Stable isotope mass balance of lakes: a contemporary perspective
J.J. Gibson a, b, *
, S.J. Birks b, c
, Y. Yi a, b
a
Alberta Innovates Technology Futures, 3-4476 Markham Street, Victoria, BC V8Z 7X8, Canada
b
University of Victoria, Department of Geography, Victoria, BC V8W 3R4, Canada
c
Alberta Innovates Technology Futures, 3608-33 St NW, Calgary, AB T2L 2A6, Canada
a r t i c l e i n f o
Article history:
Received 16 October 2014
Received in revised form
3 April 2015
Accepted 13 April 2015
Available online 6 May 2015
Keywords:
Stable isotopes
Water balance
Lakes
Latitude
Climate
Atmospheric moisture
a b s t r a c t
The theoretical basis for application of stable isotope mass balance of lakes is described for a range of
climatic situations including low latitude, high latitude, high altitude, continental and coastal systems, as
well as cases where the atmospheric boundary layer is significantly modified by the lake evaporation
process. The effects of seasonality on isotopic offset between precipitation and atmospheric vapour and
the slope of the local evaporation line are described. Atmospheric feedback and its role in labelling the
isotopic composition of the Laurentian Great Lakes and tropical lakes is discussed. Several important
considerations are suggested to improve parameterization of quantitative paleoclimatic reconstructions
including use of assumptions that are appropriate for the climatic setting, for the atmospheric feedback
situation, for salinity, and headwater setting. Potential for use of dual-isotopes to trace past changes in
seasonality and input, and a dual-lake index method that can potentially be used to trace connectivity of
lakes are presented. In cases where modern or paleo-evaporation systems may be under-defined there
are inherent limitations in the degree of quantification that can be attained.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
The investigation of stable water isotopes (mainly d18
O) records
from terrestrial material, as an alternative to marine sediments,
was propelled to the forefront of paleoclimate studies in the early
1990s (Swart et al., 1993). The development of water isotope records
from lake sediments, in substrates such as carbonates,
biogenic silica, kerogen, sedimentary cellulose, and lipids, is typically
undertaken with the goal of reconstructing the isotopic history
of lake water (Edwards et al., 2004). Analogous to marine
studies (Emiliani, 1955; Shackleton and Opdyke, 1973) stratigraphic
changes in d18
O in the lacustrine environment were initially
attributed largely to changes in lake or air temperature (Eicher and
Siegenthaler, 1976) and interpreted based on the understanding of
the temperature dependence of isotopic fraction in the formation of
carbonate (Epstein et al., 1953; Friedman and O'Neil, 1977). A
number of studies have also utilized modern analogues to develop
empirical relationships between temperature and various isotopic
proxies (von Grafenstein et al., 1996; Schleser et al., 1999; Wooller
et al., 2004). However, an increasing number of studies have
pointed out the apparent limitations of this simplified transfer
function approach, including the inherent control that water balance
and climatic conditions play in determining lake water isotopic
composition (Edwards et al., 2004; Jones et al., 2005;
Henderson and Shuman, 2009; Steinman et al., 2010a).
More recently, as an emerging trend in the paleoclimate community,
multi-disciplinary investigations have sought to gain
insight from more holistic contemporary monitoring of spatial and
temporal isotope systematics to inform the interpretation of
isotope records in the lake sediment record (Benson, 1994; Roberts
et al., 2008; Shapeley et al., 2008; Wolfe et al., 2012; Steinman et al.,
2013; Zolitschka et al., 2013). Several studies have developed
coupled hydrology and isotope mass balance (IMB) models for
specific lake systems (Hostetler and Benson, 1994; Benson and
Paillet, 2002; Shapley et al., 2008; Jones and Imbers, 2010;
Steinman et al., 2010a,b), while others have demonstrated the
sensitivity of paleo-archives to hydrological setting (Jones et al.,
2007; Shapley et al., 2009; Steinman et al., 2010b, 2012, 2013;
Steinman and Abbott, 2013). IMB models were found to be informative
for these purposes as they provide a theoretical framework
to simulate and quantitatively interpret isotopic signals in lakes
(e.g. Dincer, 1968; Gonfiantini, 1986; Gat, 1995). Increasingly, it has
been realized that utilization of IMB becomes essential for the
* Corresponding author. Alberta Innovates Technology Futures, 3-4476 Markham
Street, Victoria, BC V8Z 7X8, Canada. Tel.: þ1 250 721 7341; fax: þ1 250 483 1989.
E-mail address: jjgibson@uvic.ca (J.J. Gibson).
Contents lists available at ScienceDirect
Quaternary Science Reviews
journal homepage: www.elsevier.com/locate/quascirev
http://dx.doi.org/10.1016/j.quascirev.2015.04.013
0277-3791/© 2015 Elsevier Ltd. All rights reserved.
Quaternary Science Reviews 131 (2016) 316e328
proper interpretation of lacustrine isotope records as paleoclimate
and paleoenvironmental proxies (Cross et al., 2001; Leng and
Marshall, 2004; Anderson et al., 2007; Wolfe et al., 2007; St.
Amour et al., 2010). Other requirements include specific understanding
of local isotopeeclimate relations and substrate-specific
fractionations (e.g. Marshall, 1992; Swart et al., 1993; Kim and
O'Neil, 1997; Sauer et al., 2001; Huang et al., 2004).
This review is a process-based summary of important controls
on d18
O or d2
H in the IMB model. Here we describe IMB as applied
in many contemporary studies, discuss the assumptions made to
characterize atmospheric moisture and fractionation factors, present
calibration approaches such as use of an index lake, describe
the influence of headwater conditions, seasonality and atmospheric
feedbacks, and configurations of the IMB for specific settings
including low latitude, high-latitude, continental and coastal
systems, and chain of lakes. Appropriate assumptions for application
of IMB to paleo-environmental reconstructions are also
described.
2. Theory
2.1. Isotope mass balance
The annual water-mass and isotope-mass balance for a wellmixed
lake may be written respectively as
dV=dt ¼ I À Q À E

