Corresponding author: V. Bennington, Center for Climatic Research, University of Wisconsin-Madison, 1225 W. Dayton St., Madison, WI 53706, USA. (firstname.lastname@example.org)
 Lake Superior is the largest lake in the world by surface area, containing 10% of the world's surface freshwater. Yet, little is known about its role within the regional carbon budget. Observational studies on Lake Superior have been limited by harsh winters and the challenges of covering such a vast expanse. To date, carbon budgets extrapolated from observational studies are largely out of balance and suggest a large efflux of carbon dioxide to the atmosphere (∼3 TgC/yr) that cannot be supported by the estimated net inputs into the lake (<1 TgC/yr). We couple a hydrodynamic model of Lake Superior to an ecosystem model to understand the seasonal cycle of the partial pressure of carbon dioxide (pCO2) in the lake surface waters, the resulting air-lake carbon dioxide (CO2) fluxes, and whether spatial heterogeneity can explain the previously imbalanced carbon budget. The model sufficiently simulates lake productivity, circulation, respiration, pCO2, and chlorophyll. We find that the seasonal cycle of pCO2is generally a double sinusoidal curve during the simulated period of 1996–2001. The lake acts as a sink of carbon dioxide in summer and during late winter of cold years and as a source to the atmosphere during winter and spring. We find significant spatial heterogeneity of respiration in Lake Superior, with near-shore to offshore rates of respiration varying by two orders of magnitude. Thus, Lake Superior need not act as a significant source of carbon dioxide (∼0.5 TgC/yr) to the atmosphere in order to be consistent with in situ observations of respiration.
 The terrestrial biosphere is a natural sink of anthropogenic carbon dioxide (CO2), removing about one quarter of global anthropogenic emissions each year. Inverse models are used to pinpoint terrestrial carbon sinks, and findings suggest the North American continent is currently a large sink of carbon dioxide (although anthropogenic emissions from the continent far exceed this sink) [Field et al., 2007]. The North American Carbon Program (NACP) uses a combination of observations and models to mechanistically understand this sink and attributes it primarily to forest re-growth and a reduction in forest fires [Field et al., 2007]. To date, inverse models have set Great Lakes (and coastal oceans) carbon fluxes to zero; thus carbon fluxes from these water bodies are aliased to the land. This may either exaggerate or suppress the natural variability and seasonality of true air-land fluxes, confounding our understanding of probable future changes to this sink.
 Inland water bodies have historically been neglected by global and regional inverse modelers, either because the air-water CO2 fluxes were unknown or assumed to be insignificant. Inland water bodies were viewed simply as closed pipes, moving carbon and other nutrients from the land to the ocean where they are processed. However, using direct observations and indirect techniques to estimate partial pressure of carbon dioxide (pCO2) at the surface of global inland water bodies, Cole et al. [1994, 2007] found that 90% of the world's lakes are supersaturated with carbon dioxide and later concluded that, globally, inland water bodies are a significant source of carbon to the global atmosphere (0.75 Pg C/yr, according to Cole et al. ; updated by Tranvik et al.  to 1.4 PgC/yr). Thus, much of the carbon sunk into the terrestrial biosphere runs off into inland water bodies where it is respired and released back into the atmosphere. Only about half of the carbon entering this “pipe” makes it to the ocean. Thus, inland water bodies are a globally significant source of atmospheric carbon dioxide and should be considered in regional carbon budgets.
 The Laurentian Great Lakes cover 244,000 km2 within the United States and Canada, an area roughly the size of the United Kingdom. Primary production within the lakes (60–300 gC/m2/yr [Vollenweider et al., 1974]) is of the same order of magnitude as the surrounding forests, suggesting they may be a significant component of the regional carbon budget. Previous attempts to quantify regional terrestrial sinks of carbon dioxide have assumed a negligible contribution from the Great Lakes, for lack of a better assumption.
 Lake Superior is the largest freshwater lake in the world by surface area and contains approximately 10% of the Earth's freshwater. Situated within Michigan, Minnesota, Wisconsin, and Ontario, Lake Superior is the coldest and deepest of the Laurentian Great Lakes. Its average depth is 150 m and at its deepest point is over 400 m. Surface temperatures rarely exceed 4°C near shore before mid-April, and the open lake often does not stratify until late June or July [Bennett, 1978; Austin and Colman, 2007].
