2.1. Study Site
 This study was conducted in the Rannells Flint Hills Prairie near Manhattan, Kansas, USA (39°12′N, 96°35′W, 324 m above sea level). The site has a mixture of C3/C4 photosynthesis and is burned during the last 10 days of April every year. The vegetation was dominated by C4 grass species, primarily Andropogon gerardii, Sorghastrum nutans, and Andropogon scoparius. The C3 species included Carex, a sedge, and numerous forb species including Vernonia baldwinii, Artemesia ludoviciana, Ambrosia psilostachya, and Psoralea tenuiflora var. floribunda. The 15-year average annual precipitation is 878 mm, with 74% occurring between April and September. The average canopy height, defined as the height of the tallest vegetation structure, was about 0.6 m at peak growth in 2002 and 2003, but extended to about 1.2 m in 2004 as a result of favorable growing conditions (i.e., more precipitation).
 From 2002 to 2004, NEE and, carbon and oxygen isotope values of ecosystem respiration were measured at the ungrazed site in the Rannells prairie. Measured NEE fluxes were averaged to a half-hourly basis, while values of δ13CR and δ18OR were estimated on weekly intervals. To demonstrate the seasonal and interannual variations of measured NEE fluxes, we calculated average daytime and nighttime NEE fluxes on a weekly basis. We assume that each weekly measurement of δ13CR and δ18OR was representative of the carbon and oxygen isotope ratios of respired CO2 fluxes for that particular week.
2.2. Flux and Meteorological Measurements
 An open-path eddy covariance system consisting of a triaxial sonic anemometer (CSAT3, Campbell Scientific Inc., Logan, Utah, USA) and a CO2/H2O gas analyzer (LI-7500, LI-Cor Inc., Lincoln, Nebraska, USA) was used to measure fluxes of momentum, CO2, sensible, and latent heat above the canopy [Ham and Heilman, 2003]. A CR23X data logger (Campbell Scientific) recorded 10 Hz signals to compute 30-min average fluxes. Lai et al.  described measurements of meteorological variables, including net radiation, air temperature, relative humidity, precipitation and soil temperature, in this tallgrass ecosystem. No correction was applied to the nighttime flux data since this site is generally windy (with calm night representing 0.1% of all sampling time). More details about eddy covariance measurements are given by Ham and Heilman .
2.3. Oxygen Isotopes of Water Samples
 In May and July of 2002, two field experiments were conducted to collect samples for measuring δ18O values of ecosystem water pools. Each experiment lasted for 3 days, and samples of water vapor, soil water, crown-root water, and bulk leaf water were collected 1–5 times a day to characterize diurnal patterns of δ18O in each water pool. We collected foliage samples by clipping the whole grass blade and storing them in glass vials immediately after collection. Three replicates of grass blades from three dominant C4 species were collected each time. We reported the average of 9 samples (±1 S.D.) as the δ18O value of canopy leaf water. Root water was sampled by collecting crown roots (the top portion of the rooting system where all fine roots converge). The δ18O value of crown-root water represents δ18O signatures of source water for this prairie. Profiles of soil samples were collected in general from the top 30 cm, with an increment of 10 cm from 5 soil pits. All water samples were stored in screw-cap glass vials carefully wrapped with Parafilm® to prevent evaporation and kept refrigerated or frozen until subsequent stable isotope ratio analyses.
 Atmospheric water vapor was cryogenically captured and analyzed for oxygen isotope ratios using the sampling protocol described by Helliker et al. . Air from three heights (0.5, 1, and 3 m above ground) was passed through sampling tubes placed in a dewar of crushed dry ice, allowing water vapor to condense on the inner walls of the glass tubing. The airflow rate was set at 5 cc s−1 with a sampling time of ∼ 20 min. Water vapor tubes were sealed with a rubber stopper, and wrapped with Parafilm® on the outside. Samples of water vapor, crown-root water, and bulk leaf water were collected concurrently every 3–4 hours between 0800 and 2000 local standard time (LST) during the two field experiments.
 Water samples were extracted in the laboratory using a cryogenic vacuum distillation apparatus [Ehleringer et al., 2000]. Each water sample equilibrated with dilute CO2 (CO2:N2 = 1:9) for 48 hours at 25°C. Batches of 9 samples were calibrated against 3 working water standards during each analysis run using an EA-CF-IRMS method described by Fessenden et al. . Precision of the δ18O analyses is ±0.2‰.
