To better understand the variations over time of precipitation water isotopes measured in polar ice cores, we have developed an intermediate complexity model (ICM) of atmospheric water vapor transport and associated isotopic distillation. The model builds directly from earlier work by D. Fisher and M. Hendricks and is calibrated against the measured modern spatial distribution of δD and deuterium excess (d). Model improvements include a correction to the equation governing advective transport, which solves a major puzzle arising from the earlier work. The new model shows isotopic data to be consistent with dominance of eddy diffusive transport at high latitudes. Model experiments are used to show that a wide variety of climate changes in subtropical source regions can affect Antarctic d and that such d changes are consistently anticorrelated with changes of δD. Magnitudes of ΔδD/Δd are ∼−1 to −5 and are much higher at the ice sheet margin than in the interior of the continent. Changes in the relative dominance of diffusive and advective transport are also shown to cause anticorrelated changes of similar magnitude. Isotopic sensitivities to temperature change (ΔδD/ΔT) are shown to also vary spatially, with low values in marginal zones and higher values inland. Effects of ocean surface relative humidity on Antarctic d are shown to be nearly uniform across the continent (in contrast to earlier results given by Petit et al. ) but quantitatively small. The method used by Vimeux et al.  for folding humidity effects into source temperature effects is supported. We draw attention to a pervasive misapplication of marine composition corrections to Antarctic δD records. Arguments are made in support of simple interpretations of calibrated ice core isotopic time series in terms of temperature changes despite the potential complexities in the system.
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 The isotopic ratios δ18O and δD of precipitation provide an important and versatile tool for investigating both paleoclimatic conditions and characteristics of the global hydrological cycle. Despite the widespread use of these indicators (here collectively called δ), the factors that control their spatial and temporal variations are incompletely understood, as evidenced in particular by recent discussions of temporal sensitivities of polar δ to climate variables [e.g., Aristarain et al., 1986; Cuffey et al., 1995; Johnsen et al., 1995; Boyle, 1997; Fawcett et al., 1997; Krinner et al., 1997; Cuffey, 2000; Hendricks et al., 2000; Holdsworth, 2001; Kavanaugh and Cuffey, 2002]. To date, most investigations into the controls on δ have utilized either Rayleigh distillation models or general circulation models (GCMs) equipped with isotopic tracers. Both have contributed valuable insights [e.g., Jouzel and Merlivat, 1984; Jouzel et al., 1987; Johnsen et al., 1989; Petit et al., 1991; Charles et al., 1994; Hoffmann et al., 1998; Delaygue et al., 2000], but both also have disadvantages. Rayleigh models do not include crucially important factors like evaporative recharge and atmospheric transport properties, and make limited use of the constraints provided by climatological data. GCMs, in contrast, allow the inclusion of both important physical mechanisms and detailed climatological conditions, making them powerful tools for exploring the isotopic response to climate changes. Their complexity, however, limits their usefulness for exploring how variations in single climate parameters, or in fundamental characteristics of the isotopic distillation system, directly affect δ of polar precipitation.
 It is therefore useful to supplement the information from Rayleigh model and GCM studies with insights from models of intermediate complexity [Fisher and Alt, 1985; Hendricks et al., 2000; Kavanaugh and Cuffey, 2002]. The goal of such intermediate complexity models (ICMs) is to provide conceptual, and possibly quantitative, insight into the relationship between water vapor transport, climate, and the isotopic content of precipitation. The intent of this study is to improve the quality and utility of ICMs, by constructing a revised ICM for investigating the factors that control the δ18O, δD, and deuterium excess (defined as d = δD − 8δ18O) of Antarctic precipitation. We will also use this ICM to further examine controls on the temporal shifts in δ seen in ice core data, with relevance to understanding the magnitudes of isotopic sensitivities (∂δ/∂T) and their use in the joint interpretation of δ18O and δD time series [Cuffey and Vimeux, 2001; Vimeux et al., 2001].
1.2. Precedent and Puzzles
 The use of ICMs to examine precipitation isotopes was pioneered by D. Fisher [Fisher, 1990, 1991, 1992; Fisher and Alt, 1985], who connected the geographic variations of δ to zonally averaged climate quantities (temperature (T), precipitation (P), and evaporation (E)) and to the partitioning of atmospheric transport between advective (mean flow) and diffusive (turbulent eddy) components (following the study of Eriksson ). Hendricks et al.  subsequently created the state-of-the-art ICM by explicitly and consistently linking water vapor transport to both the δ and the climate variables. They used this model to calculate δ values along a transport path leading to central East Antarctica, for both purely advective and purely diffusive atmospheres. To highlight fundamental system properties, this model treated all isotopic fractionations as equilibrium processes and omitted kinetic effects on evaporation and ice condensation. These effects are, however, important for calculation of the deuterium excess. The major contribution of the Hendricks et al.  analysis is its demonstration that the strong evaporative recharge of the low and middle latitude atmosphere with isotopically heavy vapor can limit the variability of δ over the polar ice sheets. In particular, the sensitivity of δ values to temporal changes in temperature is modeled to vary spatially; sensitivity is low at the ice sheet margins and increases inland, even though the modern spatial gradient (∂δ/∂T calculated using modern climate data from different locations) across the ice sheet may be uniform.
 The analysis of Hendricks et al.  left two major puzzles. First, model results suggested that a purely advective atmosphere provides a good fit to observed δ–θ (latitude) and δ–T (temperature) data [Hendricks et al., 2000, Figure 2], whereas it is generally thought that diffusive transport dominates in regions poleward of the Hadley Cell [Hartmann, 1994, p. 150]. Second, while the modeled advective atmosphere provided a good fit to observed δ relationships, the modeled diffusive atmosphere better matched observed deuterium excess values [Hendricks et al., 2000, Figure 3]. We will revisit these issues in section 2.4 of this paper.
Kavanaugh and Cuffey  subsequently used the advective-only version of the Hendricks et al. model (with some modifications) to examine the covariation of δD and d in Antarctic precipitation induced by vapor source region climate changes. They showed that, in the context of this model, a wide range of such source region climate changes causes anticorrelated variations of δD and d over the ice sheet, a result that lends support to ice core data analyses that use d to correct δD for nonlocal effects to derive a temperature time series at the ice core site [Cuffey and Vimeux, 2001; Vimeux et al., 2001].
1.3. Goals of This Paper
1.3.1. A New State-of-the-Art Model
 One goal of this paper is to present a modified version of the Hendricks et al.  model that we hope will be useful as a new state-of-the-art ICM.