m3
$year

(1)
V
ddL
dt
þ dL
dV
dt
¼ IdI À QdQ À EdE

‰$m3
$year

(2)
where V is the volume of the lake, t is time, dV is the change in
volume over time interval dt, I is instantaneous inflow where
I ¼ IU þ IR þ IG þ PL; IU is channelized inflow from upstream
lakes, IR is surface inflow from the catchment area, IG is
groundwater inflow, PL is precipitation on the lake surface;
Q ¼ QY þ QZ is instantaneous outflow where QY is surface
outflow, QZ is groundwater outflow; E is evaporation; dL is the
isotopic composition of the lake; dI, dU, dR, dG and dP are the
isotopic compositions of total inflow and its components, i.e.
channelized inflow from upstream lakes, surface inflow,
groundwater inflow, and precipitation, respectively; and dQ, dY
and dZ are the isotopic compositions of total outflow and its
components, i.e. surface outflow and groundwater outflow,
respectively. Here, d values are defined as isotopic ratios
reflecting deviation in per mil (‰) from Vienna-SMOW (Standard
Mean Ocean Water), where dSAMPLE ¼ 1000((RSAMPLE/
RSMOW) À 1), and R is 18
O/16
O or 2
H/1
H. Values presented here are
normalized on the SMOW-SLAP (Standard Light Arctic Precipitation)
scale.
Note that dI ¼ (dUIU þ dRIR þ dGIG þ PLdP)/I and dQ ¼ (dYQY þ dZQZ)/
Q, the latter of which, dQ and its subcomponents, dY and dZ will be
identical and approximately equal to dL in well mixed lakes to
maintain the isotope balance. Three main hydrologic settings can
be distinguished including (i) desiccating water bodies (dV/dt < 0),
where inflow occurs once or periodically, and water bodies at hydrologic
steady state (dV/dt ¼ 0), including (ii) terminal lakes,
where inflow is balanced by evaporation (I ¼ E), and (iii)
throughflow lakes, where inflow is balanced by evaporation and
outflow (I ¼ E þ Q) (Fig. 1; see also Horita, 1990; Gat, 1981).
Based on the linear resistance model of Craig and Gordon (1965)
and using the convention of Gonfiantini (1986) for describing the
equilibrium fractionation aþ
as a quantity slightly greater than 1, dE
can be estimated by:
dE ¼
dL À εþ
aþ
À hdA À εK
!,

1 À h þ 10À3
$εK

ð‰Þ (3)
where h is the relative humidity normalized to water surface
temperature (decimal fraction), dA is the isotopic composition of
atmospheric moisture, εþ
is the equilibrium isotopic separation
(see Horita and Wesolowski, 1994) being related to aþ
by
εþ
¼ (aþ
À 1)1000, and εK ¼ q$CK(1Àh) is the kinetic isotopic
separation, where q is a transport resistance parameter, commonly
assumed to be unity when dA and h are measured or estimated close
to the interface (Gat,1995). q ¼ 1 indicates that the evaporation rate
is controlled by molecular transport of water through the laminar
sublayer (see Horita et al., 2008). CK is a kinetic constant described
later on. Note that airewater isotopic exchange will proceed and
the lake water will enrich (or deplete) to an isotopic steady-state
reflective of the isotopic and hydrologic characteristics of the system,
as described below.
Substitution of eq. (3) into eq. (2) assuming well-mixed conditions
yields:
V
ddL
dt
þ dL
dV
dt
¼IdI À QdL À
E
1 À h þ εK=1000
Â
dL À εþ
aþ
À hdA À εK
!

‰$m3
$year
 (4)
which under constant atmospheric and hydrologic conditions (i.e.
hydrologic steady state, such that dV/dt ¼ 0) simplifies to
(Gonfiantini, 1986):
ddL=dt ¼ À
Â
ð1 þ mxÞdL À dI À xd*
Ã
ðI=VÞ ð‰Þ (5)
where x ¼ E/I is the fraction of lake water lost by evaporation,
1Àx ¼ Q/I (being the fraction of water lost to liquid outflows), and
m ¼

h À 10À3
$

εK þ εþ
.
aþ
0

1 À h þ 10À3
$εK

ðdimensionlessÞ
(6)
is the temporal enrichment slope, and
d*
¼

hdA þ εK þ εþ
.
aþ
0
h À 10À3
$

εK þ εþ
=aþ

ð‰Þ
(7)
is the limiting isotopic composition. It is significant to note that d* is
the isotopic composition that a desiccating water body would
approach under non-steady-state conditions as it dries up (i.e.
V / 0).
Integrating eq. (5) with respect to time, assuming constant
values for dI, dA, εþ
, εK, h, I, Q, E yields (Gonfiantini, 1986):
dLðtÞ ¼ dS À ðdS À d0Þexp½ À ð1 þ mxÞðIt=Vފ ð‰Þ (8)
where dL(t) describes the change in isotopic composition of the lake
with time t, d0 is the initial isotopic composition of the lake at t0,
and dS is the steady-state isotopic composition that the lake approaches
as t / ∞. The steady state isotopic composition dS is given
by Gonfiantini (1986) and Gat (1995) as:
dS ¼ ðxmd* þ dIÞ=ð1 þ mxÞ ð‰Þ (9)
which can be rearranged to provide an expression to estimate x (or
E/I):
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328 317
x ¼ ðdS À dIÞ
0
À
m
À
d*
À dS
ÁÁ
ðdimensionlessÞ (10)
where x ¼ 1 corresponds to a terminal lake, and values of x between
0 and approaching 1 reflect varying degrees of throughflow.
The steady state isotopic composition dS is commonly used to
represent lake water in paleoclimatic scenarios where short-term
or seasonal variations are assumed to be minor given the resolution
of the records. Perturbations from steady state are commonly
observed due to normal variability in atmospheric and hydrologic
conditions.
Other hydrological parameters of interest may also be characterized
including watershed runoff R
R ¼ IR þ IG ¼ E=x À P À IU

