2.2.1. Laboratory Analysis
 All stable isotope measurements were carried out at the G.G. Hatch Isotope Laboratory of the University of Ottawa within 4 months of sample collection. To measure δ13CDIC, a syringe was used to inject water samples into an evacuated reaction vessel that contained H3PO4, and therefore, dissolved inorganic carbon (DIC) was quickly converted into gaseous CO2. A magnetic stirrer was used to facilitate CO2 release from the water. The released CO2 gas was purified cryogenically and kept in a 6 mm Pyrex tube for isotope analysis. The 13C:12C ratios were measured on a VG Isogas SIRA-12 triple-collector mass spectrometer with reproducibility of ±0.1‰.
 To measure δ18ODO, a helium headspace was first created in each sample bottle [Wassenaar and Koehler, 1999]. Sample bottles were placed in an anaerobic chamber, the chamber was sealed, and the air was replaced with He gas. Bottles were then uncapped, 10 mL of water was withdrawn using a syringe, and the bottles were immediately recapped securely. The high solubility of He gas facilitates O2 release from the water into the headspace. Dissolved O2 in the sample was equilibrated with the headspace using a shaker for ∼2 h. The 18O:16O ratio was measured from the O2 gas drawn from the headspace by a gastight syringe. Approximately 0.5 mL of headspace gas was injected into an elemental analyzer (CE Instruments EA 1110). O2 was separated by using a molecular sieve 3A GC packed column, and 18O:16O was measured using a Finnigan Delta Plus mass spectrometer. Repeated analysis of air-equilibrated (at 25°C) water samples produced δ18ODO of 24.3‰ ± 0.3‰, which is close to the assumed value of 24.2‰ [Lane and Dole, 1956; Benson and Krause, 1984].
2.2.2. Interpretation of Stable Isotopes
 Both the degree of oxygen saturation, O2sat, and the stable isotopic composition of dissolved oxygen, δ18ODO, are reflective of the relative amounts of production, respiration, and atmospheric exchange of oxygen in the aquatic ecosystem. Stable isotopes of dissolved oxygen have been used in several large rivers to examine the balance between production and respiration [i.e., Quay et al., 1995]. When temperature and pressure are held constant, the process of photosynthesis will increase the degree of O2 saturation, while respiration will decrease it (Figure 2a). The average isotopic composition of atmospheric oxygen is ∼23.5‰ [Lane and Dole, 1956]. The dissolution of oxygen is a fractionating process that produces dissolved atmospheric O2 with an isotopic value of ∼24.2‰ [Benson and Krause, 1984]. Respiration preferentially consumes the light isotope of oxygen and leaves the dissolved oxygen pool enriched in 18O, while photosynthesis converts oxygen in a water molecule into O2 without fractionation. Since the oxygen in H2O in the study area has an isotopic composition of about −8.5‰ [Lee and Veizer, 2003], the photosynthetically generated O2 has a depleted isotopic composition (Figure 2a).
Figure 2. (a) General effects of production, respiration, and atmospheric exchange on the isotopic composition of dissolved oxygen, δ18ODO, and the degree of oxygen saturation. (b) Carbon isotopic signature of various components of the carbon cycle in rivers. The effects of biogeochemical processes on δ13C are shown with arrows. White rectangles indicate δ13C measurements specific to the Mississippi. Adapted from Dubois et al. .
