This study investigates the response of the global mean and spatial variations of the δ18O value of atmospheric CO2 (δCa) to changes in soil CO2 hydration rates, relative humidity, the δ18O value of precipitation and water vapor, visible radiation, temperature, and ecosystem flux partitioning. A three-dimensional global transport model was coupled to a mechanistic land surface model and was used to calculate isotopic fluxes of CO2 and H2O and the resulting δCa. The model reproduced the observed global mean and north-south gradient in δCa. The simulated seasonal amplitude and phases of CO2 and δCa agreed well at some but not all locations. Sensitivity tests with relative humidity increased by 3.2% from its original value decreased δCa by 0.21‰. Similarly, a global 3.3‰ decrease in the isotopic composition of both precipitation and water vapor (δWP and δWAV, respectively) caused a 2.6‰ decrease in δCa. A 1 K increase in atmospheric temperatures also affected δCa, but there was a very small δCa response to realistic changes in light levels. Experiments where leaf and soil CO2 fluxes were repartitioned revealed a nontrivial change to δCa. The predicted north-south δCa gradient increased in response to an increase in soil CO2 hydration rates. However, the δCa gradient also had a large response to global changes in δWP and δWAV. This result is particularly important since most models fail to deplete δWP enough at middle and high latitudes, where the influence of δWP and δWAV on the δCa gradient is strongest.
 Land use changes and rising levels of industrial activity have increased the atmospheric CO2 concentration over the past several decades [Denman et al., 2007; Ballantyne et al., 2012]. Nevertheless, terrestrial photosynthesis and respiration still play a dominant role in the seasonal cycling of CO2, annually exchanging 21% of the atmospheric stock [Sarmiento and Gruber, 2002]. A number of approaches have been developed to attribute observed atmospheric CO2 concentration variations to its various surface sources and sinks, including inversions [Gurney et al., 2003, 2004], bottom-up approaches [Denman et al., 2007], and isotopic tracers (13C, 14C, and 18O) [Quay et al., 1992; Fung et al., 1997; Peylin et al., 1999; Ogée et al., 2004; Naegler et al., 2006; Rayner et al., 2008]. This study focuses on the sensitivity of the 18O/16O composition of atmospheric CO2 (hereafter δCa, where δ = R/RStandard − 1 and R is the molar ratio of heavy to light isotopes, in the case of 18O/16O) to changes in climate forcing. Since δCa variations are believed to be driven primarily by terrestrial respiratory and photosynthetic fluxes, combined with the 18O content of water in soils and plant leaves [Francey and Tans, 1987; Farquhar et al., 1993; Ciais et al., 1997a; Cuntz et al., 2003a], δCa is a potentially valuable atmospheric tracer of global interactions between the water and carbon cycles and of the separate contributions of each gross terrestrial carbon flux.
Francey and Tans  used global atmospheric observations to argue that terrestrial carbon fluxes were the most important influence on the north-south gradient in δCa. Farquhar et al.  confirmed this inference through a pioneering global model analysis, which showed that terrestrial ecosystem fluxes largely determine the spatial structure of δCa. Studies using more complex global-scale models have concluded that both the north-south gradient and the seasonal cycle in δCa are almost entirely determined by land ecosystem fluxes and atmospheric transport [Ciais et al., 1997a, 1997b; Peylin et al., 1999; Cuntz et al., 2003a, 2003b; Wingate et al., 2009]. The strong influence of ecosystem fluxes is in part due to the equator-to-pole gradient in the 18O/16O composition of precipitation and water vapor. Furthermore, Still et al.  demonstrated through site-level observations and an isotope-enabled land model a range of linkages between δCa and the atmospheric hydrological cycle (such as humidity and cloud cover variations). Similarly, Buenning et al.  and Welp et al.  showed observational evidence of a possible connection between δCa and both relative humidity and precipitation δ18O values on interannual time scales. Buenning et al.  also concluded that global mechanistic models would be needed to test their proposed hypotheses. Wingate et al.  presented global model experiments that showed how an increased soil CO2 hydration rate reduced discrepancies between observed and modeled δCa. In particular, their results suggested that high CO2 hydration rates in soils are necessary to correctly simulate the north-south gradient in δCa. However, their study did not evaluate how other variables could also change the simulated gradient to better match observations. In fact, there remains a need to obtain and provide extensive, model-based quantitative estimates of the response of δCa and the north-south δCa gradient to changes in environmental conditions. In this study, we used a global-scale model of CO2 and CO18O exchanges to examine the sensitivity of the annual mean and spatial variations of δCa to changes in climatic variables that could potentially influence δCa.
 In Appendix B, the δCa budget is examined and the potential driving variables are identified as relative humidity, δ18O values of precipitation and vapor, radiation levels, temperature, and ecosystem flux partitioning. To evaluate the climatic and ecosystem influences on δCa, land simulations were performed using an isotope-enabled version of the National Center for Atmospheric Research (NCAR) Land Surface Model (ISOLSM) [Bonan, 1996; Riley et al., 2002, 2003; Lai et al., 2006], similar to that used by Still et al. . The simulations used predicted global surface-to-atmosphere fluxes from ISOLSM as input to the NCAR Community Atmosphere Model (CAM) to estimate δCa. This model configuration allows us to easily conduct the sensitivity experiments described below. A comparison between a control simulation and observed δCa is presented to demonstrate model performance. We conducted sensitivity experiments with the model to determine how changes in soil CO2 hydration, relative humidity, the δ18O value of precipitation and water vapor, light levels, temperature, and ecosystem CO2 fluxes can affect the annual mean and spatial δCa variations via changes in gross CO2 fluxes and/or the isotopic composition of leaf and soil water.
2 Model and Experiments
2.1 The Land Surface Model (ISOLSM)
 Land Surface Model simulates the exchanges of energy, momentum, H2O, and CO2 between the atmosphere and the terrestrial biosphere. Riley et al. [2002, 2003] developed integrated modules within LSM1.0 (together called ISOLSM) to compute the exchanges of CO18O and H218O to and from the terrestrial biosphere. The model calculates canopy water vapor, vertically resolved soil water, and shaded and sunlit leaf water, as well as the 18O (and 2H) isotopic composition of each pool. Nine model layers are used for the simulations, with increasing thickness with depth (dz = 0.04, 0.04, 0.04, 0.1, 0.2, 0.4, 0.8, 1.6, and 3.2 m).
 ISOLSM accounts for 18O in water and CO2 exchanges by including various kinetic and equilibrium fractionation processes [Riley et al., 2002]. A steady state estimate of canopy vapor and its isotopic composition is calculated via a mass balance equation dependent on fluxes and the isotopic content of atmospheric vapor, canopy transpiration and evaporation, and soil evaporation [Riley et al., 2002, equation (11)]. A canopy turnover time (3 h) is then applied to the steady state value and the values from the previous time step. The leaf water model in ISOLSM employs a time-dependent mass balance that includes a transpiration-dependent leaf turnover time scale to calculate δWl [Dongmann et al., 1974; Still et al., 2009]. The model uses an advective transport model for soil water, nonfractionating root water uptake, and surface boundary layer resistance to predict the soil water isotopic ratio. The δ18O value of CO2 within leaves and the soil column is predicted considering gaseous diffusion, surface boundary layer resistance, and the following temperature-dependent equilibration between gaseous CO2 and water [Brenninkmeijer et al., 1983]:
where Ts (K) is surface temperature (i.e., ground or leaf temperature). Kinetic isotopic fractionation associated with CO2 diffusion across the leaf stomata and modified for the leaf boundary layer is weighted by CO2 concentration gradients from the canopy to the chloroplasts (following Farquhar and Lloyd ). A similar kinetic fractionation is applied to diffusion during transport of gas phase CO2 through the soil. The CO2 diffusion module within ISOLSM is based on Tans  and described in detail in Riley et al.  and Riley . Similarly, the isotopic kinetic fractionations during soil evaporation are dependent on near-surface turbulent intensity as well as the ratio of H218O diffusivity to H2O diffusivity [Mathieu and Bariac, 1996].
 The model computes gross CO2 leaf fluxes from the atmosphere-to-leaf, Fal (mol m−2 s−1), and from leaf-to-atmosphere, Fla, as [Ciais et al., 1997a]:
where Ci is the CO2 concentration inside the stomatal pores. The CO18O fluxes from leaves are calculated as follows:
where αl is the diffusive fractionation factor across the laminar leaf boundary layer and through the stomata, and Rl is the CO18O to CO2 ratio within the leaves after equilibration with leaf water. The value of αl is a weighted mean of fractionation factors for diffusion in the stomata, through the mesophyll cell wall, and through the laminar boundary layer and into the air space above the canopy. Note that this simplified estimates does not factor in recent findings of the strong kinetic effect from canopy-scale turbulent diffusion [Lee et al., 2009]. The nonleaf CO2 and CO18O respiration fluxes (Fr and 18Fr, respectively) are calculated as the sum of microbial, growth, and root and stem maintenance respiration.
 Detailed in Still et al. , previous studies have tested ISOLSM simulations at the site level. These include studies that have validated ISOLSM's predictions of H2O and CO2 fluxes at different locations and different ecosystems [Suyker and Verma, 2001; Riley et al., 2003; Cooley et al., 2005; Lai et al., 2006; Aranibar et al., 2006; Still et al., 2009]. ISOLSM's isotopic predictions have also been validated; comparing observed and simulated δ18O values of ecosystem water pools and ecosystem H2O and CO2 fluxes throughout the Great Plains [Riley et al., 2003; Still et al., 2005; Still et al., 2009; Lai et al., 2006].