m3
$year

(11)
For a headwater lake, where IU ¼ 0 we can define annual runoff
or water yield WY as
WY ¼ R=WA$1000 ðmm$yearÞ (12)
where WA is land surface area of the watershed. Runoff ratio Z can
then be computed as:
Z ¼ R=PWA ðdimensionlessÞ (13)
where PWA is precipitation on the watershed. Given that the volume
of the reservoir can be measured or estimated the residence time of
water can estimated using isotopic data as:
t ¼ xV=E ðyearsÞ (14)
An IMB schematic for a lake is shown in Fig. 2a, a typical scenario
for a small, well-mixed lake that does not significantly influence the
humidity or isotopic composition of the atmosphere into which it
evaporates. Note that atmospheric fluxes should be evaporationflux
weighted (Gibson, 2002a; Gibson et al., 2008) and liquid water
fluxes should be amount-weighted. Also note that lake water,
inputs and outputs are normally sampled in the field, or in the case
of outputs from a well-mixed lake, are assumed to be representative
of lake water values.
While short-term or seasonal variations in lakewater isotopic
composition can also be accurately simulated with IMB, factors
such as residence time of lake water (Jones et al., 2005) and resolution
of archives (Steinman et al., 2013) are inherent limitations in
these types of assessments. However, such models may still be very
useful for understanding seasonally-biased signals, as for wetedry
seasonal systems (e.g. Kirby et al., 2002; Vonhof et al., 2013).
2.2. Atmospheric moisture
A simple approximation is shown in Fig. 2a whereby atmospheric
moisture upwind of the lake is assumed to be in equilibrium
with precipitation during the evaporation season (see also
Gibson et al., 2008). Other approaches for characterizing atmospheric
moisture include direct measurement (Yamanaka and
Shimizu, 2007; Iannone et al., 2010; Aemisegger et al., 2012;
Good et al., 2012), evaporation pans (Gibson et al., 1999) and use
of an index lake.
The index lake approach was proposed for terminal lakes by
Dincer (1968) but can essentially be used for any lake with known
water and isotope balances. Calibration of the limiting isotopic
enrichment, d*, in this case is given by:
d*
¼ ðdS À dIÞ=xm þ dI ð‰Þ (15)
where isotope ratios here refer to values in the index lake. A recent
example of use of a terminal index lake is presented by Gibson and
Reid (2014).
As lake surface area increases, it becomes more common for the
evaporation flux from the lake to impact its own boundary layer and
modify the overlying humidity and isotopic composition of atmospheric
moisture. An IMB schematic for a typical lake with atmospheric
feedback is given in Fig. 2b, and is described in Section 2.5.
2.3. Fractionation factors
The equilibrium isotopic fractionation factors aþ
and isotopic
separations εþ
for oxygen and hydrogen are temperaturedependent
but these are fairly well-constrained by laboratory experiments
in the range of 0e350 C. Many studies use the values
proposed by either Horita and Wesolowski (1994) or Majoube
(1971). Horita and Wesolowski (1994) give experimental values of:
aþ
ð18
OÞ ¼ exp
h
À 7:685
.
103
þ 6:7123=ð273:15 þ TÞ
À 1666:4
.
ð273:15 þ TÞ2
þ 350410
.
ð273:15 þ TÞ3
i
(16a)
aþ
ð2
HÞ ¼ exp
h
1158:8

ð273:15 þ TÞ3
.
1012

À 1620:1
Â

ð273:15 þ TÞ2
.
109

þ 794:84

ð273:15 þ TÞ
.
106

À 161:04
.
103
þ 2999200
.
ð273:15 þ TÞ3
i
(16b)
for oxygen-18 and deuterium, respectively, where T is temperature
in C. The temperature used should correspond to the water surface
Fig. 1. Schematic showing main hydrologic settings for lakes including (i) desiccating pond, (ii) terminal lake, where inflows are balanced by evaporation, and (iii) throughflow lake
or straight-exchange sea (after Horita, 1990).
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328318
temperature (usually close to the airewater mean temperature). It
has been suggested that surficial cooling effects (up to 4 C) may
play a role, particularly for high rates of evaporation (Cappa et al.,
2003), although this seems to be less important under natural
conditions (Horita et al., 2008). Use of the correct form of the
equilibrium fractionation factors has been the primary source of
confusion among previous studies. Note that the equilibrium fractionation
factors aþ
used above are defined by the convention of
Gonfiantini (1986) as the ratio in liquid versus vapour, i.e. aþ
¼ RL/
RV > 1, where RL and RV are the isotope ratios in liquid and vapour,
respectively, rather than a* ¼ RV/RL < 1 as proposed by Craig and
Gordon (1965) and subsequently used by many others (see also
Gat, 1996). For clarity, we also include the alternate formulation of
eq. (3) for using a*:
dalt
E ¼
À
a*
dL À hdA À ε*
À εK
Á.
1 À h þ 10À3
$εK

