We examined carbon cycling in the Mississippi River using stable isotopes of inorganic carbon and dissolved oxygen. Eighteen sites were sampled along the river and its tributaries over 1 year. We estimate using a conservative approach that the flux of CO2 to the atmosphere (1 × 1013 g C yr−1) approximately equaled the flux of alkalinity to the Gulf of Mexico (9.7 × 1012 g C yr−1) and greatly exceeded the flux of dissolved organic carbon (1.5 × 1012 g C yr−1). Though only a first-order estimate, our work shows that the atmospheric flux of CO2 is significant and should not be ignored when examining the carbon budget of the Mississippi River. As expected, because of the large area covered by the Mississippi watershed, the isotopic composition of dissolved inorganic carbon, δ13CDIC, varied widely. In the Ohio and upper and lower Mississippi basins, δ13CDIC indicates that the source of inorganic carbon in the rivers is primarily from carbonate dissolution by soil CO2. Dissolved inorganic carbon in the Missouri River was enriched in 13C, and the isotopic composition of dissolved oxygen in this river suggests that this results from an excess of aquatic photosynthesis over respiration.
 An improved assessment of the anthropogenic effects on global climate necessitates a better understanding of global carbon cycle. Rivers play an important role as conduits of carbon from terrestrial reservoirs to the oceans and the atmosphere. Worldwide, rivers transport approximately 1.0 Gt carbon annually, in particulate and dissolved forms, from continents to oceans [e.g., Amiotte Suchet et al., 2003]. Moreover, recent studies have shown that rivers can degas significant amounts of carbon to the atmosphere as well [Richey et al., 2002; Yao et al., 2007; Zhai et al., 2007].
 As North America's largest river, the Mississippi has been studied intensely, and fluxes of alkalinity and organic carbon to the Gulf of Mexico have been well quantified [e.g., Raymond and Cole, 2003; Bianchi et al., 2004, 2007; Cai et al., 2008]. Likewise, the effect of climate changes on both inorganic and organic carbon fluxes have also been estimated [Raymond and Oh, 2007]. However, fluxes of CO2 from the Mississippi to the atmosphere have not been, as yet, well quantified.
 Because of the complexity of biogeochemical reactions that occur within watersheds, tracing the origin of carbon in fluvial systems can be convoluted. Stable isotopes of carbon can be powerful tools to constrain the sources of carbon in rivers [e.g., Brunet et al., 2005; Hélie and Hillaire-Marcel, 2006; Doctor et al., 2008]. The isotopic composition of dissolved inorganic carbon in a river, δ13CDIC, reflects both the sources of inorganic carbon and in-river processes, such as respiration, photosynthesis, and atmospheric exchange. In addition, stable isotopes of dissolved oxygen (DO), δ18ODO, can be utilized as tracers of the metabolic balance of aquatic systems [Luz and Barkan, 2000; Quay et al., 1995; Venkiteswaran et al., 2007]. Yet, stable isotopes have rarely been used on a large scale to examine sources of carbon in the Mississippi [e.g., Kendall et al., 2001].
 The objectives of this study are (1) to constrain the sources of inorganic carbon in the Mississippi River and (2) to quantify fluxes of carbon associated with weathering in river metabolism and atmospheric exchanges using δ13CDIC and δ18ODO. For this, we estimated fluxes of dissolved organic carbon (DOC), alkalinity, and CO2 at 18 sites along the Mississippi and its tributaries over 1 year and measured stable isotopes of dissolved inorganic carbon and dissolved oxygen.
2. Materials and Methods
2.1. Study Area and Sampling
 The Mississippi River basin is the largest drainage system in North America. It covers more than 3.2 × 106 km2 in the United States and Canada [Canadian National Committee for the International Hydrological Decade, 1978; Seaber et al., 1987]. The basin consists of four tributary drainages: the Missouri, the Ohio (including the Tennessee), the upper Mississippi, and the lower Mississippi (including the Arkansas-White-Red (Figure 1)). In terms of terrestrial carbon cycling, Lee and Veizer  suggested that the basin has a balanced long-term CO2 budget, with fluxes of carbon associated with net primary productivity (1.2 Pg C yr−1) and heterotrophic soil respiration (1.1 Pg C yr−1) being approximately equal. Because of its vast areal coverage, heterogeneities in climate, land cover, and basement geology are considerable. In terms of hydrological conditions, precipitation is higher for the south and the east while decreasing toward the west and the north of the basin. Therefore, river discharge is highest in the Ohio and comparatively smaller in the Missouri [Alexander et al., 1996].