 ISOLSM simulations were forced with two sets of meteorological data: radiation, precipitation, height, wind speed, and sea-level and surface pressure from data generated by Qian et al. ; and temperature and relative humidity from the Global Summary of the Day, which was obtained through the World Meteorological Organization and the National Climatic Data Center Climate Services Branch. The Qian et al.  data set merges data from station measurements, remote sensing, and model simulation, using different products for each variable. A method similar to the Cressman  objective analysis was used to interpolate the station observations onto the model grid. Appendix C contains a brief description of this data set and a comparison with other gridded data to demonstrate why it was preferred. It is important to note that although the model is forced with two different data sources, both are constrained by observations that are subject to the same meteorological conditions. The δ18O value of precipitation (δWP) was prescribed from a data set described in detail by N. H. Buenning and D. C. Noone (An evaluation of annual mean and seasonal timing of local and non-local processes controlling the isotopic composition of precipitation from observations and comprehensive models, manuscript in preparation, 2014), which was constructed using a regression/Fourier transform approach and was constrained by global observations [Isotope Hydrology Section, 2006]. The isotopic composition of atmospheric vapor (δWAV) was prescribed from the above δWP using the offset between precipitation and vapor as modeled by the Melbourne University General Circulation Model [Noone and Simmonds, 2002]. The reasoning for these choices of δWAV and δWP are described in more detail in section 4.
2.2 Ocean and Anthropogenic Fluxes
 The global distribution of net CO2 fluxes between the ocean and the marine atmosphere, Fo (mol m−2 s−1), and sea-air CO2 partial pressures, po and pa (Pa), were taken from a data set produced by Takahashi et al.  and Gurney et al. . However, the one-way CO2 fluxes (atmosphere-to-ocean (Fao) and ocean-to-atmosphere (Foa)) must be considered independently (like the leaf fluxes), as their isotopic compositions differ. To calculate the two one-way fluxes (equations (6) and (7)), the air-sea gas exchange coefficient, Kex, was first calculated [Ciais et al., 1997a] (equation (5)):
 The ocean-to-atmosphere CO18O flux (mol m−2 s−1), 18Foa, was calculated as follows:
where Ro is the 18O/16O ratio of dissolved CO2 and αw is the fractionation associated with CO2 crossing the air-sea interface, using the value Vogel et al.  measured at 0°C of +0.8‰ (αw = 1 + εw, εw = +0.8‰). The ratio Ro was calculated as
where αeq is the temperature-dependent equilibrium fractionation factor, Ts is sea surface temperature, and Row is the 18O/16O ratio of ocean surface water. Using reconstructed sea surface temperatures, Ts, from the NOAA_ERSST_V3 (data provided by the NOAA/OAR/ESRL PSD) [Smith et al., 2008], the value of αeq(Ts) was calculated using equation (1). The values of Row were obtained via data compiled by LeGrande and Schmidt . This data set was constructed using local (rather than global) relationships between ocean water δ18O values and salinity from 50 years worth of available data. LeGrande and Schmidt  found that their gridded estimates performed well in general but found errors in the deep ocean, locations near sea-ice, and regions that exhibit large seasonality. These last two regions and areas where observational constraints were sparse will likely cause some bias in our modeling results.
 Emissions from fossil fuel combustion, Ff, were acquired from the data set produced by Andres et al. . Also included in the model were fluxes from biomass burning Fb, using the Global Fire Emissions Database version 2 (GFEDv2) [Van der Werf et al., 2006]. This flux does not include regrowth, and as Ciais et al. [1997a] points out, the regrowth can likely be neglected because of the small magnitude relative to Fla and Fal and the gross flux has an almost trivial disequilibrium with the atmosphere. Both of the anthropogenic fluxes were assumed to have the isotopic ratio of atmospheric oxygen, RO2 (where δO2 = −17‰), which assumes no fractionation as CO2 is sourced to the atmosphere. Thus, the CO18O fluxes from both fossil fuel emissions and biomass burning were calculated as
2.3 Atmospheric Transport Model (CAM)
 Atmospheric concentrations of CO2 and CO18O were simulated using the NCAR Community Atmosphere Model (CAM) [Collins et al., 2006]. Taking into account the processes of the terrestrial biosphere, the ocean, and the anthropogenic sources, the temporal changes of CO2 and CO18O can be written as
where Ra is the instantaneous ratio of atmospheric CO18O to CO2 (18Ca/Ca) and Ma is a conversion factor (with units of moles of air m−2). While all fluxes in equation (12) were computed by either ISOLSM or calculated from data sets, the atmosphere-to-surface CO18O fluxes in equation (13) were dependent on Ra, and were thus calculated at every time step within the atmospheric transport model CAM. Specifically, by allowing the atmosphere to interact with the surface fluxes, a steady state δCa can be found (i.e., simulated local annual mean δCa stays relatively constant). Note that this interactive approach slightly differed with other δCa models that solely used CO2 fluxes from offline calculations (e.g., Ciais et al. [1997a, 1997b] and Peylin et al. ). On the other hand, the model framework used here is not a complete fully coupled model used by Cuntz et al. [2003a, 2003b]. Nonetheless, to resolve the three-dimensional δCa field, account needs to be made for the advection tied to the mass evolution on the left-hand side, a task for which CAM is well suited.
 ISOLSM simulations ran twice through the 1979–2004 period, to fully spin-up the model's deep soil layers. The 12 (January through December) monthly mean surface fluxes of CO2 and CO18O were computed using the last 36 years of the simulation (i.e., the second cycle through the 1979–2004 period). Because ISOLSM does not have a dynamic coupling between carbon uptake and respiration, a correction was used to adjust the (nonleaf) respiratory fluxes so that the surface ecosystem CO2 fluxes were close to being balanced for every grid point in a manner similar to Denning et al.  and Riley et al.  (i.e., a method similar to the so-called “R*” approach). Global respiration was slightly adjusted even further such that simulated CO2 concentrations gradually rose at a rate consistent with observations during the 1990s (3.2 GtC yr−1) [Denman et al., 2007], implying a slight terrestrial uptake of CO2. These fluxes and the fluxes described in section 2.2 were then used as input for CAM. Additional tracers were used in CAM to quantify the contribution of each surface-to-atmosphere flux to the simulated CO2 and CO18O concentrations. CAM simulations ran for 30 years with the last 10 years used for the analysis of the steady state conditions.
 Fourteen experiments were performed to compute the sensitivity of the climatological δCa values to each of the quantities that influence the fluxes described by equations (12) and (13). The experiments aimed to evaluate separately the influence of soil CO2 hydration, atmospheric relative humidity, isotope hydrology, light levels, temperature, and CO2 flux partitioning on spatial δCa variations. Table 1 gives a brief explanation of each experiment along with the experiment name, which is used hereafter. For comparison with Wingate et al. , we conducted two similar experiments where soil CO2 hydration rates were increased by factors of 20 and 300 (HYD20 and HYD300, respectively). Station observed relative humidity was shown [Buenning et al., 2011] to gradually increase within the Asia Pacific and the Tropical Americas by an average of 3.3% from 1993 to 1997 (a similar increase was observed in central Europe, western North America, and Siberia), a brief interval of time where δCa decreased at nearly every station [Ishizawa et al., 2002; Flanagan, 2005]. As such, a sensitivity experiment was preformed that increased the prescribed relative humidity at each grid point by 3.3% units globally (RH) and only within the tropics (equatorward of 20°N and 20°S, RHTROP). Also, observations in the Asia Pacific and Tropical Americas show a 3.2‰ decrease in δWp during the same 1993 to 1997 period, and precipitation data sets within these tropical regions depict an increase in precipitation that is consistent with the so-called amount effect (δWp anticorrelates with precipitation) [Buenning et al., 2011]. To examine the influence of isotope hydrology on δCa, a global 3.2‰ reduction was applied to the prescribed δ18O values of precipitation (PREC). To examine how much of the response was from the tropics, the region that dominates terrestrial CO2 exchanges, another experiment was performed in which the reduction was only applied within the tropics (PRECTROP). The same specifications were applied to the δ18O values of water vapor only (WV and WVTROP) and then to both δ18O values of precipitation and water vapor (PRECWV and PRECWVTROP) to further disentangle the role of hydrological isotopic forcing on δCa. To estimate the influence of light levels on δCa, 7.5% of the prescribed direct radiation was repartitioned to diffuse radiation (a 15% total change), while the total radiation was lowered by 4% (denoted as LIGHT). The sizes of these anomalies were chosen to be comparable to those following the eruption of Mount Pinatubo, as inferred by Robock  and Gu et al. . The eruption of Mount Pinatubo also affected global air temperatures, and the role of temperature changes on δCa was evaluated through an experiment in which global surface air temperatures were increased by 1 K (TEMP). In the TEMP experiment, relative humidity was kept unchanged; thus, there was also a slight increase in specific humidity. To evaluate how a change to the assimilation/respiration partitioning may influence δCa, an experiment was conducted where photosynthetic leaf fluxes were increased globally by 3.6% (offline from both ISOLSM and CAM) without any change to nonleaf respiration (ASSIM). Another experiment was conducted that increased nonleaf respiration globally by 3.6% without any change to photosynthetic leaf fluxes (RESP). Buenning et al.  estimated the 3.6% increase by weighting radiation changes (from 1993 to 1997) within the tropics by predicted Net Primary Production from the Carnegie-Ames-Stanford Approach biosphere model [Potter, 1999; Potter et al., 1999]. This estimate also takes into account the fraction of the tropics that contributes to global NPP.
Table 1. List of the Experiment Names With a Brief Description
Soil CO2 hydration is increased by a factor of 20 globally
Soil CO2 hydration is increased by a factor of 300 globally
Global relative humidity is increased by 3.3%
Relative humidity is increased by 3.3% between 20°S and 20°N
Reduced the prescribed δ18O of precipitation by 3.2‰ globally
Reduced the prescribed δ18O of precipitation by 3.2‰ between 20°S and 20°N
Reduced the prescribed δ18O of atmospheric water vapor by 3.2‰ globally
Reduced the prescribed δ18O of atmospheric water vapor by 3.2‰ between 20°S and 20°N
Reduced the prescribed δ18O of precipitation and atmospheric water vapor by 3.2‰ globally
Reduced the prescribed δ18O of precipitation and atmospheric water vapor by 3.2‰ between 20°S and 20°N
Repartitioning 7.5% of the direct radiation to diffuse and a 4% reduction in global downwelling solar radiation
Global temperatures are increased by 1 K
Global 3.6% increase in Fla and Fal without any change to Fr
Global 3.6% increase in Fr without any change to leaf fluxes
3 Simulated CO2 and CO18O
 To facilitate later discussion and demonstrate model performance, the results from an unperturbed control simulation are presented first. Figure 1 shows model results for the first 20 years of the simulation at two grid cells associated with Mauna Loa (155.58°W, 19.54°N) and South Pole (24.80°W, 89.98°S). Modeled δCa came to a quasi-steady state at about 5 years at these two locations (Figure 1). The time evolution of δCa in Figure 1 demonstrates that treating the first 20 years of the simulation as spin-up is more than adequate. The global annual average quasi-steady state δCa at the lowest level in the model (typically corresponding to a mean level of approximately 70 m above the Earth's surface) was found to be 0.48‰ (VPDB), which agrees reasonably well with the observed value of about 0.9‰ (e.g., NOAA/Global Monitoring Division data presented by Cuntz et al. [2003b]).
 Figure 2a shows observed and modeled (control simulation) zonal mean δCa at the ground level as well as the contributions from the five components of the total surface-to-atmosphere flux. Both observed and simulated values of δCa in Figure 2 were offset so that South Pole values equal 0‰, as is conventional in previous global model studies [Ciais et al., 1997b; Peylin et al., 1999; Cuntz et al., 2002b; Wingate et al., 2009]. Each station data point in Figure 2a was calculated by taking the mean of all monthly values (from the NOAA database) from 1990 to 2007; because not all stations started observations at the same time and have the same missing values, the station means will not span the same time intervals. The model simulated a north-south δCa gradient that agrees well with observations, as is reflected in the high correlation coefficient in Figure 2a (r = 0.970; correlating 45 observed station annual means [White and Vaughn, 2009] with simulated values from the nearest grid cell). In general, these results suggest that the model's control simulation reasonably captured the north-south gradient of δCa.
 It was found that forcing the model with δWP data that were closely constrained by observations (N. H. Buenning and D. C. Noone, manuscript in preparation, 2013) was important for this successful model/data agreement. Previous runs of the model using simulated δWP from models developed at Melbourne University (MUGCM) [Noone and Simmonds, 2002], the Max Planck Institute for Meteorology (ECHAM) [Hoffmann et al., 1998], and the Goddard Institute for Space Studies (GISS) [Jouzel et al., 1987] resulted in north-south δCa gradients that were lower than what is observed (Figure 2b). Indeed, Noone and Sturm  and N. H. Buenning and D. C. Noone (manuscript in preparation, 2013) report that these models underestimate the depletion of δWP in parts of the northern middle and high latitudes, which caused the simulated gradients in δCa to be too low.
 Additional tracers were implemented into CAM to quantify the contribution from each surface-to-atmosphere CO2 flux, though the additional tracers are all subject to the same interactive atmosphere-to-surface fluxes (e.g., the fossil fuel tracer can be removed by atmosphere-to-leaf fluxes.). Unlike the results of Cuntz et al. [2002b], the model predictions implied very small contributions to the gradient from biomass burning and fossil fuel consumption likely due to differences in modeled global means (and therefore ecosystem isofluxes), and only about a 0.2‰ global contribution from ocean fluxes. Terrestrial ecosystem respiration contributed the most to the gradient, while leaf-to-atmosphere fluxes caused a stronger equator-pole gradient (i.e., not necessarily a pole-to-pole overall north-south gradient). This contribution from leaves was similar to the findings of Cuntz et al. [2002b] and contrasts with the model results of Peylin et al. , whose low-latitude photosynthesis contribution to the equator-to-pole gradient was nearly canceled out by the contribution from high northern latitude photosynthesis. Because the isotopic composition of atmospheric vapor and precipitation are generally not depleted enough in GCMs (discussed above), it is likely that the discrepancy is due to differences in the isotopic composition of atmospheric vapor and precipitation, and thus more positive midlatitude and high-latitude leaf isofluxes to the atmosphere when forced with GCM water isotopologues.
 In agreement with a wide range of other transport modeling studies, the highest annual mean surface CO2 concentrations for the control simulation were in the Northern Hemisphere, specifically over the northeastern United States and Eastern Europe (Figure 3a), a pattern that is consistent with a seasonal “rectifier effect” [Denning et al., 1996]. These regions also had large differences in CO2 concentrations between boreal winter (mean of December-January-February (DJF)) and summer (June-July-August (JJA)), with high CO2 concentrations during the Northern Hemisphere winter when there was little photosynthetic activity (Figure 3b). Yet the largest difference between DJF and JJA were simulated over western tropical Africa, partially due to large seasonal variations in biomass burning.
 The 18O/16O composition of CO2 (Figure 3c) was lowest over northern middle- to high-latitude forests where the δ18O value of precipitation is relatively depleted and thus carbon fluxes deplete δCa. These areas included the boreal forests of North America, Asia, and Eastern Europe. The high-latitude depletion is often characterized primarily as a result of the very negative soil respiration isoflux. However, if the δ18O value of precipitation—and thus leaf water—is depleted enough, even leaf exchange fluxes can deplete the 18O/16O composition of back CO2. As noted by Still et al. , the isotopic composition of chloroplast CO2 (δCc) needs to exceed ~7‰ before the retro-diffused flux enriches δCa. The simulations of Ciais et al. [1997b] showed high levels of depletion in the Northern Hemisphere's boreal forests, as well as in the Amazon, the Congo, and Southeast Asia, which were attributed to ecosystem fluxes; however, the simulations of Cuntz et al. [2003b] had only slightly depleted values over the Amazon, and to a lesser extent Southeast Asia with enriched values over the Congo. The simulated tropical δCa shown here (Figure 3c) agrees better with the results of Cuntz et al. [2003b] than with Ciais et al. [1997b] with slight depletion over the Amazon and Southeast Asia and enrichment over the Congo.
 The DJF-JJA difference in δCa (Figure 3d) was similar to that of CO2 (Figure 3b) with large differences over some highly productive broadleaf forests like those in tropical Africa, and South America, as well over the northern boreal forests. The model also predicted the largest δCa DJF-JJA differences in the high latitudes (especially in Canada and Russia), which was due to large seasonal variations in isotopically depleted ecosystem CO2 fluxes. For instance, when ecosystem fluxes were highest over North America during June, July, and August, δCa decreased locally because those fluxes acted to lower δCa at middle and high latitudes. During winter months, ecosystem fluxes were depleted but very small, which allowed δCa to slowly approach the global mean of δCa via large-scale transport, thus causing large seasonal amplitudes.
 Simulated seasonal cycles of CO2 and δCa were compared to observed cycles at 45 NOAA sites [White and Vaughn, 2009] where there were the most δCa observations for the 1990–2007 period (Figures 4 and 5). For each station, the 12 monthly means were calculated from each monthly value provided by the NOAA database. As with other studies [Ramonet and Monfray, 1996; Cuntz et al., 2003b], some model grid cells have been shifted to take into account different sampling methods (e.g., Barrow and Cape Grim). It is also common for modeling studies to compare data from high elevation stations with model levels farther up in the atmosphere (e.g., Mauna Loa). Results from the lowest, fourth, and seventh model levels are shown in the figures to demonstrate the simulated seasonal cycles near the surface, the top of the boundary layer, and within the free troposphere, respectively. Model results away from the surface are also shown because many of the observing stations collect air samples when meteorological conditions favor a free atmosphere measurement (thus, limiting the influence of local fluxes). Making the comparison in this way is perhaps better at eliminating local effects than shifting to ocean grid cells, as seasonal changes in ocean fluxes in some regions can be large (e.g., summer ocean fluxes are high near Barrow but close to zero during the winter). To quantify the model's performance, correlation coefficients were calculated for the observed monthly means and the corresponding simulated monthly means at the model's surface, fourth, and seventh levels (corresponding to r1, r4, and r7, respectively). These values are shown in Figures 4 and 5 for each station. Also, the seasonal range (maximum minus minimum) was computed at each station for both the observed and modeled values, and all model-observation differences are given in Tables D1 and D2. Similarly, the phase of the first harmonic (defined as the day of the seasonal maximum) of each seasonal time series was computed using Fourier transforms, and the first harmonic phase differences between model and observations are given in Tables D1 and D2. Furthermore, the CO2 and δCa model/observation differences are shown as a scatter plot in Figure 6 for both the amplitude and phase. It is important to note that the values given in Figures 4 and 5 and Tables D1 and D2 provide a quantification of the model's ability to predict the seasonal cycles, which is rarely done in global modeling studies of δCa (though Peylin et al.  calculated amplitude differences). These values can also serve as reference of comparison for future modeling studies.
 For the Northern Hemisphere stations, observed monthly CO2 concentrations mostly fell on the curves derived from modeled surface values or in between the surface and the free atmosphere; thus, the model accurately captured the seasonal amplitude and phase of atmospheric CO2. For example, at Cape Kumakahi, the seasonal cycle was modeled well at all three layers, as is reflected in the correlation coefficients (r1, r4, and r7 equal 0.991, 0.991, and 0.989, respectively) and the low model-observation differences (Table D1). On the other hand, at Niwot Ridge, simulated amplitudes and phases matched up better with observations at the fourth and seventh levels (reflected in the r values and the differences in Table D1), as this station is at an elevation of 3475 m and the model did not resolve topography well for this region. Indeed, the fifth model level is the layer at which the average geopotential height is closest to the station's elevation. One model weakness found here was inaccurate simulation of CO2 amplitudes in the Southern Hemisphere. An additional model simulation was performed where all ocean fluxes were set to zero, and the results suggest that the Southern Hemisphere CO2 amplitude discrepancy was likely due to inaccurate ocean fluxes and not a problem with calculated land fluxes from ISOLSM. However, the large model amplitude near the tropics and Southern Ocean could also be due to inadequate transport within CAM, advecting too much CO2 from the Northern Hemisphere into the Southern Hemisphere.