(3a)
and in this case eqs. (6) and (7) become
malt
¼

hÀ10À3
$
À
εK þε*
Á0
1Àhþ10À3
$εK

ðdimensionlessÞ
(6a)
and
d*alt
¼
À
hdA þ εK þ ε*
Á
0
h À 10À3
$
À
εK þ ε*
Á
ð‰Þ (7a)
where ε* ¼ (1 À a*)$1000. For lakes, kinetic constants CK are
commonly assumed to be 14.2‰ for oxygen-18 and 12.5 for
deuterium (Horita et al., 2008) representing fully turbulent, openwater
conditions. For laminar flow conditions, diffusioncontrolled
settings (i.e. evaporation from soils) or for mixed conditions
(i.e. evaporation through leaves), alternate formulations
have been proposed based on proportionate weighting of diffusivity
ratios and turbulence (see Horita et al., 2008). Note that an
alternate kinetic fractionation scheme proposed by Merlivat and
Fig. 2. Schematic showing major water fluxes and isotopic compositions for a well-mixed lake (a) without atmospheric feedback, and (b) with atmospheric feedback. Note that
atmospheric parameters are preferably evaporation-flux weighted whereas liquid fluxes to the lake are amount-weighted, and discharge acquires the isotopic signature of the lake
water. A simple approximation for atmospheric moisture is also shown that assumes equilibrium with upwind precipitation. Note that atmospheric feedback modifies the isotopic
composition and humidity of the overlying air mass. Kinetic and equilibrium exchange between the lake and atmosphere, as shown, are conceptual. These occur in the near-surface
boundary layer.
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328 319
Jouzel (1979) uses separate wind speed-dependent algorithms for
smooth and rough surfaces, and is widely applied by the GCM
community for simulating evaporation from oceans and continental
surface waters (see Schmidt et al., 2005; Lee et al., 2007; Risi
et al., 2012). The fundamental influence of using different parameterization
schemes in GCMs versus the Craig and Gordon (1965)
model has been discussed only recently (Haese et al., 2013), and
needs to be kept in mind when GCM outputs are compared to IMB
simulations or paleoclimate data.
2.4. Seasonality effects
For non-seasonal climates, where evaporation occurs consistently
throughout the year, it is often suitable to assume that atmospheric
moisture is in equilibrium with precipitation:
dA ¼

dP À εþ
.
1 þ 10À3
$εþ

(17)
as shown in Fig. 3a, which is an example of an evaporating system
with an evaporation line slope close to 3.5. Here, dP is mean annual
precipitation which is assumed to be the isotopic composition of
input to the lake.
In seasonal climates, where evaporation may be highly seasonal,
or lakes may even be frozen for a significant part of the year (e.g.
Canada or Russia), it is less appropriate to use the equilibrium
approximation. For this situation, the atmosphere is better represented
by equilibrium with precipitation during the evaporation
season, ideally using evaporation flux-weighted values of dP to estimate
dA (Gibson, 2002a; see Fig. 3b). In this case, the typical
evaporation line slope is 5 or higher, and the effective isotopic
separation between amount-weighted precipitation (falling near
the intersection of local evaporation line and meteoric water line)
and evaporation-flux weighted moisture, is less than the equilibrium
separation. This is termed the effective precipitation-vapour
separation (εeffective), as illustrated in Fig. 3b. Gibson et al. (2008)
illustrated this concept on a global basis from analysis of the International
Atomic Energy Agency's Global Network for Isotopes in
Precipitation database, as we present in Fig. 4. Overall, the precipitation
e atmospheric moisture separation (εeffective) is slightly
compressed at high latitude due to this effect. It is important to note
that such maps, while useful for illustrating the global and regional
patterns of precipitation and atmospheric moisture, should be
interpreted cautiously and are not recommended for interpolating
values for individual sites. For seasonal settings where continuous
records of dA are not available, a ‘selected’ equilibrium model
applied to mean annual precipitation dP may be more appropriate
using:
dA ¼