2.4. Flask Sampling and Isotope Analyses
 Air samples from three heights (0.1, 0.4, and 3 m) were collected using an automated sampling system, capable of filling 15 flasks on the basis of the specification of a data logger [Schauer et al., 2003]. Two flasks were collected 5-min apart in the midafternoon (usually between 1430 and 1530 LST) from the top intake. This flask pair was averaged for CO2 concentration and δ13C to estimate daytime canopy air. Beginning in March 2003, an extra pair of daytime flasks was collected on a separate day every week. Nighttime air samples were collected to attain a gradient of CO2 concentration ≥50 ppm over the course of a night using 100 mL flasks (Kontes Glass Co., Vineland, New Jersey). Flasks were sealed with vacuum-tight Teflon stopcocks. The specified CO2 range was typically achieved during the growing season. Nighttime sampling started an hour after sunset to avoid effects of photosynthesis, and air was drawn from 2 heights: 0.1 m and 0.4 m above ground. Flasks were filled at 5-min intervals, cycling between the bottom and middle inlets. A “panic” mode was initiated one hour before sunrise which filled all the remaining empty flasks before any photosynthetic uptake. If the specified CO2 gradient was not met, the sampler resets and repeats the same procedure the following day. In general, there are 11 flask samples for each Keeling plot. Air was dried by flowing through a magnesium perchlorate trap before collection to minimize storage effect on the δ18O of CO2 [White et al., 2002]. The majority of air samples were typically collected within the first 2 hours (∼2000–2200 LST) after the sampling started. A field person then checked on the data logger and collected flasks the next day if they were successfully filled the night before.
 Flasks were collected for isotope analyses on weekly intervals between May and November and on a monthly basis for the rest of the year [Lai et al., 2003, 2004, 2005]. Carbon and oxygen isotope ratios of CO2 were analyzed on a continuous flow isotope ratio mass spectrometer (Finnigan MAT 252, San Jose, California), while CO2 concentration was measured to a precision of 0.3 ppm using a bellow/IRGA system in 2002 [Lai et al., 2003]. Beginning in 2003, a GC-IRMS system was deployed to analyze a flask for δ13C, δ18O and concentration of atmospheric CO2. Measurement precision was determined to be 0.06‰ for δ13C, 0.11‰ for δ18O and 0.48 ppm for CO2 concentration [Schauer et al., 2005]. Precision of the GC-IRMS system significantly improved isotope ratio analyses (by ∼0.05‰) but slightly degraded the precision for CO2 concentration measurements (by ∼0.2 ppm). This analytical modification improves the overall accuracy of the Keeling plot analysis because of the relative greater improvements in isotope precision as compared to a smaller decrease in the precision of concentration measurements.
 In this study, we report carbon isotope ratios on the VPDB scale; oxygen isotope ratios in water and CO2 are both reported relative to the VSMOW scale [Coplen, 1996].
2.5. Isotope Ratios of Ecosystem Respiration
 A two-source mixing line approach, first developed by Keeling [Keeling, 1958, 1961], can be used to estimate the isotopic composition of ecosystem respiration (δR):
where C represents mixing ratios of CO2. Subscripts m and b represent measurements collected within the nocturnal boundary layer and the background atmosphere, respectively. In theory, equation (1) can be applied for both carbon (δ13CR) and oxygen (δ18OR) isotopes; indeed, many ecosystem studies have adopted the mixing line approach to estimate δ13CR [Flanagan et al., 1999; Buchmann et al., 1997; Buchmann and Ehleringer, 1998; Bowling et al., 2002; Ometto et al., 2002; Pataki et al., 2003] and δ18OR [Flanagan et al., 1997, 1999; Buchmann and Ehleringer, 1998; Harwood et al., 1999; Bowling et al., 2003a, 2003b]. In this study, if the standard error of an estimated δ13CR value was greater than 2‰ (3‰ for δ18OR), we excluded it from our analyses. We excluded 10 and 22% of the measured δ13CR and δ18OR values on this basis.
2.6. Brief Descriptions of ISOLSM
 The isotope submodels in ISOLSM simulate the dominant processes impacting the δ18O value of the soil and leaf H2O and CO2 fluxes: advection and evaporation of H218O in soil water, CO2 and C18OO soil-gas transport, leaf water enrichment, interactions between soil and leaf H218O and CO2, and the δ18O value of canopy air space vapor. We have applied ISOLSM to examine (1) impacts of the atmospheric δ18O value of H2O and CO2 on ecosystem discrimination against C18OO [Riley et al., 2003], (2) impact of the enzyme carbonic anhydrase in soils [Riley et al., 2002], (3) impacts of gradients in the δ18O value of near-surface soil water on the δ18O value of the soil-surface CO2 flux [Riley, 2005; Riley et al., 2003], (4) impacts of land use change on regional surface CO2 and energy fluxes and near-surface climate [Cooley et al., 2005], and (5) uncertainties associated with the use of 18O in CO2 measurements to estimate gross CO2 fluxes from net ecosystem exchange measurements and atmospheric C18OO measurements [Riley and Still, 2003].
