Can we determine what controls the spatio-temporal distribution of d-excess and 17 O-excess in precipitation using the LMDZ general circulation model?

Abstract. Combined measurements of the H218O and HDO isotopic ratios in precipitation, leading to second-order parameter D-excess, have provided additional constraints on past climates compared to the H218O isotopic ratio alone. More recently, measurements of H217O have led to another second-order parameter: 17O-excess. Recent studies suggest that 17O-excess in polar ice may provide information on evaporative conditions at the moisture source. However, the processes controlling the spatio-temporal distribution of 17O-excess are still far from being fully understood. We use the isotopic general circulation model (GCM) LMDZ to better understand what controls d-excess and 17O-excess in precipitation at present-day (PD) and during the last glacial maximum (LGM). The simulation of D-excess and 17O-excess is evaluated against measurements in meteoric water, water vapor and polar ice cores. A set of sensitivity tests and diagnostics are used to quantify the relative effects of evaporative conditions (sea surface temperature and relative humidity), Rayleigh distillation, mixing between vapors from different origins, precipitation re-evaporation and supersaturation during condensation at low temperature. In LMDZ, simulations suggest that in the tropics convective processes and rain re-evaporation are important controls on precipitation D-excess and 17O-excess. In higher latitudes, the effect of distillation, mixing between vapors from different origins and supersaturation are the most important controls. For example, the lower d-excess and 17O-excess at LGM simulated at LGM are mainly due to the supersaturation effect. The effect of supersaturation is however very sensitive to a parameter whose tuning would require more measurements and laboratory experiments. Evaporative conditions had previously been suggested to be key controlling factors of d-excess and 17O-excess, but LMDZ underestimates their role. More generally, some shortcomings in the simulation of 17O-excess by LMDZ suggest that general circulation models are not yet the perfect tool to quantify with confidence all processes controlling 17O-excess.


Introduction
Water-stable isotopic measurements in ice cores have long been used to reconstruct past climates. In particular, the H 18 2 O and HDO isotopic ratio (expressed, respectively through δD and δ 18 O) in polar ice cores have long been used as a proxy of past polar temperature (Johnsen et al., 1972;Lorius et al., 1979;Jouzel, 2003). Combined measurements of H 18 2 O and HDO isotopic ratio in precipitation, leading to second-order parameter D-excess (d-excess = δD − 8 δ 18 O, Dansgaard, 1964), have provided additional constraints on past climates compared to the H 18 2 O or HDO ratios alone. Its interpretation is however more complex. First interpreted as a tracer of relative humidity conditions at the moisture source (Jouzel et al., 1982), it was later interpreted in terms of the the effect of this combination of processes, isotopic GCMs are invaluable. For example, isotopic GCM simulations have been exploited to understand how δ 18 O and d-excess relate to the origin of water vapor (e.g. Delaygue, 2000;Werner et al., 2001;Noone, 2008;Masson-Delmotte et al., 2011). The drawback of these GCM studies is however the difficulty of GCMs to simulate some aspects of observed d-excess variability. For example, simulated daily d-excess variations in the water vapor or in the precipitation are too flat (Risi et al., 2010b;Steen-Larsen et al., 2013) and simulated d-excess variations at the paleo-climatic scale are always of opposite sign compared to δ 18 O even when observed variations are of the same sign (Werner et al., 2001;Noone, 2008). This difficulty reflects the complexity of the d-excess variable and our lack of understanding of its major controlling factors. This difficulty is expected to be even more severe for 17 O-excess.
To our knowledge, this is the first time 17 O-excess simulations with a GCM are being documented. The first goal of this paper is thus to document the performance of GCMs in capturing observed spatio-temporal variations in 17 O-excess. This allows us to better assess the feasibility of using a GCM to investigate what controls 17 O-excess. For features that the model can capture well, we use the GCM to disentangle the different processes controlling 17 O-excess and contrast them with processes controlling δ 18 O and d-excess. For features that the model cannot capture well, we suggest possible causes of mismatches. As a first study of 17 O-excess in a GCM, we focus on latitudinal gradients, seasonal variability and difference between the Last Glacial Maximum (LGM) and present-day (PD).
In Sect. 2, we describe the model simulations, data sets and methodology. In Sect. 3, we evaluate the model isotopic simulations. In Sect. 4, we quantify the factors controlling the δ 18 O, d-excess and 17 O-excess distributions simulated by LMDZ and discuss implications for the factors in the real world. In Sect. 5, we summarize our results and present perspectives for future work.

