Accurate quantification of CO2 flux across the air-water interface and identification of the mechanisms driving CO2 concentrations in lakes and reservoirs is critical to integrating aquatic systems into large-scale carbon budgets, and to predicting the response of these systems to changes in climate or terrestrial carbon cycling. Large-scale estimates of the role of lakes and reservoirs in the carbon cycle, however, typically must rely on aggregation of spatially and temporally inconsistent data from disparate sources. We performed a spatially comprehensive analysis of CO2 concentration and air-water fluxes in lakes and reservoirs of the contiguous United States using large, consistent data sets, and modeled the relative contribution of inorganic and organic carbon loading to vertical CO2 fluxes. Approximately 70% of lakes and reservoirs are supersaturated with respect to the atmosphere during the summer (June–September). Although there is considerable interregional and intraregional variability, lakes and reservoirs represent a net source of CO2 to the atmosphere of approximately 40 Gg C d–1 during the summer. While in-lake CO2 concentrations correlate with indicators of in-lake net ecosystem productivity, virtually no relationship exists between dissolved organic carbon and pCO2,aq. Modeling suggests that hydrologic dissolved inorganic carbon supports pCO2,aq in most supersaturated systems (to the extent that 12% of supersaturated systems simultaneously exhibit positive net ecosystem productivity), and also supports primary production in most CO2-undersaturated systems. Dissolved inorganic carbon loading appears to be an important determinant of CO2 concentrations and fluxes across the air-water interface in the majority of lakes and reservoirs in the contiguous United States.
 The majority of inland waters contain dissolved CO2 in excess of atmospheric concentrations and are therefore net sources of carbon dioxide to the atmosphere [Cole et al., 1994]. Global estimates of net lake emissions range from 0.07 to 0.53 Pg C yr–1 as CO2 [Cole et al., 1994, 2007; Tranvik et al., 2009], with reservoirs emitting an additional 0.3 Pg C yr–1 [St. Louis et al., 2000]. CO2 supersaturation has generally been attributed to in-lake respiration of terrestrially derived organic matter (OM), resulting in net heterotrophy (respiration exceeding photosynthesis) [Cole and Caraco, 2001; Cole et al., 2000; Duarte and Prairie, 2005]. Several studies report a positive correlation between dissolved organic carbon (DOC), potentially an indicator of terrestral OM inputs, and pCO2,aq in widely distributed lakes [Jonsson et al., 2003; Larsen et al., 2011; Roehm et al., 2009; Sobek et al., 2005]. However, negative correlations between these parameters have also been observed in Arctic lakes [Tank et al., 2008]. There is also growing evidence that hydrologic inputs of dissolved inorganic carbon (DIC) may be responsible for CO2 supersaturation in some net autotrophic systems [Finlay et al., 2010; López et al., 2011; Stets et al., 2009; Striegl and Michmerhuizen, 1998].
 Accurate characterization of ecological carbon sequestration requires detailed estimates of current CO2 fluxes from lakes and reservoirs on regional scales [Zhu et al., 2010]. The primary goal of this study is to develop these regional estimates for the contiguous United States. We combine water chemistry data for more than 1000 lakes and reservoirs collected during the summer of 2007 by the U.S. Environmental Protection Agency [U.S. Environmental Protection Agency (EPA), 2009a] with a recently developed high-resolution regional inventory of the 3.5 million lakes and reservoirs (>0.001 km2) present in the contiguous United States [McDonald et al., 2012] to quantify summertime CO2 concentrations and estimate atmospheric exchange in these systems.
 The secondary goal of this study is to determine the relative influence of organic and inorganic allochthonous carbon inputs on pCO2,aq and CO2 flux across the air-water interface. We hypothesize that in regions of the contiguous United States where high-alkalinity waters are prevalent (e.g., the Great Plains), DIC is the dominant control on pCO2,aq, whereas in low-alkalinity areas (e.g., New England) respiration of allochthonous DOC dominates. We analyze patterns of lake chemical and physical properties to identify regional variability in the drivers of lake and reservoir pCO2,aq. We also present a carbon balance model incorporating hydrologic DIC inputs, net ecosystem productivity (NEP), and carbonate equilibrium chemistry. The model is applied to nearly 1000 lakes and reservoirs, and results are used to assess regional variability in the relative importance of inorganic carbon loading, respiration of allochthonous organic matter, and photosynthesis in determining in-lake CO2 concentrations and fluxes across the air-water interface.
 Sign conventions for carbon fluxes vary with context and discipline. Here we consider the water, exclusive of particulate constituents, to be our frame of reference. Therefore, for air-water gas transfer, positive is out of the lake. For NEP, positive indicates that gross primary productivity exceeds community respiration.
2.1 Water Chemistry and pCO2,aq
 Water chemistry data were obtained from the U.S. EPA's National Lakes Assessment (NLA) [EPA, 2009a]. The NLA used a probability-based survey design to select 1028 lakes and reservoirs (hereafter referred to collectively as “lakes”) that were representative of the 68,223 lakes in the contiguous United States that met the following criteria: (a) are greater than 4 ha in area with a minimum of 0.1 ha of open water, (b) are at least 1 m deep, and (c) are not treatment or disposal ponds, brackish, or ephemeral [EPA, 2009a]. Some states opted to sample additional water bodies meeting the same criteria. The final 1157 sampled lakes are shown in Figure 1. The Laurentian Great Lakes were not included. Sampling took place during the summer of 2007; 50% of the samples were obtained between 12 July and 23 August, and nearly all (99%) were obtained between 1 June and 30 September. Ninety-five of the target lakes were sampled twice. In the current study, we use averaged data for revisited sites. NLA data can be accessed at http://water.epa.gov. Data were partitioned geographically according to the slightly modified Level II Ecoregions shown in Figure 1 [Omernik, 1987; Zhu et al., 2010]. These regions represent areas of similar land use, topography, natural vegetation, and soils.
 Many physical, biological, and chemical indicators were measured for the NLA [EPA, 2009a]; we utilized only a subset of these data. Temperature, pH, and dissolved oxygen were measured in the field, and 2 m depth-integrated (surface) samples were obtained for water chemistry analyses [EPA, 2007]. Laboratory analyses were performed at the Willamette Research Station analytical laboratory in Corvallis, OR, following laboratory standard operating procedures (David Peck, personal communication, 2011). DOC was analyzed using a Phoenix 8000 carbon analyzer. Chlorophyll was determined fluorometrically with a Turner Fluorometer. Ions were analyzed using inductively coupled plasma-mass spectrometry (Thermo Fisher IRIS Intrepid II). Acid-neutralizing capacity was measured via titration with HCl, and was assumed to be equivalent to alkalinity (i.e., the contribution of particulates to alkalinity was assumed to be negligible). Information on quality assurance is provided by EPA [2009b].
 Although many studies ignore the contribution of noncarbonate alkalinity to total alkalinity when calculating pCO2,aq, parallel calculations utilizing alkalinity/pH/temperature and DIC/pH/temperature have indicated that doing so generally leads to an overestimation of pCO2,aq, and subsequently, CO2 fluxes [Hunt et al., 2011]. In typical naturally occurring fresh waters, the only major contributor to noncarbonate alkalinity is organic acid, primarily humic, and fulvic acids [Lozovik, 2005]. The concentration of free organic anions was estimated for the NLA lakes as a function of pH and DOC concentrations using the empirical relationships of Oliver et al. , and their contribution to alkalinity was then calculated according to Lozovik . Although the parameters of the Oliver et al. equation have been shown to vary regionally [Driscoll et al., 1989], we chose the more general Oliver et al. parameterization to apply to the NLA data set. The fraction of alkalinity attributable to organic anions was generally small (mean = 2%, median = 0.4%). However, in 5% of the samples organic anions were estimated to be responsible for more than 5% of measured alkalinity, and in 2% of the samples organic anions were estimated to be responsible for more than 10% of measured alkalinity.
 Dissolved CO2 was computed as a function of alkalinity, pH, and temperature according to carbonate equilibrium chemistry [Stumm and Morgan, 1981]. Dissociation constants of carbonic acid were estimated according to Harned and Davis  and Harned and Scholes . The total dissolved inorganic carbon concentration was optimized (Microsoft Excel Solver, simplex method) such that the calculated alkalinity was equal to observed alkalinity. CO2 concentrations were converted to partial pressures using Henry's law constants calculated from water temperature according to Plummer and Busenburg .
 Because flux calculations were to be performed using mean pCO2,aq values, the data were examined for extreme values prior to computation. After sorting calculated pCO2,aq by Ecoregion (but prior to averaging values for revisited sites), we removed any observations that fell outside of the interval [Q1 – 3*IQR, Q3 + 3*IQR], where IQR is the interquartile range and Q1 and Q3 are the first and third quartiles, respectively. This resulted in the removal of 77 observations, so that the final working data set comprised 1089 sites (1175 observations).
2.2 CO2 Fluxes
 CO2 flux across the air-water interface, JCO2 (mol m–2 d–1) was calculated as
where k is the gas transfer velocity (m d–1), [CO2]aq is the dissolved concentration of CO2 (mol L–1), KH is Henry's law constant (mol L–1 µatm–1), and pCO2,air is the atmospheric partial pressure of CO2 (µatm). Atmospheric pCO2 was estimated as a summer (June–September) average from five monitoring locations throughout the U.S. for which 2007 surface CO2 flask measurements were made: Key Biscayne (FL), Niwot Ridge (CO), Southern Great Plains (OK), Wendover (UT), and Trinidad Head (CA) (mean = 382.9 µatm, SD = 1.2 µatm). These data are available from http://www.esrl.noaa.gov.
 The gas transfer velocity was calculated according to Cole and Caraco , using an exponent of −0.67 to relate k600 (the gas transfer velocity at a Schmidt number of 600) to kSc, where Sc is the Schmidt number calculated for each region as a function of water temperature [Wanninkhof, 1992]. Mean summer (June–September) wind speeds at 10 m (u10) for each Ecoregion were determined from NASA surface meteorology and solar energy data set (http://eosweb.larc.nasa.gov/sse/) and ranged from 2.97 m s–1 in Ecoregion 8.3 (Southeastern Plains) to 4.43 m s–1 in Ecoregion 9.4 (South Central Semi-Arid Prairies). Lake surface areas are tabulated for each Ecoregion in McDonald et al. .
2.3 Statistical Analysis
 Many of the parameters involved in these calculations violate normality assumptions. Therefore, nonparametric confidence intervals (95%) on the mean were determined using the bias-corrected and accelerated method on 1 million ordinary bootstrap replicates [Efron, 1987]. Confidence intervals on calculated parameters were determined via propagation of uncertainty. The nonparametric Spearman's rank correlation coefficient (ρ) was calculated for pCO2,aq vs. DOC, DO, chlorophyll a, and Ca2+ in each region (Ecoregion 15 was excluded from the correlation analysis because it contains only a single NLA lake, Lake Okeechobee).
2.4 Model Development
2.4.1 Model Overview
 A steady state, coupled mass balance and geochemical speciation model was developed to describe the roles of hydrologic DIC and DOC inputs in determining dissolved CO2 concentrations in the NLA lakes (Figure 2). A simple physical framework was utilized, representing a completely mixed epilimnion (for stratified lakes) or lake (for unstratified lakes) during average summertime conditions, inflow/outflow, and evaporation. Equilibrium chemistry was modeled using PHREEQC [Parkhurst and Appelo, 1999]. The model computes DIC concentration and speciation in the lake considering the alkalinity, pH, and temperature of incoming hydrologic inputs/outputs and lake water, air-water gas exchange (computed according to equation (1)), and NEP (calibrated parameter, as explained below). The model was implemented and run in Matlab 7.12.
2.4.2 Model Inputs
 Lake alkalinity, pH, and temperature measurements were obtained from the NLA data set as described in section 2.1. For each lake, maximum depth was obtained from the NLA data set, and the depth of the thermocline was identified as the depth at which depth-resolved temperature profiles exhibited the greatest gradient. The volume of the epilimnion was then estimated by approximating the shape of the lake basin as an inverted cone and using similar geometries (i.e., subtracting the hypolimnetic volume from the total volume). The total conic volume was used for unstratified lakes.
 Inflow was determined using runoff data from the NHDPlus data set (http://www.horizon-systems.com/nhdplus). The 8 digit hydrologic unit(s) in which each NLA lake is located was identified, and the corresponding mean annual unit runoff was calculated from cumulative runoff and cumulative drainage area (NHDPlus). The actual basin areas (NLA), including lake surface area, were then used to estimate mean annual inflow to each lake. Monthly averaged climatic data (temperature, relative humidity) were obtained from the NASA surface meteorology and solar energy data set (section 2.2). Evaporation from the water surface was calculated according to the method outlined by Chapra [1997, pp. 284–285], where the dew-point temperature was determined according to Lawrence . Evaporation and the gas transfer coefficient (k) were modeled on an Ecoregional basis, and KH was computed for each lake individually. Outflow from each lake was determined as the sum of inflow and evaporation, such that water volume was conserved. In the cases where calculated evaporation was greater than estimated inflow (n = 178), inflow was set equal to 150% of evaporation. This situation occurred most frequently in the northern Great Plains, where hydrology is often groundwater-dominated. Considering only surface water chemistry in model inputs was a conservative choice (i.e., the model is likely underestimating hydrologic inputs of DIC). Direct groundwater inputs (which are typically higher in DIC than surface water) are a significant component of hydrologic and carbon budgets in some lakes [Stets et al., 2009, 2010]. On the other hand, precipitation falling directly on lake surfaces is implicitly assumed to contain DIC concentrations equal to those of surface waters, which is an overestimate, but this input is typically small in the NLA lakes (median lake:basin area ratio = 0.03).
 Summertime (June–September) river alkalinity, pH, DOC, and temperature data were compiled for the approximately 10,800 sites in the USGS National Water Quality Information System (http://waterdata.usgs.gov/nwis) for which all three parameters have been simultaneously measured [Butman and Raymond, 2011]. Kriging was used to spatially interpolate these data, and values corresponding to each NLA lake were obtained from the resulting raster surfaces.
 Kriged mean annual river alkalinity was generally greater than observed alkalinity in the NLA lakes (median [alkalinityriver – alkalinitylake] = 392 μEq). Calcite precipitation [Otsuki and Wetzel, 1974] and calcification [McConnaughey et al., 1994] can be responsible for reducing alkalinity in situ in some systems. It seems unlikely, however, that these mechanisms are responsible for a widespread discrepancy, especially considering that the greatest difference between river and lake alkalinities occurs in the lowest alkalinity regions, where precipitation is least likely (e.g., Atlantic Highlands (5.3), Marine West Coast Forest (7.1)). It seems possible that this pattern is instead due to lakes being diluted during periods of high surface runoff that are not represented in discrete water-quality data. However, in lakes that were resampled, there was little evidence of the increasing trend that would be expected if this were the case (median increase in alkalinity of 1%). If significant and widespread calcite precipitation is in fact partially responsible for the disagreement between riverine and lake alkalinity concentrations, then an additional hydrologic source of CO2 is being attributed to NEP in the model, leading to conservative model predictions with respect to the role of DIC inputs.
 Because major differences between alkalinity in lakes and inflows in model input would prevent steady state operation of the model, lake alkalinities (corrected for evaporation) were assigned to the inflows. River pCO2,aq was calculated (see section 2.1) for each site using kriged river alkalinity, pH, and temperature data, and inflow pH was adjusted using the Nelder-Mead simplex direct search method [Lagarias et al., 1998] so that the CO2 concentrations in the modeled inflows were equal to calculated values. This approach likely further underestimates hydrologic DIC inputs, and again leads to conservative model predictions regarding the role of these inputs in lacustrine carbon cycling.
2.4.3 Model Execution and Calibration
 The model was run using a 1 day time step. At each time step, PHREEQC calculates DIC speciation within the lake considering daily inflow, evaporation, and addition or removal of CO2 from the system via flux across the air-water interface (calculated according to equation (1)) and NEP. The model was run until numerical stability was achieved. This occurred in less than 20 days in most cases, although some lakes required nearly 100 days to stabilize. In some cases (n = 63), estimated river and lake chemistry were dissimilar enough to cause an internal nonconvergence error in PHREEQC, and in 29 cases model output had not stabilized after 100 days. Additionally, there were 38 sites where the specified inflow and volume resulted in a residence time of less than one day. All of these sites were discarded from model output. NEP was calibrated for the remaining 959 sites using the Nelder-Mead simplex direct search method to match the modeled to observed (i.e., calculated) CO2 concentrations.
3.1 Dissolved CO2 and Air-Water Flux
 The majority (67%) of the lakes examined were supersaturated in CO2 with respect to the atmosphere (Figure 3a). The frequency distribution of pCO2,aq is skewed toward high values, so that the mean (1043 µatm) is higher than the median (646 µatm). With the exception of Ecoregions 15 (Everglades) and 6.2 (Western Cordillera), regional median lake pCO2,aq values are all greater than pCO2,air (Figure 3c). Significant differences in pCO2,aq exist among Ecoregions (Kruskal-Wallace test, P < 0.001). Yet, regional variability in pCO2,aq is small compared with the regional variability in alkalinity and pH (Figure 3b and Table 1).
Approximate carbonate alkalinity; total alkalinity corrected for the contribution of organic acids (see Methods).
 It has been shown that epilimnetic pCO2,aq tends to decrease during the summer, as it is utilized for photosynthesis [e.g., Maberly, 1996]. Of the NLA lakes that were resampled (n = 95), however, this phenomenon was not clearly observed. The difference between samplings (second – first) was in fact slightly negative (mean = −14 µatm, median = −20 µatm), but there was a great deal of variability in this value (SD = 2808 µatm). Furthermore, pCO2,aq actually increased in nearly half (45%) of the lakes. Thus, although our assumption of constant summertime pCO2,aq is clearly not realistic for a single lake, it does appear to be a reasonable approximation when modeling patterns across a large population of lakes, as we have done here.
 Mean summer CO2 fluxes from lakes are variable among regions (Figure 4a and Table 2), ranging from being a sink of 0.05 g C m–2 d–1 in Ecoregion 15 (Everglades, i.e., Lake Okeechobee) to a source of 0.61 g C m–2 d–1 in Ecoregions 9.4 (South Central Semi-Arid Prairies) and 8.3 (Southeastern USA Plains). The gas transfer velocity is fairly consistent among regions, with a mean value of 1.1 m d–1 (Table 2). Regional variability in CO2 calculated fluxes is therefore largely a reflection of variability in dissolved CO2 (Table 1).
Table 2. Regional Estimates of CO2 Flux Across the Air-Water Interfacea
Level II Ecoregion
Mean [CO2] (μM)
Transfer Velocity (m d–1)
Mean CO2 flux (g C m–2 d–1)
Mean CO2 Mass Flow Rate (Gg C d–1)
Mean Regional CO2 Yield (mg C m–2 d–1)
Presented as mean [95% confidence interval]. Positive values indicate flux out of the lake.
 The Ecoregional surface area of lakes is also highly variable, ranging from 689 to 17,900 km2 [McDonald et al., 2012]. Taking this into account, mean total CO2 mass flow rates (i.e., net CO2 transfer across the air-water interface per unit time) range from −0.1 to 10.6 Gg C d–1 among Ecoregions, and exhibits a greater degree of regional variability than does CO2 flux (Figure 4b and Table 2). The total summer mass flow rate for the entire contiguous United States is 40.3 Gg C d–1. Because the sizes of the Ecoregions themselves are also variable, ranging from 22,600 to 106,000 km2 [McDonald et al., 2012], normalizing to Ecoregion area to develop an estimate of CO2 emissions in units of mg C m–2 d–1, henceforth referred to as yield, is instructive. Yields ranged from −3.9 to 13.4 mg C m–2 d–1 (Figure 4c and Table 2).
 Correlations (Spearman's ρ) between pCO2,aq and DOC, DO, chl a, and Ca2+ were generally weak, but 28 out of 60 comparisons resulted in a correlation that was significant at α ≤ 0.1 (Table 3). Dissolved oxygen is significantly negatively correlated with pCO2,aq in 13 out of 15 regions, and in some regions in which the median chlorophyll concentration is large, a significant negative correlation between chlorophyll and CO2 also tends to occur (Tables 1 and 3). DOC, on the other hand, was only significantly correlated with pCO2,aq in a single region (Ecoregion 8.4), and in this case the correlation is negative.
Table 3. Correlations Between pCO2,aq and Selected Parameters
 Of the modeled sites, 73% were estimated to be CO2-supersaturated with respect to the atmosphere, which agrees well with direct calculations (section 3.1). Of the supersaturated sites, 88% had negative modeled NEP, while 12% had positive NEP (Figure 5). All but one of the undersaturated sites had positive modeled NEP. The majority of plotted (Flux, NEP) pairs fall above the 1 : –1 line, indicating some degree of hydrologic support (Figure 5a).
 Figure 5b shows the difference between flux and NEP (i.e., the vertical distance from a point to the 1 : –1 line in Figure 5a) normalized to flux. This may be interpreted as the fraction of CO2 flux out of the lake attributable to hydrologic DIC inputs, while the remainder can be inferred to be attributable to net respiration of allochthonous DOC inputs. Of the 73% of lakes that were supersaturated with CO2 the overall median was 0.06 indicating that hydrologic DIC inputs are typically only responsible for about 6% of lake CO2 emissions. However, on a regional basis the median value was much higher. In Ecoregion 8.4 (Ozark, Ouachita-Appalachian Forests), for example, the median contribution of hydrologic DIC to lake CO2 emissions is 36% (Figure 5b). Overall, in 19% of supersaturated lakes hydrologic DIC can account for 50% of more of CO2 emissions, and in 12% of supersaturated lakes hydrologic DIC can account for greater than 100% of CO2 emissions (i.e., these lakes are supersaturated despite positive NEP). Again, there is significant regional variability in these values (Figure 5b).
 For supersaturated lakes, Figure 5c also shows the difference between flux and NEP, but in this case is normalized to NEP, so that it may be interpreted as the fraction of NEP supported by hydrologic DIC (as opposed to atmospheric CO2). The overall median of this statistic is 0.26, indicating that in the typical undersaturated lake, over one fourth of the NEP is supported by hydrologic DIC. Again, there is a large degree of regional variability (Figure 5c), with medians ranging from 0.05 (Ecoregions 9.3, 10.1, and 11.1) to 0.69 (Ecoregion 8.2).
 The mean calculated pCO2,aq in this study (1043 µatm) is consistent with the mean value for global lakes reported by Cole et al.  (1036 µatm) , but is considerably greater than the summer epilimnetic values (680 µatm) in their study. As expected, most lakes throughout the U.S. are supersaturated in carbon dioxide with respect to the atmosphere, and thus represent a source of atmospheric carbon. However, the fraction of lakes in this study that were found to be at or below atmospheric equilibrium (27–33%) is higher than the 7–10% reported in previous studies [Cole et al., 1994; Sobek et al., 2005]. This is presumably due to samples from throughout the year being included in those estimates, whereas our data are limited to summertime observations, when surface CO2 concentrations tend to be lower than average [Cole et al., 1994; Huotari et al., 2011; Riera et al., 1999; Striegl and Michmerhuizen, 1998].
 Artificial water bodies contain significantly greater concentrations of CO2 than natural lakes (medianartificial = 706 µatm, mediannatural = 611 µatm; one-sided Wilcoxon rank sum test, P = 0.01; meanartificial = 1170 µatm, meannatural = 890 µatm). Reservoirs have previously been identified as major sources of greenhouse gases to the atmosphere [Barros et al., 2011; St. Louis et al., 2000]. It is not possible to distinguish artificial from natural water bodies in the NHD [McDonald et al., 2012], and thus we cannot explicitly distinguish between the two in our calculations. However, certain regions of the USA contain mostly artificial water bodies, whereas others contain mostly natural water bodies (Figure 1). Because the composition of the NLA data set for each region reflects the relative abundance of natural and artificial water bodies, differences in CO2 flux from lakes and reservoirs are implicitly accounted for in net regional flux estimates.
 The mean summertime flux of CO2 to the atmosphere from lake surfaces in the contiguous U.S. was 0.26 g C m–2 d–1. While summertime CO2 emissions have been quantified with reasonable certainty, extrapolating to an annual scale is not a straightforward task. Lakes in the northern half of the contiguous U.S. experience some duration of annual ice cover, while those in the southern half are monomictic or polymictic [Hostetler and Small, 1999]. In dimictic lakes, CO2 tends to build up in the hypolimnion during summer and under ice cover in winter and subsequently be released during fall turnover or ice-out. However, few studies have quantified the relative impact of these episodic events on total annual flux [e.g., Anderson et al., 1999; López Bellido et al., 2009; Riera et al., 1999; Striegl and Michmerhuizen, 1998]. The impact of these events varies widely among lakes, but can represent a major fraction of annual emissions, and in some cases cause lakes that are sinks for atmospheric CO2 during the summer to be net annual sources [Riera et al., 1999; Striegl and Michmerhuizen, 1998]. Even less is known about the seasonality of CO2 flux from polymictic or monomictic lakes. López et al.  documented a shift from CO2 uptake during stratification to emission during mixing in a large monomictic reservoir in Spain, but this pattern appeared to be driven by carbonate precipitation in the epilimnion. Although the available data do not allow us to accurately account for these seasonal phenomena, a rough approximation of annual CO2 emissions from the lakes and reservoirs of the contiguous U.S. may be developed by simply extrapolating the daily summertime flux to an entire calendar year. This approach results in an annual estimate of CO2 mass flow from lakes to the atmosphere of 14.7 Tg C yr–1. Extrapolation of this value to the global scale using the lake and reservoir surface area estimates of McDonald et al.  gives 300 Tg C yr–1, which is slightly lower than recent global-scale estimates of 350–710 Tg C yr–1 [Tranvik et al., 2009; Cole et al., 2007].
 Although the Laurentian Great Lakes were not considered in this study, their massive surface area (160% of all other inland lakes in the contiguous U.S. combined [McDonald et al., 2012]) makes them a potentially important source of emissions. Despite recent advances in modeling the carbon cycle of Lake Superior [Bennington et al., 2012], however, CO2 emission estimates for the entire system remain very poorly constrained, currently ranging from less than 1 Tg C yr–1 to over 30 Tg C yr–1 [McKinley et al., 2011].
 Regardless of the contribution of the Great Lakes, lakes and reservoirs appear to comprise a smaller portion for total aquatic emissions than streams and rivers (recently estimated by Butman and Raymond  to be 97 ± 32 Tg C yr–1). Combined, however, the magnitude of aquatic CO2 emissions is clearly great enough to be relevant to continental-scale carbon budgets. Pacala et al.  estimated that the terrestrial U.S. (accounting for sediment burial in and export via aquatic systems but excluding aquatic C gas exchange) was a net carbon sink of between 300 and 580 Tg C yr–1. Zhang et al.  estimated that the Great Plains region of the U.S. alone was a carbon sink of 336 Tg C yr–1. More recently, the U.S. Department of Agriculture  estimated that forests and agriculture in the U.S. constituted a net carbon sink of 173 Tg C yr–1. The inclusion of aquatic CO2 fluxes could alter all of these estimates considerably.
 The correlations between DO, chl a, and pCO2,aq suggest that intraregional variability in NEP is linked to variability in epilimnetic CO2 in lakes throughout the contiguous U.S., and the supersaturated state of the majority (~70%) of these lakes implies an external subsidy of carbon. Several studies have found that DOC concentrations are generally positively correlated with pCO2,aq and that respiration of allochthonous organic carbon supports CO2 supersaturation [Jonsson et al., 2003; Larsen et al., 2011; Roehm et al., 2009; Sobek et al., 2005]. Given the evidence for the biological influence on pCO2,aq observed in nearly every region in this study, such a relationship might be expected to exist here as well. However, virtually no evidence of a relationship between these two variables was found. DOC is only significantly correlated with pCO2,aq in one region, and in that case the correlation is negative (Table 3). Although adjusting measured alkalinity for the effect of organic anions significantly reduced calculated pCO2,aq in a small fraction of lakes, most lakes were only slightly affected. Omitting this correction from our calculations has a negligible effect on the correlation between DOC and pCO2,aq. Combining all of the lakes into a single data set does result in a very weak but statistically significant positive relationship (ρ = 0.06, P =0.04) between DOC and pCO2,aq. Given the lack of a relationship within regions, however, this result seems likely to be spurious.
 There are several possible explanations for the lack of a relationship between DOC and CO2. An observed positive correlation for a set of lakes implies that lacustrine DOC concentrations are consistently proportional to the allochthonous carbon subsidies being respired within the lakes. If, however, the composition and photodegradation potential of DOC sources varies significantly among the lakes being compared, this relationship may not hold. Even given DOC of similar biodegradability, variability in hydraulic residence (i.e., processing) time may obscure a relationship between DOC and CO2. The production of autochthonous DOC originating from primary productivity, which can vary among lakes independently of allochthonous DOC inputs, may further complicate the DOC-CO2 relationship. The presence of autochthonous and allochthonous DOC might be expected to correlate inversely with pCO2,aq (i.e., the presence of autochthonous DOC should be correlated with uptake of CO2 via primary production, while the presence of allochthonous DOC should be correlated with greater CO2 production via respiration of this OM source), and thus correlations may be obscured in lakes containing significant proportions of both types of DOC. These different behaviors may also be reflecting the effect of variation in residence time related to precipitation and/or different regional hydrologic characteristics (e.g., dominance of seepage vs. drainage lakes) on in-lake DOC processing in these regions.
 Perhaps the most surprising result of this study is the significant fraction (12%) of supersaturated lakes that appear to have positive NEP (overall, 35% of the lakes were estimated to have NEP > 0). Supersaturation is commonly assumed to imply negative NEP, while the observation of supersaturated lakes with positive NEP [e.g., Stets et al., 2009], has been viewed as an exception to this rule. Yet, a significant fraction of the lakes in this study appear to fall into this category (Figure 5b). In these lakes, biological activity is acting as a net sink for inorganic carbon, but the magnitude of this sink is not sufficient to draw dissolved CO2 concentrations down to atmospheric levels. In other words, hydrologic inputs of DIC are more than sufficient to support primary production in the lake, and influx of atmospheric CO2 is unnecessary for net positive NEP.
 On the other hand, undersaturation nearly always implies positive NEP. Although the fraction of net photosynthesis supported by hydrologic DIC inputs approaches zero for some lakes, it is generally higher (median = 0.26, mean = 0.34; Figure 5c), and in 42% of undersaturated lakes the fraction is greater than 0.5. Therefore, it appears that a significant fraction of photosynthetic carbon fixation, even in undersaturated lakes, is supported by hydrologic DIC inputs. Essentially, the concentration of CO2 originating from allochthonous sources must be depleted to below atmospheric levels before primary production will be augmented by an influx of atmospheric CO2. This study emphasizes the connectivity between terrestrial and aquatic ecosystems given that on average, the majority of productivity in aquatic systems appears to be supported by relocated terrestrial carbon, regardless of whether it enters the lake in organic or inorganic form.
 Many studies directly linking CO2 supersaturation to net heterotrophy are performed in regions underlain by shield rock (such as the northeastern North America and the Nordic regions [Amiotte Suchet et al., 2003]) and having relatively low-alkalinity, high-DOC waters. In Ecoregion 5.2 (Mixed Wood Shield), which fits this description, both correlation analysis and modeling suggest that lake CO2 is largely derived from respiration of allochthonous organic matter. Although a direct correlation between DOC and pCO2,aq was not observed, correlations between pCO2,aq, DO, and chlorophyll (Table 3) suggest that intraregional variability in pCO2,aq here is indeed a function of variability of biological activity. Among the supersaturated lakes in this region, model results suggest a relatively small contribution of hydrologic DIC to overall CO2 flux out of lakes (Figure 5b).
 Our results do not clearly indicate, however, that the importance of hydrologic DIC inputs in the carbon cycle of a lake is related to total DIC concentrations. Positive correlations between Ca2+ (an indicator of weathering intensity) and pCO2,aq were observed in some high-alkalinity regions, but the presence or absence of this relationship appears unrelated to DIC concentrations (i.e., alkalinity, Tables 1 and 3). Model results suggest a variable role for hydrologic DIC among regions, but there is no relationship between the fraction of flux or NEP supported by hydrologic DIC and alkalinity (Figures 5b and 5c, and Table 1). The apparently minor contribution of hydrologic DIC to CO2 emissions from the lakes in the Great Plains (Ecoregions 9.2, 9.3, and 9.4), which generally have very high alkalinity, is particularly surprising, although it is worth noting that these lakes also contain high concentrations of DOC and chlorophyll (Table 1).
 The modeling approach employed here is simple, and does not take into account factors such as hypolimnetic storage of CO2, temporal variability in hydrologic DIC inputs and lake water chemistry, or calcite precipitation. Nonetheless, the large and spatially comprehensive NLA data set has allowed us to perform a robust analysis, and the results unambiguously highlight the widespread importance of DIC loading in determining the CO2 content of lakes. Our results also highlight the importance of considering carbonate equilibrium chemistry in any analysis of CO2 in lakes, even in low-alkalinity waters or highly productive systems. However, these model results have not been verified by a sufficient number of direct field observations, and field studies focused on historically undersampled regions are needed.
 Approximately 70% of the lakes and reservoirs in the contiguous United States are CO2-supersaturated during the summertime. In sum, contiguous U.S. lakes and reservoirs represent a source of CO2 to the atmosphere on the order of 40 Gg C d–1 during the summertime and ~15 Tg C annually. There is significant regional variability in the concentrations, fluxes, and drivers of CO2 in lakes, and large-scale lake carbon flux estimates should take this into consideration. Indicators of biological activity suggest that intraregional variability in pCO2,aq is typically determined by variability in NEP. Surprisingly, however, our analysis did not reveal a direct link between summer epilimnetic DOC and pCO2,aq in the lakes and reservoirs in the majority of the contiguous United States. Given the geographic scope and consistency of our data, this finding has major implications for our current understanding of carbon cycling and the DOC-CO2 relationship in lakes and reservoirs throughout the world.
 Taking DIC inputs and carbonate equilibrium chemistry into account, model results indicate widespread support of lake pCO2,aq by hydrologic DIC inputs, regardless of whether NEP is positive or negative. Approximately one third of the lakes and reservoirs in the contiguous United States appear to have positive NEP during the summer, including approximately 12% of CO2-supersaturated systems. Although respiration of allochthonous DOC likely contributes to CO2-supersaturation in all systems, the overall influence of this mechanism appears to be smaller in many regions than it is in the oft-studied low-alkalinity systems of northeastern North America and the Nordic countries. The paradigm of CO2 dynamics in lakes driven primarily by NEP needs to be updated to account for the potentially large role of hydrologically derived DIC in the majority of inland waters.
 This work was supported by a USGS Mendenhal postdoctoral fellowship and the USGS LandCarbon Ecosystem Carbon Sequestration Project. We thank Brian Pellerin and two anonymous reviewers for useful comments, and Sydney Wilson for assisting with Figure 2. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.