 ISOLSM is forced with measurements of air temperature, pressure, and vapor content, wind speed, CO2 concentration, downward shortwave and longwave radiation, precipitation amount and its isotopic ratio, and the δ18O value of above-canopy vapor (δ18Ov) and CO2. We estimated downward longwave radiation using measured air temperature, shortwave radiation (SW) from measurements of photosynthetically active radiation (PAR), and a conversion factor (CF) of 0.46 with the relationship: SW = PAR/CF. Using satellite data, Pinker and Laszlo  derived relationships between PAR and SW for the globe. They showed that, in most cases, CF is between 0.44 and 0.50, with the mean and median values being 0.46. For comparison, meteorological measurements from the ARM Central Facility (ww.arm.gov) between May and October of 2003 indicate a midday mean (standard deviation) of 0.43 (0.07), indicating that our choice is within the range of values expected for this area. In the absence of continuous measurements of δ18Ov we assumed a value 11‰ less than the predicted isotopic composition of source water. This assumption was based on averages of δ18Ov and source water δ18O measured during the two experiments in May and July 2002. The averaged δ18Ov was −12.3‰ (±1.2; n = 11) and −16.6‰ (±1.2; n = 10), while the averages of source water δ18O were −2.0‰ (±1.3; n = 99) and −5.1‰ (±1.8; n = 90) in May and July, respectively. Many factors other than evapotranspiration (e.g., horizontal and vertical atmospheric advection) impact δ18Ov, which can have diurnal variations of up to 4‰ in this area [Helliker et al., 2002]. Our measurements in this grassland also showed diurnal variations about 4‰ in the two experimental periods in 2002. We assumed constant δ18Ov values relative to the source water δ18O in the ISOLSM simulations.
 We do not have δ18O measurements of precipitation (δ18Op) at this site, so we relied on two data sources for estimates of δ18Op values. Welker  reported arithmetic averages of δ18Op from 3 years (1989–1991) at sites representative of the Gulf of Mexico storm track from Gulf coast of Texas, western Oklahoma, western Nebraska, and into southeastern Montana. We expect δ18Op values in Rannells Prairie to have similar seasonal characteristics and magnitude as those monitoring stations because it is in the pathway of this storm track. The averaged δ18Op values along this storm track ranged between −2 and −10‰ from Texas to Montana. The two stations closest to our site (western Oklahoma and western Nebraska) had average δ18Op values of −5 and −8‰. Although δ18Op values showed considerable variations between summer and winter rains, summer precipitation was confined to a smaller range (less than 5‰). The second data source was based on a model output [Bowen et al., 2005], which interpolates a global precipitation data set for water isotope analyses developed by IAEA. An online calculator for oxygen and hydrogen isotopes of precipitation at any locations is available at http://www.waterisotopes.org. On the basis of this model, δ18Op values varied between −4.4 and −5.5‰ between the month of May and August at our site (39.12°N, 96.35°W, elevation = 324 m), with an average of −5‰. Hence we assumed a constant δ18Op of 5‰ in our model simulation throughout the growing season for all 3 years. The short-term variability of δ18Op is not considered in the model, which contributes to the uncertainty in the modeled soil and leaf water δ18O, and consequently, the modeled δ18O of net CO2 fluxes.
 The ISOLSM simulations predict δ18O values of leaf water on the basis of predicted δ18O values of source water and canopy water vapor using the Craig–Gordon model [Craig and Gordon, 1965] with modifications for leaves as described by Flanagan et al. . Gillon and Yakir [2000a, 2000b, 2001] showed that the presence of carbonic anhydrase is lower in C4 relative to C3 plants. Consequently, there is a lower degree of 18O exchange between CO2 and leaf water in C4 grasses. We have used ISOLSM to evaluate the impact of incomplete equilibration between leaf water and CO2 on ecosystem discrimination in a tallgrass prairie [Riley et al., 2003]. For the work presented here we assume complete equilibration between CO2 and leaf water; this assumption will not impact our results since our focus is on nighttime respiration.
 CO2 in the soil profile approaches equilibrium with soil water with a characteristic time on the order of an hour [Riley, 2005]. It is important to note that the δ18O of CO2 in canopy air is influenced by the δ18O value of the net soil-surface CO2 flux, which, in turn, is impacted by the δ18O value of CO2 in the soil profile. The δ18O value of soil-respired CO2 (δ18Os) will reflect (1) the δ18O value of CO2 in complete equilibration with soil water at depth (δ18Ose); (2) the δ18O value of CO2 in partial equilibrium with near-surface soil water; and (3) a theoretical diffusional fractionation, ɛD, of 8.7‰. Consequently, δ18Os will equal δ18Ose depleted in 18O by some kinetic fractionation (ɛDf) between −8.7 and 0‰ [Amundson et al., 1998], i.e.,
Miller et al.  determined an effective kinetic fractionation of CO2 diffusing out of the soil to be 7.2‰ (with respect to water at about 10 cm depth) on the basis of a dynamic chamber experiment.
 Riley  recently used a model simulation in a tallgrass prairie to show that gradients in the δ18O value of near-surface soil water have significant impacts on the δ18O value of the soil-surface CO2 flux. For the work presented here, we use the relationship developed in that study with near-surface water-filled pore space (W (%)) to estimate ɛDf: