This study evaluates the potential impact of clouds on ecosystem CO2 and CO2 isotope fluxes (“isofluxes”) in two contrasting ecosystems (a broadleaf deciduous forest and a C4 grassland) in a region for which cloud cover, meteorological, and isotope data are available for driving the isotope-enabled land surface model (ISOLSM). Our model results indicate a large impact of clouds on ecosystem CO2 fluxes and isofluxes. Despite lower irradiance on partly cloudy and cloudy days, predicted forest canopy photosynthesis was substantially higher than on clear, sunny days, and the highest carbon uptake was achieved on the cloudiest day. This effect was driven by a large increase in light-limited shade leaf photosynthesis following an increase in the diffuse fraction of irradiance. Photosynthetic isofluxes, by contrast, were largest on partly cloudy days, as leaf water isotopic composition was only slightly depleted and photosynthesis was enhanced, as compared to adjacent clear-sky days. On the cloudiest day, the forest exhibited intermediate isofluxes: although photosynthesis was highest on this day, leaf-to-atmosphere isofluxes were reduced from a feedback of transpiration on canopy relative humidity and leaf water. Photosynthesis and isofluxes were both reduced in the C4 grass canopy with increasing cloud cover and diffuse fraction as a result of near-constant light limitation of photosynthesis. These results suggest that some of the unexplained variation in global mean δ18O of CO2 may be driven by large-scale changes in clouds and aerosols and their impacts on diffuse radiation, photosynthesis, and relative humidity.
 While spatial and temporal variations in atmospheric CO2 and its 13C/12C composition have received considerable attention from the carbon cycle community [e.g., Ciais et al., 1995; Fung et al., 1997; Rayner et al., 1999, 2008; Randerson et al., 2002a, 2002b; Scholze et al., 2003], much less is known about the 18O/16O composition of atmospheric CO2 (δ18Oa; symbols defined in Table 1). Although global simulations of δ18Oa and its controlling processes have made good progress [Farquhar et al., 1993; Ciais et al., 1997a, 1997b; Peylin et al., 1999; Cuntz et al., 2003a, 2003b; N. Buenning et al., Modeling the response of the terrestrial biosphere and δ18O of atmospheric CO2 to flux, humidity, and isotope hydrology changes, manuscript in preparation, 2009], fundamental spatial and temporal variations of δ18Oa are poorly captured by state-of-the-art global model simulations. One example of unexplained behavior is the phase shift between seasonal cycles of CO2 and δ18Oa observed at high northern latitudes, though a recent study showed how this shift is sensitive to boreal forest plant functional type composition and the δ18O of plant source water [Welp et al., 2006]. A second, outstanding example of unexplained variation is the large, multiyear variation in mean δ18Oa observed at many stations. The pronounced downward excursion in global mean δ18Oa observed during the early and mid-1990s averaged ∼ −0.1‰ a−1 for extratropical, marine boundary layer stations, implying isotope fluxes, or “isofluxes,” on the order of tens of Pmol CO2‰ a−1.
Here δ = ( − 1) and Rsam and Rstd are the ratios of 18O/16O in a sample or standard, respectively. The δ18O-CO2 values are reported relative to the Vienna Peedee belemnite (VPDB) CO2 measurement scale, and δ18O-H2O values are reported relative to the VSMOW measurement scale.
Background atmosphere δ18O-CO2 (VPDB-CO2)
Diffuse fraction, the ratio of diffuse irradiance to total (global) irradiance or of diffuse PAR to total PAR
Photosynthetically Active Radiation (400–700 nm).
Leaf area index (m2/m2)
Discrimination against CO18O during photosynthesis
Kinetic fractionation during molecular diffusion of CO18O
δ18O value of CO2 in equilibrium with H2O in leaves
Ca, Ci, Cc
CO2 concentrations in the atmosphere, stomatal pore, and in chloroplasts
Gross CO2 flux from atmosphere to leaf
Gross CO2 flux from leaf to atmosphere
Net leaf photosynthesis including leaf respiration (Fal-Fla)
Atmosphere-to-leaf isoflux (δ18O in CO2)
Leaf-to-atmosphere isoflux (δ18O in CO2)
Net photosynthetic isoflux
δ18O value of leaf water (VSMOW)
δ18O composition of source water in xylem (VSMOW)
δ18O composition of soil water (VSMOW)
δ18O composition of in-canopy water vapor (VSMOW)
δ18O composition of background, above-canopy water vapor (VSMOW)
 Recent research has documented large variability in tropical cloud cover [e.g., Wielicki et al., 2002] on interannual timescales that span part of the δ18Oa record. For example, satellite measurements of earth's shortwave and longwave radiation budgets over the 1990s suggest decreases in tropical mean cloudiness [Wielicki et al., 2002], in agreement with decreases in the monthly mean global cloud fraction over the 1990s (http://isccp.giss.nasa.gov/climanal1.html). Tropical cloud cover variability may be particularly relevant for understanding global δ18Oa variations, as tropical terrestrial ecosystem CO2 fluxes comprise a large fraction of global productivity. Other satellite-based analyses document increasing spring and summer cloud cover in the Arctic region [Wang and Key, 2003]. In addition, evidence from ground-based radiometers suggests secular changes in surface global irradiance, with a total reduction of ∼4–6% from about 1960 to 1990 (“global dimming”) [Stanhill and Cohen, 2001; Liepert, 2002; Liepert et al., 2004] followed by a reversal from roughly 1990 onward that has been termed “global brightening” [Wild et al., 2005, 2007; Pinker et al., 2005; Roderick, 2006].
 Relative humidity will influence both photosynthetic CO2 fluxes and the δ18O of leaf water via impacts on stomatal conductance, and thus can have a disproportionate impact on ecosystem-atmosphere isofluxes. An increase in relative humidity generally increases stomatal conductance, which, coupled with increased shade leaf photosynthesis, should increase photosynthetic isofluxes. However, increased relative humidity will also decrease leaf water δ18O because of a greater influx of depleted vapor, and this would decrease photosynthetic isofluxes.
 Thus, the net effect of changing cloud cover on biosphere-atmosphere CO2 and CO2 isofluxes exchanges is difficult to assess without high-frequency ecosystem CO18O flux measurements. However, these data are currently being collected at only a few sites at present [Griffis et al., 2008; McDowell et al., 2008]. The focus of this study instead is to examine potential ecosystem isoflux responses using observed cloud cover, radiation, meteorological and water isotope data to drive an isotope-enabled ecosystem model (ISOLSM). We chose to focus on two contrasting ecosystems in the Southern Great Plains over a short time period for intensive investigation of the mechanisms underlying the modeled canopy isoflux response to changing cloud cover. For our analyses, we selected a 12-day period from 11 to 22 July 2004 (day of year (DOY) 193–204,) during which strong variations in daytime thick cloud cover occurred at our study site, from less than 10% on clear days to 100% on a cloudy day. In addition to cloud cover variations, we selected this period using the following criteria: constant LAI, only trace amounts of precipitation (since precipitation δ18O is a primary driver of CO2 isofluxes), and no large changes in air temperature and specific humidity due to the passage of differing air masses associated with storm fronts. By limiting variability from these factors, we decomposed the predicted isoflux response to cloud cover into its component processes.
2.1. Site Description
 To capture the relevant processes that determine the net impact of clouds on ecosystem CO18O isofluxes, we employed a comprehensive, isotope-enabled ecosystem model (ISOLSM) [Riley et al., 2002, 2003; Still et al., 2005] in the DOE Atmospheric Radiation Measurement (ARM) program's Climate Research Facility (ACRF) in the 140,000 km2 Southern Great Plains (SGP) region of Oklahoma and Kansas [Ackerman and Stokes, 2003]. The SGP region is particularly amenable for such a study because of the great diversity of cloud property, aerosol, radiation, and meteorological measurements available, with the most intensive data collection at the Central Facility (CF) site near Lamont, OK (36° 36.30′N, 97° 29.10′W, 320 masl). Analysis of atmospheric data collected at the CF has shown large changes in irradiance driven by cloud cover from 1997 to 2004 [Dong et al., 2006]. The SGP region also contains natural and agricultural ecosystems representing a variety of photosynthetic pathways and growth forms, including tallgrass prairies, broadleaf forests along riparian areas, and crops such as winter wheat, milo, and corn. Because we wanted to explore the impact of cloud cover variations on ecosystem-atmosphere isofluxes in two globally important but strongly contrasting natural vegetation types also represented within the SGP region, we chose broadleaf deciduous forests and C4 grasslands for our model simulations.