dP À kεþ
.
1 þ 10À3
$kεþ

ð‰Þ (18)
where k typically ranges from 0.5 for highly seasonal climates to
values approaching 1 for non-seasonal climates. In case studies
where both oxygen and hydrogen isotope data are available, the
selected equilibrium approach has been used to fit dA to match the
observed slope of the local evaporation line (Bennett et al., 2008;
Gibson and Reid, 2014).
As lower slopes predicted by the equilibrium model (Fig. 3a) do
not generally match the observed slopes for seasonal climates,
evidently due to improper (or lack of) weighting for the dA À dP
separation, it is appropriate to use the selected equilibrium
assumption that accounts for the fact that evaporation and isotope
exchange does not occur during periods of ice cover or that the
process is seasonally variable. An interesting point that is especially
relevant for paleoclimate studies is that temporal changes in seasonality
likely contributed to a continual shift in the slope of the
local evaporation line in the past.
While many paleoclimate studies are based on oxygen-18 only,
it is thought-provoking to note that, where possible, use of dual
oxygen-18 and deuterium records in lake sediments would provide
a method for tracing changes in paleoslope of the evaporation line
and therefore potentially offer a basis for examining past seasonality
in the lake sediment record. Regression of paleoslopes to the
intersection with the meteoric water line could also be used to
constrain precipitation input signatures more precisely. Without
dual isotopes, paleoclimate studies using oxygen-18 alone might at
least consider use of a selected equilibrium assumption to avoid
systematic scaling issues in quantification of water balance in
seasonal settings. For modern water balance applications, the use of
evaporation-flux-weighted dA and evaporation-flux-weighted exchange
parameters is required to avoid substantial errors in
computed long-term values for evaporation to inflow ratios,
particularly for strongly seasonal climates where errors may be as
high as 50% for low throughflow, high evaporation lakes. One other
implication is that slope of local evaporation lines:
Fig. 3. Schematic d2
Hed18
O plots showing isotopic composition of water and vapour in
an ideal lake undergoing evaporation. Two cases are shown including (a) non-seasonal
climate where atmospheric moisture is in equilibrium with mean annual precipitation,
and (b) seasonal climate, where atmospheric moisture in equilibrium with precipitation
falling during the evaporation season. Note that in the latter case, the isotopic
separation between mean annual precipitation and the effective atmospheric moisture,
termed the effective isotopic separation εeffective
, is less than equilibrium. This
situation can be modelled using a selected equilibrium approach (see text for discussion).
The MWL is the Global Meteoric Water Line of Craig (1961) (modified from
Gibson, 2002a).
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328320
Fig. 4. Maps showing isotopic compositions based on modelling of the Global Network for Isotopes in Precipitation database, (a) Mean annual isotopic composition of precipitation
(b) isotopic composition of moisture in equilibrium with mean annual precipitation, (c) evaporation-flux-weighted atmospheric moisture. Note that the separation between (a) and
(b) is significantly greater than (a) and (c), especially at high latitudes (modified from Gibson et al., 2008). This map is provided to illustrate global and regional patterns and is not
intended to be used for interpolation for individual sites.
SLEL ¼
"
hðdAÀdP Þþð1þdP $10À3
ÞðεK þεþ
=aþ
Þ
h$103ÀεK Àεþ=aþ
#
2"
hðdAÀdP Þþð1þdP $10À3ÞðεK þεþ=aþÞ
h$103ÀεK Àεþ=aþ
#
18
(19)
vary globally, with lower values near the equator and higher values
at high latitudes (Fig. 5; see also Gibson et al., 2008). Note that eq.
(19) is evaluated based on d* and the isotopic composition of inflow
dP assuming lakes fed by precipitation-derived waters. In general,
the evaporation slope based on eq. (19), which is atmospherically
controlled, can serve as a useful diagnostic variable to determine
the appropriate parameterization scheme for both modern and
paleoclimate applications. However, it is important to acknowledge
that LEL slopes are slightly non-linear and also weakly dependent
on water balance when evaluated in the range of dP to dS as shown
in Fig. 6. Caution should also be used when applying slope diagnostics
for arid climates where humidity is below 50% as isotopic
enrichment becomes unconstrained.
An example of the expected steady-state isotopic enrichment
for lakes located in the same climatic zone but under different
water balance conditions, as well as differences in evaporate is
shown in Fig. 6a, The scenario assumes constant temperature and
humidity (T ¼ 10 C, h ¼ 0.7), constant inflow of precipitationderived
waters with delta values of d18;2
I ¼ ðÀ20 ‰; À150 ‰Þ, and
constant atmospheric moisture of d18;2
A
¼ ðÀ25:1 ‰; À180:9 ‰Þ
which assumes dA ¼ (dP À 0.75εþ
) (1 þ 10À3
$0.75εþ
). Under
changing humidity, temperature and water balance, the slope of
the LEL is shown to be strongly dependent on the humidity,
moderately dependent on the temperature, and weakly dependent
on the water balance (Fig. 6b).
2.5. Atmospheric feedback
For lakes, especially large lakes, where evaporation has a significant
influence on the boundary layer, the humidity, atmospheric
moisture feedback, and effect on the kinetic fractionation need to
be considered. In general, the isotopic composition of the atmosphere
above the lake is modified by admixtures of evaporate according
to:
d
0
A ¼ ð1 À f Þ$dA þ f $dE ð‰Þ (20)
where d
0
A is the modified isotopic composition of the atmospheric
admixture and f is the fraction of evaporate added. It is important to
note that eq. (20) describes the effect of turbulent mixing between
evaporate and the overlying air mass, whereas q describes the effect
on isotopic fractionation in the near-surface boundary layer. Gat
(1996) discussed the implications of q in situations where atmospheric
feedback is significant. He noted that the transport
parameter q ¼ (1 À h')/(1 À h) is appropriate for situations with
atmospheric feedback (q has been shown to have a value close to
0.88 in the vicinity of the Great Lakes and 0.5 for the eastern
Mediterranean; Gat (1996), but is expected to be close to 1 for small
lakes). The modified isotopic composition of evaporate in a feedback
system then becomes:
d
0
E ¼