 Examining the simulated δCa seasonal cycle (Figures 5 and 6 and Table D2) revealed that the simulated amplitude and phase at the lowest model level agreed well with observations at some stations (e.g., Baltic Sea and Cold Bay), while most stations agreed better with the fourth or seventh atmospheric layer (e.g., Alert, Barrow, and Mauna Loa), and others were not accurately predicted at any atmospheric layer, particularly continental stations that are likely influenced by a range of other surface properties and are less representative of free-troposphere values (e.g., Ulaan Uul, Wendover, and Mount Waliguan). There was also good agreement at stations in the Southern Hemisphere like the South Pole, Cape Grim, and American Samoa, locations where the seasonal cycle is primarily driven by shifts from Northern-to-Southern Hemisphere CO2. The agreements in δCa at these stations and the model's inaccurate CO2 amplitudes at the same locations might indicate possible shortcomings in the spatial distribution of net exchanges with either the ocean or land ecosystems. Alternatively, at Barrow and Alert, the modeled surface amplitude was too large and the phase led the observations by about 2 months (63.5 days for Barrow) when comparing with the model surface level, although there was much better agreement at higher levels in the atmosphere (30.3 days). Figure 6 shows that the model predicts too large of a seasonal amplitude in both CO2 and δCa near the surface at the high northern latitude stations (red points on Figure 6a), a possible indication that the summer drawdown is too large in the high latitudes, which would also over-deplete atmospheric CO2 in 18O. The values in Table D2 reveal that in general, the model led observations at northern middle- and high-latitude locations, a common model shortcoming in previous studies, while slightly lagged the observations in the high latitudes of the Southern Hemisphere. Conversely, the phase differences were smallest in the tropics and subtropics. Based on the correlation coefficients in Figure 5 and the amplitude and phase differences, the stations where the model performed the worst were at Mount Waliguan and Wendover, Utah, where both the amplitudes and phases were inaccurately simulated. It was found that the model better captured the seasonal cycle at these locations when comparing the observations with levels farther up in the atmosphere beyond the seventh level, which suggests that the model/observation mismatch is likely due to the model not resolving certain topographic features well for these mountainous regions. The mismatch could also be due to local fluxes that are unresolved in the model. However, there does not appear to be a clear relationship between phase differences in both δCa and CO2 (Figure 6b). The modeling of the δCa seasonal cycle remains a challenge in the modeling community as this study and others [Ciais et al., 1997b; Peylin et al., 1999; Cuntz et al., 2003b; Wingate et al., 2009] have failed to demonstrate accurate modeling of the cycle at every location around the world, particularly the phase at high-latitude stations. Because the model best predicted the global mean and north-south gradient of δCa, the sensitivity of the δCa seasonal cycle is only briefly discussed in section 5.
 Validation of the control simulation provides some assurance that sensitivity calculations are meaningful; however, as in all modeling studies, we are cautious not to overstate the accuracy of any particular prediction. We have shown that many of the basic features of the CO2 and δCa climatology were well captured by this model. Nonetheless, no model is perfect, and one can certainly identify shortcomings in the reproduction of the existing observations. To minimize the influence of model shortcomings in our findings, the model experiments were designed to test the robustness of the mechanistic calculations that underpin the computed CO2 and CO18O fluxes, while atmospheric transport accounts for the nonlocal influences of those fluxes. Buenning et al.  argued that this type of approach was required to compliment observational work that can only provide limited assessment of mechanisms. As such, the focus of the model experimental results are on large-scale δCa features, rather than on regional or local changes, since the modeled circulation is more reliable on large spatial scales, as demonstrated in the relatively accurate predicted mean and north-south gradient of δCa.
4 Sensitivity of δCa
4.1 Sensitivity to Soil CO2 Hydration Rates
 The HYD20 and HYD300 simulations globally increased the soil CO2 hydration rates at all locations. Like the experiments of Wingate et al. , the increased hydration resulted in a decrease in the global mean δCa (Table 2) and an increase in the north-south δCa gradient (Figure 7a). The decrease in global mean δCa due to increased hydration rates was a result of the invasion flux being accounted for in ISOLSM [Riley et al., 2003; Riley2005]; this explanation is consistent with that reported by Wingate et al. .
Table 2. Changes in the Global Annual Means of Transpiration (QV), Evaporation (QE), Photosynthesis (PSN), Fla, Fr, δWl, δWS, δFla, δFr, and δCa
 The north-south δCa gradient increased by 0.29‰ and 0.48‰ for the HYD20 and HYD300 experiments, respectively, which agrees well with the results of Wingate et al. . Figure 8 shows that the largest change in δCa for the two experiments occurred in high northern latitudes. The largest change to annual mean δCa occurred over northern Siberia, where soil water δ18O values were especially depleted [Ciais et al., 1997a]. Despite the simulated increase in the north-south gradient in δCa found here, the experiments did not result in a better agreement with the observations in both the global mean (0.68‰ too low for HYD300) and the north-south gradient (0.58‰ too steep for HYD300), as it did in Wingate et al. . Additionally, there is very little observational basis for such increased soil CO2 hydration rates across a range of ecosystems. And, as was shown by Riley et al.  and Riley , increasing soil hydration rates in those ecosystems with sharp gradients in upper soil water isotopic composition from evaporation can also enrich δCa. In the following subsections, we show that the modeled north-south gradient is also sensitive to other variables that affect the δCa budget and not considered by Wingate et al. .
4.2 Sensitivity to Relative Humidity
 Transpiration is driven by the diffusion of vapor from leaves, and that rate is driven by the difference between the vapor pressure in the interior of plant leaves and the vapor pressure of the surrounding air. As such, transpiration (and latent heat exchange in general) is expected to change when atmospheric relative humidity increases, as has been seen in observations during the mid-1990s for some high-flux regions [Buenning et al., 2011]. Indeed, when relative humidity was increased by 3.3% (on an absolute basis), the global mean transpiration decreased by 3.6% (Table 2) due to a decrease in the vapor pressure gradient.
 A similar result was found for soil water where increased humidity caused a 2.9% reduction in evaporation and a slight increase (1.4%) in soil moisture. These changes in latent heat fluxes likely caused a change to the CO18O isoflux to the atmosphere from the leaves (Ila) and respiration (Ir), which can be quantified by:
 It can be seen from equations (14) and (15) that the isofluxes are dependent on both the magnitude and the isotopic composition of the fluxes, δFla and δFr (note that both δF values factor in kinetic fractionation). Because the isotopic composition of the flux is strongly related to the isotopic composition of leaf and soil water, changes to δWl and δWS are first evaluated, followed by an assessment of changes from leaf and respiration fluxes (Fla and Fr).
 The predicted decrease in transpiration from increased relative humidity is consistent with an effective reduction in kinetic fractionation (equation (B4)). This change reduced leaf water 18O enrichment, resulting in a reduced enrichment of the CO2 molecules in equilibration within the stomatal cavity. The global changes in the isotopic compositions of leaf and soil water following a 3.3% absolute increase in relative humidity were −0.38‰ and −0.081‰, respectively. Differentiating equation (B4) with respect to humidity gives an upper limit to the expected relationship between leaf water 18O/16O content and humidity; for typical values of δWX, δWCV, and the fractionation coefficients, ∂δWl-CG/∂hl ≈ −0.36‰ %−1. ISOLSM predicted that the 3.3% increase in relative humidity only caused a 2.0% increase in photosynthesis-weighted hl. This change in hl caused a global reduction in photosynthesis-weighted δWl to be slightly over half the theoretical value expected from the Craig and Gordon  steady state model. This difference was partially due to the fact that ISOLSM used the time-dependent leaf water model rather than the steady state model, and partially due to the inclusion of leaf boundary layer effects [Still et al., 2009]. The nonsteady state model reduced the diurnal amplitude of leaf water enrichment and in particular restricted the otherwise extreme enrichment during early afternoon.
 Predicted changes in leaf and soil CO2 fluxes are shown in Table 2. The increase in relative humidity caused a global increase in predicted assimilation, which in turn increased the leaf-to-atmosphere flux globally by 4.2%, and thereby increased the isoflux to the atmosphere. However, this effect was partially balanced by the reduction in δFla. The RH experiment also showed similar changes to the soil-respired CO2 fluxes, which for many regions deplete δCa. Growth respiration is related to both the leaf area index and assimilation, and because assimilation increased, growth respiration also increased, which led to an overall increase in total ecosystem respiration. For regions where soil respiration depletes δCa values, the combination of more depleted soil water (and thus decreased δFr) and increased respiration both acted to increase the depleting isoflux, Ir. Thus, it was not clear if the changes to leaf fluxes caused δCa to go up or down from equation (14) alone, though the changes to respiratory fluxes should in all cases cause δCa to decline (through equation (15)), which highlights the need to use a fairly comprehensive land surface model like ISOLSM.
 The RH experiment (where relative humidity was increased by 3.3% globally) depleted δCa by 0.21‰. Results from RHTROP (where relative humidity was increased by 3.3% only within the tropics) suggest that 0.073‰ of this response was from the tropics (Table 2), an indication that δCa is more sensitive to relative humidity in regions outside of the tropics. This was at least partly due to the uniformly high relative humidity found in most tropical areas: At high humidity, δWl is dominated by atmospheric water vapor isotopic composition and equilibrium fractionation effects, similar to the extreme case noted in Appendix B with 100% relative humidity. By contrast, in extratropical regions where relative humidity is often below 50%, the impact of soil source water and kinetic isotope effects are more important for δWl, and thus increases in relative humidity in these regions might have larger impacts. Additionally, because δFla and δFr are close to background δCa, tropical isofluxes are smaller than would be expected based on CO2 fluxes. If one were to estimate the global mean change in δCa due to changes in leaf water enrichment by means of the budget equation used by Buenning et al.  for the RH experiment (with their equation applied globally), the estimated change in δCa would be −0.63‰. This comparison indicates that feedbacks, atmospheric transport, and changes to CO2 fluxes counteracted the expected changes due to decreased δWl alone.
 The RH experiment increased the north-south δCa gradient by 0.13‰, while the RHTROP slightly decreased the gradient by 0.023‰ (Figure 7b). When the humidity was changed globally, the largest decrease to δCa occurred over northern Canada and Siberia (Figure 9a). When the relative humidity anomaly was only applied to the tropics, the change in δCa over the northern regions was relatively small (Figure 9b). Northern Canada and Siberia have strong negative isofluxes from both leaf and soil fluxes, and the relative humidity increase not only further depleted the isotopic composition of these fluxes but also increased the fluxes themselves. This response was not the case for regions within the subtropics and parts of the middle latitudes where leaf fluxes do not always deplete the atmosphere of CO18O. These results suggest that the north-south δCa gradient can be increased by global increases in relative humidity, and one might expect the change to be greater if relative humidity were only to rise in the middle and high latitudes. These results suggest the possible use of the north-south δCa gradient measurement as a sensitive proxy of flux-weighted relative humidity changes in midlatitude and high-latitude regions of the Northern Hemisphere. For instance, Buenning et al.  showed how relative humidity increased during the mid-1990s throughout most of central Europe, a broad region of Siberia, and most of western North America. This would have caused an increase in the north-south gradient; however, relative humidity also increased in the Tropical Americas and the Asia Pacific during the mid-1990s, which likely outweighed the midlatitude change.
4.3 Sensitivity to δ18O Values of Precipitation and Water Vapor
 The isotopic composition of leaf and soil water depends principally on the δ18O values of precipitation and atmospheric water vapor (δWP and δWAV), along with kinetic and equilibrium fractionation factors. The soil water 18O/16O content should be closely linked with δWP, and also with δWAV in upper soil layers subject to evaporation. The value of δWl depends on the δ18O values of soil water (via root uptake without fractionation; equation (B4)) and on the δ18O values of canopy vapor. Therefore, it is hypothesized here that decreases in δWP will reduce both δWl and δWS, which would ultimately reduce δCa.
 As described in section 2.4, two experiments were constructed to examine the effects of changes in δWP independent of changes in δWAV: (1) an overall 3.2‰ decrease in δWP (PREC) and (2) a 3.2‰ decrease in δWP in only the tropics (PRECTROP). The reduction of δWP by 3.2‰ caused δWl and δWS to decrease globally by 2.1‰ and 2.7‰, respectively (Table 2). Results from the PRECTROP simulation revealed that the tropics contributed about half of the change in photosynthesis-weighted δWl (i.e., the tropics made up about half of global photosynthesis in our simulation).
 To examine the impact of the δ18O value of atmospheric water vapor (δWAV)—independent of changes in δWP—on the isotopic composition of leaf and soil water, the same perturbations were applied to δWAV. Lowering δWAV by 3.2‰ (WV) caused a global decrease in δWl and root-weighted δWS of 1.4‰ and 0.065‰, respectively. When the change was only applied to the tropics, there was approximately no change to the global mean δWS and a decrease in δWl of 0.67‰. These results suggest that δWl is sensitive to changes in the isotopic composition of atmospheric vapor as implied by equation (B4), though soil water is not. Not surprisingly, these simulations revealed that δWS is mostly dependent on the isotopic composition of precipitation, but δWl depends on both the isotopic composition of precipitation and vapor. However, it should be noted that these dependencies are partially a result of the equations used in ISOLSM (e.g., Riley et al. [2002, equation (20)]).
 In the PRECWV simulation, where δWP and δWAV were both reduced by 3.2‰, the isotopic composition of root-weighted soil water decreased by only 3.0‰. The small discrepancy between the perturbation and the response was a result of bottom layer recharge when the soil column dried out. In the model, the recharged water carries the same isotopic composition of the bottom soil layer, so the recharge of bottom layer water was only indirectly affected by the isotopic forcing. The isotopic composition of soil water becomes even less dependent on precipitation if the rate of recharge is greater than the infiltration rate. Results from the PRECWVTROP simulation showed that 1.7‰ of the change in δWl came from the tropics, which again was a consequence of about half of global photosynthesis coming from the tropics.
 The changes in the isotopic composition of ecosystem leaf and soil water pools induced similar changes to the isotopic composition of ecosystem CO2 fluxes and subsequently of atmospheric CO2 (Table 2 and Figure 10). For the experiments in which only the isotopic composition of precipitation was reduced (PREC and PRECTROP), global and annual mean δCa decreased by 1.8‰ and 0.92‰, respectively. The reduction in δCa was not as large when only δWAV was decreased in the WV and WVTROP simulations (−0.78‰ and −0.37‰, respectively). When the isotopic composition of both precipitation and water vapor were reduced in the PRECWV and PRECWVTROP experiments, the model predicted the largest change to the global and annual mean δCa (−2.6‰ and −1.3‰, respectively). It is not likely the changes to δWP and δWAV occurred globally; however, Buenning et al.  highlighted three tropical stations (Bangkock, Darwin, and Izobamba) within the Global Network of Isotopes in Precipitation (GNIP) network that observed a decrease in δWP during the mid-1990s (note that there were only five tropical GNIP stations that have more than 90 months of data on record from 1990 to 2005). Welp et al.  showed that this decrease also occurred for a spectrally nudged simulation of the Isotope-incorporated Global Spectral Model (IsoGSM) [Yoshimura et al., 2008]. Recall that this is the same time interval in which certain tropical and midlatitude regions observed an increase in relative humidity. Thus, it is possible that tropical changes to relative humidity, δWP, and δWAV drove a large fraction of the observed decrease in δCa during the 1990s.
 The three globally perturbed experiments drove significant increases in the δCa latitudinal gradient (Figure 7c). Indeed, the largest impacts to δCa occurred over the continents, especially over northern Canada and Siberia (Figure 10). These results indicate that the north-south δCa gradient is especially sensitive to global changes in the 18O/16O composition of both vapor and precipitation (without corresponding changes to the δWp and δWAV gradients, i.e., when all values are shifted to more negative values). On the other hand, when the offset was only applied to the tropics, the opposite effect occurred. Although the tropics-only experiments caused a decrease in δCa at all latitudes (Table 2 and Figure 10), the largest decrease occurred in the Southern Hemisphere and within the tropics, thus decreasing the north-south δCa gradient. We therefore conclude that the largest increase in the δCa gradient will occur when δWp and δWAV decrease only in the northern middle and high latitudes.
4.4 Sensitivity to Radiation
 The LIGHT experiment attempted to represent light levels following the eruption of Mount Pinatubo by reducing total downwelling solar radiation by 4% and repartitioning 7.5% of the direct light to diffuse light (15% total) [Gu et al., 2003]. ISOLSM is well suited for this experiment, as it calculates both sunlit and shaded leaf photosynthesis, and shade leaf light use efficiency (LUE) is about 4 times greater than sunlit leaf LUE. Model predictions revealed that these combined radiation changes caused global mean transpiration to decrease by only 0.059%. Two additional simulations were conducted that imposed each light level change separately to better understand which change dominated the model response. Because diffuse light is able to reach the leaves deeper within the canopy, proportionally more evaporation from shade leaves can result, and thus, more diffuse light could drive an increase in ecosystem transpiration and photosynthesis when and where the leaf area index is high and midday light saturation occurs. On the other hand, the 4% reduction in total solar downwelling will cause decreases in leaf temperature and water evaporation from the mesophyll cells. Results from the additional experiments revealed that the 4% reduction caused global transpiration (mostly from sun leaves) to decrease by 1.85%, while the repartitioning from direct to diffuse radiation caused a 1.80% increase in transpiration. Thus, the two radiation changes opposed one another and resulted in a very small change in global average transpiration.
 The very small change in transpiration was not expected to greatly impact the isotopic composition of leaf water. However, photosynthesis-weighted δWl was reduced globally by 0.19‰. About 0.1‰ of the change was due to a 0.3% global increase in photosynthesis-weighted values of hl that resulted from the radiation changes. The other 0.09% was due to increases in photosynthesis, especially over the northern boreal forests where δWl was low relative to the global mean. The 0.19‰ decrease in δWl resulted in a 0.16‰ decrease in δFla. The decrease in soil evaporation lowered δWS by only 0.013‰, though the values of δFr increased globally by 0.019‰. The difference in sign between these two isotopic changes was a result of a slight decrease in soil temperatures, which slightly increased the H2O-CO2 equilibrium fractionation (equation (1)).
 The light level changes only caused a 0.048‰ decrease in the global mean δCa, which was a much smaller response compared to the relative humidity and isotope hydrology changes (Table 2). Not surprisingly, the north-south gradient also exhibited only a small change, a decrease of 0.073‰ (Figure 7d). Despite this small change, δCa was most sensitive to radiation changes in the interior of northern Canada and northern Asia (Figure 11a), the same regions where relative humidity and isotope hydrology changes caused the largest δCa response. These responses (and the responses discussed in the previous two subsections) occurred because δFla was lowest for these two northern regions (Figure 12), and thus had the most negative isoflux from leaves (equation (14)) of any continental regions (i.e., had the largest impact on δCa). Any decrease to δFla (as occurred in the global sensitivity experiments shown here) will cause the leaf retro-diffused isoflux to be even more negative and further drive down regional δCa. On the other hand, certain locations in the tropics and subtropics have δFla that are higher than δCa; thus, lowering δFla would bring the leaf-to-atmosphere isoflux closer to zero (though the atmosphere-to-leaf component will always be positive).