2.2. Model Description
 ISOLSM is based on the NCAR Land Surface Model (LSM1.0) [Bonan, 1994; Bonan et al., 1997], which was modified by Riley et al.  to simulate the carbon and oxygen isotope composition of terrestrial ecosystem-atmosphere CO2 and H2O exchanges. The model simulates canopy radiation transfer using the two-stream approximation of Dickinson  and Sellers  to calculate direct and diffuse radiation fluxes in the visible and near-infrared wave bands. The canopy is divided into sunlit and shaded leaves using an extinction coefficient that accounts for scattering within the canopy [Sellers, 1985]. The model does not vary leaf nitrogen and photosynthetic capacity between sun and shade leaves, as is done in some models [e.g., de Pury and Farquhar, 1997; Wang and Leuning, 1998]. The version of ISOLSM applied here differs from that described by Riley et al.  by several changes made to the plant photosynthesis submodels. First, low- and high-temperature inhibition factors on the maximum catalytic capacity of Rubisco (Vmax) from Sellers et al.  have been included. Second, we implemented the method of Sellers et al.  to smooth transitions between the three limiting assimilation rates (i.e., Rubisco, light, and export limited). Finally, iterations to estimate Cc and Ci, the leaf chloroplast and internal CO2 concentrations, are now performed using net photosynthesis (i.e., accounting for leaf respiration occurring inside the leaf), as opposed to gross photosynthesis, as done in the original version of LSM1. Of these changes, the last had the largest impact, resulting in values for Vmax and Ci that are much closer to measured values. Accurate Ci and Cc are critical for simulating isotopic fractionations against 13CO2 and CO18O. ISOLSM models mesophyll (or internal) conductance in C3 plants to be proportional to the maximum carboxylation capacity (Vmax (in μmol m−2 s−1)) following Evans and Loreto , but without the soil moisture dependence implemented by Randerson et al. [2002b]. During light-saturated photosynthesis in forest sun leaves, the average drawdown from Ci to Cc was ∼4 Pa over the study period, similar to the drawdown measured by Gillon and Yakir .
 We have tested ISOLSM's H2O and CO2 flux predictions against several sets of measurements: (1) in the dominant vegetation types using measurements [Suyker and Verma, 2001] performed in the SGP as part of the AmeriFlux program [Riley et al., 2003]; (2) against 3 years of surface measurements made during the FIFE campaign [Betts and Ball, 1998; Cooley et al., 2005]; (3) in a tallgrass prairie site in Kansas [Lai et al., 2006a]; (4) in an old growth conifer forest in Oregon [Aranibar et al., 2006]; and in more recent measurements in wheat, pasture, and soy (W. J. Riley et al., manuscript in preparation, 2009). We have also tested ISOLSM's isotopic predictions against available data in Great Plains grassland and cropland ecosystems (i.e., δ18O in ecosystem water pools and fluxes, and δ18O in ecosystem CO2 fluxes [Riley et al., 2003; Still et al., 2005; Lai et al., 2006a]). We have previously applied ISOLSM to examine (1) impacts of the atmospheric δ18O value of H2O and CO2 on ecosystem discrimination against CO18O [Riley et al., 2003]; (2) impact of carbonic anhydrase activity in soils and leaves [Riley et al., 2002, 2003]; (3) impacts of gradients in the δ18O value of near-surface soil water on the δ18O value of the soil surface CO2 flux [Riley et al., 2003; Riley, 2005]; (4) impacts of land use change on regional surface CO2 and energy fluxes and near-surface climate [Cooley et al., 2005]; and (5) the use of 13C measurements to improve model parameterizations [Aranibar et al., 2006]. The isotope submodels in ISOLSM simulate the dominant processes impacting the δ18O value of soil (δ18Osw) and leaf H2O (δ18Olw) and CO2 fluxes: advection of H218O in soil water and subsequent evaporation, leaf water isotopic enrichment, isotopic exchanges between H2O and CO2 in the soil and leaves, the transport of CO2 and CO18O in the soil column, and the δ18O of canopy water vapor (δ18Ocv). The xylem source water that supplies leaves, δ18Oxy, is determined in ISOLSM by the vertical distribution of δ18Osw, weighted by rooting density profiles for the various ecosystem types. δ18Ocv is calculated at each time step as a function of vapor isotope exchanges with above-canopy air (δ18Ov), as well as isotope fluxes from canopy transpiration and soil and canopy evaporation when the canopy is wet [Riley et al., 2002]. Further description of our leaf water δ18O and photosynthetic isoflux calculations is given in section 3.
2.3. Cloud Cover, Radiation, Meteorology, and Water Isotope Forcing Data
 ISOLSM is forced with meteorological and water isotope data [Riley et al., 2002, 2003], and it has recently been modified to ingest satellite measurements of vegetation characteristics such as the projected leaf area index (LAI). For the simulations reported here, radiation, cloud property, and aerosol data were acquired from instruments at the ARM Central Facility (CF) in Lamont, OK, which is the primary measurement facility within the ARM SGP region [Ackerman and Stokes, 2003]. The instrument array at the CF includes sensors to measure cloud presence and cloud radiative properties, which are necessary to explore the role of clouds in ecosystem-atmosphere CO18O exchanges. Radiation fluxes measured at the CF site include downwelling shortwave radiation (direct and diffuse) and downwelling longwave radiation. For our analysis, early morning and late afternoon values (solar angles less than 15°) were screened to minimize the impact of low solar angles on RD/RS.
 The ARM cloud data used are the daytime percent cover of clouds, as measured by the total sky imager (TSI), an instrument that measures the fractional sky coverage of thin and thick (opaque) clouds (i.e., the fraction of the hemispheric field of view that contains these cloud types) for daytime periods when the solar elevation exceeds 10 degrees. For this analysis, we focus on the percent cover of thick clouds, as these are both the dominant cloud types and have the largest impact on irradiance, RD/RS, temperature, and relative humidity. Min  showed that diffuse radiation fluxes due to optically thick clouds have a greater impact on canopy photosynthetic efficiency than do fluxes from optically thin clouds. Because of temporal limitations on these data (i.e., only daytime cloud cover fractions are available from the TSI), we have restricted our analysis to daytime periods. Although nighttime clouds can affect the surface energy budget and carbon cycle through modulation of longwave energy fluxes [e.g., Dai et al., 1999], the largest impacts of clouds on canopy isofluxes should occur during the day. Unfortunately, cloud-screened aerosol optical depth data from a Sun photometer [e.g., Niyogi et al., 2004; Oliveira et al., 2007] were not available for our study period to allow a separate assessment of aerosol impacts on isofluxes.
 The meteorological data used to force ISOLSM include air temperature, pressure, water vapor content, wind speed, and precipitation amount. These data were taken from the Oklahoma and Kansas Mesonet program. The Mesonet consists of 145 instrument platforms (as of April 2007) distributed throughout the two states. Each station measures relative humidity, wind speed and direction, air temperature, and atmospheric pressure, and reports these data as 5-min, 15-min, or half-hourly averages for the state of Oklahoma and as hourly average for the state of Kansas. Additional external data sets required by ISOLSM include the following: (1) soil type from the 1 km USGS Statsgo soils database (i.e., 20% sand, 15% silt, and 65% clay around the CF); (2) monthly mean precipitation δ18O values averaged over 2–5 years of data from analyses of archived water samples collected by the EPA National Atmospheric Deposition Program (NADP) network [Lynch et al., 1995] between 1980 and 1990 and interpolated across the Great Plains region [Welker, 2000]; and (3) the atmospheric CO2 concentration.