The LMDZ4 model and isotopic implementation
LMDZ4 (Hourdin et al., 2006) is the atmospheric component of the Institut Pierre-Simon Laplace coupled model (IPSL-CM4, Marti et al., 2005) used in CMIP3 (Coupled Model Intercomparison Project, Meehl et al., 2007). It is used here with a resolution of 2.5 • in latitude, 3.75 • in longitude and 19 vertical levels. The physical package includes the Emanuel convective scheme (Emanuel, 1991;Emanuel and Zivkovic-Rothman, 1999), coupled to a statistical cloud scheme (Bony and Emanuel, 2001) which diagnoses convective cloud fraction from a radiative point of view. Precipitation can be created either by the convective scheme or by a large-scale Clim. Past, 9, 2173-2193, 2013 www.clim-past.net/9/2173/2013/ condensation scheme. The large-scale condensation scheme is also based on a statistical cloud scheme (Letreut and Li, 1991). The impact of tuning parameters in this statistical cloud scheme on water isotopic compositions are limited to the upper troposphere . Water vapor and condensate are advected using a second-order monotonic finite volume advection scheme (Van Leer, 1977;Hourdin and Armengaud, 1999). The isotopic version of LMDZ is described in detail in Risi et al. (2010b). Equilibrium fractionation coefficients between vapor and liquid water or ice are calculated after Merlivat and Nief (1967), Majoube (1971a) and Majoube (1971b). The isotopic composition of the ocean surface evaporation flux is calculated following Craig and Gordon (1965). We take into account kinetic effects during the evaporation from the sea surface following Merlivat and Jouzel (1979) and during snow formation following Jouzel and Merlivat (1984), with the supersaturation parameter λ set to 0.004 to optimize the simulation of d-excess over Antarctica (Risi et al., 2010b). This λ value is consistent with that found to optimize the simulation of both d-excess and 17 O-excess in both Antarctica and Greenland in simpler models (Landais et al., 2012a,b). We make the simplifying assumption that over land, all evapotranspiration occurs as transpiration (e.g. Hoffmann et al., 1998), which is non-fractionating (Washburn and Smith, 1934; Barnes and Allison, 1988 Barkan and Luz, 2005;Landais et al., 2012b). The diffusivity of H 17 2 O relatively to that of H 16 2 O is assumed to be that for H 18 2 O at the power 0.518 (Barkan and Luz, 2007). We do not consider the effect of methane oxidation on the stratospheric water isotopic composition (Johnson et al., 2001;Zahn et al., 2006). This is a reasonable approximation since we focus on the isotopic composition of the precipitation and of low-level vapor. It has been shown that in Central Antarctica, stratospheric intrusions may play a role in the inter-annual variability of Vostok precipitation 17 O-excess, but the role of these intrusions in the spatial and seasonal distribution of 17 O-excess and in its LGM-to-present variation is unclear.
The implementation of stable water isotopes in the convective scheme has been extensively described in Bony et al. (2008). In convective updrafts, condensation is assumed to be a closed process (i.e. vapor-condensate equilibrium) for the liquid phase (above −40 • C) and an open process (i.e. Rayleigh distillation) for the ice phase (below 0 • C). We pay particular attention to the representation of the re-evaporation and diffusive exchanges as the rain falls, which is significantly more detailed compared to other GCMs: at each time step and at each level, the model takes into account the evolution of the compositions of both the rain and the surrounding vapor as the rain drops re-evaporate (Bony et al., 2008), whereas most GCMs take into account the evolution of the composition in the rain only. The relative proportion of evaporative enrichment and diffusive equilibration is calculated at each level depending on surrounding relative humidity following Stewart (1975). The surrounding relative humidity is calculated as φ + (1 − φ) · h ddft with h ddft being the relative humidity in the environment of the rain drops, i.e. in the unsaturated downdraft that collects the precipitation for convective precipitation, or in the large-scale environment for large-scale precipitation. The parameter φ was set to 0.9 to optimize the simulation of δ 18 O and d-excess in tropical rainfall and their relationship with precipitation rate (Risi et al., 2010b), although φ = 0.8 is in better agreement with some 17 O-excess data (Landais et al., 2010). When the relative humidity is 100 % we simply assume total reequilibration between raindrops and vapor, contrary to Stewart (1975) and , who take into account the raindrop size distribution in this particular case. To calculate fractionation coefficients, the temperature at each level in the environment of the rain drops is used, i.e. in the unsaturated downdraft for convective precipitation or in the large-scale environment for large-scale precipitation.
Our calculation of isotopic exchanges during rain reevaporation involves in the general case the numerical solution of an integral (Bony et al., 2008). The number of iterations used in this solution was chosen to be sufficient to accurately predict δ 18 O and d-excess, but was found to be insufficient to predict 17 O-excess. The number of iterations was thus multiplied by 2, which makes the simulation with H 17 2 O computationally slower than usual.

Model simulations
Due to computational limitations, all simulations are short (2-3 yr) but use as initial states outputs of simulations that have already been equilibrated for several years for all isotopes.
To compare with data sets, LMDZ is forced by observed sea surface temperatures (SST) and sea ice following the AMIP (Atmospheric Model Inter-comparison Project) protocol (Gates, 1992) for the year [2005][2006]. The year 2005-2006 was chosen to allow daily collocation with the vapor data set of Uemura et al. (2010). Horizontal winds at each vertical level are nudged by ECMWF reanalyses (Uppala et al., 2005) as detailed in Risi et al. (2010b). This ensures a realistic large-scale circulation. When comparing with the other data sets, some of the model-data difference could be attributed to the differences in the meteorological conditions between [2005][2006] and the year of the measurement. Ideally, the full period 2000-2010 should have been simulated and outputs should have been collocated with each measurement for a perfectly rigorous comparison. However, for the first GCM evaluation for 17 O-excess, we focus on broad latitudinal gradients and seasonal variations that are robust with respect to inter-annual variability.
www.clim-past.net/9/2173/2013/ Clim. Past, 9, 2173-2193, 2013 To investigate controls at paleo-timescales, we focus on the LGM period for which a large number of paleo-climate proxies are available (e.g. Farrera et al., 1999;Bartlein et al., 2010) and the forcing is relatively well-known (Braconnot et al., 2007) and strong. For the PD control simulation, LMDZ is run without nudging and forced by climatological AMIP SSTs averaged over 1979-2007. For the LGM simulation, the PMIP1 protocol is applied (Joussaume and Taylor, 1995). LMDZ is forced by SSTs and sea ice from the Lon-gRange Investigation, Mapping, and Prediction (CLIMAP, CLIMAP, 1981) forcing. Orbital parameters and greenhouse gas concentrations are also set to their LGM values. ICE-5G ice sheet conditions are applied (Peltier, 1994). This simulation is described in Risi et al. (2010b). We use CLIMAP rather than the SSTs simulated by a coupled model (as in the PMIP2 protocol, Braconnot et al., 2007), because the SSTs and sea ice simulated by the IPSL model at LGM are unrealistically warm in the Southern Ocean (Risi et al., 2010b). As a consequence, evaporative recycling over high latitude oceans is too strong and δ 18 O is unrealistically enriched at LGM (though d-excess is in slightly better agreement with observations) (Risi et al., 2010b). We are aware of the caveats of the CLIMAP forcing. In particular, the warm tropical SSTs and the extensive sea ice of the CLIMAP reconstruction have been questioned (MARGO project members, 2009). However, since our LGM evaluation will focus on Antarctica, where most of the 17 O-excess so far have been available for LGM, we prefer the caveats of CLIMAP than those of the IPSL model.