4.5 Sensitivity to Temperature
 Temperature influences the isotopic composition of leaf and soil water—and eventually that of CO2—partially through its impact on equilibrium fractionation [Majoube, 1971]:
 Differentiating equation (16) with respect to temperature results in a sensitivity of dεLV/dT = −0.099‰ K−1 at 280 K. Furthermore, in the middle and high latitudes, temperature can also constrain ecosystem fluxes [Nemani et al., 2003]. Thus, temperature influences both the isotopic composition and the magnitude of the CO2 and H2O fluxes (in often counteracting ways).
 Results from the TEMP experiment, in which global surface air temperatures were increased by 1 K, showed a change in global transpiration and soil evaporation of 0.89% and −0.63%, respectively; implying that the air temperature increase only slightly modified the partitioning of latent heat components (note that this experiment did not alter atmospheric relative humidity). δWS decreased globally by 0.055‰, which was less than the theoretical sensitivity based on equilibrium fractionation. Photosynthesis-weighted δWl decreased globally by 0.19‰. By calculating the global means of other variables (such as relative humidity and surface temperature), it was determined that 0.014‰ of the decrease was due to the decrease in δWS, 0.088‰ from the change of εLV in equation (B4), 0.010‰ from changes to photosynthesis, and about 0.055‰ due to a slightly increased relative humidity at the surface of the leaf.
 Temperature-dependent equilibrium fractionation also takes place as CO2 interacts with leaf and soil water [Ciais et al., 1997a], with a temperature sensitivity of dεeq/dT = −0.22‰ K−1 at 280 K (recall that εeq = (αeq − 1) × 1000). Both δFla and δFr decreased more than the isotopic composition of leaf and soil water, which was a result of the reduction in equilibrium CO2-H2O fractionation due to increased ground and leaf temperatures (both of which increased globally by about 0.89 K). The global mean δCa decreased by 0.16‰ (Table 2), and the north-south δCa gradient increased by only 0.054‰ (Figure 7e). As in the other experiments, the largest response was in the northern parts of Canada and Asia where the negative isoflux in the control simulation was the greatest (Figure 11b). These results indicate that the influence of changes in temperature on the isotopic composition of leaf and soil water, and thereby on the isotopic composition of ecosystem fluxes, can affect the global mean of δCa, though it has little effect on the north-south δCa gradient.
4.6 Sensitivity to Assimilation/Respiration Partitioning
δCa is commonly thought of as a tracer of the partitioning between assimilation and respiration. In the ASSIM experiment, assimilation was increased globally by 3.6% (an estimate used by Buenning et al. ), while nonleaf respiration fluxes were held unchanged relative to the control simulation. Thus, there was no change to the isotopic composition of the fluxes for this experiment, simply a change in the balance between assimilation and respiration. It should be noted that because these perturbations change the net ecosystem change (relative to the other simulations), the resulting CO2 concentrations during the spin-up interval will be different than the other simulations. Globally, the 3.6% increase in photosynthetic fluxes caused a 0.10‰ increase in δCa. Simulated global gross primary production (minus leaf respiration) was 123.9 GtC yr−1 for the control simulation, and thus, the ASSIM experiment increased FA by 4.5 GtC−1 yr−1. Given the relationship between FA and its constituent gross fluxes Fal and Fla, this change caused the magnitudes of Fal and Fla to increase by 17 and 12 GtC yr−1, respectively. This implies that the sensitivity of δCa to increases in assimilation is 0.022‰ (GtC/yr)−1 (assuming no change to nonleaf respiration). Despite the increase in mean δCa, the north-south gradient in δCa increased by 0.17% (Figure 7e), due primarily to Fal fluxes which acted to enrich atmospheric CO2 in 18O. The enriching effect caused large positive isofluxes to and from leaves in the tropics and reduced negative isofluxes poleward. Indeed, Figure 13a shows how the ASSIM simulation resulted in large changes to δCa over certain tropical locations and almost no change in some high-latitude regions (e.g., equatorial Africa and Siberia, respectively).
 Globally, the RESP experiment increased respiration by 4.4 GtC yr−1. This change to respiration decreased the global mean δCa by 0.10‰. Thus, the model results suggest that the impact of global respiration on δCa is 0.023‰ (GtC/yr)−1, assuming all other fluxes remain unchanged. In the RESP simulation, the north-south δCa gradient decreased by 0.061‰ relative to the control simulation (Figure 7e). Similar to the ASSIM simulation, the δCa change was smallest in the middle and high latitudes (Figure 13b). This pattern was due to the fact that fluxes were much larger in the tropics, and a fractional change to global fluxes has the largest influence on tropical fluxes. The larger increase in isotopically depleted respiration lowered tropical δCa, which lowered the north-south δCa gradient.
5.1 Model and Budget Prediction Comparisons
 Some of the perturbation described above can be estimated from budget CO2 and δCa equations. If there were no seasonal variation, the global steady state, δCa-ss, can be analyzed following Cuntz et al. [2003a] by taking equations (12) and (13) at steady state and solving for the atmospheric isotopic composition:
 Specifically, the steady state δCa is a weighted average of the isotopic composition of the contributing fluxes where the weighting is simply the fractional contribution for each flux to gross surface exchange. In this subsection equation (19) is used to compare with the ISOLSM/CAM modeling results for the experiments that changed ecosystem fluxes (Fla, Fal, and Fr) and those that changed the isotopic composition of precipitation and vapor (and thus δFla and δFr).
 The ASSIM experiment increased leaf fluxes by 3.6% with no change to the isotopic composition of the fluxes (i.e., changes the averaging weights in the budget equation). The budget equation predicts a δCa increase of 0.10‰, which was also the change in CAM. The results were also similar for the RESP experiment where respiration was increased by 3.6%, both predicting a δCa decrease of 0.10‰. These results demonstrate the robustness of the budget equation for predicting changes to δCa for these particular experiments.
 When both δWP and δWAV decrease by 0.32‰ (the PRECWV experiment), modeled δFla and δFr decrease by 0.32‰ and 0.39‰, respectively. This resulted in a modeled change of −2.6‰. Indeed, when the different values of δFla and δFr are factored into the budget equation, the predicted change in δCa is −2.7‰, which is not dissimilar to the results from CAM. When the change is only applied to the tropics, the values of δFla and δFr change by −1.5‰ and −1.9‰, respectively. In turn, the budget equation predicts a δCa change of −0.69‰. Interestingly though, ISOLSM/CAM predicts a δCa change of −1.3‰, almost double the estimate from the budget equation. This discrepancy shows how applying certain changes to one region or one latitudinal zone (as opposed to a global perturbation) can introduce nonlinear effects due to feedbacks within the system. This particular outcome likely resulted from the perturbation only being applied to the tropics and the fact that CO2 is quickly cycled through the ecosystem within the tropics, a feature that is unresolved with the budget equation.
5.2 Sensitivity of Simulated Seasonal Cycles of δCa
 The sensitivity experiments presented in section 4 not only changed the global mean and spatial variations of δCa but they also changed the δCa seasonal cycle. In section 3, it was shown that the model had many shortcomings when predicting the observed seasonal δCa cycle, though it is possible that one or more of the model experiments could have improved the model/observation comparison. Table 3 shows how the seasonal amplitude compares with the observations for the control simulation and each experiment at four stations (Barrow, Mauna Loa, Cape Grim, and the South Pole). The largest model/observation mismatch in the δCa seasonal amplitude occurred at the high northern latitude stations (Figure 6a). At Barrow, the simulated seasonal amplitude matched better with observations when the δ18O values of precipitation and/or vapor were decreased in the tropics only (e.g., PRECTWVTROP). This result was largely due to the fact that δCa is lowered by local ecosystem fluxes during the growing season, and returns to background values when fluxes shut off during winter months. This seasonal effect will have less of an influence if precipitation and vapor δ18O values have a reduced equator-to-pole gradient (as was done in the experiments). To a lesser extent, the amplitude also improved for the HYD300 experiment, which caused a global reduction in the isotopic composition of CO2 fluxes from soils (Table 2). This had the largest influence in the tropics, where fluxes are not as seasonal, which caused a reduction in the background δCa and thus lowered the seasonal amplitude.
Table 3. Model/Observation Difference in the Seasonal Cycle δCa Amplitude at Barrow (BRW), Mauna Loa (MLO), Cape Grim (CGO), and South Pole (SPO) for the Control and Experimental Simulationsa
Units are ‰.
 Table 4 displays the model/observation mismatch for the δCa seasonal phase at the same four stations. Unfortunately, the phase of the seasonal cycle did not change significantly for any of the model experiments at Barrow, Cape Grim, or the South Pole. There was a slight change (~ 15 days) at Mauna Loa when the both δWP and δWAV were decreased in the tropics. The seasonal phase at Mauna Loa is related to the movement of the Hadley Cell, such that it lies under tropical air for most of the year and northern midlatitude air masses during the boreal winter. The reduction in both δWP and δWAV caused a decrease in the difference between the two air masses and slightly shifts the timing of the drop in δCa. However, Mauna Loa was not a location where the phase of the δCa seasonal cycle was particularly problematic. Furthermore, these results suggest that the seasonal phase model shortcomings at middle and high latitudes are likely related to the seasonal timing of one or more δCa driving variable, rather than mean global or tropical model biases.