 Drainage basin areas of small lakes far exceed lake surface area, and respiration of externally produced (allochthonous) carbon exceeds carbon production within the lake. Thus, carbon cycling within small lakes is dominated by respiration of external inputs from the watershed. As the ratio of drainage basin area to lake surface area decreases, internal processes begin to dominate carbon cycling within the lake [Hanson et al., 2004]. Lake Superior has a watershed to lake surface area ratio of only 1.55 (Great Lakes Atlas, http://www.epa.gov/glnpo/atlas/index.html) the smallest of all the Great Lakes, suggesting that internal processes are more important than external inputs to lake-wide carbon cycling.
Alin and Johnson  show that low latitude large lakes are more likely to be a sink of atmospheric carbon dioxide, due to permanent stratification and high rates of primary production. As you move to higher latitudes, stratification and primary production tend to decrease, and this sink changes to a source. Lake Superior is situated within this transitional zone, suggesting it may be either a source or sink of carbon dioxide. Observational studies [Cotner et al., 2004; Urban et al., 2005] have suggested that Lake Superior is a source of carbon dioxide to the atmosphere, but are unable to account for the magnitude of the suggested source of carbon being respired within the lake. Observations from the nearby eddy flux tall tower in Park Falls, Wisc., suggest that Lake Superior is either a source of carbon dioxide during summer, or a smaller sink than the nearby forests [Desai et al., 2008; Vasys et al., 2011].
 The carbon budget of Lake Superior has remained imbalanced, likely due to observations being sparse in space and time, and to heterogeneity in the physical system that make extrapolation from a small area of the lake to the entire lake difficult. Harsh winters also prevent observations, and to date, no wintertime measurements of primary productivity or the partial pressure of carbon dioxide (pCO2) have been made in Lake Superior. Thus, extrapolation over an entire year is a source of significant uncertainty. From measurements primarily taken in the western arm of Lake Superior (Figure 1), Cotner et al.  estimated the lake ecosystem creates 5.3–8.2 Tg of organic carbon each year via photosynthesis and respires 13–39 TgC/yr. They estimated river and atmospheric inputs of 0.52–0.62 and 0.16–0.41 TgC/yr, respectively. Thus, even without considering outflow (0.08–0.1 TgC/yr) and burial losses (0.48 TgC/yr [McManus et al., 2003]), the lake appears to be respiring far more organic carbon than is supplied to the lake each year [Cotner et al., 2004]. Urban et al.  also estimated sources and sinks of carbon in Lake Superior from measurements of respiration and photosynthesis. Their study area was just off the Keweenaw Peninsula, within 20 km of shore in southern Lake Superior (Figure 1), but their findings were similar to those of Cotner et al. . Urban et al.  estimated a net efflux from Lake Superior of 3 TgC/yr from pCO2 observations and estimates, but again, no known source of carbon to the lake is large enough to support this magnitude of heterotrophy.
 The Environmental Protection Agency (EPA) samples the water column at 19 stations throughout Lake Superior twice per year, once in April or May and again in August or September (Figure 1). Using EPA measurements of surface alkalinity, temperature, and pH, Atilla et al.  determined the surface of Lake Superior is likely supersaturated with CO2 during April and in near equilibrium during summer. Thus, Lake Superior is likely a source to the atmosphere in April and approximately neutral in August, although the pCO2 values used to develop these estimates may be biased high. Indirect techniques of pCO2 estimation have large uncertainty (approximately 130 μatm in April and 80 μatm in summer) due to a bias in measuring pH in freshwater using an electrode [French et al., 2002] and the extreme sensitivity of pCO2 estimates to pH in freshwater. Even without any uncertainty in indirect estimates of pCO2, EPA data provide only two moments in time each year. What is occurring throughout the lake during the rest of the year? What is the entire seasonal cycle of pCO2?
 There is only one available time series of direct measurements of pCO2 in Lake Superior. Atilla et al.  summarize data from an in situ pCO2 sensor (SAMI) deployed in the far western arm during spring and summer of 2001. Kelly et al.  directly measured pCO2 directly in Thunder Bay during summer. Both sets of data suggest an uptake of CO2 during the stratified period. Although these measurements are limited in space and time, Atilla et al.  show that pCO2 is controlled by variations in DIC caused by physics and biology.