Data sets for model evaluation
To evaluate the present-day nudged simulation of δ 18 O and d-excess, we use the GNIP (Global Network of Isotopes in Precipitation) data set (Rozanski et al., 1993) as is done in all basic isotopic modelling publications (Hoffmann et al., 1998;Risi et al., 2010b). This data set was complemented with Antarctica (Masson-  and Greenland (V. Masson-Delmotte, personal communication, 2008) data and was regridded on the LMDZ grid by attributing to each LMDZ grid the average of all measurements falling into this grid.
For 17 O-excess, we use a set of meteoric water measurements compiled by Luz and Barkan (2010). This includes measurements in precipitation, snow, rivers and lakes (Table 1). We compare observed composition in the precipitation and in the snow to the simulated composition in the precipitation for the particular month of sampling. For the snow, we neglect post-depositional effects (e.g. Taylor and Renshaw, 2001;Gurney and Lawrence, 2004;Ekaykin et al., 2009;Lee et al., 2010). This is a reasonable assumption since seasonal cycles of δ 18 O, d-excess and 17 O-excess measured in shallow cores compare well with those measured directly in the precipitation (Landais et al., 2012b). We compare observed composition in river water to the simulated annual-mean composition in the precipitation. In reality, river water composition integrates precipitation water over the previous months and over the entire watershed (Kendall and Coplen, 2001). It is additionally affected by evaporative enrichment ) and by temporal variations in drainage and runoff (Dutton et al., 2005). Coupling LMDZ with the land surface model ORCHIDEE , equipped with a routing scheme (Polcher, 2003) and enabled with water isotopes , would be necessary to rigorously compare the model to river observations. This is beyond the scope of this paper, and this is why here we simply assume that river water is representative of the annual-mean precipitation. This assumption is justified by the fact that the isotopic seasonality in river water is usually strongly dampened relatively to that in the precipitation (Kendall and Coplen, 2001).
We add to this set some 17 O-excess measurements made at LSCE (Table 2): monthly-mean precipitation in the Zongo Valley in Bolivia (Vimeux et al., 2005, unpublished for dexcess and 17 O-excess), in Niamey (Niger, Landais et al., 2010), in NEEM (Greenland, Landais et al., 2012b) and in Vostok (Antarctica, Winkler et al., 2012). In Vostok the flow is taken into account in the age scale, though this has little impact on the last glacial-interglacial transition. We also add δ 18 O, d-excess and 17 O-excess measurements along an Antarctica transect . To evaluate the composition of the water vapor, we use the δ 18 O, d-excess and 17 O-excess measurements made during Southern Ocean cruises in . Finally, we use the isotopic composition measured from PD to LGM in several Antarctica ice cores: Vostok , Taylor Dome and Dome C (Winkler et al., 2012) (Table 3). The precision of these measurements is about 5 per meg (Landais et al., 2006).
Although 17 O-excess measurements are now calibrated with respect to two international standards (Schoenemann et al., 2013), there are calibration issues affecting absolute measurements of 17 O-excess (Winkler et al., 2012;Landais et al., 2012a   collected in precipitation or rivers. We did not select lakes, caves or ponds in order to avoid samples affected by re-evaporation after rainfall. Based on land surface isotopic modelling (e.g. Fekete et al., 2006;) and observations (Kendall and Coplen, 2001), we assume that river water is close to annualmean precipitation. For rivers, we thus compare with annual mean simulated precipitation composition. When several samples are taken at the same location in the same season, we present averages. Precipitation composition is first decomposed into two terms: The first term, R v , is the vapor composition. It results from all processes affecting the isotopic composition of the vapor upstream air mass trajectories. The second term is the precipitation-vapor difference. This reflects local condensation and post-condensation processes, since precipitation is produced and falls locally. In the tropics, where the precipitation is liquid, R p − R v will mainly reflect rain reevaporation and vapor-liquid exchanges during the rainfall.
At high latitudes, precipitation is solid. The diffusion of water molecules in ice is too low to allow for isotopic exchanges during the fall of snow (Jouzel, 1986). Therefore, R p − R v will rather reflect the condensation altitude, temperature and rate. It can also depend on the vertical gradient of water vapor isotopic composition between the surface and the condensation altitude.
Then, several sensitivity tests are used to understand what controls the vapor composition R v . Since 17 O-excess has been shown to be affected by evaporative conditions at the moisture source and to be sensitive to kinetic fractionation during ice condensation, we quantify preferentially these two kinds of effects. To quantify the effect of evaporative conditions, we make additional simulations in which the sea surface temperature (SST) or the relative humidity normalized by the surface temperature (RH s ) during the calculation of isotopic fractionation at ocean evaporation are fixed. This allows us to quantify the direct effect of SST and RH s at the moisture source without changing anything www.clim-past.net/9/2173/2013/ Clim. Past, 9, 2173-2193, 2013 in the dynamics or in the hydrological cycle of the simulation. We call RH s cste the simulation in which the RH s is set to 60 % during the calculation of isotopic fractionation at ocean evaporation. The effect of RH s at the source is thus R RH s = R v,control −R v,RH s cste . We call RH s SSTcste the simulation in which the SST is set to 15 • C and the RH s is set to 60 % during the calculation of isotopic fractionation at ocean evaporation. The effect of SST at the source is thus To quantify kinetic fractionation during ice condensation, we perform an additional simulation (called nokin) in which this fractionation is turned off, i.e. λ is set to 0. The effect of kinetic fractionation during ice condensation is thus Assuming that all processes add up linearly, we can thus decompose R v into four terms: (1) The first term on the right-hand side represents all the processes other than evaporative conditions and kinetic fractionation during ice condensation. In the tropics, this may represent for example convective mixing by unsaturated downdrafts (Risi et al., 2008a, more details in Sect. 4.3.1). In higher latitudes, this represents Rayleigh distillation along trajectories and mixing between vapor from different air masses. Note that the assumption that all processes add up linearly is valid for δ 18 O and for 17 O-excess, but may lead to uncertainties of up to 1 ‰ for d-excess in very cold regions (Supplement). In the remaining of the paper, we will focus on d-excess variations larger than this uncertainty.

Model evaluation
We first evaluate the simulation of the triple isotopic composition in the water vapor, and then in the precipitation.