 The model simulations also require the δ18O composition of above-canopy water vapor (δ18Ov) and background atmospheric CO2 (δ18Oa). Neither quantity is measured continuously in this region. Many factors affect δ18Ov [Lee et al., 2006], including evapotranspiration and horizontal and vertical atmospheric advection, and diurnal variations of up to 4‰ have been measured in this area [Helliker et al., 2002; Riley et al., 2003]; smaller diurnal variations (1–2‰) have been observed over temperate forests [Lai et al., 2006a; Lee et al., 2006]. Other investigators have shown strong linear or log linear relationships between specific humidity and δ18Ov [White and Gedzelman, 1984; Lee et al., 2006]. However, we have no information on this relationship in the SGP region, as extensive δ18Ov data are not available. Instead, for this set of simulations, we set δ18Ov to be in a temperature-dependent isotopic equilibrium with the most recent precipitation event [e.g., Lee et al., 2006]. Although our approach only crudely captures the processes that regulate δ18Ov, the sensitivity of ecosystem-atmosphere CO18O exchanges to diurnal variations in δ18Ov has been examined in detail by Riley et al.  and found to be small, partly because the more important vapor δ18O is that of within-canopy vapor, δ18Ocv, which interacts directly with δ18Olw. Riley et al.  also showed that diurnal variations in δ18Oa can impact CO2 isofluxes. However, since we lacked consistent diurnal measurements of δ18Oa, we imposed a constant value of −0.5‰, which is similar to the zonal annual mean value from midlatitude, northern hemisphere stations in the NOAA air sampling network [Cuntz et al., 2003b], and is close to mean values measured 3–4 km above the surface by ARM and NOAA. There is no diagnostic solution for the canopy air space CO2 and CO18O concentrations that is analogous to the H2O and H218O solution [Riley et al., 2002]. We therefore assume that canopy CO2 and CO18O concentrations are the same as above-canopy values. To properly analyze potential feedbacks between leaf and canopy CO18O fluxes, a prognostic canopy airspace model would need to be used; to our knowledge, no previous work has addressed this issue.
2.4. Model Sensitivity Experiments
 Our primary objective was to better understand the effects of cloud cover and associated environmental factors such as diffuse radiation and relative humidity on ecosystem-atmosphere CO18O exchanges for two globally important and strongly contrasting biomes that should bracket the expected range of ecosystem responses to cloud cover: broadleaf deciduous forests and C4 grasslands. The two types differ in photosynthetic pathway (C3 forest and C4 grass), life form (tree versus grass), and canopy stature (canopy heights used in ISOLSM are 20 m and 0.5 m, respectively [Bonan, 1996]), thereby allowing us to explore a wide range of potential ecosystem CO2 isoflux responses to cloud cover variations. The LAI values we used are particularly important because a higher diffuse radiation fraction is more influential with higher canopy LAI, as more leaf area is in shade during sunny conditions dominated by direct beam radiation [cf. Roderick et al., 2001; Gu et al., 2002; Alton et al., 2005; Knohl and Baldocchi, 2008]. To assess the sensitivity of our results to LAI in the broadleaf forest, we ran our base simulation with the mean value (5.0) for temperate broadleaf forests from Asner et al. . We also ran simulations with LAI values one standard deviation above and below the mean (i.e., LAI of 3.5 and 6.5, with all other driving variables were held constant). An LAI of 6.5 is not uncommon in temperate and tropical broadleaf forests, which together contribute substantially to global primary production [e.g., Field et al., 1998] and thus are particularly relevant for understanding global δ18Oa variations. We set the C4 grass canopy LAI to 3.75. This value is typical of highly productive C4 grasslands [Suyker and Verma, 2001] and C4 corn crops [Campbell et al., 1999]. To assess the C4 grass canopy LAI sensitivity, we doubled the LAI (from 3.75 to 7.5) in one simulation and reduced it by 33% (to 2.5) in another.
 We also tested the sensitivity of our results to shade leaf temperatures, as ISOLSM does not separately calculate the energy balance of sun and shade leaves. Shade leaves can experience a very different radiation environment than sun leaves, leading to leaf temperature gradients in the canopy [Gu et al., 2002; Larcher, 2003]. Shade leaf temperatures can be lower than sun leaf temperatures during sunny days. We tested the impact of this difference on our results by setting forest shade leaf temperatures to canopy air temperatures. Finally, we assessed the sensitivity of our results to the uniform distribution of leaf nitrogen and photosynthetic capacity (Vmax) between sun and shade leaves in ISOLSM. This uniformity could lead to larger shade leaf photosynthesis than would otherwise occur if these leaves become limited by Rubisco, which scales with leaf nitrogen. We halved Vmax in forest shade leaves in a separate simulation.
3. Results and Analysis
 We analyzed consecutive growing season days to understand how changes in cloud cover affected the physical environment and modeled ecosystem-atmosphere CO2 fluxes and isofluxes in a broadleaf deciduous forest canopy and a C4 grassland canopy. Our analysis is divided into four sections to clarify the processes impacting CO2 fluxes and isofluxes: (section 3.1) cloud cover effects on RD/RS, PAR, temperature, and humidity; (section 3.2) the response of photosynthesis and respiration to cloud cover; (section 3.3) the response of leaf and soil water δ18O to cloud cover; and (section 3.4) the response of CO2 isofluxes to cloud cover.
3.1. Cloud Cover Impacts on RD/RS and the Physical Environment
 During the first 3 days (DOY 193–195) of the study period, the percent of the sky obscured by thick (opaque) and thin clouds was minimal (Figure 1a). During these mostly clear days, total irradiance was high, and the PAR flux was dominated by direct beam radiation except for early in the morning and early in the evening when diffuse radiation increased (Figure 1b). In this and subsequent figures, only daytime values are plotted. These clear-sky days provided a useful basis for comparison with subsequent days (DOY 196–199), which experienced increasing thick cloud cover and midday diffuse PAR irradiance, along with reduced direct and total shortwave irradiance. The peak diffuse PAR irradiance on partly cloudy days increased more than twofold from clear days. The magnitude of midday diffuse PAR irradiance was similar to direct PAR on DOY 196, and thick cloud cover exceeded 60% for several hours. DOY 198 was by far the cloudiest day of the study period, with thick cloud cover close to 100% for much of the day (Figure 1a) and irradiance dominated by diffuse fluxes (Figure 1b). The days before and after DOY 198 were both partly cloudy, with daily maximum thick cloud cover around 60%. DOY 199 is noteworthy, as the thick and thin clouds scattered and reflected direct beam irradiance, in the process increasing the diffuse irradiance enough to produce the highest midday shortwave irradiance measured in the study period (i.e., total PAR was greater than even the clear-sky days of 193, 194, and 202). This effect of unexpectedly high midday irradiance during partly cloudy periods has been observed elsewhere [Gu et al., 1999, 2001; Urban et al., 2007].
 The period from DOY 200–203 was mostly clear, with the lowest cloud cover of the study period measured on DOY 202 (Figure 1a). On this day, direct beam PAR was very high, about the same peak magnitude as on the other very clear day, DOY 193, but diffuse PAR was slightly lower. DOY 204 was partly to mostly cloudy (cover greater than 80% for much of the day), and it had high diffuse PAR irradiance (Figure 1b). This day preceded a heavy rain event on DOY 205. Stratifying the days by cloud cover thus produces the following classifications: clear (sunny) days (DOY 193–195, 200–203), partly cloudy days (DOY 196–197, 199, and 204), and a cloudy day (DOY 198).