 A new estimate of annual primary production (9.73 TgC/yr [Sterner, 2010]) suggests that it is larger than previously estimated (5.3–8.2 TgC/yr [Cotner et al., 2004]; 3–8 TgC/yr [Urban et al., 2005]; ∼5 TgC/yr [Hecky, 2000]). This would still not balance the carbon budget if respiration estimates (13–83 TgC/yr [Urban et al., 2005]; 13–39 TgC/yr [Cotner et al., 2004]) are correct. It is unlikely that river inputs (max of ∼1 Tg/C [Urban et al., 2005]), atmospheric deposition (0.1–0.4 TgC/yr [Cotner et al., 2004; Urban et al., 2005]), or primary production are an order of magnitude greater than previously estimated, making it more likely that spatial heterogeneity in a lake larger than the state of South Carolina accounts for the imbalance in the carbon budget. Previous observational studies have been severely limited in both space and time due to the cost of lake-wide observations and harsh winter conditions in Lake Superior.
 We utilize a mechanistically driven model in an attempt to place these observations in a lake-wide and year-round context. Early oceanographic ecosystem models were data driven and included primary production by forcing simulated nutrient conditions toward observations, assuming the difference between model-simulated and mean observed nutrient concentrations to be due to production and export [Sarmiento et al., 1988]. These models relied upon adequate observations of ocean nutrient conditions but required few model parameters for production, as ecosystem structure was not included. As these models restore nutrient conditions to the mean state, with a seasonal cycle, inter-annual variability in production can only be driven by changes in circulation. Later, primary production was modeled using locally available light and nutrient concentrations, and still required no ecosystem community structure [Sarmiento and Gruber, 2006]. As community structure is necessary to address many scientific questions, its inclusion in coupled models may be important to understanding both natural and anthropogenic changes. Although these are more complex models, they are capable of incorporating more mechanistically driven changes to the system [Doney, 1999]. Here, we began with a phosphorus-based ecosystem model with a small community structure, capable of addressing more fundamental questions about Lake Superior. Additionally, we compare to an alternative ecosystem model in which phosphorus limitation is considered constant and only variations in light and temperature determine rates of primary production.
 In this work, we address the following questions: Can spatial and temporal heterogeneity account for the apparent imbalance in previous carbon budgets? What is the full seasonal cycle of pCO2and air-lake CO2fluxes in Lake Superior? What mechanisms control carbon cycling within Lake Superior? To answer these questions, we couple two unique ecosystem models to a three-dimensional (3-D) hydrodynamic model of Lake Superior. Insections 2 and 3 we describe and evaluate the model. Results are shown in section 4. We conclude in section 5.
 We couple an eddy-resolving, 3-D lake hydrodynamic model to two separate ecosystem models. Both model configurations are run from 1997 through 2001.
2.1. Physical Model
 We use the MIT general circulation model configured to Lake Superior bathymetry at 2 km horizontal resolution [Bennington et al., 2010]. The model uses a z-coordinate system, and layers within the top 50 m have thicknesses of 5 m. Layer thickness gradually increases with depth to a maximum thickness of 33 m at 200 m depth. The hydrodynamic model is forced by three-hourly atmospheric temperature, humidity, radiation, and winds from the North American Regional Reanalysis (NARR) [Mesinger et al., 2006]. For a complete description of the physical model and its evaluation, please refer to Bennington et al. .
2.2. Ecosystem Model 1
 A medium-complexity ecosystem model [Dutkiewicz et al., 2005; Bennington et al., 2009] is adapted for Lake Superior (Figure 2a). The cycles of carbon, phosphorus, oxygen, and alkalinity are explicitly modeled throughout the entire water column. The model includes two phytoplankton types (small, diatoms), a single zooplankton class that preys upon both phytoplankton groups, and an implicit microbial loop. The model traces carbon and phosphorus as they pass from inorganic to organic form and then to detritus in dissolved and sinking particulate forms. Particulate organic carbon (POC) sinks at a rate of 0.5 m/d [Chai and Urban, 2004], while the dissolved form is only subject to currents and mixing. Phosphorus is the primary limiting nutrient in Lake Superior [Sterner et al., 2004]; thus, phosphorus, light, and temperature limit primary production in the model (equations (1) and (2)):
where μmax is the maximum growth rate for phytoplankton, I is the available photosynthetically active radiation (PAR), kI is the half saturation constant for PAR, P is the concentration of soluble reactive phosphorus (SRP), and kP is the half saturation constant for phosphorus. The temperature function is from Moore et al. , where TK is the temperature in Kelvin, and tbase and Tnorm are constants. Table 1 lists all model ecosystem parameters.
