t en oxyg~ne-18 et en deuterium entre l'eau et sa vapeur. J.
Chim. Phys., 68:1423 1436.
Merlivat, L., 1978. Molecular diffusivities of H~O, HDI~O, and H~SO in gases. J. Chem. Phys., 69:
2864 2871.
Mills, R., 1973. Self diffusion in normal and heavy water in the range 1 45°C. J. Phys. Chem., 77:
685~88.
Mills, R. and Harris, K.R., 1976. The effect of isotopic substitution on diffusion in liquids. Chem.
Soc. Rev., 5:215 231.
Munnich, K.O., Sonntag, C., Christmann, D. and Thoma. D., 1980. Isotope fractionation due to
evaporation from sand dunes. 2. Mitt. Zentralinst. Isot. Stralenforsch., 29: 319~332.
Nye, P.H., 1979. Diffusion of ions and uncharged solutes in soils and soil clays. Adv. Agron.. 31:
225 272.
Penman, H.L., 1940. Gas and vapour movement in soil. Int. J. Agric. Sci., 30:437 462.
Philip, J.R., 1969. Theory of infiltration. Adv. Hydrosci., 5:215 296.
Philip, J.R., 1988. Quasianalytic and analytic approaches to unsaturated flow. In: W.L. Steffen,
O.T. Denmead and I. White (Editors), Flow and Transport in the Natural Environment:
Advances and Applications. Springer, Berlin (in press).
Philip, J.R. and De Vries, D.A., 1957. Moisture movement in porous media under temperature
gradients. Trans. Am. Geophys. Union, 38: 222-232.
Porter, L.K., Kemper, W.D., Jackson, R.D. and Stewart, B.A., 1960. Chloride diffusion in soils as
influenced by moisture content. Soil Sci. Soc. Am. Proc., 24: 46(~463.
Raats, P.A.C., 1975. Transformation of fluxes and forces describing the simultaneous transport of
water and heat in u n s a t u r a t e d porous media. Water Resour. Res., 11: 93~943.
Rodhe, A., 1987. The origin of streamwater traced by oxygen-18. Doctoral Thesis, Uppsala
University, Dept. Phys. Geogr., Div. Hydrol., Rep. Ser. A, No. 41,260 pp., plus Appendix 73 pp.
Rose, C.W., 1968. Water transport in soil with a daily temperature wave. II. Analysis. Aust. J. Soil
Res., 6:31 44.
Salhotra, A.M., Adams, E.E. and Harleman, R.F., 1985. Effect of salinity and ionic composition on
evaporation: Analysis of dead sea evaporation pans. Water Resour. Res., 9: 133~1344.
Saxena, R.K., 1987. Oxygen-18 fractionation in nature and estimation of groundwater recharge.
Doctoral Thesis, Uppsala University, Dep. Phys. Geogr., Div. Hydrol., Rep. Ser. A, No. 40, 152
pp.
Saxena, R.K. and Dressie, Z., 1983. Estimation of groundwater recharge and moisture movement
in sandy formations by tracing n a t u r a l oxygen-18 and injected tritium profiles in the unsaturated zone. Proc. IAEA Int. Symp. Isot. Tech. Water Resour. Dev., pp. 139 150.
Scott, H.D. and Paetzold, R.F., 1978. Effects of soil moisture on the diffusion coefficients and
activation energies of tritrated water, chloride and metribuzin. Soil Sci. Soc. Am., J., 42:23 27.
Scotter, D.R., 1976. Liquid and vapour phase transport in soil. Aust. J. Soil Res., 14:33 41.
Sharma, M.L. and Hughes, M.W., 1985. Groundwater recharge estimation using chloride,
deuterium and oxygen-18 profiles in the deep coastal sands of Western Australia. J. Hydrol., 81:
93 109.
Sorer, Z. and Gat, J.R., 1972. Activities and concentrations of oxygen-18 in concentrated aqueous
salt solutions: analytical and geophysical implications. E a r t h Planet. Sci. Lett., 15:232 238.
Sofer, Z. and Gat, J.R., 1975. The isotopic composition of evaporating brines: effect of the isotopic
activity ratio in saline solutions. E a r t h Planet. Sci. Lett., 26:179 186.
Sonntag, C., Thoma, G. and Munnich, K.O., 1980. Environmental isotopes in North African
groundwaters; and the D a h n a sand-dune study, Saudi Arabia. Proc. IAEA Int. Syrup. Isot. Tech.
Water Resour. Dev., pp. 77 84.
Sonntag, C., Christmann, D. and Munnich, K.O., 1985. Laboratory and field experiments on
infiltration and evaporation of soil water by means of deuterium and oxygen-18. IAEA Proc.
Stable Radioact. Isot. Stud. U n s a t u r a t e d Soil Zone, IAEA, Vienna, IAEA-TECDOC-357.
176
Sophocleous, M., 1979. Analysis of water and heat flow in unsaturated saturated porous media.
Water Resour. Res., 15: 1195~1206.
Stewart, M.K. and Friedman I., 1975. Deuterium fractionation between aqueous salt solutions and
water vapour. J. Geophys. Res., 80:3812 3818.
Taylor, S.A. and Carey, J.W., 1964. Linear equations for the simultaneous flow of matter and energy
in a continuous soil system. Soil Sci. Soc. Am., Proc., 28:167 172.
Thoma, G., Esser, N., Sonntag, C., Weiss, W., Rudolph, J. and Leveque, P., 1979. New technique of
in-situ soil-moisture sampling for environmental isotope analysis applied at Pilat sand dune
near Bordeaux. In: P. Udluft et al. (Editors), Isotope Hydrology. Proc. Syrup. Munich, Tech.
Univ. Munich, 1:191-204.
Ullman, W.J., 1985. Evaporation rate from a salt pan: Estimates from chemical profiles in nearsurface groundwaters. J. Hydrol., 79:365 373.
Vachier, P., Dever, L. and Fontes, J.-Ch., 1987. Mouvements de l'eau dans la zone non saturee et
alimentation de la Nappe de la Craie de Champagne (France): approches isotopique et
chimique. Proc. IAEA Int. Symp. Isot. Tech. Water Resour. Dev., Pap. IAEA-SM-299/53.
Walker, G.R. and Dighton, J . C , 1988. Simultaneous movement of water, salt and stable isotopes of
water during evaporation. J. Hydrol. (in prep.).
Walker, G.R., Hughes, M.W., Allison, G.B. and Barnes, C.J., 1988. The movement of isotopes of
water during evaporation from a bare soil surface. J. Hydrol., 97:181 197.
White, J., 1983. The climatic significance of deuterium/hydrogen ratios in White Pine in the
n o r t h e a s t e r n United States. P h . D . Thesis, Columbia University, 348pp.
White. J., 1985. The influence of macropores on the transport of dissolved and suspended matter
through the soil. Adv. Soil Sci., 3:95 120.
Yousfi, M., Aranyossi, J.F., Djermouni, B. and Fontes, J.-Ch., 1985. Conclusions and recommendations on the usefulness of studies of the isotopes ~O, 2H and 3H in water in the unsaturated
zone. IAEA Proc. Stable Radioact. Isot. Stud. U n s a t u r a t e d Soil Zone, IAEA, Vienna. IAEATECDOC-357.
Zimmermann, U., Ehhalt, D. and Munnich, K.O., 1967a. Soil-water movement and evapotranspiration: changes in the isotopic composition of the Water. Proc. IAEA Symp. Isot. Hydrol., IAEA
Vienna.
Zimmermann, U., Munnich, K.O. and Roether, W., 1967b. Downward movement of soil moisture
traced by means of hydrogen isotopes. G.E. Stout (Editor), Am. Geophys. Union, Geophys.
Monogr. No. 11. pp. 2~35.
Zouari, K., Aranyossi, J.F., Mamou, A. and Fontes, J.-Ch., 1985. Etude isotopique et geochimiques
des mouvements et de F~volution des solutions de la zone a e r i e des sols sous climat semi-aride
(Sud Tunisien) Proc. Stable Radioact. Isot. Stud. U n s a t u r a t e d Soil Zone, IAEA Vienna. IAEATECDOC-357.