 Observed relative humidity and the diffuse PAR fraction (RD/RS), are shown in Figure 2. (Our analysis focuses on the observed diffuse PAR fraction, which we denote with the same notation (RD/RS) as the diffuse shortwave fraction following Roderick 1999; although diffuse PAR and shortwave fractions can differ slightly, during our study period they were indistinguishable from one another). Diurnal profiles of relative humidity largely followed the pattern of air temperature, and RD/RS followed predictable patterns on clear days with higher morning and evening values (Figure 2). Midday RD/RS was highest on the partly cloudy and cloudy days. Notably, the partly cloudy days (DOY 196–197, 199, and 204) did not have temperatures or humidities dramatically different from adjacent clear-sky days. Modeled leaf temperatures in the forest simulation tracked measured air temperatures, though they were higher by 1–3 K on sunny days (not shown).
 The increasing cloud cover during DOY 196–198 increased diffuse PAR and decreased direct and total PAR irradiance, producing a positive relationship between daytime RD/RS and the thick cloud cover fraction (Figure 3). Thin clouds and aerosols might also have affected RD/RS and contributed to some of the scatter shown in Figure 3. On partly cloudy days, midday RD/RS values were ∼0.4, compared to ∼0.15 on clear days, and the highest midday RD/RS occurred on DOY 198, when it reached 1.0. The strong relationship between cloud cover and RD/RS has been observed in a variety of other studies, and results from radiation absorption, reflection and scattering by cloud droplets.
3.2. Photosynthetic Responses to Cloud Cover Changes
3.2.1. Broadleaf Deciduous Forest
 The effect of cloud cover on modeled broadleaf deciduous forest canopy photosynthesis was large. Despite the lower total PAR on partly cloudy and cloudy days (DOY 196–199, 204), simulated peak canopy photosynthesis was higher on these days than on sunny days (DOY 193–195 and 200–203; Figures 1b and 4a). This enhancement was due primarily to increases in shade leaf photosynthesis from increases in diffuse PAR on these days. There were minimal changes in modeled sun leaf photosynthesis on these days because the rate was light saturated for much of the day, and even relatively large decreases in direct PAR didn't impact sun leaf photosynthesis. During these periods, sun leaf photosynthesis was limited by the amount and capacity of the primary photosynthetic enzyme, Rubisco [i.e., Collatz et al., 1991]. Also, the leaf temperature was slightly lower on the partly cloudy days compared to the sunny days because of lower radiant heating, thereby decreasing leaf respiration and photorespiration rates. The temperature sensitivity of the maximum carboxylation capacity (Vmax) is important for sun leaf photosynthesis, as it is usually light saturated and depends directly on Vmax, while photorespiration affects both light-limited and light-saturated rates [Farquhar et al., 1980; Collatz et al., 1991].
 In contrast to sun leaves, forest shade leaves responded strongly to the altered radiation regime induced by clouds: as cloud cover increased, diffuse PAR and shade leaf photosynthesis increased in tandem because shade leaf photosynthesis was light limited. On sunny days, peak shade leaf cumulative photosynthetic fluxes were less than half of sun leaf fluxes, whereas on partly cloudy and cloudy days the shade leaf fluxes equaled or exceeded the sun leaf values (Figure 4a). The overall positive simulated forest canopy photosynthetic response to increasing cloud cover (slope 0.15, r2 = 0.37; Figure 4b) thus resulted primarily from increased shade leaf carbon uptake with increased RD/RS.
3.2.2. C4 Grassland
 The C4 grass canopy photosynthetic response to cloud variations was opposite that of the broadleaf deciduous forest canopy: increasing cloud cover generally led to decreased canopy photosynthesis. The negative response of C4 photosynthesis to increasing RD/RS was stronger than its response to cloud cover (not shown). Although grass shade leaf photosynthesis responded positively to increased cloud cover due to increased diffuse PAR, sun leaf photosynthesis responded negatively to the decrease in direct beam radiation, and sun leaf photosynthesis was much larger than shade leaf photosynthesis during almost all cloud cover conditions (Figure 5).
 The modeled C4 grass canopy photosynthesis closely followed daily irradiance patterns, in agreement with leaf and canopy-scale observations for C4 plants [Suyker and Verma, 2001; Larcher, 2003]. In general, the highest predicted C4 grass canopy photosynthesis rates occurred during the clear-sky days (DOY 193–195, 200–203), and the lowest rates occurred during the cloudiest days (DOY 196, 198, 204). The one important exception (on DOY 199, which was partly cloudy) proves the rule: peak insolation values on this day were the highest of the study period because of cloud scattering and reflection, and modeled peak C4 grass photosynthesis was also highest on this day (Figure 5). Modeled peak canopy photosynthesis was large because of the high LAI values we imposed, although there are examples of well-watered and fertilized natural C4 grassland and C4 crop canopies exhibiting even higher productivity [Piedade et al., 1991; Jones, 1992; Morison et al., 2000]. The net ecosystem exchange (NEE) values predicted by ISOLSM (not shown) ranged from −15 to −35 μmol m−2 s−1, similar to NEE measured in a C4 grass-dominated pasture in this region [Suyker and Verma, 2001].
 The fundamentally different response to cloud cover of the C4 grass canopy (as opposed to the forest canopy) was at least partly due to canopy stature and the lower effective shade leaf area (and higher effective sun leaf area) in the much shorter grass canopy. Grass leaves have a more vertical orientation (erectophile morphology), and broadleaf deciduous tree leaves have a more horizontal orientation, so that at high solar angles the sun leaf area in grass canopies is higher than the comparable sun leaf area of broadleaf deciduous tree canopies [Jones, 1992; Larcher, 2003]. Another reason for the different response to irradiance is that both sun and shade leaf photosynthetic rates are almost always limited by light in the C4 grass simulation. A hallmark of C4 plants is their dominance in high-light and high-temperature environments such as grasslands and savannas [Long, 1999; Sage et al., 1999]. Photosynthesis in unstressed C4 plants does not saturate on sunny days, unlike the typical light saturation for C3 plants [Collatz et al., 1991, 1992].
 The decline in C4 grass canopy photosynthesis with increasing cloud cover and RD/RS parallels the empirical results from eddy flux studies assessed by Niyogi et al. , who found that increasing aerosol optical depth increased RD/RS and reduced RS. This led to increases in net carbon uptake by C3 ecosystems, but strong reductions in net carbon uptake for a C4 natural grassland. Although not explicitly a response to cloud cover variations per se, this study supports our modeling results: increasing RD/RS and decreasing RS reduces C4 photosynthesis, without the diffuse light photosynthetic enhancement often seen in C3 canopies. Our predictions also agree with Turner et al. , who studied the relationship between measured gross primary production (GPP) and absorbed PAR in a cross-biome comparison. The C4-dominated tallgrass prairie displayed a nearly linear relationship between GPP and APAR, unlike other biomes, which exhibited more typical light saturation responses (i.e., a hyperbolic relationship between GPP and APAR). Thus, decreases in RS and increases in RD/RS, whether caused by clouds or aerosols, should decrease GPP in C4 grasses, but not necessarily in C3 plants.
3.2.3. Response of Canopy Light Use Efficiency to Cloud Cover and RD/RS Variations
 The response of forest photosynthesis to cloud cover and irradiance is related to how efficiently the canopy converts solar radiation to chemical energy, a quantity referred to as gross or GPP light use efficiency (LUE) (mol CO2 mol−1 APAR). The broadleaf deciduous forest gross LUE was inversely proportional to irradiance. Indeed, the forest canopy strongly increased its gross LUE as RD/RS increased (Figure 6a). The daily averaged forest gross LUE for clear/sunny days (DOY 193–195, 200–203) was 0.031 mol CO2 mol−1 APAR, for partly cloud days (DOY 196–197, 199, 204) was 0.038 mol CO2 mol−1 APAR, and for the cloudy day (DOY 198) was 0.048 mol CO2 mol−1 APAR. This pattern follows the expectations of increasing LUE with increasing cloud cover and RD/RS demonstrated previously in eddy flux [e.g., Hollinger et al., 1994; Gu et al., 2002; Rocha et al., 2004; Min, 2005] and modeling [Norman and Arkebauer, 1991; Choudhury, 2001] studies. The increase of LUE with RD/RS depends on canopy structure and openness [Alton et al., 2005], and, as we show below, on photosynthetic pathway.
 During periods of high RD/RS, both sun and shade leaves in the forest were light limited and thus displayed a linear response to APAR. The linear slope between photosynthesis and APAR is defined as the quantum yield of photosynthesis [Larcher, 2003]. In C3 plants the highest intrinsic quantum yield is ∼0.085 mol CO2 mol−1 incident PAR, and its temperature sensitivity is largely driven by photorespiration [Collatz et al., 1998; Ehleringer et al., 1997]. Therefore, canopy LUE under low light closely follows the temperature-dependent photorespiration rate. Forest LUE values reached their lowest values around midday when sun leaves were light saturated and leaf temperatures were high. Forest canopy LUE dropped nonlinearly with temperature and reached its lowest values on the sunniest, hottest days when RD/RS was lowest (Figure 6a).
 The C4 canopy maintained high gross LUE over the study period, and was relatively insensitive to variations in cloud cover, irradiance, and leaf temperature. Since C4 sun and shade leaf photosynthesis was almost always light limited, the relationship between canopy photosynthesis and APAR was linear across the entire PAR range, and thus canopy LUE was very close to the leaf quantum yield. The intrinsic modeled leaf C4 quantum yield is 0.06 mol CO2 mol−1 incident PAR [Collatz et al., 1998], although natural C4 monocots can occasionally exceed this value [Ehleringer et al., 1997]. C4 plants typically maintain nearly constant quantum yields across a range of temperatures under low-light conditions [Ehleringer et al., 1997; Collatz et al., 1998]. During most daytime hours of the study period, the C4 grass canopy LUE varied from ∼0.035–0.05 mol CO2 mol−1 APAR, and, unlike the forest canopy, there was no consistent relationship with cloud cover or leaf temperature. There was a relationship with RD/RS, although it was weak compared with the forest LUE response to RD/RS (Figures 6a and 6b).
3.3. Leaf and Soil Water δ18O Responses to Cloud Cover Changes
In this equation, δ18Oxy and δ18Ocv are the 18O/16O composition of stem xylem (source) water and within-canopy atmospheric water vapor; ɛk is the weighted mean of kinetic fractionations against H218O molecules diffusing through the stomata and across the leaf boundary layer (32 and 21‰, respectively [Cappa et al., 2003]); ε* is the equilibrium fractionation between liquid and vapor phases over a saturated surface (∼9.4‰ at 298K [Horita and Wesolowski, 1994]); and ea and ei are the water vapor pressures (Pa) in the canopy atmosphere and inside leaf stomata, respectively.
Here, τ is the leaf water time constant (s) and in practice Δt is the model time step (s). τ is calculated separately for sun and shade leaves as the ratio between the leaf stock of water interacting with transpiration (Ml) and the gross water vapor flux out of leaves:
Here, R is the universal gas constant (8.314 J mol−1 K−1), Tv is vegetation temperature (K), and gs is stomatal conductance (sun or shade leaf, m s−1). The leaf water content, Ml, of both sun and shade leaves is set to a constant value of 10 mol m−2, which is consistent with limited available observations from a temperate needleleaf forest [Seibt et al., 2006] and a tropical broadleaf forest [Förstel, 1978]. In reality, the water content of the average shade leaf is undoubtedly different from the average sun leaf, since there are well-known differences in specific leaf area between sun and shade leaves [Chapin et al., 2002; Larcher, 2003]. However, we lacked data to reliably and accurately set this difference and assumed a constant value in both biomes and leaf types.
3.3.1. Broadleaf Deciduous Forest
 Simulated nonsteady δ18Olw for forest sun and shade leaves varied by over 20‰ during the study period (Figure 7a: all δ18O-H2O values are reported relative to the Vienna SMOW (VSMOW) scale). The diurnal cycle of δ18Olw for sun and shade leaves was inversely related to canopy relative humidity. Assuming steady state and no leaf boundary layer fractionation, the change in δ18O of an evaporating leaf at steady state will be roughly −0.4‰ for each percent change in relative humidity [Craig and Gordon, 1965]. This slope will be slightly smaller when including isotopic fractionation across the leaf boundary layer and nonsteady state effects. Over the study period, the slope of the linear regression for daytime sun leaf δ18Olw versus canopy relative humidity was −0.39‰ per % change in relative humidity. By contrast, the slope for shade leaves was lower, approximately −0.28‰ per % change in relative humidity. δ18Ocv varied diurnally between −13‰ and −16‰ in response to canopy transpiration, soil evaporation, and exchange with above-canopy air. This variation was dampened by a 3-h canopy turnover time imposed to account for turbulent air mass exchange between the canopy and atmosphere [Riley et al., 2002].
 The sun and shade δ18Olw differed from the steady state (δ18Olws) and from each other during most of the day (both leaves had the same water content, were at the same temperature, and were exposed to the same canopy vapor pressure and isotopic composition). This difference occurs because the leaf water time constant depends on the stomatal conductance of each leaf type (equation (3)), which is linked to the photosynthetic rate. For much of the day, sun leaf δ18Olw was close to steady state. Shade leaf δ18Olw generally lagged sun leaf δ18Olw, with smaller lags on partly cloudy and cloudy days when shade leaf photosynthesis and transpiration were higher because of enhanced diffuse PAR (e.g., DOY 196, 204). Both sun and shade leaves remained elevated above source stem water, especially in the early evening and through much of the night.
 As is apparent from δ18Oxy (Figure 7a), variation in modeled soil water δ18O (δ18Osw) was minimal across the study period. Even in the upper soil layers where δ18Osw can strongly increase because of evaporative enrichment [Allison et al., 1983; Riley, 2005], δ18Osw did not vary greatly because transpiration dominated evapotranspiration in these high-LAI simulations. The magnitude and variability of soil-respired CO2 isofluxes was fairly minimal, in agreement with earlier Great Plains modeling studies [Riley et al., 2002, 2003; Lai et al., 2006a; Still et al., 2005], and will not be discussed further.
3.3.2. C4 Grassland
 There was an unanticipated difference between the broadleaf forest and C4 grassland δ18Olw, with peak C4 grassland δ18Olw over the period never exceeding 12‰, whereas peak forest δ18Olw routinely exceeded 18‰ (Figures 7a and 7b), despite identical precipitation δ18O, radiation, and meteorological forcing (including above-canopy relative humidity). The difference is due to feedbacks between transpiration and within-canopy relative humidity. The canopy relative humidity (not shown) was substantially higher in the C4 grassland. Canopy relative humidity is calculated in ISOLSM from the canopy temperature and vapor pressure, which depends on exchanges with background vapor pressure, as well as transpiration and soil and canopy evaporation. The canopy relative humidity in the C4 grassland simulation never dropped below 55% over the study period, whereas modeled canopy relative humidity in the broadleaf forest was only slightly elevated from the measured above-canopy humidity, reaching values below 40% near midday. The higher average daytime relative humidity in the C4 canopy (relative to the broadleaf forest canopy) depleted δ18Olw.
 The higher relative humidity in the C4 canopy was due to higher transpiration fluxes. Although C4 plants typically exhibit water use efficiencies roughly twice those of comparable C3 plants [Pearcy and Ehleringer, 1984], this difference was overcome by much higher photosynthetic fluxes in the C4 grass canopy compared to the forest canopy (Figures 4a and 5). The higher relative humidity in the C4 grass canopy was also due to a lower aerodynamic conductance between the grass canopy and overlying atmosphere compared to the taller and aerodynamically rougher forest, leading to a greater offset between the canopy relative humidity and the background atmosphere. The effect of these differences is also apparent in the greater diurnal cycle of canopy vapor δ18O (δ18Ocv) in the C4 grassland (Figure 7b), as it was more strongly influenced by transpiration. The greater diurnal cycle in δ18Ocv also contributed to the transpiration feedback on δ18Olw, although the feedback was primarily due to the change in canopy relative humidity.
3.4. Response of Photosynthetic Isofluxes to Cloud Cover and RD/RS
ɛd is the weighted kinetic fractionation accompanying diffusion of CO18O molecules across the stomata, boundary layer, and the mesophyll walls (∼7.4‰ [Farquhar and Lloyd, 1993; Gillon and Yakir, 2001]), δ18Oc is calculated from δ18Olw and a temperature-dependent fractionation factor [Brenninkmeier et al., 1983], and δ18Oa is the δ18O value of background atmospheric CO2. The term arises from mass balance of CO18O molecules, and when multiplied by net leaf uptake, quantifies the back diffusion or retro-diffusion flux of CO2 molecules, which have a different δ18O from when they entered the leaf. This change occurs because only some of the CO2 entering the leaf is fixed by photosynthesis, while the remainder diffuses out after full or partial isotopic equilibration with leaf water [Farquhar et al., 1993; Flanagan et al., 1994; Gillon and Yakir, 2001].
 These bidirectional fluxes, termed Fal (atmosphere-to-leaf) and Fla (leaf-to-atmosphere), together sum to net photosynthesis, Anet (which includes leaf respiration). Each of these global fluxes (roughly 300 and 200 Pg C a−1 for Fal and Fla, respectively [Ciais et al., 1997a]) is larger than any other carbon flux term in the contemporary carbon budget. Equation (4) can be recast as a function of Fal and Fla:
 The first, right-hand side term captures the effective discrimination associated with the return, or retro-diffused, flux from leaves, and its sign and magnitude vary directly with changes in δ18Oc. The combined net photosynthetic isoflux, in units of μmol ‰ m−2 s−1, is the product of photosynthetic discrimination (18Δ) and net leaf photosynthesis (Anet):
 Bidirectional CO2 isofluxes across leaf stomata can occur during nighttime periods [e.g., Cernusak et al., 2004; Barbour et al., 2007]. Although this effect is potentially important, accurate quantification requires a model with a canopy air space and prognostic calculations of CO2 and CO18O concentrations throughout the night [e.g., Seibt et al., 2006], along with a model that accurately predicts stomatal conductance and the concentration of CO2 in the substomatal air spaces (Ci) and inside leaf chloroplasts (Cc) when photosynthesis is zero. For this study, we focused on daytime isofluxes only.
3.4.1. Broadleaf Deciduous Forest
 The 18Δ diurnal cycle (not shown) was strongly related to δ18Olw enrichment as canopy relative humidity declined with increasing air temperature. There was a decline in 18Δ with increasing cloud cover that followed from a small decrease in δ18Olw on partly cloudy days, and a large decrease in δ18Olw on the cloudy day (Figures 1a and 7a). Neither Cc nor leaf temperature (the other components of 18Δ) varied appreciably with cloud cover for either leaf type. The bidirectional leaf CO2 fluxes, Fal and Fla, varied diurnally with photosynthesis and increased strongly with cloud cover, particularly for shade leaves. The 18Fal and 18Fla isofluxes were often in opposition: the gross flux into stomata (18Fal) always enriched atmospheric δ18Oa (i.e., was always positive in δ notation), whereas the retro-diffused flux (18Fla) depleted δ18Oa in the morning (i.e., a negative isoflux) and enriched it in the afternoon (Figure 8a). The early morning depletion occurred because δ18Olw (and thus δ18Oc) was relatively depleted from the previous night when it approached δ18Oxy (Figure 7a); also, early morning canopy relative humidity was still high, and the transpiration flux was reduced because of low light levels, thus affecting the leaf water time constant. At this site, where we imposed a fixed δ18Oa consistent with the measured annual zonal mean (−0.5‰), δ18Oc must exceed ∼7.0‰ before the retro-diffused isoflux (18Fla) has a positive isotopic forcing (i.e., enriches δ18Oa).
 As relative humidity decreased in the late morning, δ18Oc became more enriched until it exceeded the ∼7‰ threshold and the leaf-to-atmosphere isoflux (18Fla) reinforced the atmosphere-to-leaf isoflux (18Fal). The forest sun leaf δ18Olw corresponding to this δ18Oc threshold occurred at a canopy relative humidity of ∼60%. Only on the cloudiest and coolest day (DOY 198) did δ18Olw stay below this value throughout the day (Figures 7a and 8a). The greatest δ18Olw enrichment occurred on the sunniest, hottest day when canopy relative humidity was lowest (DOY 202), and 18Fla was mostly positive. Because of high leaf temperatures on DOY 202, however, Anet and net leaf isofluxes (Anet18Δ or 18Fal + 18Fla) were lowest of the study period.
 If δ18Olw and δ18Oc are sufficiently negative, the net leaf isoflux can deplete δ18Oa. The δ18Oc where negative net photosynthetic isotope fluxes (18Fal + 18Fla < 0) occur is a function of δ18Oa, the Cc/Ca ratio, and ɛd. δ18Oc values more depleted than approximately −4.2‰ caused net forest photosynthetic isofluxes to be negative. During the 12-day study period, negative CO2 isofluxes occurred only briefly on DOY 193 when δ18Olw approached δ18Oxy and photosynthesis was just beginning (Figure 8a). Because the δ18O of growing season precipitation is rarely more depleted than −5‰ at these latitudes [Welker, 2000; Bowen and Wilkinson, 2002], forest photosynthetic isofluxes will almost always enrich δ18Oa. At higher latitudes where precipitation δ18O is lower, leaf CO2 isofluxes can deplete δ18Oa [e.g., Francey and Tans, 1987; Farquhar et al., 1993; Ciais et al., 1997b], because of 18Fla outweighing 18Fal.
 The net photosynthetic isoflux (Anet18Δ, solid line in Figure 8a) generally followed the daily variations in canopy photosynthesis (Figure 4a), with larger isofluxes on partly cloudy days (DOY 196–197, 199, 204) than on clear, sunny days (DOY 193–195, 201–203), an effect driven by shade leaves. However, the cloudy day (DOY 198) exhibited intermediate CO2 isofluxes: although it had the largest peak photosynthesis, this was countered by the lowest δ18Olw and 18Δ of the study period (Figures 4a, 7a, and 8a). Partitioning the net leaf isoflux (Anet18Δ) into 18Fal and 18Fla (equation (6)) reveals the canopy response to cloud cover in more detail. The 18Fal isoflux increased strongly with increasing cloud cover because of an increase in shade leaf and canopy photosynthesis with cloud cover. By contrast, 18Fla did not exhibit a strong relationship with cloud cover during daytime hours of the study period. Indeed, both negative and positive 18Fla values occurred for a range of cloud cover, as δ18Olw and thus δ18Oc alternated from relatively depleted values in the morning to enriched values in the afternoon after they crossed the ∼7.0‰ threshold. Thus, for the sum of 18Fal and 18Fla (i.e., Anet18Δ), no clear response to cloud cover occurred. When net photosynthetic isofluxes are plotted against RD/RS, however, there was a weak negative relationship, with the highest isofluxes centered at an RD of ∼0.4. This was driven by 18Fla, which peaked around this value in our simulations; at RD/RS values above ∼0.6, 18Fla was always negative. The peak isoflux at an RD/RS of 0.4 was not driven solely by photosynthetic responses to diffuse irradiance, as peak canopy photosynthesis occurred at higher RD/RS values. Rather, it was the combination of enhanced photosynthesis with higher δ18Olw due to lower canopy relative humidity at this particular RD/RS. These conditions occurred around midday on the partly cloudy days (DOY 196, 199, 204) that have the largest peak and cumulative daily isofluxes.