 PAR is assumed to be 40% of the incoming shortwave radiation at the lake surface (I0) [Frouin and Pinker, 1995] and is attenuated within the water column by water and chlorophyll according to Beer's Law (equation (3)):
where kw and kc are the absorption coefficients of water and chlorophyll, respectively. The presence of ice reduces light penetration proportional to its spatial coverage, as in the physical model [Bennington et al., 2010]. For example, we assume that when a model grid cell is 40% ice covered, only 60% of the PAR reaches the lake surface.
 Phytoplankton ingests dissolved inorganic carbon (DIC) at a carbon to phosphorus ratio (C:P) that varies with depth according to Sterner . The ratio is maximized at the surface, where phytoplankton ingests 375 moles of carbon for each mole of phosphorus. The ratio decreases linearly to 200 at 37.5 m depth and remains at a constant value of 200 to the lake floor. As done with phosphorus, carbon passes through phytoplankton into zooplankton and detritus. The microbial loop returns autochthonous organic matter (DOC, POC) back into ingestible forms (SRP, DIC) with a time scale of 30 days, modified by temperature:
where θr is an optimized constant from Model 2 and Tcis the temperature in Celsius. The relationship between temperature and rates of remineralization accounts for increased microbial activity during summer, as well as increased exposure to sunlight, which is known to significantly photo-oxidize organic matter in oligotrophic lakes [Miller, 1998]. Mortality rates of phytoplankton and zooplankton are 1/15 days, modified by temperature similar to equation (4) but with a separate constant, θm. Upon death, 99% and 90% of small phytoplankton and diatoms enter the dissolved organic matter pool, respectively. The remainder enters the particulate pool. Zooplankton preys upon phytoplankton, and the modeled zooplankton class prefers small phytoplankton (Table 1).
 To estimate gross primary production (GPP) from net primary production, we assume the magnitude of autotrophic respiration to be 75% of the magnitude of net primary production [McDonald, 2010] and excretion to be 13% the magnitude of NPP [Baines and Pace, 1991].
 Lake alkalinity is increased by net primary production, assuming a Redfield ratio of nitrate to phosphorus of 16 [Sarmiento and Gruber, 2006]. Similarly, decomposition of organic matter reduces alkalinity locally. Chlorophyll concentrations are calculated from biomass and available light concentrations, allowing for photo-adaptation, according toequation (5) [Dutkiewicz et al., 2005]:
We ignore any impact of nutrient concentrations on chlorophyll, as Model 2, described below, does not trace phosphorus. Due to C:P ratios that vary with depth, the chlorophyll parameterization is non-ideal for Model 1 but is kept consistent between the two models.
 The partial pressure of carbon dioxide (pCO2) at the lake surface is calculated from the local temperature and concentrations of alkalinity and DIC according to CO2sys [Lewis and Wallace, 1998]. The air-lake flux of carbon dioxide is driven by the gradient inpCO2across the air-lake interface and wind speed. Atmospheric concentrations of carbon dioxide are taken from observations at the WLEF tall tower in Park Falls, Wisc. [Desai et al., 2008], and smoothed, interpolated, and extrapolated to 8-day values by GLOBALVIEW-CO2 [Cooperative Atmospheric Data Integration Project, 2011]. We correct for water vapor pressure according to Weiss and Price . We assume a quadratic relationship between flux and wind speed according to Wanninkhof , because the significant fetch of Lake Superior results in high wind speeds, and fluxes calculated assuming a cubic relationship to wind speed overestimate fluxes at high wind speeds [Ho et al., 2006].
2.2.1. Sensitivity of Model 1 to Ecosystem Parameters
 The coupled physical-biogeochemical Model 1 is computationally expensive.McDonald et al.  optimized many of the ecosystem parameters (Table 1) using a Markov Chain Monte Carlo approach in a one-dimensional setting where sufficient observations exist for constraint. These parameters were an improvement over hand-tuned parameters when utilized in the three-dimensional model setting [McDonald et al., 2012]. However, the optimization is limited by the ecosystem model formulation and available observations. As primary production is not adequately observed and model parameters under-constrained, phytoplankton half saturation constants, mortality rates, and maximum growth rates were hand-tuned to best simulate the seasonal cycle of primary production observed bySterner .