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 The isotopic composition of dissolved inorganic carbon in a river, δ13CDIC, reflects the sources of inorganic carbon. The major input of DIC into a river is due to rainwater that has equilibrated with soil CO2 and reacted with carbonate rocks during subsurface weathering [Raymond et al., 2008]. The carbon isotopic composition of DIC input from carbonate dissolution can be calculated from the relative proportions of soil and carbonate-derived DIC. The soil DIC is mainly produced by the respiration of organic matter, and its isotopic signature is therefore inherited from the organic matter. The isotopic signature of organic matter is primarily dependent on the photosynthetic pathway of the plant from which it is derived: −27‰ for C3 plants and −14‰ for C4 plants [O'Leary, 1988]. Lee and Veizer  estimate that C3 plants account for 84% of the vegetation in the Missouri, 77% in the Ohio, 68% in the upper Mississippi, and 68% in the lower Mississippi, suggesting that the isotopic composition of organic matter in the rivers would average −24.9, −24.0, −22.8, and −22.8, respectively. Overall, Lee and Veizer  estimated the relative distribution of C3 and C4 plants for the Mississippi River basin as 72.7% and 27.3%, respectively; therefore, CO2 produced from respiration in the soil is expected to have an isotopic signature of ∼−23.5‰. Soil CO2 may be subject to isotopic enrichment from diffusion of approximately +4.4‰, producing more positive values [Cerling et al., 1991], and an additional kinetic isotopic enrichment of ∼0.85‰ during gas transfer may also occur [Zhang et al., 1995]. Dissolution of CO2 into water and subsequent conversion into DIC are a temperature- and pH-dependent fractionating process [Mook et al., 1974]. At pH 7.9 and 15°C, the resulting HCO3−, the dominant DIC species, will have a δ13C value of −14.6‰ or slightly higher because of enrichment during diffusion or kinetic isotope effects. When HCO3− from soil CO2 reacts with carbonate rocks during subsurface weathering, the carbon isotopic composition of DIC input can be calculated from the relative proportions of soil and carbonate-derived DIC. Carbonates have an isotopic composition near 0‰, and thus, DIC derived from carbonate dissolution by soil CO2 has an isotopic value that is an intermediate between the two sources of carbon. Hence, the above 1:1 mixture should theoretically have a δ13C value of HCO3− near −7.3‰. The δ13CDIC can be calculated from pH, and the temperature-dependent fractionation factors for carbonate dissolution.
 In a river, respiration, photosynthesis, and atmospheric exchange also effect the isotopic composition of DIC (Figure 2b). Aquatic photosynthesis preferentially consumes 12C, leaving the residual carbon dioxide pool enriched in 13C [Baird et al., 2001] with the magnitude of the enrichment depending on the amount of CO2 available to photosynthesizing organisms. As a result, the organic matter produced by aquatic photosynthesis is isotopically depleted. Reported fractionation factors for photosynthesis vary widely and range from 0‰ to 20‰ lighter than the isotopic composition of the dissolved CO2 [Leggett et al., 1999; Bade et al., 2006; Cole et al., 2002]. The competing process, respiration, consumes this depleted organic matter and produces CO2 with a similarly depleted isotopic composition [Keough et al., 1998]. When an aquatic system is oversaturated in CO2, degassing under nonequilibrium conditions can lead to 13C enrichment of the remaining DIC pool [Doctor et al., 2008]. Finally, exchange with atmospheric CO2 can also affect δ13CDIC. In the Northern Hemisphere, atmospheric CO2 has a δ13C value around −8‰ Vienna Pee Dee belemnite (VPDB). Dissolution and gas transfer into water are both isotopically fractionating processes yielding δ13C values near 0‰ for DIC that is in equilibrium with atmospheric CO2 [Mook et al., 1974].
2.2.3. Atmospheric Flux of CO2
 We estimated evasion of CO2 to the atmosphere from the flux equation
where F is the diffusive flux of CO2 to the atmosphere, k is the gas transfer coefficient, Ceq is the concentration of dissolved CO2 in equilibrium with the atmosphere, and C is the measured concentration of dissolved CO2.
 As k was not measured, we calculated F with several flux constants taken from the literature and a suit of empirical functions to better constrain our estimates of the CO2 flux. The greatest uncertainty associated with calculating CO2 flux is related to the gas exchange coefficient, which is not well constrained in rivers [Raymond and Cole, 2001]. Gas exchange coefficients are dependent on wind speed, temperature, and turbulence and can be influenced by weather conditions such as rainfall. Richey et al.  found the average measured k in the Amazon to be 3.6 m d−1, a value representative of moderately stirred water [Mook, 1970]. Guérin et al.  measured k in the Sinnamary River and found that it averaged 3.0 m d−1. Several functions based on empirical observations have been proposed to estimate the gas exchange coefficient as a function of wind speed and temperature [Wanninkhof, 1992; Raymond and Cole, 2001; Borges et al., 2004]. The three functions give significantly different k at the same wind speed and temperature. At the average monthly wind speeds reported in the Mississippi basin by the National Climactic Data Center, the function presented by Wanninkhof  gives an average k of 3.9 m d−1, similar to observations in both the Amazon River [Richey et al., 1990] and the Sinnamary River [Guérin et al., 2007]. The function presented by Raymond and Cole  gives an average of 6.4 m d−1, while Borges et al.  give an average k of 11.9 m d−1. Because the gas diffusion coefficients calculated from Wanninkhof  are closest to observational data from large rivers [Richey et al., 1990; Guérin et al., 2007], we calculated carbon dioxide fluxes using k from Wanninkhof  and presume these fluxes are minimum estimates of the CO2 flux.