184.108.40.206. Modified Physics
 We have identified an error in the Hendricks et al.  model, which we here explain and correct. A critical term in the model is the horizontal advective water flux divergence , calculated using vertically integrated water content and effective velocity values. The advective (mean flow) water flux is
in which is the vertically integrated water content
The effective vertically integrated horizontal water transport velocity is by definition
and the corresponding advective divergence is
which, together with the divergence of the eddy diffusive flux, must balance the net evaporation minus precipitation at steady state. Hendricks et al.  omitted the second term on the right in (4). A velocity divergence term does not appear in three-dimensional (3-D) calculations of incompressible flows, but must be retained in vertically integrated formulations (note that ∇ · is the divergence of the horizontal fluxes only) and in compressible flows. In the present context the flow of water is both vertically integrated and not constrained by incompressibility, and so this term must be included. This change proves to be important.
 To illustrate why this change is necessary, consider the hypothetical example of a purely advective atmosphere. In such a case, the Hendricks et al.  formulation requires, for a spatial distribution of precipitation and evaporation given by P and E at latitude θ, that (where R is the mean radius of the Earth), and thus that = 0 where P = E. This implies conceptual problems. For the desert belts, which are evaporation-dominated and hence sources of water to the higher latitudes (Figure 1), this formulation forces the transport velocity to change direction at the boundary of the desert belt, so that all of the transport within this source region is away from the pole. It is conceptually more reasonable to allow the direction of transport to change in the middle of the source region rather than at its edge (Figure 1), and in fact data show this to be the case [Piexoto and Oort, 1984, p. 389]. Another difficulty arises over the center of the Antarctic ice sheet, where w is a minimum and ∂w/∂θ = 0. Here, the Hendricks et al.  formulation would require infinite transport velocity (because P − E ≠ 0), whereas one would expect = 0 at this point of symmetry in the global water flux field.
220.127.116.11. Other Improvements
 Three additional model improvements incorporated here are less fundamental but nonetheless important. The first two were introduced by Kavanaugh and Cuffey . First, isotopic fractionation factors during evaporation and condensation include kinetic effects (following the studies of Johnsen et al. [1989, and references therein] and Jouzel and Merlivat [1984, and references therein]). Second, we examine a second, more relevant water vapor transport path. By “path,” we mean a particular spatial distribution of climate variables, expressed as a function of latitude. The specific distributions used will be different depending on the geographic pattern of ocean, land, and topography above which water vapor is transported. The transport path used by Hendricks et al.  starts in the southern Pacific Ocean and traverses Antarctica from the west, along the Antarctic Peninsula, and across West Antarctica to central East Antarctica. The second path used here originates in the southeastern Indian Ocean, and directly approaches central East Antarctica from the north. Moisture transported along this path accounts for approximately 50% of precipitation at Vostok according to GCM estimates, compared to ∼20% for the western path [Delaygue et al., 2000].
 In this paper we have allowed for a mixture of advective and diffusive transport mechanisms, determined by data over the subtropics and by model calibration over Antarctica. This has enabled us to produce a calibrated model that matches observed δ–θ, δ–T, and d–δD relationships along both transport paths. In previous work [Hendricks et al., 2000; Kavanaugh and Cuffey, 2002], only end-member models with purely advective or diffusive atmospheres were examined.
1.3.2. Model Applications
 The second major goal of this paper is to further explore how variations in a number of climate variables are reflected in changes of δ and d values over Antarctica. By prescribing climate perturbations from the calibrated base model, we ask a number of questions relevant to ice core interpretation and utility of the ICM:
How does the model respond if forced only by changes in marine isotopic composition? These results do not involve changes of climate variables and so can be directly compared to those obtained by GCMs. To be credible, the ICM should give similar results.
Are the conclusions of Kavanaugh and Cuffey  still valid following correction of the advective divergence formulation and incorporation of mixed advective and diffusive transport into the model?
How does varying the relative strengths of the advective and diffusive transport mechanisms change the δ and d relationships?
How do variations in the mean ocean surface relative humidity affect the deuterium excess of precipitation over the ice sheet? Using a Rayleigh model, Petit et al.  derived the puzzling result that the impact of oceanic relative humidity on precipitation d diminishes significantly toward the interior of the ice sheet, whereas source temperature effects on d do not diminish. This deserves reexamination.
Is it still valid to conclude [Hendricks et al., 2000] that isotopic sensitivity to local temperature change is low near the ice sheet margin and increases inland?
Are isotopic sensitivities influenced significantly by the nature of any precipitation and evaporation changes that occur in coincidence with temperature changes? For example, are isotopic sensitivities dependent on geographic shifts of precipitation and evaporation zones that might accompany climatic temperature changes? In their calculations, Hendricks et al.  assumed no changes of P and E.
Does the sensitivity of δ to source region temperature change also vary spatially? Does it also depend on coincident changes of P and E?
 We will address each of these questions specifically in section 3 and briefly summarize their implications for ice core interpretation in section 4.
1.4. An Important ICM Caveat
 Although we think that ICMs are very useful tools for gaining insight into the dependence of δ values on climatological parameters, we also wish to emphasize that the ICMs are not climate models. The climate variables and their interdependence are prescribed in an ICM rather than calculated as in the case of GCMs. Therefore ICMs are inferior to GCMs for deriving quantitative values for isotopic sensitivities, and for quantitatively examining the covariance of δD and d. The purpose of the model calculations presented here is to seek generalized patterns and conceptual insight, and to provide rough estimates of the effect of variations in climatological parameters on δ and d values of Antarctic precipitation.
2. A Revised Model
2.1. Model Physics
 The isotopic composition of atmospheric water vapor is calculated by accounting for the water balance along the transport path for each isotopic species. In steady state, conservation of water vapor mass requires that the divergence of the local 3-D atmospheric water flux is balanced by the net water vapor source :
Separating the vertical component (qw,z) from and integrating vertically over the atmospheric column yields
where ∇H is the del operator for the horizontal dimensions. Evaluating the second term in (6) at its integration limits gives qw,z(z = ∞) − qw,z(z = 0) = 0 − E = −E, and the third term is simply the precipitation (changes in cloud mass being negligible). We can thus write
The horizontal water vapor flux is broken down into two components. The first component accounts for water vapor transport due to turbulent eddies, which is modeled as a diffusive process with latitude-dependent diffusivity k. The second component describes advective moisture transport by prevailing winds, with representing the mean horizontal transport velocity (also a function of latitude). The steady state expression for the vertically integrated horizontal water vapor transport in a given atmospheric column is thus
The reduction of the 3-D water balance expression (5) to two dimensions (8) by vertical integration of the transport and source terms greatly reduces the complexity and computational expense of the model and is justified conceptually by Hendricks et al. . The model is further reduced to a single independent integration variable by zonal averaging to eliminate terms accounting for divergence of zonal transport. This approach is exact if the zonal average is taken over a complete circuit of the globe, as done by Fisher . More generally, this approach gives a good approximation provided that the average is taken across a sufficiently wide range of longitudes so that the time-averaged zonal divergence is small compared to that for the meridional divergence (outside of the tropics, the longitude range must be broader than the wavelength of stationary waves). If we label the atmospheric divergence due to eddy processes Dk and the divergence due to mean flow Dv, we can rewrite (8) in spherical polar coordinates as
The relative strengths of the two transport mechanisms Dk/Dv can be prescribed in accordance with observations in order to calculate k(θ) and (θ); we will discuss the choice of this ratio below. The expression for Dv shown in (9c) differs from that that would be obtained if the second term in (4) were omitted (in which case the first term within the square brackets would not appear).
 Closely following the study of Hendricks et al. [2000, p. 852], (9a), (9b), and (9c) are recast in terms of δ values by writing its equivalent separately for each isotope-bearing water and by assuming that the water contents and HDO are both significantly smaller than . The resulting expression for steady state latitudinal variations in the isotopic composition of atmospheric water vapor is found to be identical to the steady state version of equation (3) of Hendricks et al.  (although with a different w) and is
The term Δe = δe − δa is the difference in isotopic composition between the evaporate and atmospheric water vapor, and Δp = δp − δa gives the difference between the precipitate and atmospheric water vapor. These differences are due to fractionation, such that (1 + δp) = α(1 + δa) and (1 + δe) = α−1(1 + δm) (where δa, δp, δe, and δm are the atmospheric, precipitative, evaporative, and oceanic surface water isotopic composition values, respectively, and α is a fractionation factor). Details on the fractionation factors used to determine values for Δe and Δp in (10), including the treatment of kinetic effects associated with evaporation and condensation, can be found in Appendix A. This appendix also describes the parameterizations used to determine both the condensation temperature and ice–liquid composition of the formed precipitate, both of which affect Δp.
 As mentioned in section 18.104.22.168, we will investigate δ values along two transport paths. The first of these paths, which we will refer to as path 1, was used by Hendricks et al. ; the second, referred to as path 2, was added by Kavanaugh and Cuffey . Additional information about these paths can be found in Appendix A. Also discussed in this appendix are details of the climate data used in the model calculations and a description of the numerical solution method employed in the calculations.
2.2. Diffusive and Advective Divergences
 The diffusive and advective divergences Dk(θ) and Dv(θ) are determined as follows. Over the oceans, the relative contribution of each of the two transport mechanisms to the total divergence E − P is relatively well known, and values for Dk and Dv from the study of Hartmann [1994, p. 150] are used. Over the ice, where the relative strength of the two mechanisms is more poorly constrained by data, we prescribe a spatially invariant diffusive fraction fk such that Dk = fkDtotal = fk(E − P). Thus Dv = (1 − fk)(E − P) and each transport mechanism contributes a fixed proportion of the total high-latitude divergence. This total is fairly well known from ice accumulation rate data.
2.3. Model Calibration
 Calibration to establish a base model was accomplished by adjusting five tunable parameters, which are the atmospheric δa18O and δaD at the low-latitude limit, the high-latitude diffusive fraction fk, and the cloud supersaturation coefficients c and F (see Appendix A, section A2). These parameters were adjusted by using the following constraints (on path 2): (1) The low-latitude atmospheric δa18O and δaD were adjusted so that the precipitate composition matched field measurements of δp18O and dp [Fricke and O'Neil, 1999]. Specifically, values used here were δp18O = −3.0‰, δpD = −14.0‰, and dp = +10.0‰. (2) The high-latitude diffusive fraction fk = 0.65 was adjusted to match the modern δpD value for Vostok of −440‰ [Petit et al., 1999]. (3) Cloud supersaturation factors c = 1.04 and F = 0.003 were adjusted to match the modern δpD − dp relationship at δpD = −200‰ and −350‰ [Dahe et al., 1994]. Identical values for all five tuning parameters were used for both transport paths.
2.4. New Base Model and Solutions to Two Puzzles
 Modeled δp18O, δpD, and d values for precipitation along paths 1 and 2 are shown in Figures 2 and 3 respectively. These results were obtained using the tuning parameter values given above for both transport paths. The modeled relationships are imperfect, but are in reasonably good agreement with the measured isotopic values, both as functions of latitude and as functions of surface temperature. Recall that the path 2 model results are fixed by calibration at both ends, so it is the pattern of variation in between, and the match for path 1, that are significant. The value fk = 0.65 is also encouraging, as it implies that eddy transport of water vapor dominates at high latitudes, as expected from meteorological data. The numbers c = 1.04 and F = 0.003 imply that cloud supersaturation ratios attain values around 15% over the coldest heart of Antarctica, a number that cannot be verified independently at present but which is similar to values obtained by GCM calibrations of the same parameters (c = 1.00, F = 0.003 were obtained by Jouzel et al. ).
 As these results show, the correction of the advective divergence equation (4) solves the first puzzle arising from the Hendricks et al. analysis; the δp data can now be matched with an atmosphere that is dominantly diffusive at high latitudes. One result of this is that inclusion of kinetic isotope effects allows modeled δp and dp to be simultaneously fit to the field data. Note that δpD at Vostok is strongly sensitive to fk but only very weakly sensitive to c and F, whereas the deuterium excess is strongly sensitive to c and F. Another result is that the low-latitude boundary can be chosen to be in the middle of the desert belt, rather than at its edge (compare Figure 2 to Figure 2a, advection-only case, in the study of Hendricks et al. ).
Figure 4 plots the deuterium excess as a function of δpD for the two paths. The observed rise of dp in the Antarctic interior is an inevitable consequence of the substantial depletion of δD relative to that for δ18O, combined with the fractional character of distillation (a differential change in δ having the proportionality dδ ∝ [1 + δ]). Thus the proper way to evaluate the goodness-of-fit of a deuterium excess model is to compare d to the total distillation (measured as δD or δ18O as done here), rather than to external variables like T. The second puzzle arising from the Hendricks et al.  analysis (modeled excess matched a diffusive atmosphere whereas modeled δ matched an advective atmosphere) is therefore an artifact that arose from comparing d to T [Hendricks et al., 2000, Figure 3]. For a diffusive atmosphere, their modeled δD values are too high at a given T (the distillation is insufficient) and hence their d are too low. The d(T) relationship misleads.