dL À εþ
.
aþ
À hd
0
A À εK
0
1 À h þ 10À3
$εK

ð‰Þ
(21)
noting that εK ¼ (1 À h')/(1 À h)CK(1 À h) or εK ¼ CK(1 À h') to
account for atmospheric feedback. Equations (20) and (21) can be
solved iteratively using isotope mass balance by converging on a
Fig. 5. Simulated slope of local evaporation lines for precipitation-fed lakes showing steepening of slopes, particularly at northern high latitudes (modified from Gibson et al., 2008).
This map is provided to illustrate global and regional patterns and is not intended to be used for interpolation for individual sites.
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328322
matching value for evaporation for both d2
H and d18
O, as demonstrated
by Jasechko et al. (2014).
An IMB schematic for a lake with atmospheric feedback is
shown in Fig. 2b.
3. Regional scenarios and examples
There are several informative reviews of lake isotope balance
studies (e.g. Dincer, 1968; Gat, 1981; Gonfiantini, 1986) and many
other case studies available in the scientific literature (e.g.
Zimmerman, 1979; Hostler and Benson, 1994; Sachs, 2002; Tyler
et al., 2007; Longinelli et al., 2008; Brooks et al., 2014). Terrestrial
water balance at the regional scale derived from lake isotope
compositions has also been described (Jasechko et al., 2013). While
informative, these studies do not offer significant insight into IMB
systematics related to specific climatic regions under study. Variations
expected in dP,dS,dA and dE are shown for a variety of regional
climate scenarios including low latitude, high latitude, temperate
regions, large lakes, and coastal lakes (Fig. 7). These examples are
included to inform selection of appropriate IMB parameterization
schemes for paleoclimatic reconstructions using stable water isotopes.
We use constant values of input as a reference case so that
direct comparisons can be readily made between scenarios.
Example spreadsheet calculations for the scenarios in Fig. 7 are
provided as Supplementary material.
3.1. Low latitude lakes
Gat (pers. comm.) described a reference evaporation system in
low latitude regions as one that is non-seasonal, characterized by
input from precipitation that is in isotopic equilibrium with local
vapour, and a lake with throughflow that is well-mixed, in hydrologic
steady state, and losing water by surface evaporation. In this
case, humidity does not significantly affect the slope of the evaporation
line but higher humidity tends to limit the overall offset
from the meteoric water line along the local evaporation line
(Fig. 6a,b). Ideal examples of the low-latitude (non-seasonal) systems
are few, but this model is most suitably applied where slopes
of local evaporation lines are approximately 3.5 (see Gibson et al.,
2008). However, in almost all cases, subtle seasonal shifts can
result in slight departure from precipitationevapour equilibrium
resulting in weak humidity dependence of the local evaporation
line. Vallet-Colomb et al. (2008) describe atmospheric moisture
conditions over a tropical lake, but find that vapour is not in isotopic
equilibrium due to atmospheric feedback effects, and evaporation
line slopes are steeper, as discussed later on. The idealized
scenarios shown here assume dP of À20‰ for d18
O and À150‰ for
d2
H, a mean annual temperature of 20 C, and dA À dP equilibrium.
Two humidity cases are shown, for 55% (Fig. 7a: aridzone) and for
80% (Fig. 7b; humid zone).
3.2. High latitude lakes
High latitude lakes in strongly seasonal climates are considered
as another reference scenario whereby evaporation occurs under
conditions where the effective isotopic separation (εeffective) is less
than the equilibrium separation. This is due to the seasonality effect
as described in Fig. 3b. In general, evaporation slopes are steeper
than low latitude cases (Fig. 5), with a steeper slope associated with
higher humidity and enhanced seasonality (Fig. 7c,d) While temperature
is also typically lower than for low latitude lakes, its effect
on isotopic enrichment is minor. Many contemporary studies have
been conducted at high latitudes in both arctic and subarctic regions
(Gibson et al., 1993, 1996, 1998, 2005; Gibson and Edwards,
2002; Ichiyanagi et al., 2003; Leng and Anderson, 2003; Yi et al.,
2008; Brock et al., 2009; Jonsson et al., 2009; Gibson and Reid,
2010, 2014; Turner et al., 2010; Anderson et al., 2013; Tondu
et al., 2013). A review of IMB highlighting cold regions processes
is given by Gibson (2002b). High latitude lakes in continental regions
tend to display pronounced evaporative enrichment during
the thaw season due to seasonally arid conditions, although this is
more limited in coastal areas (Gibson et al., 2005). The scenarios
shown here assume a dP of À20‰ for d18
O and À150‰ for d2
H, an
evaporation season temperature of 5 C, and a dA À dP separation
(εeffective) equal to 50% of equilibrium. Two humidity cases are
shown, for 65% (Fig. 7c; semi-arid zone) and for 80% (Fig. 7d; humid
zone).
3.3. High altitude lakes
Similar highly seasonal responses are expected for high-altitude
lakes, often with the additional need to consider the effect of glacial
meltwater input (This can also occur in some high altitude systems,
although not in the reference examples presented above). In general,
glacial meltwater is expected to be depleted in isotopic
composition relative to precipitation on the lake due to the altitude
effect and conceivably due to colder climate when it was deposited.
Fig. 6. (a) Deuterium-oxygen-18 plot showing steady-state isotopic composition for
lakes under constant temperature (T ¼ 10 C), humidity (h ¼ 0.7), constant dI
18,2
(À20‰, À150‰, d18;2
A ¼ ðÀ25:1 ‰; À180:9 ‰Þ. The scenario simulates selected equilibrium
conditions, i.e (dA z dP À 0.75εþ
). (x ¼ 0) denotes the isotopic composition of
first evaporate of water with precipitation composition (b) Dependance of slope of LEL
on water balance, showing scenarios for T ¼ 10 C and T ¼ 25 C. Note that water
balance, temperature, and humidity have an increasing importance in determining the
slope of LEL. Solid lines depict 10 C scenarios and dashed lines depict 25 C scenarios.
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328 323
Fig. 7. Schematic d2
Hed18
O plots showing isotopic composition of water and vapour for various lake water balance scenarios including low latitude, high latitude, temperate, and
coastal systems. Note that the MWL is the Global Meteoric Water Line of Craig (1961).
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328324
While glacial input may augment or even dominate inflow, it may
also produce steepening of local evaporation lines by making net
input more isotopically depleted. This is expected to make the
effective isotopic separation (εeffective) smaller by making net input
more similar to the evaporation-flux-weighted moisture (see
Fig. 3b). Studies of contemporary hydrology of high altitude lakes
include Guerrieri and Furniss (2004) who traced groundwater exchange