 Samples of river water were obtained through collaboration with the U.S. Geological Survey National Stream Quality Accounting Network (NASQAN) program. The NASQAN program has been in place since 1973 and during the period of study operated 18 stations for sampling river water in the Mississippi River (Figure 1). For the purposes of this paper they have been divided into the lower Mississippi (including the St. Francisville, Melville, and Arkansas sites), upper Mississippi (Thebes, Grafton, and Clinton), Missouri (Hermann, Louisville, Omaha, Pierre, Garrison Dam, Sidney, and Culbertson), and Ohio (Grand Chain, Paducah, New Harmony, Cannelton Dam, and Greenup Dam) rivers. The sampling stations were selected to fully represent a possible spatial variation of riverine systems in the Mississippi drainage basin. For the majority of stations, monthly to bimonthly samples of river water were taken by NASQAN from May 2000 to May 2001. The Sydney, Culbertson, and Louisville stations were closed in October 2000, and the Paducah, New Harmony, and Grand Chain stations were closed in January 2001, and thus, fewer data are available from these stations. Additional information on sampling is available from Lee and Veizer .
 At each sampling station, a depth-integrated water sample was taken from the center of the river. Upon sampling, river water was immediately sealed, refrigerated, and transported to the laboratory located in each district office, where the water was then filtered through a 0.45 μm glass fiber filter and subsampled into 100 mL amber glass bottles poisoned with mercuric chloride to inhibit microbial growth. Sampling was done in two stages to prevent contamination of field sites with HgCl2. Water temperature, pH, alkalinity, O2 concentration, and specific conductance were measured in the field at each sampling site. The pCO2 was calculated from pH, temperature, and alkalinity according to Henry's law. Detailed descriptions of sampling techniques, site characteristics, and measurements of water properties are available from NASQAN (http://water.usgs.gov/nasqan/). Supplementary information such as discharge, DOC, and sulfate is also available at the NASQAN home page.
2.2. Stable Isotopes
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).
 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.
2.3. Statistical Analysis
 All statistical tests and confidence intervals are reported at the α = 0.05 critical level. The precision of chemical and isotopic measurements are reported as ±1 SE of the mean of n determinations multiplied by Student's t distribution (t) for n − 1 degrees of freedom, where SE = SD/(n)1/2 and SD is the standard deviation. Variables used in linear regressions were tested against the standard normal distribution with a chi-square goodness of fit test. Nonnormal variables were log transformed and used as such in multiple regressions. For linear regressions, all regression parameters were bootstrapped 1000 times, and standard errors are reported. All means are reported as discharge-weighted averages.
3.1. Missouri River
 At Mississippi pH values, which averaged 7.9 ± 0.1, alkalinity is dominated by bicarbonate and is reported as mg C L−1 following Raymond and Cole . In the Missouri River basin, discharge-weighted average alkalinity was 32.8 ± 1.5 g C m−3 (Table 1 and Data Set S1 in the auxiliary material) and was negatively correlated with discharge (Figure 3 and Data Set S2 in the auxiliary material). The pCO2 in the Missouri ranged from 73 to 3015 μatm with a discharge-weighted mean of 812 ± 159 μatm (Figure 4a). The discharge-weighted mean dissolved organic carbon concentration (DOC) was 4.0 ± 0.3 g C m−3 (Figure 4b).
Table 1. Discharge-Weighted Average Physiochemical Properties Measured in the Four Subbasinsa
T, Temperature (°C); pH; alk, alkalinity (g C m−3), pCO2 (μatm); H2CO3, dissolved carbon dioxide (g C m−3); DOC, dissolved organic carbon (g m−3); Cond, conductivity (μS cm−1); SO42−, sulfate (g m−3); O2sat, oxygen saturation; the isotopic composition of δ13CDIC, dissolved inorganic carbon (‰ VPDB), and δ18ODO, dissolved oxygen (‰ VSMOW).