Water vapor isotopic composition
Few observations are available for 17 O-excess in the water vapor. We compare LMDZ with water vapor isotopic composition measured in the near-surface vapor along Southern Ocean transects (Uemura et al., , 2010. When going poleward, observed δ 18 O decreases consistently with the distillation of air masses (Fig. 1a, red). At the same time, dexcess and 17 O-excess decrease (Fig. 1b, c). This is consistent with the effect of evaporative conditions on d-excess and 17 O-excess (Vimeux et al., 2001a;Landais et al., 2008;Risi et al., 2010c). The RH s increases poleward (Fig. 1d) while the SST decreases. Both RH s and SST effects contribute to the poleward decrease of d-excess and 17 O-excess (Appendix A).
The Merlivat and Jouzel (1979) Merlivat and Jouzel (1979) closure equation, the "total" slope corresponds to the regression lines shown in blue and green in Fig. 1e, f. The "RH s effect" is calculated by the difference between the "total" slope and the slope that we would obtain if RH s was set to 60 % everywhere (RH s cste simulation for LMDZ). The "SST effect" is calculated by the difference between the slope that we would obtain if RH s was set to 60 % everywhere, and the slope that we would obtain if RH s was set to 60 % everywhere and if SST was set to 15 • C everywhere (RH s SSTcste simulation for LMDZ). ture some processes, such as boundary layer mixing with the free troposphere, act to dampen the 17 O-excess sensitivity to evaporative conditions. The water vapor composition at the lowest model level simulated by LMDZ is compared to the data for each measurement day and location. LMDZ captures the RH s distribution as a function of latitude well, with an increase in RH s with latitude (Fig. 1a, Table 4). The lack of sensitivity of dexcess to RH s in LMDZ was already noticed when comparing to water vapor measurements in Greenland (Steen-Larsen et al., 2013).
This lack of sensitivity could be due to several kinds of problems. First, there could be problems in the composition of the evaporation flux. However, this does not appear to be the case, since the Merlivat and Jouzel (1979) closure approximation, which applies the same Craig and Gordon (1965) equation as in LMDZ, is in good agreement with the observations (Fig. 1e, f). Using the RH s SSTcste and RH s cste simulations, we estimate that LMDZ underestimates the RH s and SST effects in similar proportions: 37 and 31 %, respectively (Table 4). This suggests that in LMDZ, the sensitivity to SST and to RH s are dampened by some atmospheric processes that are unrelated to evaporative conditions. Second, there could be some altitude mismatch between the near-surface vapor collected on the ship (a few meters), and the vapor of the first layer of the model (0-130 m). This hypothesis is supported by the fact that the simulated δ 18 O latitudinal gradient in the low-level vapor is steeper than in that observed in the near-surface vapor (Fig. 1a). As a simple interpolation, we calculate near-surface vapor δ 18 O as www.clim-past.net/9/2173/2013/ Clim. Past, 9, 2173-2193, 2013  Uemura et al. (2008Uemura et al. ( , 2010 and simulated by LMDZ, as a function of surface relative humidity RH s . Model outputs were collocated with the measurements. Regression coefficients for both simulated and observed values are indicated in Table 4. For comparison, the d-excess and 17 O-excess of surface water vapor predicted by the Merlivat and Jouzel (1979) closure approximation (Appendix A) is also shown in green. For clarity, we show only the regression line. Sensitivity tests using the LMDZ model (purple and cyan) are detailed in the text a mixture between the low-level vapor and the evaporation flux. When doing so, the δ 18 O latitudinal gradient becomes less steep (Fig. 1a, cyan). Quantitatively, adding 7 % of surface evaporation appears optimal to match the observed variations in near-surface δ 18 O. However, adding 7 % of evaporation flux has little influence on d-excess and 17 O-excess (Fig. 1b, c, cyan). Therefore, the altitude mismatch is unlikely to explain the d-excess and 17 O-excess mismatch. Third, there could be problems in the boundary layer parameterization. If the boundary layer mixing is too strong, then the evaporative signal in the near-surface vapor may be dampened by advection of free-tropospheric air. Simulated latitudinal gradients of d-excess and of 17 O-excess in the free troposphere are smoother (or even reverted in the case of mid-and upper tropospheric d-excess) than near the surface (Fig. 2). A weaker vertical mixing might thus improve the results. To test this hypothesis, the mixing length scale used in the boundary layer parameterization is halved (Fig. 1 purple). However, this does little to improve d-excess or 17 O-excess.
Fourth, there could be all kinds of other problems affecting the latitudinal gradients in the free-tropospheric vapor, which is entrained into the boundary layer. In particular, some pro- cesses in the subtropics that lower the tropospheric d-excess and 17 O-excess could be oversimulated in the model (e.g. liquid condensation for d-excess, mixing for 17 O-excess), and other processes that increase the tropospheric d-excess and 17 O-excess could be undersimulated (e.g. rain drop reevaporation). The range of processes that could be misrepresented is very large and the sensitivity tests that we have done so far have not allowed us to identify the culprit yet. Measurements of horizontal and vertical gradients in water vapor composition during cruises and aircraft campaigns would be useful to elucidate this problem. In the meanwhile, when interpreting the results in Sect. 4, we need to remember that the effect of evaporative conditions will be likely underestimated.

Spatial distribution
The simulated spatial patterns of annual mean δ 18 O, d-excess and 17 O-excess in precipitation are compared with observations in Fig. 3. The latitudinal gradients are summarized in Fig. 4. In the latter figure, model outputs and observations are collocated for a more quantitative comparison.
The simulated annual mean spatial and zonal distribution of δ 18 O and d-excess were already extensively evaluated in Risi et al. (2010b). Spatial patterns of δ 18 O are very well captured, including the main "effects" that have long been documented (Dansgaard, 1964;Rozanski et al., 1993): latitudinal gradient associated with the temperature effect, the land-sea contrast with more depleted values over land associated with the continental effect, and the depletion of the South Asia-Western Pacific region, associated with the amount effect. The root mean square error of simulated δ 18 O is 3.5 ‰ globally. The latitudinal gradient in polar regions is underestimated, due to the warm bias in these regions (Risi et al., 2010b   Spatial patterns for d-excess are also relatively well captured: a minimum in the Southern Ocean and over the coasts of Antarctica, a minimum over northwestern America and Alaska, a minimum over the Sahel region (associated with rain re-evaporation; Risi et al., 2008b) and a maximum over the Mediterranean and Middle East region (interpreted as the effect of strong kinetic fractionation during sea surface evaporation in a dry environment, Gat et al., 1996). Even the land-sea contrast with higher values over land, traditionally interpreted as the effect of fractionation during continental recycling (Gat and Matsui, 1991), is well captured by the model even without representing this process. The latitudinal structure, with a local minimum near the equator, maxima in the subtropics, a strong poleward decrease in midlatitudes, and a poleward increase in high latitudes (> 60 • ), are well captured (Fig. 4). The root mean square error is only 3.2 ‰ globally.
It is surprising that LMDZ simulates the latitudinal gradient of precipitation d-excess well, while it had difficulties simulating it in the vapor. In particular in the subtropics, precipitation d-excess has the right mean value in spite of the va- It could be that d-excess in precipitation reflects the d-excess in the vapor at a level where LMDZ would agree better with observations, if such observations existed. It could also be that the correct values of precipitation d-excess arises from a compensation of errors. In particular, the parameter φ controlling kinetic fractionation during rain re-evaporation was tuned to optimize precipitation d-excess (Risi et al., 2010b). Simultaneous measurements of d-excess in both vapor and precipitation would be very helpful to ensure that tuning φ does not lead to error compensations.
No coherent spatial pattern for 17 O-excess emerges from the sparse data available. Measured values range from about 0 to 50 per meg. The values simulated by LMDZ are within this range, except in Antarctica and Greenland where values are underestimated by about 40 per meg. Outside these two regions, the root mean square error is 13 per meg. The underestimate of 17 O-excess in subtropical water vapor source (Sect. 3.1) could contribute to the underestimate of polar 17 O-excess. As will be detailed in Sect. 4.4, uncertainties in supersaturation parameter λ and in the equilibrium fractionation and diffusivity coefficients may also contribute to LMDZ difficulties in simulating polar 17 O-excess.

Seasonal variations
The 2.7 ‰. In the tropics, precipitation is more depleted during the wet season, consistent with the amount effect. Poleward of 35 • latitude, precipitation is more depleted in winter, consistent with the temperature effect (Dansgaard, 1964). The broad pattern of d-excess seasonality is well captured. In most regions of the globe, observed d-excess is lower in summer of each hemisphere, especially in the subtropics. This is also the case in LMDZ, but with less noise. The root mean square error is 4.8 ‰. The d-excess seasonality in high latitudes has often been interpreted as the effect of evaporative conditions at the moisture source (e.g. Delmotte et al., 2000). It is surprising that although LMDZ underestimates the d-excess sensitivity to evaporative conditions (Sect. 3.1), LMDZ is able to capture the observed d-excess seasonality in northern high latitudes. This may be because d-excess seasonality in these regions arises at least partly from processes other than changes in evaporative conditions. LMDZ fails to simulate the higher d-excess in winter in Central Antarctica. As will be detailed in Sect. 4.4, this could be associated with uncertainties in the supersaturation parameter λ.
We have only three sites where seasonal cycles of 17 Oexcess in precipitation are available: in Greenland, Antarctica and Bolivia. Observed 17 O-excess is 15 per meg lower in summer in Greenland, a few per meg higher in winter in Antarctica, and 22 per meg lower during the dry season in Bolivia. LMDZ fails at capturing the correct seasonality at all sites.
Simulated d-excess and 17 O-excess in tropical regions are very sensitive to the choice of the re-evaporation parameter φ. Figure 6 shows the sensitivity of δ 18 O, d-excess and 17 O-excess to this parameter. When φ = 0, the relative humidity around rain drops is that of the environment and kinetic fractionation is stronger. In this case, δ 18 O increases  and d-excess and 17 O-excess decrease especially in dry regions. Over the Bolivian site however, tuning φ is not sufficient to reach model-data agreement. In observations, 17 Oexcess is 22 per meg lower during the dry season than during the wet season, possibly due to more rain re-evaporation during the dry season. However, even with φ = 0 (maximum kinetic fractionation during re-evaporation), 17 O-excess is only 3 per meg lower during the dry season than during the wet season. Therefore, processes other than re-evaporation may be at play in this region, and LMDZ does not capture them. For example, the observed 4 ‰ higher d-excess during the dry season may be associated with a higher proportion of the moisture arising from bare soil evaporation upstream, which is characterized by higher d-excess (Gat and Matsui, 1991). LMDZ does not simulate this effect.

Last glacial maximum
LGM-PD variations for δ 18 O and d-excess were extensively evaluated in Risi et al. (2010b). We focus here on LGM-PD variations in Antarctica where most of the LGM 17 O-excess data are available. LMDZ simulates qualitatively well the observed depletion at LGM in Antarctica, and it captures the increased depletion towards the interior (Fig. 7a). However, the depletion magnitude is underestimated by 20 % in Dome C and up to 45 % in Vostok and Taylor Dome (Table 3). Although simulating d-excess signals with the same sign as δ 18 O has proven difficult for some models (Werner et

Fig. 7.
LGM minus present-day difference in precipitation δ 18 O, dexcess and 17 O-excess in Antarctica observed in ice cores (colored circles) and simulated (shaded) by LMDZ over Antarctica. Numerical values are given in Table 3. 2001; Noone, 2008), LMDZ is able to simulate the lower d-excess at LGM over most of Antarctica (Fig. 7b). In observations, the decrease of d-excess from PD to LGM is all the larger as we go poleward. However, LMDZ simulates the opposite, with an increase over Central Antarctica from PD to LGM. When using the LGM SST forcing based on the IPSL climate simulation, the decrease of d-excess from LGM to PD is 1 ‰ stronger but has a similar shape (Risi et al., 2010b). LMDZ captures the lower 17 O-excess observed at LGM at most sites (Fig. 7c). In observations, the decrease of 17 Oexcess from PD to LGM is all the larger as we go poleward, as for d-excess. This is also well captured by LMDZ. However, LMDZ overestimates the 17 O-excess decrease from PD to LGM at all sites, and simulates the wrong sign near the coast. Note that stratospheric intrusions may contribute to the LGM-PD difference in 17 O-excess (Winkler et al., 2013), but their effects are neglected in LMDZ.

Understanding what controls precipitation 17 O-excess
We now use LMDZ simulations to understand what controls δ 18 O, d-excess and 17 O-excess in the model. In doing so, we keep in mind the strengths and weaknesses highlighted by the model-data comparison: we have good confidence in the δ 18 O distribution both for PD and LGM. We have relatively good confidence in the annual-mean d-excess distri-bution and in the broad latitudinal pattern of d-excess seasonality. Finally, we have moderate confidence in the LGM-PD changes in d-excess and 17 O-excess in Antarctica. All other features are subject to more caution, as they are either misrepresented in LMDZ, or difficult to evaluate given the lack of data. Figure 8 shows the decomposition of the latitudinal variations of annual mean δ 18 O, d-excess and 17 O-excess into four effects (Sect. 2.4): (1) precipitation-vapor difference (green); (2) evaporative conditions associated with SST and RH s (orange); (3) effect of supersaturation (dashed pink); and (4) all other processes (red). The sum of all these contributions make the total signal (black). Figure 9 and 10 shows the same decomposition for seasonal and LGM-PD variations, respectively.

Precipitation-vapor difference
The contribution of precipitation-vapor difference to the precipitation signal is shown in green in Figs. 8-10.

Rain re-evaporation
In the tropics, in the absence of rain re-evaporation, the precipitation reequilibrates with the vapor as it falls (Risi et al., 2008a). Variations in precipitation-vapor difference are thus mainly associated with rain re-evaporation.
As rain re-evaporates, δ 18 O increases in the rain (Risi et al., 2008a(Risi et al., , 2010a. This process is the main reason for the so-called amount effect (Risi et al., 2008a), i.e. the decrease of δ 18 O as precipitation amount increases. Regarding the latitudinal gradient, the green and black curves have similar shapes for δ 18 O (Fig. 8a). This means that rain re-evaporation explains much of the latitudinal variations in precipitation δ 18 O. In particular, rain reevaporation explains the slight local minimum in δ 18 O in the equatorial region (around 0 • N) where the air is moist, and the larger values in the subtropics (around 30 • N and 35 • S) where re-evaporation is strong. Regarding seasonality, in the tropics, the green and black curves also have a similar shape for δ 18 O (Fig. 9). This means that the effect of rain reevaporation dominates the seasonality in δ 18 O, with larger values during the dry season (Fig. 9a, Risi et al., 2008b). At LGM, LMDZ simulates only small changes in δ 18 O in the tropics, but the latitudinal distribution of these changes mirror those in precipitation-vapor difference.
As rain re-evaporates, in parallel to the δ 18 O increase, dexcess and 17 O-excess both decrease (Risi et al., 2010a;Barras and Simmonds, 2009;Landais et al., 2010). In the tropics, this explains much of the latitudinal variations, in particular the local maxima in d-excess and 17 O-excess in the equatorial region and the lower values in the subtropics (Fig. 8b, c). Rain re-evaporation also dominates the seasonality in 17 Oexcess (and to a lesser extent in d-excess), with lower values during the dry season (Fig. 9b, c). This seasonal evolution www.clim-past.net/9/2173/2013/ Clim. Past, 9, 2173-2193, 2013 of the triple isotopic composition of precipitation is consistent with that observed during the transition from dry to wet season in the Sahel (Risi et al., 2008b;Landais et al., 2010). At LGM also, the small changes in d-excess and 17 Oexcess in the tropics reflect the changes in rain re-evaporation (Fig. 10b, c).

Effect of fractionation coefficients
In high latitudes, precipitation falls as snow and is thus not affected as much by post-condensational processes. The precipitation-vapor difference is thus associated with condensation processes. As temperature decreases, the fractionation coefficients increase, but the coefficient for δ 18 O increases faster than that for δD. Therefore, precipitation-vapor difference for d-excess becomes more negative at colder temperatures. This contributes to the lower d-excess in polar regions, during winter and during the LGM (Figs. 8b, 9b and  10b). During winter, this effect is not major and does not Hemisphere, higher in winter in the Southern Hemisphere, higher during the wet season in the northern tropics, higher during the dry season in the southern tropics). When the colored curves are of the same sign as the black curves, then the corresponding process contributes positively to the total seasonal signal.
prevent d-excess to be higher in winter. During the LGM in contrast, this effect appears as the main process contributing to the lower d-excess in polar regions. Similarly, the precipitation-vapor difference in 17 O-excess increases at lower temperatures. This is due to the fact that the slope of the meteorologic water line (0.528) is lower than the logarithm of the ratio of the fractionation coefficients ( ln(α O17 ) ln(α O18 ) = 0.529). This fractionation coefficient effect contributes to the increase of 17 O-excess in polar regions, in winter and at LGM. This effect might however be overestimated in LMDZ. Observations at the NEEM station in Greenland shows that 17 O-excess is only 3 ± 13 per meg higher in the snow than in the vapor (Landais et al., 2012b), compared to 41 per meg higher as predicted by LMDZ (not shown). This may be due to ln(α O17 ) ln(α O18 ) being actually closer to 0.528 than to 0.529 for vapor-solid equilibrium (Landais et al., 2012b). However, even in LMDZ, this equilibrium fractionation effect is not dominant since it is overwhelmed by other effects (green and black curves do not have similar shapes and often have opposite signs on Figs. 8c, 9c and 10c).

Evaporative conditions
The contribution of evaporative conditions (SST and RH s ) to the precipitation signal is shown in orange in Figs between the solid and dashed lines correspond to the role of SST only. For δ 18 O, evaporative conditions play little role in the latitudinal gradient and in LGM-PD differences, but they do contribute to the seasonality of δ 18 O in high latitudes. This is mainly due to the RH s being drier in summer.
Evaporative conditions play a more important role for the distribution of d-excess. In particular, the poleward decrease in d-excess from 30 • to 60 • in the Southern Ocean is due to evaporative conditions (Fig. 8b). SST and RH s account each for about half of this decrease. The broad latitudinal distribution of d-excess seasonality was characterized both in observations and LMDZ by lower values in summer in the subtropics and mid-latitudes of each hemisphere (Sect. 3, Fig. 5). This pattern is similar to that of the evaporative condition contribution, in particular the effect of RH s at the moisture source (Fig. 9b). Therefore, the observed d-excess pattern could be due to the RH s seasonality at the moisture source or to seasonal shifts in moisture sources. In high latitudes, the contributions of "other processes" (red curve, detailed in Sect.4.3) and of supersaturation (pink curve) effects are large and largely compensate each other (later discussion in Sect. 4.3). Beside these two components, the dominant cause for d-excess seasonality in polar regions is RH s conditions at the moisture source (Fig. 9b). The importance of evaporative conditions could be even stronger in nature than in LMDZ, since LMDZ underestimates the effect of RH s and SST on d-excess.
Regarding LGM-PD differences, in LMDZ changes in evaporative conditions play little role in decreasing d-excess at LGM. This is because RH s and SST do not vary as much between LGM and present as during a seasonal cycle. This contradicts the suggestion that higher RH s at the LGM (Jouzel et al., 1982) or lower SST at the moisture source (Stenni et al., 2001) contribute to the lower d-excess in Antarctica. It is possible that the contribution of evaporative conditions was significant at LGM, that it is underestimated by LMDZ, and that LMDZ gets the right sign of d-excess change through compensation of errors. This study just shows that the lower d-excess at LGM can be explained without change in evaporative conditions, provided that a significant supersaturation parameter is chosen.
For 17 O-excess, the solid and dashed orange lines are identical, since SST has no impact on 17 O-excess at evaporation (Risi et al., 2010c). LMDZ simulates a small role for evaporative conditions in the latitudinal gradient of 17 O-excess (Fig. 8c). However, we have shown in Sect. 3.1 that LMDZ underestimates the slope of 17 O-excess as a function of RH s . Therefore, in nature the role for evaporative conditions might be stronger. For LGM-PD differences, the evaporative condition effect is not negligible in Antarctica. The effect of RH s at the moisture source leads to lower 17 O-excess by 5 per meg at Vostok. If LMDZ had a more realistic RH s -17 O-excess slope (i.e. about 4 times larger), the RH s contribution might have been larger, in better agreement with Landais et al. (2008). LMDZ can however simulate the observed lower 17 O-excess at LGM without an important role of evaporative conditions, provided that an adequate supersaturation parameter is used (Sect. 4.4).

Convective processes, distillation and mixing between vapors of different origins
The sum of all effects other than supersaturation, precipvapor difference and evaporative conditions is shown in red.

Convective processes
In the tropics, the air temperature is relatively uniform horizontally (Sobel and Bretherton, 2000) so the temperature effect is small (Rozanski et al., 1993). Large variations in humidity can however be associated with vertical motions (Sherwood, 1996). Since δ 18 O decreases with altitude (e.g. Ehhalt, 1974), subsidence of air in unsaturated downdrafts of convective systems (Risi et al., 2008a) and the subsidence at the large scale in dry regions (Frankenberg et al., 2009;Galewsky and Hurley, 2010) both deplete the water vapor. In addition, rain re-evaporation and rain-vapor interactions in moist conditions can also deplete the vapor Worden et al., 2007). Therefore, in the tropics, the red curves in Figs. 8-10 correspond to the combined effects of large-scale dynamics, of unsaturated downdrafts and of rain re-evaporation on the vapor. We can see that these effects are the major contribution to explain the seasonality in δ 18 O in the tropics (Fig. 9). This is consistent with the important role www.clim-past.net/9/2173/2013/ Clim. Past, 9, 2173-2193, 2013 of unsaturated downdrafts in the amount effect (Risi et al., 2008a). For d-excess, the vertical gradient in the tropics remains an open question. LMDZ simulates a decrease with altitude ( Fig. 2a), whereas theoretical considerations (Bony et al., 2008) and indirect evidence based on upper-tropospheric measurements (Sayres et al., 2010) and high-frequency measurements (Lai and Ehleringer, 2011;Welp et al., 2012;Wen et al., 2010) suggest that d-excess increases with altitude. Therefore, the role of convective-scale subsidence on d-excess is unclear. In contrast, it is more certain that rain reevaporation and rain-vapor interactions increase the d-excess of the vapor (Landais et al., 2010). This process explains the maximum of d-excess in equatorial convective regions (Fig. 8b). This is also a major contribution to the seasonality in d-excess in the tropics (Fig. 9b).
For 17 O-excess, the vertical gradient in the tropics also remains an open question. As for d-excess, rain re-evaporation and rain-vapor interactions increase the 17 O-excess of the vapor (Landais et al., 2010). This process is the major contribution to explain the seasonality in 17 O-excess in the tropics (Fig. 9c).

Distillation and mixing
In high latitudes, the above-mentioned processes play a minor role. Therefore, the red curves represent the combined effects of distillation and mixing between vapor of different origins (hereafter shortened as "mixing"). In particular, mixing includes evaporative recycling along trajectories, i.e. mixing between vapor undergoing distillation during its poleward transport and newly evaporated vapor from the ocean surface.
Distillation decreases δ 18 O. Simple Rayleigh distillation calculations based on LMDZ temperature show that if there was only distillation, the δ 18 O latitudinal gradient would be four times larger than actually simulated (not shown). In reality and in the simulations, this latitudinal gradient is dampened by evaporative recycling along trajectories. As expected, distillation and mixing (red curve) dominate the δ 18 O latitudinal gradient, consistent with the traditional temperature effect (Dansgaard, 1964). It also dominates the seasonality and the LGM-PD difference in δ 18 O.
For d-excess, Rayleigh distillation increases d-excess at low temperature (Jouzel and Merlivat, 1984). This explains the polar increase of the red contribution (Fig. 8b). For the same reasons, in high latitudes, the Rayleigh effect contributes to the increased d-excess in winter (Fig. 9b) and at LGM (Fig. 10b).
For 17 O-excess, the poleward decrease of the red contribution in high latitudes (Fig. 8c) may be due to the effect of evaporative recycling. The effect of evaporative recycling on 17 O-excess is due to the fact that mixing of two air masses with very different δ 18 O leads to 17 O-excess values that are lower than both end-members (Risi et al., 2010c).
The fact that LMDZ underestimates 17 O-excess in polar regions (Sect. 3.2) may be due to the fact that the advection scheme is too diffusive. Indeed, in the Van Leer (1977) advection scheme, advection of vapor from one grid box A to neighboring grid box B is represented as mixing between of vapor A and B into grid box B.
Note that there is persistent uncertainty on vapor-solid fractionation used for distillation at very low temperature. Vapor-solid fractionation coefficients have been measured only down to −34 • C and are extrapolated beyond (Majoube, 1971a), leading to some uncertainty. There are also disagreements between different experimental measurements (Ellehoej, 2011). This may contribute to difficulties simulating dexcess and 17 O-excess in polar regions.

Supersaturation
The effect of supersaturation is shown in dashed pink in Figs. 8-10.
Supersaturation occurs at cold temperatures, in polar regions, and this partially compensates the effect of distillation. When supersaturation occurs, δ 18 O decreases less along trajectories than expected. The supersaturation effect has, however, relatively little effect on δ 18 O ( Fig. 8a; pink).
For d-excess and 17 O-excess, supersaturation has a larger effect. The distillation/mixing and supersaturation effects are both very large and largely compensate each other (Fig. 8b,c). When supersaturation occurs, d-excess and 17 Oexcess increase less along trajectories than expected. As a consequence, the sign of the seasonality and of LGM-PD variations results from a balance between distillation effects and supersaturation effects. Regarding seasonality for example, in Greenland where LMDZ captures the sign of the dexcess seasonality, the distillation effect dominates and this leads to higher d-excess values in winter when the distillation is stronger. In Vostok in contrast, d-excess is higher in winter in observations but lower in winter in LMDZ. This suggests that in observations, the distillation effect dominates, but that in LMDZ, the supersaturation effect is too strong and dominates. In observations, 17 O-excess is higher in winter in Greenland and lower in winter in Antarctica. This suggests that the supersaturation effect dominates in Antarctica but not in Greenland. In LMDZ, the seasonality is misrepresented in both regions.
Summing up large effects of different signs without having good confidence in their magnitude leads to strong uncertainty. Estimating their magnitude calls for laboratory experiments. In particular, d-excess and 17 O-excess in polar regions is extremely sensitive to the choice of λ, consistent with simple model studies (Ciais and Jouzel, 1994;Winkler et al., 2012;Landais et al., 2012a,b). Risi et al. (2010b) chose λ to optimize the latitudinal gradient in polar d-excess. If λ was lower, the agreement would be better for 17 O-excess, but d-excess would be overestimated in Central Antarctica (Fig. 11b,c). In LMDZ, we cannot tune λ to agree both with Clim. Past, 9, 2173-2193, 2013 www.clim-past.net/9/2173/2013/ LGM-PD changes difficult. Any observed change at a given location can be reproduced by any model by tuning λ. Setting λ = 0.004 leads to a good agreement with the LGM-PD variations, but a lower value of λ can lead to a reversal of the sign of the d-excess and 17 O excess LGM-PD variations (Fig. 11e,f). In addition, there are uncertainties on the diffusivity coefficients. Cappa et al. (2003) and Merlivat and Jouzel (1979) found different values and Luz et al. (2009) suggest that they may actually vary also with temperature. Therefore, the combined uncertainties on supersaturation, equilibrium fractionation, and diffusivity coefficients make it difficult to interpret d-excess and 17 O-excess data and to identify the culprit in the shortcomings of the d-excess and 17 O-excess simulation in polar regions. In addition, stratospheric intrusions cannot be ruled out to explain at least part of the measured signals in 17 O-excess (Winkler et al., 2013).

Conclusion and perspectives
We used the LMDZ GCM to simulate the PD and LGM distributions of precipitation δ 18 O, d-excess and 17 O-excess. LMDZ correctly captures the δ 18 O distribution and climatic variations. After appropriate tuning of supersaturation, it captures reasonably well the d-excess distribution and the average LGM-PD variations in Antarctica. For 17 O-excess, the lack of data makes it difficult to evaluate the spatio-temporal distribution. LMDZ underestimates the 17 O-excess latitudinal gradient in the Austral Ocean water vapor and has difficulties to simulate seasonal variations on some stations.
We propose a methodology to quantify the controlling factors of the associated latitudinal, seasonal and LGM-PD variations. Table 5 summarizes the main factors controlling the different aspects of the δ 18 O, d-excess and 17 Oexcess spatio-temporal distribution depending on latitude. In the tropics, rain re-evaporation and convective processes explain the main features of the δ 18 O, d-excess and 17 O-excess spatio-temporal distributions. In mid-and high-latitude, as expected, the distillation effect is the first-order control on δ 18 O. D-excess and 17 O-excess are affected by distillation, but also by other processes. Evaporative conditions play a role for d-excess, and may also play a role for 17 O-excess if LMDZ was more sensitive to RH s and SST. The sensitivity to evaporative conditions is an added value of d-excess compared to δ 18 O, consistent with previous studies (e.g. Vimeux et al., 1999Vimeux et al., , 2001bGat, 2000;Stenni et al., 2001;Masson-Delmotte et al., 2005). 17 O-excess also features this added value, but an additional particularity is its sensitivity to mixing between vapor of different origins along distillation trajectories. 17 O-excess seems to be sensitive to a much broader www.clim-past.net/9/2173/2013/ Clim. Past, 9, 2173-2193, 2013  Tables 2 and 3. range of processes. Determining the controlling factors in nature with more confidence would however require much more data to more comprehensively evaluate GCM simulations of 17 O-excess. Continuous, in situ water vapor measurements are needed in order to improve the understanding of the driving mechanisms of d-excess and 17 O-excess. In this regard the new laser-based techniques are extremely helpful for in situ isotope measurements of water vapor. Yet, it is not possible, at least so far, to determine 17 O-excess with the required precision (≤ 5 per meg) using this technology. Such measurements would be very helpful. Supersaturation effects play a major role on both d-excess and 17 O-excess, leading to a large uncertainty in their interpretation. At LGM in polar regions, distillation and mixing effects tend to increase d-excess and 17 O-excess values, while supersaturation effects tend to decrease them. The balance between these two large effects is very sensitive to the assumed supersaturation function. Using a supersaturation function that leads to d-excess and 17 O-excess consistent with PD observations, LMDZ is able to simulate the lower d-excess and 17 O-excess at LGM without requiring any effect of changes in evaporative conditions at the moisture source. The choice of the supersaturation function, together with uncertainties in equilibrium fractionation and dif-fusivity coefficients, remain a key uncertainty in interpreting d-excess and 17 O-excess, since its choice determines the sign of LGM-PD changes. Measurements of vapor and precipitation along Antarctica transects would be very helpful to better constrain this function. New laboratory experiments focused on fractionation during ice formation in cold conditions would also be helpful.
We acknowledge the limitations inherent to our GCM simulations. The sensitivity of d-excess and 17 O-excess to ocean evaporative conditions is underestimated, for reasons that we do not understand but that are more likely related to freetropospheric processes. Vertical profiles or latitudinal gradients of 17 O-excess in the free-tropospheric vapor would be helpful to diagnose the cause of these problems. Alternatively, comparison with other isotopic GCMs that do not feature the same bias, if these exist, could provide some insight. Finally, taking into account fractionation during bare soil evaporation (e.g. Gat and Matsui, 1991) may be necessary to interpret d-excess and 17 O-excess patterns over land.
Finally, the methodology presented here to decompose the isotopic signals into the different physical processes will remain valid for all GCMs. Applying this methodology to other GCMs will help extract robust features among models. If in the future, some GCMs are able to better simulate d-excess and 17 O-excess, applying this methodology to these GCMs will help understand what controls d-excess and 17 O-excess with more confidence.

Appendix A
Predicting the isotopic composition of the boundary layer vapor using the closure assumption The simplest equation to predict the isotopic composition of the boundary layer vapor is the Merlivat and Jouzel (1979) closure. Although it fails to predict the absolute values of δ 18 O and d-excess (Jouzel and Koster, 1996), it has been shown to accurately predict the sensitivity of the isotopic composition to ocean surface conditions (Uemura et al., , 2010Risi et al., 2010c). We recall here the derivation of this equation and the underlying assumptions.
The isotopic composition R E of the evaporation flux from the ocean is given by the Craig and Gordon (1965) equation: where α K is the kinetic fractionation coefficient, α eq is the liquid-vapor equilibrium fractionation coefficient and R oce is the isotopic ratio of the ocean surface. The relative humidity at the surface, RH s is the relative humidity of near-surface air at the temperature of the ocean surface T s : RH s = RH a · q sat (T a ) q sat (T s ) , Clim. Past, 9, 2173-2193, 2013 www.clim-past.net/9/2173/2013/ where q sat is the specific humidity at saturation and RH a and T a are the relative humidity and temperature of the nearsurface air, respectively. If we assume that (1) the only source of vapor in the boundary layer is the surface evaporation and (2) the sinks of vapor from the boundary layer do not fractionate (i.e. have the composition of the boundary layer, e.g. air flux going out of the boundary layer), then at stationary state R v = R E . Combined with Eq. (A1), this leads to : . Supplementary material related to this article is available online at: http://www.clim-past.net/9/2173/ 2013/cp-9-2173-2013-supplement.pdf.