3.4.2. C4 Grassland
 There were large differences in leaf isofluxes between the forest and C4 grassland simulations that arose from differences in the internal CO2 concentrations between these different physiological types, as well as differences in their δ18Oc values (section 3.3). Comparing chloroplast CO2 concentrations between C3 and C4 plants is difficult since the C4 pathway concentrates CO2 around Rubisco in the bundle sheath cell chloroplasts, and raises CO2 concentrations to much higher levels than occur in mesophyll cell chloroplasts of C3 plants [von Caemmerer and Furbank, 2003]. For these simulations, we used the Ci value calculated in ISOLSM. Typical Ci/Ca ratios for C4 plants range from 0.2 to 0.4, whereas those for most C3 plants are 0.6–0.8 [Pearcy and Ehleringer, 1984; Collatz et al., 1991, 1992]. At similar photosynthetic rates, Fla can be much higher in C3 than C4 plants [Still et al., 2005; Hoag et al., 2005]. For example, a Ci/Ca ratio of 0.8 produces a Fla four times larger than a ratio of 0.2 produces for the same net leaf flux.
 The C4 grass photosynthetic isoflux, dominated by 18Fal from sun leaves, is almost always larger and less variable than the forest isoflux (Figure 8b). However, 18Fla is smaller in the grass than in the forest, and it remains negative throughout the day and never reinforces 18Fal, except for three brief periods on DOY 199, 203, and 204 (Figures 8a and 8b). This negative isotopic forcing on the atmosphere is due to the lower δ18Olw (Figures 7a and 7b) and the larger ɛd in the C4 grass simulation. δ18Oc must exceed a threshold value of ∼7.9‰ before the 18Fla from C4 plants has a positive isotopic forcing on the atmosphere. However, because leaf temperatures exceeded 30°C on the days with highest δ18Olw (DOY 199, 200, 202), and the CO2-H2O fractionation has a sensitivity of −0.2‰ K−1 [Brenninkmeier et al., 1983; Ciais et al., 1997a], 18Fla is almost always negative during the study period (Figure 8b).
 Because the magnitude of 18Fla will be much smaller in C4 plants compared to C3 plants because of lower Ci/Ca ratios [Still et al., 2005] and reduced equilibration between CO2 and H2O from lower carbonic anhydrase activity [Gillon and Yakir, 2001], photosynthesis by C4 plants will almost always enrich δ18Oa. The positive isotopic forcing associated with 18Fal will in almost every case be much larger than the negative isotopic forcing from 18Fla. Because C4 plants are largely restricted to tropical and subtropical savannas and grasslands [Still et al., 2003], the δ18O of precipitation and thus of plant xylem water (δ18Oxy), is relatively enriched [Bowen and Wilkinson, 2002]. For example, Ometto et al.  measured Amazonian C4 pasture grasses with δ18Oxy values between −3‰ and −9‰, and mean values around −5‰. These values, and measurements from C4-dominated tallgrass prairies in Oklahoma and Kansas [Helliker et al., 2002; Riley et al., 2003; Lai et al., 2006b], are similar to the mean predicted δ18Oxy at our site (Figure 7). Given a typical midday C4 plant Ci/Ca ratio of 0.3 and assuming complete equilibration, δ18Oc at this site would have to be below approximately −17.3‰ for net C4 photosynthetic isofluxes to deplete δ18Oa. Using precipitation δ18O regressions from Bowen and Wilkinson , δ18Olw and thus δ18Oc values that are sufficiently depleted occur above ∼60°N. Although C4 plants do grow north of 50° N [e.g., Schwarz and Redmann, 1988; Beale and Long, 1995], they are uncommon and do not substantially affect regional carbon fluxes.
 While C4 canopy photosynthesis decreased slightly with increasing cloud cover, net photosynthetic isofluxes (Anet18Δ) exhibited no clear relationship with cloud cover. 18Δ did not vary with cloud cover, as an increase in the Fal component of 18Δ due to an increase in Cc with cloud cover was countered by a decrease in the Fla component of 18Δ driven by the slight decrease of δ18Olw and δ18Oc with cloud cover. Over the study period, the flux-weighted mean C4 grassland canopy 18Δ was ∼12‰, with ∼2/3 of this from ɛd. There was a weak negative response of Anet18Δ to increasing RD/RS, just as there was between C4 canopy photosynthesis and RD/RS. In both cases, peak uptake occurred at RD/RS values between 0.2 and 0.4, and declined sharply above 0.4. There was a strong positive relationship (slope = 0.46; r2 = 0.89) between the net C4 photosynthetic isoflux and incident PAR (i.e., the canopy isotope light response curve; Figure 9).
3.5. Sensitivity to Leaf Area Index
3.5.1. Broadleaf Deciduous Forest
 We examined the sensitivity of our results to LAI given the importance of this canopy characteristic in the response to clouds and RD/RS as highlighted by earlier studies [e.g., Rocha et al., 2004; Urban et al., 2007; Knohl and Baldocchi, 2008]. We altered LAI values throughout the study period, with other model driving data unchanged from control simulations. Relative to the control, forest canopy photosynthesis and transpiration declined in the low-LAI simulation and increased in the high-LAI one, driven by the shade leaf response. The changes in canopy transpiration lowered or raised canopy relative humidity by a few percent relative to the base case. The impact of changing LAI on canopy relative humidity and δ18Olw was most dramatic on the cloudy day (DOY 198) when RD/RS and diffuse PAR were highest. This day exhibited the highest peak shade leaf and canopy photosynthesis in the base LAI simulation, and also the greatest humidification of the canopy from transpiration (since wind speed and exchange with the atmosphere was not different from adjacent days). On DOY 198, peak daytime steady state δ18Olw values were raised by 1.4‰ in the low-LAI (3.5) simulation relative to the base case, and lowered by 0.3‰ in the high-LAI (6.5) simulation.
 Taken in isolation, this transpiration feedback on δ18Olw would increase (decrease) 18Δ in the lower- (higher-) LAI simulations. However, the retroflux scalar (equation (4)) was lowered in the reduced LAI simulation as the relative contribution of shade leaves with slightly higher Cc values declined relative to the base LAI. The effect of these differences was to quantitatively reduce the importance of 18Fla in the reduced LAI simulations, and as a result, net photosynthetic isofluxes (Anet18Δ) were more dominated by 18Fal. Because 18Fal scales with leaf photosynthesis and is unaffected by δ18Olw, it exhibited a positive correlation with cloud cover; as LAI was reduced, a coherent relationship between Anet18Δ and cloud cover emerged. Indeed, in the low-LAI simulation, net photosynthetic isofluxes on DOY 198 reached higher peak values than on the partly cloudy days (DOY 196, 199, 204) that had the highest isofluxes in the base LAI case (Figure 10). This resulted from a combination of enhanced shade leaf photosynthesis and enriched δ18Olw due to a reduced transpiration feedback on canopy relative humidity. δ18Olw and δ18Oc were even high enough on DOY 198 in the low-LAI simulation to briefly surpass the ∼7.0‰ forest threshold (section 3.4.1), and 18Fla reinforced 18Fal to enrich δ18Oa (Figure 10).
3.5.2. C4 Grassland
 We also assessed the sensitivity to LAI in the C4 grass canopy, with other driving variables held constant. For these simulations, we decreased the LAI from the base case by one third (to a LAI of 2.5) and increased it twofold (to a LAI of 7.5). The reduced LAI lowered canopy photosynthesis and transpiration in the C4 grassland relative to the base case. The expected response led to several changes that modified photosynthetic isofluxes, primarily via the same transpiration feedback on canopy relative humidity and δ18Olw that was found for the forest simulations. In particular, δ18Olw values increased in the reduced LAI simulations as the transpiration flux was lowered and the canopy relative humidity more closely tracked the observed, above-canopy humidity shown in Figure 2. Unlike the forest simulations, reducing LAI did not strengthen the relationship between leaf isofluxes and cloud cover. The negative response of C4 photosynthesis to increasing cloud cover and RD/RS was similar for the different LAI values, and the isotope light response curve remained linear in all LAI simulations (Figure 9).
4. Discussion and Conclusions
 Terrestrial ecosystems are likely to respond to changes in irradiance, temperature, relative humidity, and RD/RS driven by changes in cloud cover. For example, Min and Wang  showed that interannual cloud cover variations drive interannual carbon fluxes in a temperate broadleaf forest. Clouds influence other ecological processes like shoot growth and reproduction [Graham et al., 2003], photosynthesis of understory species [Johnson and Smith, 2006, 2008], tree growth [Williams et al., 2008], and range boundaries [Fischer et al., 2009]. At the leaf scale, diffuse light is used less efficiently for photosynthesis than direct light [Brodersen et al., 2008], whereas at the canopy scale, the opposite response is observed. Yakir and Israeli  documented how artificially reducing irradiance reduced growth but increased 13C discrimination in an experimental plantation; this result is buttressed by work showing that increasing RD/RS in a multilayer canopy model increases Ci/Ca and 13C discrimination [Knohl and Baldocchi, 2008].
 Our results illustrate the myriad impacts that clouds have on biosphere-atmosphere CO18O exchanges. We examined a sequence of midsummer days in which the light intercepted by the canopy varied from irradiance dominated by direct beam radiation (sunny) to days with high total irradiance but an increasing diffuse fraction (partly cloudy) to days in which almost all irradiance was diffuse (cloudy). This variation allowed a detailed examination of the mechanisms that drive ecosystem isotopic states and exchanges, and to explore how ecological properties influence the mechanisms and responses. Although this study only examined a portion of the growing season, we can hypothesize that, when integrated to a larger scale, clouds have a substantial impact on biosphere-atmosphere CO18O exchanges through their varied impacts on direct and diffuse radiation, leaf temperature, relative humidity, leaf water enrichment, and bidirectional leaf fluxes (Fal and Fla). These effects vary strongly with canopy structure, LAI, precipitation δ18O, and photosynthetic pathway.
 The forest canopy increased photosynthesis with increasing cloud cover and RD/RS, whereas the C4 grass canopy exhibited a negative response to both increasing cloud cover and RD/RS. The LUE of the forest canopy was strongly related to RD and leaf temperature, whereas the grass canopy LUE was relatively insensitive to environmental conditions. Compared to sunny conditions, the forest canopy exhibited larger photosynthetic isofluxes on partly cloudy days. The response of forest leaf isofluxes to cloud cover depends strongly on LAI, primarily via a feedback of transpiration on canopy relative humidity and δ18Olw. Whereas the relationship between forest canopy photosynthesis and cloud cover (i.e., Figure 4b) became stronger with increasing LAI, the relationship between canopy photosynthetic isofluxes (Anet18Δ) and cloud cover weakened with increasing LAI.
 In contrast, photosynthesis and isofluxes in the C4 grass canopy declined with increasing cloud cover and RD/RS, regardless of LAI. This opposite response resulted primarily from the lower effective shade leaf LAI in the lower-stature grass canopy compared to the broadleaf forest, as well as the near-constant light limitation on photosynthesis in C4 sun and shade leaves. These different responses represent a fundamental functional distinction between these globally important vegetation types.
 It is important to acknowledge some of the modeling limitations in the work reported here. One deficiency is the lack of a separate energy balance and leaf temperature calculation for shade leaves. High LAI values are not uncommon in many forests, and the fraction of canopy photosynthesis attributable to shade leaves increases with LAI. An incorrect shade leaf temperature will impact canopy CO18O exchanges in several ways. First, δ18Olw is sensitive to leaf temperature because of its impact on the saturation vapor pressure inside leaves. Second, each 1°C increase in leaf temperature reduces the equilibrium liquid-vapor fractionation by ∼0.07‰ for typical ambient temperatures [Horita and Wesolowski, 1994], and also reduces the equilibration fractionation between CO2 and H2O by −0.2‰ [Brenninkmeier et al., 1983]. Leaf temperature also influences the leaf surface relative humidity and stomatal conductance, which in turn impacts Ci and bidirectional CO2 fluxes across stomata. Finally, leaf temperature affects photosynthesis and respiration [Collatz et al., 1991, 1992]. However, we tested the sensitivity of our results by varying shade leaf temperature and found the impact to be small (not shown).
 We also tested the impact of varying photosynthetic capacity (Vmax) between sun and shade leaves. When we halved shade leaf Vmax in the forest simulation, there was no change in shade leaf or total canopy photosynthesis, simply because shade leaf photosynthesis is always light limited. This prediction confirms the results of Leuning et al. , who showed with a multilayer canopy model that total photosynthesis of shaded leaves is insensitive to the nitrogen distribution within a canopy. And, as shown by de Pury and Farquhar , even with nitrogen and photosynthetic capacity distributed between sun and shade leaves as a function of optical depth in the canopy, the photosynthetic rate of shade leaves is always limited by light (i.e., by electron transport rate) and not by Rubisco.
 We contend that these model limitations have small impacts on our conclusions. One could test this assumption by conducting similar site-scale analyses with a one-dimensional, multilayer canopy models that also included turbulent transport and leaf nitrogen variations within the canopy [e.g., Baldocchi and Bowling, 2003; Knohl and Baldocchi, 2008]. However, for predictions of the impact of cloudiness on ecosystem-atmosphere CO18O exchanges at regional to global scales, a sun/shade model like ISOLSM that has already been integrated into global climate models [Noone et al., 2004; Buenning et al., manuscript in preparation, 2009] is preferable for computational reasons.
 Although the differences in the response to cloudiness between C3 and C4 vegetation is largely due to differing Fal and Fla and photosynthetic rates, there are additional physiological and anatomical differences that would further impact CO18O exchanges that we did not consider. The differences between forest and grassland isofluxes would have been even larger if we had reduced the C4 grass carbonic anhydrase activity [Gillon and Yakir, 2001]. For the work presented here we assumed complete equilibration between CO2 and δ18Olw for both vegetation types, as we were interested primarily in ecosystem responses to changes in cloud cover as mediated by canopy structure and photosynthetic pathway. Also, we lacked field data on equilibration in this region, and recent studies suggest conflicting results for assigning appropriate values in modeling studies. Gillon and Yakir  suggest a mean equilibration value of 0.4 for C4 grasses; recent work with C4 corn plants suggests values closer to C3 plants [Affek et al., 2005]. Laboratory measurements with both wild-type and transgenic individuals of a C4 dicot also suggest higher values from in vitro carbonic anhydrase assays [Cousins et al., 2006]. Moreover, a recent phylogenetic analysis suggests that reduced carbonic anhydrase activity may not be simply a trait of grasses with the C4 photosynthetic pathway, but may be more widespread among tropical grass lineages, including several widespread and productive C3 grass species [Edwards et al., 2007]. We also did not consider the large δ18Olw enrichment observed along leaf veins of C4 grasses [Helliker and Ehleringer, 2000], which can affect leaf CO18O fluxes.
 This study demonstrates the complex responses of terrestrial ecosystems to changes in cloud cover, particularly with respect to oxygen isotope fluxes of CO2. The broadleaf forest and C4 grassland are predicted to have fundamentally different responses to changes in cloud cover. Our findings also identify a potentially important feedback of transpiration on canopy relative humidity, δ18Ocv, and δ18Olw, and thus on leaf-to-atmosphere CO2 isofluxes. We believe that some of the unexplained variation in δ18Oa is driven by changes in clouds given the strong responses we show here and decadal-scale changes in cloud cover and aerosols observed in many locations.
 We gratefully acknowledge support from the NOAA Climate Program Office (grant NA03OAR4310059). Data were obtained from the Atmospheric Radiation Measurement program sponsored by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, Environmental Sciences Division. We also acknowledge meteorological data support provided by the Oklahoma and Kansas Mesonet program. The U.S. Network for Isotopes in Precipitation (http://www.uaa.alaska.edu/enri/usnip/index.cfm) contributed δ18O data for our simulations and was supported in part by NSF Earth System History program (0080952). Comments from anonymous reviewers and the associate editor improved the manuscript.