in a Colorado Lake using non-steady mass balance methods,
Yonge et al. (1989) who examined the altitude effect in lakes and
streams in a transect across the Western Cordillera from Calgary to
Vancouver, Canada, and Schurch et al. (2003) who describe the
rationale for the Swiss national isotope network. In general, evaporative
enrichment is more subdued in high alpine areas, with
isotopic composition being controlled by groundwater exchange or
glacial contributions. Various alpine climate and hydrology reconstructions
using d18
O have also been demonstrated, including
studies tracing monsoon cycles and atmospheric circulation patterns
(Mckenzie and Hollander, 1993; Barker et al., 2001; Jones
et al., 2006), paleo-altitude of orogenic belts (Rowley et al., 2001),
paleohydrology and paleohumidity (Wolfe et al., 2001) and residence
time and evaporation (Fontes et al., 1993).
3.4. Temperate lakes
Temperate regions, located between the tropics and the Polar
regions, tend to have an intermediate response compared to low
latitude and high latitude systems. As a result evaporation slopes
tend to be intermediate (often in the 4e5 range) and are moderately
humidity-dependent. There are many examples of isotope
balance studies in temperate zones. One recent study presents
variation in water balance across the contiguous United States
(Brooks et al., 2014). Henderson and Shuman (2009) demonstrate
slopes of 4e5 for lakes located at seasonal sites with freezing
winters in the United States, which is consistent with weaker
seasonality than observed in Canada or Russia.
Other studies presenting long-term datasets also describe parameterizations
for temperate lakes (Gat, 1970; Lewis, 1979;
Zimmerman, 1979; Hostetler and Benson, 1994; Sachs, 2002;
Tyler et al., 2007; Longinelli et al., 2008). Temperate lakes tend to
have a range of evaporative enrichment as determined by evaporation
loss and throughflow status. Here we summarize two
temperate scenarios, for a large lake with and without humidity
buildup. These scenarios assume a dP of À20‰ for d18
O and À150‰
for d2
H, an evaporation season temperature of 10 C, and a dA À dP
separation (εeffective) equal to 75% of equilibrium. Two relative humidity
cases are shown, for 70% (Fig. 7e; temperate) and for 80%
(Fig. 7f; temperate, with humidity buildup). The specific effect of
humidity buildup, which may occur more often for large lakes, is
described in the following section.
3.5. Large lakes with humidity buildup
Large lakes, such as the Laurentian Great Lakes (Jasechko et al.,
2014), have been shown to modify their own boundary layer on an
ongoing basis due to admixture of evaporate into the overlying air
mass. From an isotopic perspective, this has been addressed using
the modified evaporation equations presented in Section 2.5. For
the Great Lakes, Jasechko et al. (2014) estimated that between 15%
and 40% of water vapour over the lakes is contributed by lake
evaporate. Using precipitation records, Gat et al. (1994) estimated
that 5e16% of moisture at precipitation stations downwind of the
lakes were derived from lake effect moisture (i.e. q ¼ 0.88 as discussed
previously). Together these studies suggest a larger effect
over the lakes themselves. This has a significant effect on the isotopic
enrichment of the lake, as shown in Fig. 7f for the case of 35%
moisture feedback. The evaporation slope is shown to steepen
relative to the non-feedback scenario (Fig. 7f) and tends to be
steeper at lower values of x (i.e. higher throughflow). The influence
of the isotopic composition of evaporate on the overlying atmosphere
and humidity are both influential. The steepening of the
evaporation slope (see Supplementary material) also contributes to
limited overall offset of the lake from the meteoric water line (see
Laurentian Great Lakes; Fig. 8) and has created the Great Lakes
Water Line, sub-parallel to the GMWL (Fig. 8; see also Jasechko
et al., 2014). This steepening and limited offset was also observed
by Vallet-Colomb et al. (2008) for a moderately large tropical lake
(115 km2
) with significant vapour feedback. It is important to note
that failure to account for atmospheric feedbacks over such lakes
would have resulted in substantial underestimation of x. For paleoclimate
reconstruction, representative humidity for characterizing
isotopic changes in large lakes is expected to be up to 30% or so
higher than the ambient humidity in near-shore areas. Note that
water balance of individual lakes can be strongly influenced by
inflows from upstream elements. In the case of the Great Lakes
water from upstream lakes is itself enriched relative to the MWL
which needs to be considered when solving the isotope mass balance
(see Jasechko et al., 2014).
3.6. Coastal lakes
The isotopic response of coastal lakes has not been given much
attention in the peer-reviewed literature. While regional surveys of
continental lakes often display evaporation lines that lie below the
meteoric water line, coastal lakes often plot along the meteoric
water line (Fig. 8). This unique response is shown for a spatial
survey of small lakes in coastal British Columbia, Canada in comparison
with a similar survey in northern Saskatchewan, Canada
(Gibson et al., 2010). Overall, Gibson et al. (2010) report that variations
in the British Columbia survey are more closely linked to
variations in precipitation with altitude along the mountainous
coastline, whereas variations in Saskatchewan and neighbouring
provinces (Alberta and Manitoba) are driven more by variations in
the water balance of lakes. It is also important to appreciate the
Fig. 8. d2
Hed18
O plot showing characteristic differences between lakes from coastal
environments and continental environments, as well as large lakes with humidity
buildup. Note that the BC lakes (Canada) plot along the MWL (Global Meteoric Water
Line; Craig, 1961), Saskatchewan lakes (Canada) plot along a well-defined local evaporation
line with slope close to 5, and Laurentian Great Lakes (Canada/USA) plot along
a trend parallel to but below the MWL.
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328 325
unique vapour regime associated with coastal areas, especially due
to the fact that the atmosphere may oscillate from being oceanvapour
dominated to continental-vapour dominated. Under
ocean-dominated conditions, dA may become unusually enriched
compared to dP leading to isotopic exchange and potential for
extreme evaporative enrichment along the meteoric water line,
although the latter is likely constrained somewhat by high humidity
(Fig. 7g). For continental dominated moisture intervals, the
enrichment proceeds along a fairly steep slope, with departure
from the meteoric water line constrained by high humidity
(Fig. 6h). In addition, as humidity increases towards 100% and
evaporation stops, the kinetic effects become negligible. In this
situation a lake may tend toward an isotopic signature reflecting
isotopic equilibrium with the atmosphere, and water balance information
is therefore not recorded. Fortunately, humidity intervals
close to 100% are usually short-lived. The scenarios shown here
assume a dP of À20‰ for d18
O and À150‰ for d2
H, an evaporation
season temperature of 10 C, a dA À dP separation (εeffective) equal to
75% of equilibrium, and a humidity of 80% (Fig. 7g,h). Oceandominated
moisture is assumed to be close to À4‰ for d18
O
and À22‰ for d2
H, representative of oceanic evaporate (Craig and
Gordon, 1965, p. 99), It is important to note that changes in
dominance of oceanic versus continental air masses over time, and
the overprinting of both precipitation and evaporative enrichment
signals along or close to the meteoric water line, makes interpretation
of coastal isotopic records potentially more complex.
3.7. Saline lakes
The salt effect in saline lakes has been described in detail by
Gonfiantini (1986) and Gat (1995) with many informative case
studies. While beyond the scope of this article, it is important to be
aware that salt decreases the thermodynamic activity of water and
its evaporation rate, causes hydration sheaths to form which
contain a different isotopic composition to that of free water, and if
saturation occurs, salts may precipitate and remove crystallization
water that has a different isotopic signature than the remaining
liquid (Gonfiantini, 1986). Important modifications to the steadystate
balance equations shown here have been applied to account
for the thermodynamic activity effects in saline lake case studies
(see Gat and Levy, 1978; Horita, 1990). This involves normalization
of the humidity (i.e. substitution of h with h/aW, where aW is the
thermodynamic activity of water).
3.8. Chain of lakes
The theoretical case of non-headwater chain lakes has been
described in detail by Gat and Bowser (1991) and two recent case
studies have also been reported (Gibson and Reid, 2010, 2014). The
first case study, reporting IMB results from the continental subarctic
near Yellowknife, Northwest Territories, Canada, showed
how records from two nearby lakes can be used to reconstruct
changes in the degree of connectivity of a string-of-lakes watershed
over almost two decades of observation. This approach relies on
simultaneous monitoring of a terminal lake and a nearby creek
(Baker Creek) draining a watershed comprised of 370 intermittently
connected lakes. In general, it was found that as upstream
lakes became disconnected, the isotopic composition of Pocket
Lake and Baker Creek became more similar (Fig. 9), and this was
used quantitatively to estimate the effective drainage area of the
Baker Creek watershed, which ranged from about 27% to 88% of the
topographically delineated drainage area. Similar strategies could
potentially be applied in paleoclimate studies providing a suitable
high-closure lake can be identified in the vicinity of a chain of lakes
of interest.
The second example is provided by Gibson and Reid (2014) who
showed propagation of water down a chain of lakes in a tundra
watershed, and illustrated application of the method to track evolution
of water yield, runoff ratios and evaporation losses along a
chain of several lakes that were continuously connected during the
thaw season over a 20-year period. A similar approach to reconstruction
of water balance along a chain of paleolakes is also
possible as described by Yu et al. (2002). In this case the upstream
lake can be used to define dU, the middle lake defines dS, and the
downstream lake defines dQ. Both Gibson and Reid (2010, 2014) also
estimated evaporation as a percentage of evapotranspiration from
the watersheds. Such metrics that capture the balance between the
vapour loss mechanisms, and more clearly portray the role of lakes
in the regional hydroclimate system, have yet to be applied in the
paleohydrologic reconstructions, in many cases due to difficulty in
obtaining good control on past changes in some properties such as
lake levels and watershed areas. In fact, dating control on lake
sediments remains a primary limitation on combined interpretation
of co-located lake records. But the potential exists to carry out
this kind of study.
4. Summary
Isotope mass balance of contemporary systems can provide
considerable insight into expected responses observed in the
paleoenvironmental archives, and is an important consideration
when using quantitative models to simulate past water balance
conditions. An examination of modern systems shows that basic
assumptions about atmospheric moisture and humidity can have a
large impact on signatures registered in lake sediments. Several
important considerations to improve realism of quantitative paleoclimatic
reconstructions include use of an isotope mass balance
model that is appropriate for the climatic setting, for the atmospheric
feedback situation, for salinity, and headwater conditions.
We also show potential for use of dual-isotope tracers to trace past
changes in seasonality and input, and a dual-lake index method
that can be used to trace effective drainage basin areas of lakes. Use
of physical water balance information on lakes of interest, tied to
Fig. 9. Crossplot showing isotopic composition (d18
O) of Pocket Lake (a terminal lake)
versus Baker Creek (outlet of Martin Lake) sampled during the open water season
during 1991e2013. Baker Creek drains a 137 km2
basin containing 370 intermittently
connected lakes. Note that the isotopic composition of the lakes becomes more similar
as effective drainage area decreases in the Baker Creek watershed, which was applied
by Gibson and Reid (2010) to quantify connected area of the watershed.
J.J. Gibson et al. / Quaternary Science Reviews 131 (2016) 316e328326
modern isotope balance analogues, is a reasonable strategy for
paleoclimate studies of lakes to improve realism of the reconstructions.
Nevertheless, in cases where modern or paleo systems
are under-defined there are inherent limitations in the degree
of quantification that can be attained. But as reflected on by Gat
(1996), paleoclimatic applications of isotope hydrology have been
a greater incentive for the study of stable isotopes in the hydrologic
cycle, yielding more useful hydrological information as a byproduct,
than hydrological sciences applications directly. We contend
that these communities have much to learn from one another.
Acknowledgements
Funding for this research was provided by grants from Alberta
Innovates Technology Futures, Indian and Northern Affairs Canada,
the Cumulative Environmental Management Association, and the
Natural Sciences and Engineering Research Council of Canada
(CRD357130-07). We thank Paul Eby AITF for analysis of the stable
isotopes of water.
Appendix A. Supplementary data
Supplementary data related to this article can be found at http://
dx.doi.org/10.1016/j.quascirev.2015.04.013.
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