Table 4. Model/Observation Difference in the Seasonal Cycle δCa Phase at Barrow (BRW), Mauna Loa (MLO), Cape Grim (CGO), and South Pole (SPO) for the Control and Experimental Simulationsa
Units are days.
5.3 Additive Influence of Variables
 Additional experiments were performed that examined how certain variables that are related to one another affect the simulated δCa. The purpose of the additional simulations is to examine the degree to which the response of modeled δCa to multiple variable changes is additive. These simulations were done with respect to the simulation that increased global atmospheric temperatures by 1 K, the TEMP experiment. Assuming that vapor and precipitation δ18O values also increase according to the approximate slope of 0.7‰ K−1 [Johnsen et al., 1989], two experiments were conducted that applied a 0.7‰ increase to the water isotopologues, both with and without the 1 K increase. Another set of experiments decreased relative humidity by 4% (which is approximately the relative humidity change at 20°C and a relative humidity of 70%), both with and without the temperature change.
 When both δWP and δWAV increase globally, δCa responds by increasing by 0.612‰, which is consistent with the results of the PRECWV simulation, but scaled down. When this isotopic forcing perturbation is applied with the 1 K increase in temperature, the model predicts a global δCa change of 0.48‰. Though dependent on the choice of the temperature-isotope slope (which others have predicted to be lower), these model results would suggest that the influence on δCa from the 1 K increase in air temperatures would get outweighed by the subsequent increase in precipitation and vapor δ18O values. Furthermore, the results from section 4.4 showed how δCa decreased globally by 0.13‰ with only a 1 K increase in global atmospheric temperatures. Thus, the additional simulations indicate that the response of δCa to both the temperature and isotope hydrology perturbations is similar and almost identical to the additive response to each perturbation.
 Another additional experiment decreased relative humidity by 4% (4 percentage points), while increasing air temperature by 1 K. The global change in δCa from this experiment was an increase of 0.13‰. When only the decrease in relative humidity was applied to the forcing, the global mean value of δCa increased by 0.27‰. Again, because increasing temperatures by 1 K alone caused δCa to decrease by 0.13‰ implies that the two influences are nearly linear. However, unlike the previous scenario, the temperature influence was slightly stronger (though only by 0.01‰) when combined with the relative humidity change.
 A mechanistic, isotope-enabled land model (ISOLSM) was used to simulate global terrestrial fluxes of CO2, including their oxygen isotope composition. These were then combined with additional CO2 fluxes such as ocean gas exchange and fossil fuel emissions in a three-dimensional global transport model (CAM) to simulate atmospheric CO2 and CO18O. This framework accurately captured the global mean, north-south gradient, and to a lesser extent, the seasonal cycle of δCa. To develop an understanding of the controls on observed annual mean and spatial variations in δCa, model sensitivity experiments were performed to examine the effects of changes in soil CO2 hydration rates, relative humidity, δ18O values of precipitation and water vapor (δWP and δWAV), radiation levels, temperature, and assimilation/respiration partitioning on δCa. The sizes of each of the perturbations were based on observed variations discussed elsewhere [e.g., Robock, 2000; Gu et al., 2003; Buenning et al., 2011].
 The results presented here suggest that δCa is strongly dependent on hydrologic changes, such as changes to relative humidity and isotope hydrology (i.e., δWP and δWAV), an indication that the global mean δCa responds principally to changes in the isotopic composition of leaf and soil water rather than global changes to ecosystem CO2 fluxes. Our results are consistent with recent studies that have suggested that water isotope forcing and relative humidity had the largest influence on the observed interannual δCa variations [Buenning et al., 2011; Welp et al., 2011].
 The other main objective of this study was to characterize controls on the spatial variations of δCa, and in particular the north-south δCa gradient. Wingate et al.  showed that the simulated gradients were increased and better matched with observations when soil CO2 hydration rates were increased by factors of 20 and 300. Similar to their results, the model used in this study showed an increase in the gradient (of comparable magnitude) when hydration rates were increased by the same factors. However, it did not improve the global and zonal mean data model comparison; in fact, it made the comparisons worse. Our model experiments suggested that the gradient could also be increased by decreases in global or middle- and high-latitude values of δWp and δWAV (which also decreased global mean δCa). To a lesser extent, increased global and middle- and high-latitude relative humidity also caused nontrivial increases to the north-south δCa gradient. Variations to the CO2 flux partitioning also caused the north-south δCa gradient to change, such that the gradient increased when leaf fluxes increased (and nonleaf respiration remained unchanged relative to the control) and decreased when nonleaf respiration increased (but photosynthesis was not changed).
 The isotope hydrology experiments are particularly interesting in the context of the simulations of Wingate et al. , in that many isotope-equipped global models fail to simulate the proper depletion in δWp at middle and high latitudes. Noone and Sturm  showed that, over northern Canada and Siberia, GCMs commonly simulated precipitation δ18O values that were not low enough. Furthermore, the results shown here suggest that the gradient is most sensitive to δWp and δWAV, especially in the middle and high latitudes. So it is not surprising that a modeled north-south gradient would be too low if both δWp and δWAV were too high outside of the tropics and subtropics, which might have been the case for the control simulation of Wingate et al.  (which simulated a too-weak north-south gradient). Recall that the values of δWp and δWAV used here were constrained by GNIP observations, so such a bias did not occur for the model used in this study, and in turn, the CTRL simulation accurately captured the north-south δCa gradient. This study does not contradict findings elsewhere for a strong potential influence of soil CO2 hydration rates on the north-south δCa gradient, but rather our control simulation already captured the gradient accurately, likely due to correct water isotope gradients. In fact, the model results presented here suggest that even modest changes to the global mean or spatial variations of δWp and δWAV can strongly influence the north-south δCa gradient.
CO2 mixing ratio in the atmosphere, mole fraction.
CO18O mixing ratio in the atmosphere, mole fraction.
CO2 mixing ratio at the surface chloroplast within leaf stomata, mole fraction.
CO2 mixing ratio inside the stomatal pores, mole fraction.
CO2 flux into leaves, mol m−2 s−1.
CO18O flux into leaves, mol m−2 s−1.
CO2 flux into the ocean surface, mol m−2 s−1.
CO18O flux into the ocean surface, mol m−2 s−1.
CO2 flux from biomass burning, mol m−2 s−1.
CO18O flux from biomass burning, mol m−2 s−1.
CO2 flux out of leaves, mol m−2 s−1.
CO18O flux out of leaves, mol m−2 s−1.
CO2 flux due to fossil fuel consumption, mol m−2 s−1.
CO18O flux due to fossil fuel consumption, mol m−2 s−1.
Gross Primary Product minus leaf respiration, mol m−2 s−1.
Net flux of CO2 from ocean water, mol m−2 s−1.
CO2 flux from the ocean surface, mol m−2 s−1.
CO18O flux from the ocean surface, mol m−2 s−1.
CO2 flux from soil respiration, mol m−2 s−1.
CO18O flux from soil respiration, mol m−2 s−1.
Relative humidity at leaf surface, range of 0 to 1.0.
Isoflux from leaf-to-atmosphere fluxes, ‰ mol m−2 s−1.
Isoflux from soil respiration, ‰ mol m−2 s−1.
Air-sea gas exchange coefficient, mol m−2 s−1 Pa−1.
Unit conversion factor, moles of air m−2.
Partial pressure of CO2 in the atmosphere, Pa.
Partial pressure of CO2 at ocean surface, Pa.
Photosynthesis, mol m−2 s−1.
Soil evaporation, µmol m−2 s−1.
Transpiration from vegetatoin, µmol m−2 s−1.
18O isotopic ratio of leaf water.
18O isotopic ratio of CO2 equilibrated with leaf water.
18O isotopic ratio of CO2 equilibrated with surface ocean water.
18O isotopic ratio of surface ocean water.
18O isotopic ratio of atmospheric O2.
18O isotopic ratio of root-weighted soil water.
18O isotopic ratio of CO2 equilibrated with root-weighted soil water.
18O isotopic ratio of canopy water vapor.
18O isotopic ratio of atmospheric water vapor.
2.08835 × 10−3, 2.0052 × 10−3.
Surface temperature of either: ocean, soil, or vegetation, K.
Temperature-dependent CO2 equilibration factor.
Effective kinetic fractionation factor for CO18O diffusion in and out of the stomata.
Effective kinetic fractionation factor for CO18O diffusion in and out of surface ocean water.
δ18O-CO2 value of free air, ‰ versus VPDB-CO2.
δ18O-CO2 value of CO2 equilibrated with leaf water, ‰ versus VPDB-CO2.
δ18O-CO2 value of CO2 equilibrated with surface ocean water, ‰ versus VPDB-CO2.
δ18O-CO2 value of CO2 equilibrated with soil water, ‰ versus VPDB-CO2.
δ18O-CO2 value of leaf-to-atmosphere CO2 flux, ‰ versus VPDB-CO2.
δ18O-CO2 value of soil respiration, ‰ versus VPDB-CO2.
δ18O value of atmospheric water vapor, ‰ versus VSMOW-H2O.
δ18O value of canopy water vapor, ‰ versus VSMOW-H2O.
δ18O value of leaf water, ‰ versus VSMOW-H2O.
δ18O value of leaf water using the Craig-Gordon estimation, ‰ versus VSMOW-H2O.
δ18O value of precipitation, ‰ versus VSMOW-H2O.
δ18O value of root-weighted soil water, ‰ versus VSMOW-H2O.
Effective kinetic fractionation factor for CO18O diffusion in and out of the stomata, ‰.
Effective kinetic fractionation factor for CO18O diffusion in and out of surface ocean water, equal to +0.8‰.
Temperature-dependent CO2 equilibration factor in δ notation.
H218O kinetic fractionation factor for molecular diffusion.
The temperature-dependent equilibrium fractionation of H218O during the liquid-vapor phase transition.
Determining Potential Drivers of δCa
 Five fluxes are principally responsible for CO2 variations in the atmosphere, and these processes also dominate the global δCa budget [Farquhar et al., 1993; Ciais et al., 1997a, 1997b]: photosynthetic assimilation, soil respiration, ocean exchanges, fossil fuel emissions, and biomass burning. Considering just these exchanges, the global budget for δCa can be written as
where Ca is atmospheric CO2 mixing ratio, Ma is a flux conversion factor (mol air m−2), F stands for CO2 fluxes (mol m−2 s−1), Δ refers to (apparent) discriminations against CO18O (in ‰). Subscripts A, r, o, f, and b refer to assimilation, respiration, ocean, fossil fuel, and biomass burning, respectively. The first two terms within the brackets of equation (B1) can be written as [Farquhar et al., 1993; Ciais et al., 1997a]
where CC is the CO2 mixing ratio at the surface of the chloroplast within leaf stomata, ε values are kinetic fractionation factors associated with diffusion, and subscripts l and S refer to leaves and soil, respectively. It can be seen from equations (B1) to (B3) that δCa can be affected by changes in the magnitude of terrestrial CO2 fluxes and in the isotopic composition of leaf and soil CO2.
 Assimilation and stomatal conductance are principally sensitive to the photosynthetic photon flux density, relative humidity, air temperature, and CO2 concentrations [Jarvis, 1976; Wong et al., 1978; Stewart, 1988; Jones and Higgs, 1989; Collatz et al., 1991]. The photosynthesis-temperature relationship is particularly complicated because it involves both direct and indirect effects (through changes in relative humidity) that oppose one another. Nonetheless, these three variables (photon flux density, humidity, and temperature) can directly alter leaf CO2 fluxes and thereby cause changes in δCa.
 Root growth and maintenance respiration and heterotrophic respiration produces CO2 in the soil that takes on the isotopic signature of local water (i.e., either root or bacterial medium soil water) via the dissolution and hydration of CO2 molecules within soil water. The isotopic composition of soil-respired CO2 is modified by differences in diffusion rates of CO2 and CO18O through the soil column, and concurrent isotopic equilibration with soil water [Hesterberg and Siegenthaler, 1991]. Another process that influences δCa is the “invasion effect” in which atmospheric CO2 diffuses into the top layer of the soil, attains the isotopic signature of the surface soil water through rapid isotopic equilibration, and diffuses back to the atmosphere [Tans, 1998; Riley, 2005]. This invasion process is influenced by soil temperature, soil water content, the hydration rate, and atmospheric mixing conditions adjacent to the surface, which in turn are influenced by radiation, evaporation, and the concentration of CO2 immediately above the soil surface [Tans, 1998; Miller et al., 1999; Stern et al., 2001; Riley, 2005; Henderson-Sellers et al., 2006; McDowell et al., 2008; Wingate et al., 2009].
 The 18O compositions of leaf and soil CO2 are controlled by the isotopic composition of leaf and soil water pools, respectively. In leaves, the 18O exchange occurs primarily in the water of the mesophyll cells (adjacent to the stomatal cavity) [Farquhar and Lloyd, 1993; Gillon and Yakir, 2000]. In the presence of the ubiquitous enzyme carbonic anhydrase, the catalyzed reaction occurs almost instantaneously [Gillon and Yakir, 2001]. During transpiration, the lighter water isotopologue evaporates and diffuses through the stomata more efficiently than the heavy isotopologue, thereby enriching leaf water in the heavy isotopes of hydrogen and oxygen. Craig and Gordon  formulated a model to predict the isotopic composition of evaporating surface waters, which can be modified for leaves [Flanagan et al., 1991] to show that during steady state conditions, the isotopic composition (δWl-CG) at the evaporation site can be written as
where εLV is the temperature-dependent equilibrium fractionation of H218O during the liquid-vapor phase transition [Majoube, 1971], εk is the kinetic fractionation of H218O during the diffusion of vapor across the stomata and leaf boundary layer [Cappa et al., 2003; Luz et al., 2009], hl is relative humidity above the evaporating surface, δWX is the isotopic composition of xylem water, and δWCV is the isotopic composition of canopy vapor (a complete list of the variable notation is provided in Appendix A). This simple mass balance equation shows that the isotopic composition of leaf water (δWl) is related to that of stem/xylem water (δWX) and canopy vapor (δWCV), the relative humidity at the leaf surface (hl), and leaf temperature (through equilibrium fractionation). Other factors can influence δWl, including the Péclet effect [Farquhar and Lloyd, 1993] and leaf water content. In the extreme case of a relative humidity equal to zero causes the leaf water isotopic ratio to depend only on δWX (i.e., transpiration is assumed to be a one-way flux out of the leaf). Likewise, a relative humidity of 100% creates a thermodynamic equilibrium between water in the leaf and the ambient vapor and the kinetic isotope effect is eliminated, with δWl dependent only on δWCV and εLV. Therefore, changes in humidity can have significant impacts on the isotopic composition of leaf water, and consequently δCl and potentially δCa.
 Xylem water is derived from soil water, and δWX reflects a convolution of vertical variations in root water uptake and the 18O/16O composition of soil water (δWS) in the absence of stem capacitance with a differing isotope composition. δWS depends primarily on the isotopic composition of precipitation (δWP) and soil evaporation. As such, any variation in δWP could potentially cause changes in the isotopic composition of soil, stem, and leaf water (via equation (B4)). Similarly, the isotopic composition of canopy vapor is primarily controlled by the isotopic composition of above-canopy atmospheric vapor (δWAV), although Still et al.  showed how canopy transpiration in low-stature and high aerodynamic resistance canopies can provide a feedback on the isotopic composition of in-canopy vapor. These relationships indicate that δCS, δCl, and subsequently δCa could be sensitive to changes in the isotopic composition of precipitation and atmospheric vapor (i.e., changes in isotope hydrology). Thus, δCa could be influenced by many carbon and water cycle variables, and the focus of this study is to quantify how the global mean and spatial structure of δCa responds to changes in these variables.
World Meteorological Organization Forcing Data
 A Cressman-like objective analysis [Cressman, 1959] is used to interpolate World Meteorological Organization (WMO) station observations onto a grid. The procedure entails finding the weighted mean value of some quantity X (e.g., relative humidity or temperature) on a grid, given a number of values Xj with irregularly distributed positions λj, φj. That is,
where A is the area of each grid cell, and included for quantities needed in per unit area. An example is where a probability distribution of observational points is desired and where X is set to one for all points j, and the resulting field has units of probability per unit area. The weight W is a function of the great circle distance (dj) between each grid cell center and each observation,
where Rc is a critical radius that ensures W is positive for all dj larger than the critical radius, Rc. The shape of the weighting is modified by the “pinching” factor (γ), such that the mean radius of the weighting is reduced with smaller values.
 This method results in missing values when the critical radius is small enough. On the other hand, the spatial structure of a variable may be compromised due to over smoothing when the critical radius is too big. To avoid these problems, the objective analysis is looped 6 times for each day, such that the critical radius goes from large to small (Rc = 5000, 1000, 800, 600, 400, and 200 km), and the pinching factor starts extremely small and only gets larger for the first two loops (γ = 0.0002, 0.002, 0.02, 0.02, 0.02, and 0.02). Thus, the previous value with the larger radius is used to fill in grid cells with missing values. This approach ensures that local-scale features are retained where data coverage is good, but provides an interpolated value where observations are sparse.
 The chosen grid has a horizontal resolution given by triangular truncation of the spherical harmonic spectrum at wave number 62, which corresponds to a Gaussian grid of about 1.875° longitude × 1.875° latitude. The computational grid is the same as the reanalysis data set of Qian et al. , which has eight time samples per day. For each day and for each grid cell in the Qian et al.  data set, daily means were calculated and removed for each of the eight time samples. The remaining “anomalies” are then added to the interpolated WMO data, thus imposing a diurnal cycle onto the observed daily means.
 To demonstrate that this method accurately captures the station observations, Figure C1 compares examples of the observed seasonal cycle with the nearest neighbor grid cell for the interpolated data set, the data set of Qian et al. , and the National Centers for Environmental Prediction (NCEP) reanalysis [Kalnay et al., 1996]. The comparison is done for three stations in three separate regions (two tropical and one midlatitude). The station chosen for the comparison were ones with long observational records that show clear interannual variability and seasonal cycles. For both tropical regions, the two reanalysis data sets overpredict the amplitude of the seasonal cycle, with wet-season values that are too high and close to 100%. The interpolated data set accurately matches the station observation. In the midlatitudes, the seasonal cycle in relative humidity is not as clear with no monsoon to bring in a dry and wet season. Instead, the variations are dominated by atmospheric waves that bring in moisture every 5 to 7 days on average. This particular midlatitude region does observe an annually occurring dry period during the late spring/early summer. In the reanalysis data, the dry period is slightly later in the year, and thus, the seasonal cycle is not accurately captured. The interpolated data again matches up well with the stations observations, and the timing of the dry period is correct. These comparisons are the reason why the interpolated data set is preferred over the reanalysis data to force ISOLSM. Given the importance of relative humidity found here, it is particularly important to force the model with realistic relative humidity.
 Tables D1 and D2 contain the amplitude and phase differences between the observations and the model for CO2 and δCa, respectively. These differences were calculated from the curves shown in Figures 4 and 5.
Table D1. Model-Observation Differences in CO2 Seasonal Cycles
 We acknowledge with appreciation support from the NOAA Climate Program Office (award NA03OAR4310059). This research was also supported by the Director, Office of Science, Office of Biological and Environmental Research, Climate and Environmental Science Division, of the U.S. Department of Energy under contract DEAC02-05CH11231 to Berkeley Lab. We thank the associate Editor and two anonymous reviewers for their extensive and valuable comments and suggestions.