14.0 ± 2.4
8.1 ± 0.1
32.8 ± 1.5
812 ± 159
0.66 ± 0.12
4.0 ± 0.3
608 ± 42
144.0 ± 19
0.96 ± 0.03
−6.8 ± 0.4
22.5 ± 0.2
15.5 ± 3.1
7.6 ± 0.1
16.3 ± 3.0
1216 ± 251
0.63 ± 0.15
2.9 ± 0.3
319 ± 44
55.5 ± 6.7
0.94 ± 0.05
−9.1 ± 0.4
23.0 ± 0.3
14.4 ± 3.7
7.8 ± 0.1
32.5 ± 1.9
1586 ± 330
1.04 ± 0.29
5.6 ± 0.5
456 ± 44
48.4 ± 9.6
0.89 ± 0.05
−9.3 ± 0.4
23.3 ± 0.3
15.8 ± 3.3
7.6 ± 0.1
20.9 ± 2.1
1362 ± 267
0.77 ± 0.17
4.5 ± 0.5
378 ± 47
40.1 ± 6.0
0.89 ± 0.05
−10.0 ± 0.4
23.3 ± 0.3
15.4 ± 1.5
7.7 ± 0.1
23.5 ± 1.6
1335 ± 129
0.58 ± 0.09
4.2 ± 0.2
408 ± 29
55.4 ± 9.9
0.91 ± 0.02
−9.3 ± 0.3
23.0 ± 0.2
 The δ13CDIC in the Missouri River and its tributaries ranged from −9.1‰ to −3.3‰ with a discharge-weighted mean of −6.8‰ ± 0.4‰ (Figure 5). According to Lee and Veizer , 84% of the vegetation in the Missouri River watershed is C3 so that a 1:1 mixture of soil and carbonate-derived DIC theoretically has a δ13C value of HCO3− of −7.9‰. The δ13CHCO3− in river water can be calculated from δ13CDIC, pH, and temperature-dependent fractionation factors for carbonate dissolution. In samples from the Missouri River, average δ13CHCO3− was −6.4‰ ± 0.4‰. This is significantly enriched when compared to the theoretical value, indicating that carbonate dissolution is not the only process that affects the isotopic composition of DIC in the Missouri River. Stepwise multiple linear regression shows that O2sat and δ18ODO explain approximately 20% of the variability in δ13CDIC in the Missouri River. The δ13CDIC was also significantly positively correlated with sulfate in the Missouri River (r = 0.35, n = 38, p = 0.01 (Figure 6)).
 Oxygen saturation in the Missouri River (Figure 7) had a discharge-weighted mean of 0.96 ± 0.03, not significantly different from atmospheric equilibrium. The δ18ODO ranged from 20.4‰ to 24.0‰ and with a discharge-weighted mean of 22.5‰ ± 0.2‰ was significantly less than the 24.2‰ expected from atmospheric O2 (p < 0.01, n = 51).
3.2. Ohio River
 In the Ohio River basin, alkalinity ranged from 8.5 to 48.0 g C m−3 with a discharge-weighted mean of 16.3 ± 0.3 g C m−3 (Figure 3 and Table 1). Alkalinity was significantly negatively correlated with log of discharge in the Ohio River. Alkalinity concentrations were notably higher at the Wabash station, where the discharge-weighted average was 38.2 ± 6.3 g C m−3. The pCO2 in the Ohio River had a discharge-weighted mean of 1216 ± 251 μatm, and DOC concentrations averaged 2.9 ± 0.3 g C m−3 (Figure 4).
 The δ13CDIC ranged from −12.2‰ to −6.5‰ with a discharge-weighted mean of −9.1‰ ± 0.4‰ (Figure 5). Seventy-seven percent of the vegetation in the Ohio River watershed is of the C3 type [Lee and Veizer, 2003], and thus, a 1:1 mixture of soil and carbonate-derived DIC has a theoretical δ13C value of HCO3− of −7.8‰. The discharge-weighted mean of δ13CHCO3− in the Ohio River samples was −8.4‰ ± 0.4‰, not significantly different from the theoretical value.
 In the Ohio River, oxygen saturation (Figure 7) had a discharge-weighted mean of 0.94 ± 0.05 and differed statistically from atmospheric equilibrium (p < 0.01, n = 39). The δ18ODO ranged from 21.0‰ to 24.9‰ with a discharge-weighted mean of 23.0‰ ± 0.3‰, significantly less than atmospheric equilibrium (p < 0.01, n = 41).
3.3. Upper Mississippi
 In the upper Mississippi River basin, alkalinity ranged from 18.2 to 48.2 g C m−3 with a discharge-weighted mean of 32.5 ± 1.9 g C m−3 and was negatively correlated with discharge (Figure 3 and Table 1). The pCO2 in the upper Mississippi had a discharge-weighted mean of 1586 ± 330 μatm, and DOC averaged 5.6 ± 0.5 g C m−3 (Figure 4).
 The δ13CDIC ranged from −11.5‰ to −7.8‰ with a discharge-weighted mean of −9.3‰ ± 0.4‰ (Figure 5). Sixty-eight percent of the vegetation in the upper Mississippi River watershed is of the C3 type [Lee and Veizer, 2003], and thus, a 1:1 mixture of soil and carbonate-derived DIC has a theoretical δ13C value of HCO3− of −7.0‰. The discharge-weighted mean δ13CHCO3− in the upper Mississippi River samples was −8.5‰ ± 0.4‰, similar to the theoretical value. Multiple linear regression shows that approximately 60% of the variability in δ13CDIC in the upper Mississippi River is accounted for by changes in temperature, conductivity, and pCO2. The δ13CDIC was also significantly correlated with sulfate (r = 0.54, n = 31, p < 0.001 (Figure 6)).
 Oxygen saturation in the upper Mississippi averaged 0.90 ± 0.05 and was significantly less than atmospheric equilibrium (p < 0.01, n = 24 (Figure 7)). The δ18ODO ranged from 21.4‰ to 28.6‰ with a discharge-weighted mean of 23.3‰ ± 0.3‰ and was also significantly less than atmospheric O2 (p < 0.01, n = 24).
3.4. Lower Mississippi
 In the lower Mississippi watershed, alkalinity ranged from 7.2 to 32.2 g C m−3 with a discharge-weighted mean of 20.9 ± 2.1 g C m−3 (Figure 3 and Table 1). There was no significant correlation between alkalinity and discharge. The pCO2 in the lower Mississippi River had a discharge-weighted mean of 1363 ± 267 μatm, and DOC averaged 4.5 ± 0.5 g C m−3 (Figure 4).
 The δ13CDIC ranged from −11.5‰ to −7.0‰ with a discharge-weighted mean of −10.0‰ ± 0.4‰ (Figure 5). According to Lee and Veizer , 68% of the vegetation in the lower Mississippi is C3, and thus, a 1:1 mixture of soil and carbonated-derived DIC has a theoretical δ13C value of HCO3− of −7.1‰. The discharge-weighted mean δ13CHCO3− in the lower Mississippi River samples was −9.1‰ ± 0.4‰. This is considerably depleted when compared to the theoretical value, indicating that carbonate dissolution is not the only process that affects the isotopic composition of DIC in the lower Mississippi River. There was a significant negative relationship between δ13CDIC and log of discharge, log of pCO2, and δ18ODO in the lower Mississippi. The δ13CDIC was also significantly correlated with sulfate (r = 0.40, n = 33, p = 0.01 (Figure 6)).
 Oxygen saturation in the lower Mississippi averaged 0.89 ± 0.05, and δ18ODO ranged from 22.1‰ to 24.7‰ with a discharge-weighted mean of 23.3‰ ± 0.3‰ (Figure 7). Both average O2sat and δ18ODO were significantly less than atmospheric values (p < 0.01, n = 30).
3.5. Carbon Fluxes
 Annual flux of alkalinity at St. Francisville, the farthest downstream station, was 9.7 × 1012 g C yr−1 (Table 2), similar to the estimate of alkalinity flux from the Mississippi to the Gulf of Mexico reported by Raymond and Cole . The annual alkalinity flux at Thebes, the farthest downstream station on the upper Mississippi, was 5.7 × 1012 g C yr−1, greater than the flux from the Ohio (4.0 × 1012 g C yr−1) or the Missouri (2.0 × 1012 g C yr−1). At most of the stations sampled, alkalinity flux per day was at a maximum in the spring and a minimum in the fall and winter.
Table 2. Alkalinity, Dissolved Organic Carbon, CO2 Flux per Square Meter of River Area, and Annual CO2 Fluxes at Each of the Sampling Sites in the Missouri, Ohio, Upper Mississippi, and Lower Mississippi Riversa
Alk, alkalinity (109 g C yr−1); DOC, dissolved organic carbon (109 g C yr−1); CO2 flux (m−2), CO2 flux per square meter of river area (g C m−2 yr−1); CO2 flux, annual CO2 fluxes (109 g C yr−1); M, Missouri River; OH, Ohio River; UM, upper Mississippi River; LM, lower Mississippi River, The mean annual CO2 flux per square meter of river area in each subbasin is also shown (mean FCO2 (m−2), g C m−2 yr−1). The number of samples collected is indicated by n, and the surface area of water included in each sampling station's watershed (km2) is indicated by SA.
2250 ± 1245
416 ± 217
1182 ± 390
738 ± 588
Missouri (at Hermann)
739 ± 478
Ohio (at Grand Chain)
1202 ± 543
Upper Mississippi (at Thebes)
2286 ± 1311
Lower Mississippi (at St. Francisville)
1077 ± 407
1182 ± 390
 Annual flux of DOC at St. Francisville, the farthest downstream station, was 1.5 × 1012 g C yr−1 or 16% of the annual flux of alkalinity (Table 2). When all the stations were considered, the DOC flux averaged 17.8% ± 2.0% of the alkalinity flux. The annual flux of DOC from the upper Mississippi was 8.8 × 1012 g C yr−1, greater than the flux from the Ohio, 6.6 × 1012 g C yr−1, or Missouri, 3.3 × 1012 g C yr−1. Over the year, DOC flux was lowest in October and highest in the early spring.
 Average CO2 flux per square meter of river surface area varied widely across the Mississippi River basin, ranging from 101 to 3595 g C m−2 yr−1 and averaging 1182 ± 390 g C m−2 yr−1 (Table 2 and Figure 8). Average annual flux was significantly lower in the Missouri River (739 ± 478 g C m−2 yr−1) than in the upper Mississippi (2286 ± 1311 g C m−2 yr−1), lower Mississippi (1077 ± 407 g C m−2 yr−1), and Ohio (1202 ± 543 g C m−2 yr−1). From estimates of surface area covered by river water [U.S. Army Corps of Engineers, 1991a, 1991b, 2002, 2003a, 2003b, 2006, 2007], the total annual atmospheric flux of CO2 was 3.3 × 1012 g C yr−1 from the Missouri River, 2.2 × 1012 g C yr−1 from the Ohio, 6.3 × 1012 g C yr−1 from the upper Mississippi, and 1.5 × 1012 g C yr−1 from the lower Mississippi. Our conservative estimate of the annual flux of CO2 from the Mississippi River and its tributaries to the atmosphere is 1 × 1013 g C yr−1.
4.1. The pCO2
 Near-neutral pH in the Mississippi and its tributaries lead to moderate pCO2, with an discharge-weighted average of 1335 ± 130 μatm. For comparison, in the Ottawa River, pCO2 averaged 1200 μatm [Telmer and Veizer, 1999]. The pCO2 in the Changjiang River Estuary ranged from 650 to 1440 μatm but was higher in the Huangpujiang River, 1000–4600 μatm [Zhai et al., 2007]. In the Xinjiang River, a subtropical monsoon river in China, Yao et al.  found that pCO2 ranged from 600 to 7200 μatm in the mainstream and from 700 to 11000 μatm in the tributaries. In the Amazon, pCO2 ranged from 2950 μatm to over 44,000 μatm on the mainstream floodplain [Richey et al., 2002].
4.2. The δ13CDIC
Raymond et al.  have shown that 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. As shown in section 2.2.2, the carbon isotopic composition of DIC input from carbonate dissolution can be calculated from the relative proportions of soil and carbonate-derived DIC. In the Ohio and upper Mississippi subbasins, average was not significantly different from the theoretical calculated value of from a 1:1 mixture of soil and carbonate-derived DIC (Figure 5) consistent with the proposition that dissolution of carbonates by soil CO2 is the primary source of DIC in these rivers. However, in the Missouri River basin, average was enriched when compared to the theoretical value of and in the lower Mississippi, was significantly depleted when compared to the theoretical value of indicating that carbonate dissolution is not the only process that affects the isotopic composition of DIC in these basins.
 In the Missouri River, the invasion of atmospheric CO2 (δ13CDIC ≈ 0‰) would lead to enriched δ13CDIC, yet this seems an unlikely source as the majority of the samples are oversaturated in pCO2. Degassing of isotopically light CO2 can also produce 13C enrichment in DIC in rivers as, under open system conditions favorable for the rapid exchange of CO2, kinetic isotope fractionation can result in greater isotope enrichment than is expected in equilibrium conditions. Marlier and O'Leary  observed kinetic isotope fractionation as large as 14.7‰. Doctor et al.  found δ13CDIC increased between 3‰ and 5‰ in the first 500 m of the Sleepers River, concomitant with decreasing riverine pCO2. This isotope enrichment was found to be the result of CO2 outgassing. However, in the Missouri River, there was no significant relationship between δ13CDIC and pCO2 or CO2sat.
 In the Missouri, one possible source of enriched inorganic carbon is the dissolution of carbonate minerals by acidity that is unrelated to a source of carbon, such as sulfuric acid, which would generate with a δ13C signature identical to the carbonate (∼0‰). Concentrations of sulfate were higher in the Missouri than in the other watersheds sampled, and a significant relationship between sulfate and δ13CDIC was observed in the Missouri and across the Mississippi (Figure 6). Another possible source is an excess of photosynthesis over respiration, which may also be responsible for the isotopic enrichment (Figure 2). In the Missouri River samples, while O2sat was not significantly different from equilibrium, δ18ODO was significantly less than atmospheric values, suggestive of an excess of photosynthesis over respiration [Venkiteswaran et al., 2007]. Furthermore, δ13CDIC was positively correlated with oxygen saturation and negatively correlated with δ18ODO, again indicating that aquatic production and respiration influence the isotopic composition of DIC in the Missouri.
 In the lower Mississippi River, was significantly depleted when compared to the theoretical value of (Figure 5). The negative correlations between δ13CDIC and pCO2 and δ18ODO and DOC and the positive relationship with O2sat suggest that respiration of organic matter adds 13C depleted C to the inorganic carbon pool in the lower Mississippi.
4.3. Oxygen Saturation and δ18ODO
 In the Ohio and upper and lower Mississippi (Figure 7 and Table 1), oxygen saturation was significantly less than values expected from atmospheric equilibrium. Yet, in all the river basins, δ18ODO was significantly less than atmospheric oxygen values. Together, these observations suggest that atmospheric exchange is the dominant process controlling the isotopic composition of DO in these rivers [Venkiteswaran et al., 2007]. In the Missouri River, O2sat was near equilibrium, but δ18ODO was significantly less than atmospheric values, suggesting that photosynthesis dominates over respiration and atmospheric exchange is rapid [Venkiteswaran et al., 2007].
4.4. Carbon Fluxes
 Literature values of CO2 fluxes for rivers vary widely, as does the importance of atmospheric CO2 flux relative to total carbon export. Richey et al.  found that outgassing of CO2 to the atmosphere was an important source of carbon loss in the Amazon basin, equal to 120 ± 30 g C m−2 of water surface yr−1. In the Xinjiang River atmospheric CO2 fluxes ranged from 830 to 1560 g C m−2 yr−1 [Yao et al., 2007]. CO2 degassing was less significant in the Changjiang River, with fluxes ranging from 186 to 411 g C m−2 yr−1. This represented only 2%–4.6% of the DIC exported into the East China Sea [Zhai et al., 2007]. In the Ottawa River, Telmer and Veizer  estimate the flux of CO2 to the atmosphere to be 170 g C m−2 yr−1 or 30% of the river's annual flux of DIC. Minimum estimates of CO2 outgassing from the Nyong River in Cameroon were 1487 g C m−2 yr−1 or 115% of the flux of DIC [Brunet et al., 2009]. Our estimate of CO2 flux in the Mississippi was comparable at 1182 ± 390 g C m−2 yr−1 or ∼130% of the flux of DIC (Table 2).
 It should be noted that while our estimates of CO2 flux to the atmosphere (Table 2) are a significant portion of the carbon budget in the Mississippi, they represent minimum estimates of CO2 flux as these estimates were generated with a small gas diffusion coefficient. Because the gas diffusion coefficients calculated from Wannikhof  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 . However, using the gas diffusion coefficient calculated from Raymond and Cole , on average 6.4 m d−1, would increase estimates of CO2 flux to the atmosphere by 63%. Applying the gas diffusion coefficient form Borges et al. , on average 11.9 m d−1, would increase the estimated CO2 flux even further.
 Further, when calculating CO2 fluxes, we presumed a constant concentration of carbon dioxide in the atmosphere of 380 ppm. Of course, atmospheric CO2 concentrations are variable both spatially and temporally. Data from T. J. Conway et al. (Atmospheric carbon dioxide dry air mole fractions from the NOAA ESRL Carbon Cycle Cooperative Global Air Sampling Network, 1968–2008, version: 2009–07–15, 2009, available at ftp://ftp.cmdl.noaa.gov/ccg/co2/flask/event/) reveals that between 2003 and 2008, CO2 concentrations in the southern Great Plains varied on average by 11.2 ppm yr−1. Applying the monthly average CO2 values to our data increases annual CO2 fluxes by an average of 0.6%.
 In the Mississippi River and its tributaries, atmospheric efflux of CO2 varies widely. While most sampling sites were continually oversaturated in CO2, the Yellowstone River at Sidney and the Platte River at Louisville, both tributaries of the Missouri, were undersaturated in CO2 in May and June. At most of the sampling sites, CO2 efflux was highest in February and lowest in September. All rivers were sources of CO2 to the atmosphere over the sampled year; CO2 efflux averaged 1182 ± 390 g C m−2 yr−1 (Table 2). Estimating that the surface area of the Mississippi River and its tributaries covers approximately 9000 km2 [U.S. Army Corps of Engineers, 1991a, 1991b, 2002, 2003a, 2003b, 2006, 2007], this translates to an annual efflux of approximately 1 × 1013 g C yr−1. Though this is only a first-order estimate, this flux of CO2 approximately equals the sum of the DIC and DOC flux at St. Francisville, showing that the CO2 flux from the Mississippi to the atmosphere is not negligible and should be considered when examining the CO2 budget of the river.
 When our estimates of alkalinity flux (9.7 × 1012 g C yr−1) and dissolved organic carbon flux (1.5 × 1012 g C yr−1) are combined with the particulate organic carbon flux measured by Bianchi et al.  (9.3 × 105 t C yr−1) and with estimates of carbon dioxide loss (1 × 1013 g C yr−1), we propose that the net loss of carbon from the Mississippi River is 2.2 × 1013 g C yr−1. Forty-five percent of this loss is through atmospheric exchange. While this estimate of atmospheric loss seems large when compared to other carbon fluxes, it is not unprecedented. Richey et al.  found atmospheric fluxes of carbon in the Amazon basin that were an order of magnitude larger than fluxes of organic carbon. In the Nyong river of Cameroon, Brunet et al.  found that atmospheric fluxes were 4 times the river's annual flux of DIC and 115% of the river's annual DOC flux.
 Many continental- and global-scale carbon flux estimates involve “inversion” of measured atmospheric CO2 and δ13C [e.g., Rayner et al., 2008], which requires an accurate characterization of the sources and sinks of CO2 and associated isotopic effects. Our study indicates that atmospheric exchange of riverine CO2 fluxes and associated isotope effects may provide an additional factor that needs to be incorporated into models describing global carbon cycling.
 Our estimate of alkalinity, CO2, and DOC fluxes combined with the particulate organic carbon flux measured by Bianchi et al.  enables an estimate of the net flux of carbon from the Mississippi River as 2.2 × 1013 g C yr−1. This loss is 44% through alkalinity, 12% through organic carbon, and 45% through atmospheric losses. Though only a first-order estimate, our work shows that the atmospheric flux of CO2 is significant and should not be ignored when examining the carbon budget of the Mississippi basin.
 Stable isotopes of dissolved inorganic carbon indicate that in the Ohio and upper Mississippi rivers the source of inorganic carbon is primarily carbonate dissolution by soil CO2. In the Missouri River, DIC is enriched in 13C, indicating that additional processes affect the isotopic composition of DIC. Here the δ13CDIC is positively correlated with oxygen saturation and negatively correlated with δ18ODO, and δ18ODO is significantly less than atmospheric values, suggesting that an excess of production over respiration in the river leads to the 13C enrichment. In the lower Mississippi River, DIC is depleted in 13C, likely the result of the respiration of organic matter in the river.
 The U.S. Geological Survey NASQAN Program provided samples of river water for this study. A special thanks is given to Rick Hooper, Valerie Kelly, Carol Kendall, and technicians at the sampling stations. Wendy Abdi, Paul Middlestead, and Gilles St. Jean of the G.G. Hatch Isotope Laboratory helped with the isotope analysis. This study was financially supported by the Natural Sciences and Engineering Research Council of Canada and by the Chair in Earth Systems sponsored by the Canadian Institute for Advanced Research, Noranda, G.G. Hatch and Associates, and NSERC.