3. Numerical Experiments
 In the following sections, we use perturbation experiments to address the questions posed in the introduction (section 1.3.2). Results for the calibrated base model are compared to results obtained by adjusting one or a few of the model parameters or climatic inputs.
3.1. Marine Composition
 Model response to a unit increase (+1‰) of marine δm18O with no change of marine excess (i.e., ΔδmD = +8‰) or of climate is shown in Figures 5a and 5b (short dashes) and Table 1. The change Δdp at Vostok (−2.99‰) is nearly identical to that predicted by GCMs (Δdp = −2.9‰ according to the study of Delaygue ). This close match demonstrates that there are no fundamental problems with the model or the numerics that pervert results. The modeled change ΔδpD = +4.6‰ at Vostok shows that the initial source region signal is depleted to 58% of its source region value, which is very close to the 56% depletion implied by the modern Vostok δpD = −440‰. This is an important point that has been neglected in most published analyses [for example, see Petit et al., 1999, p. 431; Jouzel et al., 1993, p. 408]. To apply a simple correction for marine composition variations (using marine core data δm18O) to a δpD ice core time series, one must use δpD − ε8δm18O with ε ≈ 0.56 rather than δpD − 8δm18O as done by Petit et al.  and Jouzel et al. .
Case 1: +1‰ change in marine δm18O with no change in marine deuterium excess. Case 2: +1‰ change in initial (low-latitude) atmospheric δa18O with no change in initial atmospheric deuterium excess. Case 3: Increased source region precipitation. Case 4: Decreased source region precipitation. Case 5: Source region cooling, P and E unchanged. Case 6: Source region cooling, P and E scaled. Case 7: 10% increase in high-latitude diffusive transport fraction. Case 8: 10% decrease in high-latitude diffusive transport fraction. Case 9: Global 10% reduction in relative humidity Rh. Case 10: 0°C to −10°C surface cooling; water content w = w(T0) scaled with temperature, P and E unchanged. Case 11: 0°C to −10°C surface cooling; water content w = w(T0), precipitation P = P(T0), and evaporation E = E(T0) scaled with temperature. Case 12: −5°C to −10°C surface cooling; water content w = w(T0) scaled with temperature, P and E unchanged. Case 13: 0°C to −10°C surface cooling; water content w = w(T0) and evaporation E = E(T0) scaled with temperature, precipitation P = P(∂w/∂θ) scaled with latitudinal water content gradient (long dashes). Case 14: −5°C to −10°C surface cooling; water content, evaporation, and precipitation scaled as in Case 13. Case 15: Global −10°C surface cooling; water content, evaporation, and precipitation scaled as in Case 13.
3.2. Source Region Perturbation Experiments
 In their study of generalized controls on the deuterium excess of Antarctic precipitation, Kavanaugh and Cuffey  demonstrated that the deuterium excess is affected by a wide variety of source region changes. In addition, they showed that all of the modeled source region climate changes that resulted in variations in Antarctic dp also caused anticorrelated changes in δpD, and that the ratio ΔδpD/Δdp ≈ −1.4 to −3.5. In Appendix B, we discuss a number of experiments designed to determine whether the conclusions of that study hold true for the corrected and mixed advective diffusive model developed here. These experiments reaffirm that the dp of Antarctic precipitation responds to changes in a variety of source region parameters. Furthermore, the experiments again show that source region changes result in anticorrelated changes in δpD and dp, with ΔδpD/Δdp = −1 ∼ −4. These calculations support the conclusions of Kavanaugh and Cuffey .
3.3. Advective Diffusive Transport
 A factor not considered by Kavanaugh and Cuffey  is the relative strength of the advective and diffusive transport mechanisms. The base models shown in Figures 2 and 3 were obtained with an atmosphere in which eddy diffusive processes account for 65% of the total high-latitude atmospheric divergence. Here we investigate the effects of varying the diffusive fraction fk by ±10%. Increasing the diffusive transport component to fk = 75% results in changes for ΔδpD of ∼+26‰ and for Δdp of ∼−5.6‰ (Figures 6a and 6b (short dashes) and Table 1). Conversely, decreasing the diffusive fraction to fk = 55% results in changes with similar magnitude but opposite sign: for this perturbation, ΔδpD ≈ −30‰ and Δdp ≈ +7.7‰ (Figures 6a and 6b (long dashes) and Table 1). These results show that the δpD values at Vostok are highly sensitive to the characteristics of high-latitude vapor transport, as the ∼25‰ variations in δpD seen for the imposed 10% change in the diffusive fraction is of comparable order of magnitude to the ∼40–50‰ change recorded between glacial and interglacial periods. These experiments yield ΔδpD/Δdp of ∼−4.5. Thus, as with the source region variables, changes in δpD over the ice sheet are again observed to be anticorrelated with changes in dp.
3.4. Relative Humidity
 In their pioneering work on deuterium excess in ice cores, Jouzel et al.  interpreted Antarctic dp changes to be largely controlled by relative humidity conditions over the oceans. Analyses of Johnsen et al. , however, clarified how polar dp depends on source temperature and water content, with the result that attention shifted to temperature as a primary control on the excess, and this was confirmed for Antarctica by Petit et al. . Petit et al.  used a Rayleigh model (with some parameterized variable source) to argue that the Rh effect on the excess diminishes toward the interior of the ice sheet. For comparison, we here investigate the effect of a 10% global reduction in relative humidity; no other climate changes are imposed (Figures 6c and 6d (short dashes) and Table 1). This change results in an increase of dp values that is nearly uniform over the ice sheet, a different result from that of Petit et al. .
 Our calculations give a sensitivity of the excess to relative humidity (in %) of −0.4‰ (%)−1. In addition, changes in dp for this scenario are anticorrelated with changes in δpD, with values of ΔδpD/dp averaging ∼−0.6 for the two transport paths.
3.5. Spatial Variation of Isotopic Sensitivity
 The new ICM is here used to examine whether the isotopic response ΔδpD to a given local climatic temperature change ΔTl depends on geographic position, with small responses at the low-latitude margins and larger responses inland (as indicated by Hendricks et al. ) (i.e., that the temporal isotopic sensitivity γ = ∂δp/∂T increases toward higher latitude). This behavior is driven by fundamental system properties (at locations proximal to the zones of strong evaporative recharge, the magnitude of isotopic changes must be limited) and so is not expected to change with the revised model. Indeed, this effect is seen consistently in model results, although with local deviations. The results also clearly indicate that the temporal sensitivity γ differs substantially from the spatial gradient in some circumstances, and is difficult to ascertain a priori.
 We illustrate these properties by imposing several contrived climate change scenarios on the model. First, suppose there is a cooling over the entire model domain, with a magnitude that decreases from −10°C at Vostok to 0°C at the low-latitude limit as shown in Figures 7a and 7b (solid lines). The form of these cooling functions were chosen to give identical temperature change gradients at low and middle latitudes for the two modeled transport paths while maintaining similar cooling magnitudes at Vostok. The resulting γ(θ) depend on what prescription is used for coincident changes in P and E (see Figures 7c and 7d), but all increase inland from the ice margin, and most increase by approximately a factor of 2 between the ice margin and Vostok. Similar patterns result from choosing one prescription for P and E changes but increasing the cooling magnitude at the low-latitude limit to −5°C and −10°C (Figures 7e and 7f; see Figures 7a and 7b for cooling functions).
3.6. Hydrologic Effects on Isotopic Sensitivity
 Results shown in Figures 7c and 7d also demonstrate that isotopic sensitivities are dependent on meridional shifts of the hydrologic zones defined by zonal mean P and E. Retraction of these zones toward the equator during global climatic cooling would expand the distillation regions that are poleward of the evaporation-dominated recharge zone. Such a change would likely be recorded in Antarctic precipitation as higher values for the isotopic change magnitude is ∣ΔδpD∣ and higher values for the sensitivity γ. Would this be a strong effect or a weak one? Discussion of this point appears to be absent from the literature. The short-dashed curve in Figures 7c and 7d results from the same climatic cooling as the other curves, but in the former the P and E at given latitude have been recalculated to preserve the modern observed P(T) and E(T) relationships. This corresponds to an effective meridional contraction of approximately 4° of latitude, and results in an increase in γ of between 20% and 60% (depending on location and path). This is thus a fairly strong effect. In contrast, little effect of P and E on the δp change is observed if E(T) is preserved but P is changed in proportion to changes of the water content gradient.
 Of course, whether meridional contraction of P and E zones is important or not depends on whether such contraction of climate zones really happens in nature. There are strong physical limits to how closely the desert belts can approach the equator, but the midlatitude and high-latitude climate zones are known to have moved toward the equator in response to growth of the Pleistocene ice sheets. GCM climate simulations are required to further explore this.
3.7. Isotopic Sensitivity to Source Region Climate
 As argued elsewhere [Vimeux et al., 2001; Cuffey and Vimeux, 2001], the temporal isotopic sensitivity γ = ∂δp/∂T can, as a first-order approximation, be decomposed into a sensitivity to local temperature change over the ice sheet (γl) and a source region sensitivity (γs)
where ΔTl and ΔTs are the local and source region temperature changes, respectively. The parameter γs is very important for the deuterium excess correction to δpD time series. Figures 7g and 7h shows γs values inferred from the model experiments discussed in section 3.5. Two interesting points emerge: (1) There is a spatial variation of γs from ice sheet marginal zones to the interior, with a magnitude of variation of approximately a factor of 2. (2) The magnitude of γs appears to depend strongly on the covariation of hydrologic changes (P and E) with temperature changes. The climatic inputs we use are ad hoc, so it would be inappropriate to interpret these results quantitatively; GCM experimentation is again needed.
4. Concluding Summary and Discussion
 Building on previous work by Fisher and by Hendricks et al. , we have constructed a new ICM for use in investigating controls on stable isotopes in Antarctic precipitation. The model incorporates a correction to the equation governing advective atmospheric water vapor divergence, includes kinetic fractionations during evaporation and ice condensation, and examines transport along the geographic path most relevant to precipitation at Vostok in central East Antarctica. Calibration against modern isotopic data and numerical experiments yield the following results:
 1.To match isotopic data for Antarctic precipitation, water vapor transport in the high-latitude atmosphere must be modeled as dominantly eddy diffusive. This agrees with expectations from meteorologic data and illustrates that simple Rayleigh models (which are equivalent to purely advective transport) fundamentally misrepresent the character of polar isotopic distillation. The good agreement found by Hendricks et al.  between isotopic data and advective transport is shown to have resulted from an error in their expression for divergence of vertically integrated advective transport.
 2.To match Antarctic deuterium excess data, it is necessary for the ICM to incorporate kinetic fractionation during ice crystal growth, as proposed by Jouzel and Merlivat  and used in GCMs and Rayleigh models. The modeled excess is very sensitive to the two tuning parameters c and F used in this formulation, and this suggests that fractionation at very low temperatures is still poorly understood.
 3.Results from the revised ICM confirm that, in addition to being sensitive to the temperature and relative humidity, the Antarctic deuterium excess responds to a variety of source region climate characteristics [Kavanaugh and Cuffey, 2002] that do not involve changes in the deuterium excess of oceanic evaporation. Further, the resulting changes in Antarctic excess are anticorrelated with changes in δpD caused by these same source region variations, with a magnitude ΔδpD/Δdp of order −1 to −4. The consistency of the anticorrelation implies that the deuterium excess is a robust, if quantitatively imprecise, tool for correcting ice core δpD time series for source region effects. Consider a set of source region climate variables Cj. When these change, Antarctic δpD and d also change such that
Given that each βj is related to the corresponding γj by a proportionality of order 1, specifically βj ≈ ζγj with ζ−1 in the range −1 to −4, then the local Antarctic temperature change can be estimated as
The strongest control on Antarctic δpD exerted by source region climate is due to the temperature (with changes ΔTs) (see section 3.2). Given that changes in other source region climate parameters will almost certainly covary with ΔTs due to the strong couplings in the climate system, it is reasonable to replace (12) and (13) with
provided that the magnitudes of γs and βs are estimated from GCMs that explicitly calculate changes in other source region climate variables. This approach was used by Vimeux et al.  and Cuffey and Vimeux . If an additional term is included to account for changes in marine isotopic content (see point 6 below), this approach, though imperfect, is the best one available at present.
 4.In our model, the ocean surface relative humidity affects central Antarctic d at a magnitude of approximately −0.4‰ (%)−1. In contrast to results presented by Petit et al. , we find no evidence that this effect diminishes in the interior of the continent. Regardless, the magnitude of the relative humidity effect is small enough that source temperature effects most likely dominate. If, as suggested by GCM results [Vimeux et al., 2001], the correlation between Rh and ocean surface temperature does not significantly change over time, then the net sensitivity of d to Ts changes is
The magnitude of the second term on the right is approximately (−0.4) · (−0.5) = 0.2‰ (C°)−1, whereas the magnitude of ∂d/∂Ts is approximately 1–1.5‰ (°C)−1 [Cuffey and Vimeux, 2001, and references therein]. Therefore, we accept Vimeux's approach of including the humidity effects in βs as the best one at present for ice core interpretation.
 5.Changes in the relative magnitude of diffusive and advective transport at high latitudes also cause anticorrelated changes in δpD and d at Vostok, such that ΔδpD/Δdp ≈ −4. The sensitivity of δpD to fk is fairly high.
 6.To interpret polar ice core time series of δp, the most justifiable approach at present is to use (15) with a term included for marine composition
in which we define γ as the net thermal isotopic sensitivity at a given ice core site. This quantity can also be expressed as
Superficially, (18) is a gross simplification of reality, given that numerous variables that can affect δp are not explicitly represented (as discussed abundantly in the literature) [e.g., Dansgaard, 1964; Jouzel et al., 1997; Cuffey, 2000; Holdsworth, 2001]. Despite this limitation, the simple approach has consistently proven to be reasonably accurate in polar ice when tested against independent temperature reconstructions [e.g., Cuffey et al., 1995; Johnsen et al., 1995, Severinghaus et al., 1998], even though the magnitude of γ is not known a priori. More specifically, application of (18) has yielded ΔTl time series that strongly covary with the true temperature history, but for which the magnitude of temperature variations ΔTl is uncertain to within a factor of ∼2. The separation of γ into source and local components in (18) is probably central to understanding the magnitude of γ in many cases.
Cuffey  has suggested that the ability of ΔδpD in (18) to covary with the true local temperature change ΔTl is due to covariation of all of the variables that control δp. This is a consequence of the strong couplings within the climate system: climate changes generally involve numerous climate variables rather than one or a few in isolation. This is demonstrated conclusively by multiproxy ice core time series [e.g., Petit et al., 1999; Cuffey and Brook, 2000] and by GCMs. Nonetheless, a partial failure of the simplest assumption, Δδp = γΔTl (with constant γ), was demonstrated by Cuffey and Vimeux . For the most recent 150 ka of the Vostok ice core time series, separating γ into local and source region terms γl and γs modified the ΔTl reconstruction such that the covariation of ΔTl with other variables changed by ∼20%. The separate treatment of ΔTs and ΔTl in (19) therefore also can have important consequences for the form of the reconstructed time series in some cases.
 We emphasize that (18) is viable (despite its simplicity) partly because ΔTl and ΔTs serve as proxies for the combined effects of changes in (possibly numerous) local and source region climate variables, respectively. The combined effects of both temperature and nontemperature variables are incorporated in the magnitudes of the sensitivities γl and γs. It should also be emphasized that the choice of temperature as the “proxy” is fundamental, not arbitrary; the physics of isotopic distillation dictate that temperature is a dominant control on δ through the temperature dependence of atmospheric water vapor content [Dansgaard, 1964].
 With reference to the model results discussed in Appendix B and Figure 5, comparing the magnitudes of the different source region effects, it is clear that source temperature changes have a greater capacity to alter the precipitation composition over the ice sheet than do purely hydrologic changes or changes in the isotopic composition of atmospheric vapor at the low-latitude limit. This is encouraging for the interpretation of ice core deuterium excess records in terms of source temperature rather than other variables. The very weak effect of purely hydrologic changes results from compensating changes in transport strength that must occur to establish a new steady state atmosphere, given that w has not changed. The modestly weak effect of the low-latitude boundary composition results from dilution of this signal by evaporative recharge along the oceanic part of the transport path.
 The magnitudes of the γ are obviously of great interest. Although analyses using GCMs equipped with isotopic tracers are necessary to quantitatively explore the combined effects of changes in multiple climate variables, ICM analyses can provide insight and guidance. Our ICM analyses have shown that:
 1.As proposed by Hendricks et al. , the net sensitivity γ does vary spatially, with generally lower values near the ice sheet margin and higher values in the interior. A factor of 2 variation in γ across Antarctica appears to be plausible. We have further shown that γs varies spatially (by a factor of 1.5–2), with larger values in the marginal zones, reflecting greater control there by oceanic source regions (Figures 7g and 7h). In contrast, γl appears to have little spatial variation (Figures 7i and 7j). The spatial variation in the net γ is therefore largely due to spatial variation of γs and to the magnitude of the ratio ΔTs/ΔTl in the imposed climate change scenarios (see equation (19)). The spatial variations in γ and γs indicate that ice cores taken from coastal sites like Law Dome should record climate changes differently than should cores taken from central East Antarctica.
 2.The modeled magnitudes of γ, γs, and γl depend significantly on changes in the geographic distribution of P and E. If contraction of P and E zones toward the equator occurs when the climate cools, γ is significantly higher and γs significantly lower than if P and E do not change or if P changes are controlled by changes in the meridional water content gradient.
 3.In central East Antarctica, the magnitude of γ is modeled to be similar to the magnitude of ∂δpD/∂T (measured as the modern spatial gradient of approximately 7‰ (°C)−1), though model results vary from ∼3‰ to ∼8‰ (°C)−1.
 4.Due to the substantial distillation of the marine signal, the magnitude of γm is approximately 4.5‰ (‰)−1, significantly less than 8. Erroneous use of γm = 8 has been nearly pervasive in earlier literature, including some of the most widely cited ice core manuscripts [Jouzel et al., 1993; Petit et al., 1999]. The magnitude of the marine correction has thus been consistently overestimated. To the best of our knowledge, credit for first correcting this error should be given to Vimeux et al. , although these authors do not draw attention to the error in earlier literature.
A1. Fractionation Factors
 Isotopic fractionation upon evaporation and precipitation are prescribed as follows. The isotopic composition δe of evaporation from the ocean surface is calculated assuming that the total fractionation factor for each isotopic species is the product of an equilibrium fractionation factor and a kinetic factor that accounts for the effects of vapor transport across a boundary layer separating the ocean surface from the free atmosphere [Merlivat and Jouzel, 1979]; thus α = αeαk. Equilibrium fractionation factors used for 18O and D are from the study of Horita and Wesolowski , and kinetic fractionation factors are from the study of Merlivat and Jouzel . In ice-covered regions of Antarctica, ice wastage is due largely to sublimation rather than evaporation, and recharge of atmospheric water vapor by this mechanism is assumed to occur without additional fractionation. Thus, the effect of sublimation in ice-covered regions is to simply reduce the net accumulation (P − E).
 Isotopic fractionation during condensation of rain droplets is assumed to be an equilibrium process and is calculated using factors from the study of Horita and Wesolowski . Fractionation during snow formation is thought to be influenced by the degree of supersaturation Si within the clouds [Jouzel and Merlivat, 1984]. Here the supersaturation is assumed to be linearly related to the cloud temperature Tc such that SI = c − FTc (here Tc is expressed in degrees Celsius). The strength of this kinetic effect is poorly constrained and is determined in this study by tuning the values of c and F (see section 2.3). Fractionation factors for ice–vapor equilibrium are from the studies of Majoube [1971a, 1971b].
A2. Condensation Temperature and Precipitate Composition
 The range of altitudes over which precipitation forms at a given latitude depends on such factors as the vertical temperature structure, atmospheric water vapor content, and strength of convective mixing within the air column. As a result, precipitate formation can occur over a significant vertical distance (and therefore temperature range), and thus precipitation collected at the Earth's surface comprises a mixture of condensates formed at different elevations. The isotopic content of this mixture will be a weighted average of the values of its constituents, modified by partial reequilibration that occurs as the precipitate falls to the surface. This reequilibration will in turn depend on such factors as the rate of fall, the temperature profile within the air column, and the condensate size. Rather than attempting to capture the complexity of this system, we adopt a very simple approach to prescribe the temperature of condensation; we assume that condensation everywhere occurs at an effective altitude of 1 km over the ground surface. Consequently, condensation over the ocean occurs at a temperature 6°C cooler than the mean annual ocean surface temperature. Over the ice sheet, condensation is assumed to occur at a temperature 6°C cooler than that at the top of the surface inversion layer. The lapse rate of −6° km−1 implied by this parameterization is appropriate for a moist atmosphere. If a lapse rate of −10° km−1 is assigned to ice-covered regions (corresponding to a dry adiabat), results similar to the base model (Figures 2 and 3) can be obtained by reducing the supersaturation parameter c to 1.02 (compared to c = 1.04 for the base model). Because the effective condensation elevation is poorly constrained, we will not consider this issue further in this study.
 Depending on ambient air temperature conditions, precipitation will form as either a liquid, a solid, or a mixture of these two phases. In this study, we assume that only solid precipitate is formed at temperatures lower than −40°C and that only liquid condenses above 0°C. Between these temperatures, the proportion of ice and liquid is prescribed as a smoothly varying error integral, scaled such that an even mixture of snow and ice occurs at a temperature of −20°C [cf. Ciais and Jouzel, 1994].
A3. Modeled Transport Paths
 In this study, we have examined water vapor transport along two different trajectories, which follow the path taken during the 1990 International Trans-Antarctica Expedition [Dahe et al., 1994]. This choice of trajectories allows comparison of modeled δp and dp values with measurements taken during the survey. The purpose of defining two distinct trajectories is primarily to capture the different surface temperature distributions T(θ) along them and the different positions of the boundary between ice and open ocean. Both of these differences arise from asymmetry of the Antarctic continent about the Vostok region. The oceanic portions of the two trajectories have minor differences in climatic parameters, but these are found to have only minor effects on the calculated δ.
 The first trajectory, which we refer to as path 1, was used by Hendricks et al.  and starts in the southern Pacific Ocean, traversing Antarctica from the western hemisphere. The second, more relevant trajectory examined here was introduced by Kavanaugh and Cuffey  and will be referred to as path 2. This path originates in the southeastern Indian Ocean and traverses Antarctica directly from the north. As mentioned above, moisture transported along path 2 accounts for approximately 50% of precipitation at Vostok compared to ∼20% for that for path 1 [Delaygue et al., 2000]. Model integration along both paths begins at a latitude of 25.5°S, which is within the equatorial evaporation-dominated zone. Because the Antarctic Plateau is not symmetric about the South Pole, minimum values for T, , P − E, and δp are not reached at the pole but rather at a location near Vostok (which is located near the center of the Antarctic Plateau at 78°28′S, 106°48′E). For this reason, we adopt the shifted coordinate system of Hendricks et al.  and Kavanaugh and Cuffey  in which Vostok is defined as the model “South Pole” (i.e., the point of symmetry with respect to vapor transport). Because path 2 rises directly from the Indian Ocean onto the East Antarctic Plateau, much higher values for ∂T/∂θ characterize the ice sheet portion of this path than is the case for path 1, which traverses the entire West Antarctic ice sheet. Correspondingly, the oceanic portion of the path 2 trajectory is substantially longer than that for path 1. The pattern of net precipitation (P − E) on the ice sheet, which is known from ice accumulation rate measurements (see below), also differs. In oceanic regions, the relationship between T and the variables , P, and E is taken to be the same for both paths, so spatial differences in these arise only from differences in T(θ) (see below).
 For path 2, Antarctic temperature and net accumulation are, respectively, from the studies of Dahe et al.  and Huybrechts'  application of Fortuin and Oerlemans . Oceanic surface temperatures are taken as the average of mean January and July temperatures for the southern Indian Ocean region from the study of Shea . In this region P and E are calculated from T using the P(T(θ)) and E(T(θ)) relationships from path 1.
 The atmospheric water content (θ) for both paths is a prescribed function of the surface temperature T, also from the study of Hendricks et al. . In ice-covered regions, the decreased atmospheric height over the Antarctic plateau and the positive lapse rate within the surface temperature inversion layer are also taken into account. The relative humidity Rh(θ) at the ocean surface is calculated as a function only of ocean surface T, as a linear relationship with dRh/dT = −0.5%(°C)−1. This provides a rough match to the humidity data shown by Broecker .
A5. Solution Method
 Model integration was performed using an explicit fourth-order Runge–Kutta numerical solver. First, the diffusivity k(θ) and horizontal water vapor transport velocity v(θ) are calculated by integrating the expressions for the diffusive and advective divergences Dk and Dv ((9b) and (9c)). Integration of these equations begins at the model pole (Vostok) and proceeds toward the equator. Initial integration values ∂k/∂θ = 0 and = 0 at the pole result from the assumption of zonal symmetry about the pole. After k(θ) and v(θ) have been determined, the expression for latitudinal δ variations (10) is integrated to calculate δp18O(θ) and δpD(θ). At the low-latitude limit, initial δa values are prescribed (as described above), and integration proceeds to the model pole. The solution is obtained by iteratively solving for the initial low-latitude value of ∂δa/∂θ that yields ∂δa/∂θ = 0 at the pole for each of the two isotopic species (as required by the assumption of zonal symmetry about the pole).
B1. Source Region Perturbation Experiments
Kavanaugh and Cuffey  demonstrated that the deuterium excess d is affected by a wide variety of source region changes, and that modeled source region climate changes that give rise to variations in Antarctic dp result in anticorrelated changes in δpD, with values of ΔδpD/Δdp of ≈−1.4 to −3.5. In this appendix, we investigate whether these conclusions hold true for the corrected and mixed advective diffusive model developed herein.
 The first source region perturbation examined is that of a simple change in the isotopic composition of atmospheric water vapor at the low-latitude boundary. Increasing these atmospheric δa18O and δaD values by +1.0‰ and +8‰, respectively, preserves the deuterium excess da of the base model at this location. As in the study of Kavanaugh and Cuffey , this causes a measurable change in deuterium excess over the ice sheet even without any change in deuterium excess of either the evaporation or initial atmospheric water vapor (Figures 5a and 5b (long dashes) and Table 1). Changes in δpD and dp over the ice sheet are anticorrelated.
 The next two experiments involve changing the amount of precipitation in the source region (i.e., the entire oceanic portion of the path), with no other along-path changes. In the first case, precipitation is increased as follows: At the low-latitude limit, a 100 mm a−1 (∼15%) increase is prescribed. The precipitation increase is reduced linearly to the ice edge, where no increase is prescribed. Precipitation over the ice sheet is unchanged. The increased source region precipitation results in an atmosphere in which net distillation over the ocean is increased, resulting in slightly lower δpD values and increased dp values at Vostok (Figures 5c and 5d (short dashes) and Table 1).
 In the second case, precipitation at the low-latitude limit is decreased by 100 mm a−1, and the magnitude of this decrease is reduced linearly to the ice edge, where there is no change in precipitation. Precipitation over the ice sheet is again unchanged. As a result of these changes, the relative importance of evaporative recharge is increased over the oceans, yielding decreased net distillation in the source region and producing changes with similar magnitude but opposite sign to those observed in the previous scenario (Figures 5c and 5d (long dashes) and Table 1). In both of these scenarios, anticorrelated changes in δpD and dp over the ice sheet are seen.
 The following two experiments explore the effects of a source region cooling. For these experiments, a 5°C cooling of the surface is prescribed at the low-latitude limit. The magnitude of cooling decreases linearly to 0°C at the ice edge, and ice sheet temperatures are unchanged. In the first of these two experiments, the atmospheric water content is scaled with the surface temperature such that w = w0(T), where w0(T) is the water content–surface temperature relationship in the unperturbed case. No changes to the precipitation P or evaporation E are made. This source region cooling scenario results in decreased fractionation, higher δpD values and lower dp values (Figures 5e and 5f (short dashes) and Table 1).
 In the second source region cooling experiment, both the water content and the evaporation are scaled with the surface temperature, such that w = w0(T) and E = E0(T). In addition, the precipitation is scaled by the change in the latitudinal water content gradient:
In comparison with the previous case, these changes cause an even greater decrease of net distillation, yielding greater changes in δpD and dp (Figures 5e and 5f (long dashes) and Table 1). As in the previous source region perturbation experiments, these temperature change scenarios result in anticorrelated changes in δpD and dp.
 All of these calculations support the conclusions of Kavanaugh and Cuffey . The dp of Antarctic precipitation responds to changes in a variety of source region parameters, some of which are unrelated to the deuterium excess of the evaporate. This arises from the dependence of distillation on both temperature-dependent fractionation factors and on cumulative distillation itself (specifically, on 1 + δ), which are both different for 18O and D. Furthermore, the effects of source region changes on δpD and dp are anticorrelated.
Cloud supersaturation parameter
Source region climate variable
Deuterium excess of atmospheric water vapor
Deuterium excess of ocean water
Deuterium excess of precipitate
Zonally averaged total atmospheric divergence
Zonally averaged diffusive atmospheric divergence
Zonally averaged advective atmospheric divergence
Zonally averaged mean annual evaporation
Zonally averaged mean annual evaporation, base model
Diffusive transport fraction
Cloud supersaturation parameter
Zonally averaged latitude-dependent diffusivity
Zonally averaged mean annual precipitation
Zonally averaged mean annual precipitation, base model
Total local 3-D atmospheric water flux
Total local 3-D atmospheric water flux, vertical component
Vertically integrated advective atmospheric water flux
Mean radius of the Earth
Degree of cloud supersaturation
Local ice region surface temperature
Source region surface temperature
Height-dependent advective atmospheric water transport velocity
Vertically integrated advective atmospheric water transport velocity
Height-dependent atmospheric water content
Vertically integrated atmospheric water content
Vertically integrated atmospheric water content, base model
Total fractionation factor
Equilibrium fractionation factor
Kinetic fractionation factor
Total temporal sensitivity of d to temperature changes
Temporal sensitivity of d to source region climate variable Cj
Temporal sensitivity of d to local ice sheet temperature changes
Temporal sensitivity of d to source region temperature changes
Total temporal sensitivity of δD to temperature changes
Temporal sensitivity of δD to source region climate variable Cj
Temporal sensitivity of δD to local ice sheet temperature changes
Temporal sensitivity of δD to changes in marine isotopic composition
Temporal sensitivity of δD to source region temperature changes
Relative change in the isotopic ratio for a given species
Relative change in the atmospheric isotopic ratio for a given species
Isotopic composition difference between evaporate and atmospheric water vapor
Isotopic composition difference between precipitate and atmospheric water vapor
Relative change in the evaporative isotopic ratio for a given species
Relative change in the marine isotopic ratio for a given species
Relative change in the precipitative isotopic ratio for a given species
Marine sediment core correction factor
Ratio of isotopic sensitivities βj/γj
Local net water vapor source rate
 We are grateful to Melissa Hendricks for helpful discussions and for supplying us with inputs for the model runs to make possible direct comparison to her results. We also thank the efforts of W. Reeburgh, J. Severinghaus, and an anonymous reviewer in improving the manuscript. This work was supported in part by NSF OPP-018035.