 There is a trade-off between parameters impacting primary production in Model 1. Increasing maximum growth rates will allow for a rapid increase in spring production but results in a rapid decrease in P availability and an earlier decline in primary production (PP). Although one would expect a decrease in half saturation constants to prolong a bloom, it also leads to a more rapid decline in P availability through increased growth rates and does not successfully maintain high rates of PP through summer. Model 1 is limited by the mass of P in the system. Once SRP is converted to biomass, it is no longer available for production. Thus, to maintain higher growth rates through summer, the phytoplankton must rapidly die and the organic matter rapidly returned to inorganic nutrients within the mixed layer. Thus, a large portion of deceased phytoplankton and grazed matter is prescribed to enter the dissolved organic matter pools (Table 1), to keep nutrients from sinking out of the euphotic zone. High, but realistic, mortality rates are used, and the implicit microbial loop rapidly decomposes organic matter to provide inorganic nutrients for production. Still, summer modeled production is nutrient limited (Figure 3) and lower than suggested by observations (Figure 4).
2.3. Ecosystem Model 2
 We update the optimized ecosystem of McDonald et al. to include the air-lake exchange of carbon dioxide (Figure 2b). Sterner  observations show that although production in Lake Superior is limited by phosphorus concentrations, 93% of the variance in production can be explained by light and temperature conditions. This result suggests that in the open lake, the limitation of nutrients remains relatively constant compared to the changes in growth rates caused by changes in light and temperature. Thus, in Model 2, primary production is determined by light and temperature according to the empirical relationship of Sterner :
where T is temperature in Kelvins, I is PAR, and Popt, α, and Ea are constants (Table 2). Although the equation of Sterner  is employed, using this equation for integrated light within a gridded, time step system does not yield the same magnitude of primary production as Sterner  (section 3.1). While Model 2 is unable to capture production changes in regions with highly variable P concentrations (river mouth, upwelling areas), it is a highly constrained method of simulating the large-scale impacts of biological production on lake carbon.
Remineralization rate of allochthonous (t) and refractory (r) organic matter
1/30 y−1 1/180 y−1
 Carbon passes from DIC to the single phytoplankton class (PHY) to particulate (POC) and dissolved (DOC) detritus. This autochthonous carbon returns back to its inorganic form with a time scale of 30 days, modified by temperature as Model 1. Lake alkalinity is increased by net primary production, assuming a carbon to nitrate ratio of 12.5. Similarly, decomposition of organic matter reduces alkalinity locally. Rates of phytoplankton mortality and organic matter remineralization are increased by warmer temperatures as in Model 1 (Table 2). Calculation of pCO2and the air-lake fluxes of carbon dioxide are computed identically as in Model 1.
2.4. River Inputs
 Without an external supply of carbon, the lake would eventually equilibrate with the atmosphere. For the lake to be a source of atmospheric carbon, it must be effluxing carbon from its watershed. Groundwater supplies to Lake Superior have historically been considered negligible, as lake water supplies have been explained without their inclusion [Croley and Lee, 1993]. Atmospheric deposition supplies an estimated 0.1–0.4 Tg C each year [Cotner et al., 2004; Urban et al., 2005] and would cause a primarily spatially homogeneous increase in lake carbon. Rivers are estimated to supply ∼1 Tg C [Thompson, 1978] to local river mouths each year and constitute the largest known source of external carbon to the system.
 River inputs of DOC were previously believed to be recalcitrant and of little impact on the carbon cycle of the Arctic Ocean. However, recent studies suggest that significant amounts of labile DOC reach the Arctic Ocean via rivers and likely impact coastal carbon cycling on the Arctic shelf [Raymond et al., 2007; Holmes et al., 2008]. Decreases in river alkalinity are present during high flow conditions in the Arctic [Cooper et al., 2008] and it is likely that similar occurs in the tributaries to Lake Superior. Seasonal cycles of pH in Lake Superior tributaries have been observed [Keller, 1983]. River DOC increases with flow in the Arctic [McClelland et al., 2007; Raymond et al., 2007; Holmes et al., 2008] and has been shown to increase with river flow in tributaries to Lake Superior [Urban et al., 2005]. Such seasonality may cause an influx of low alkalinity, high DOC, and high DIC waters during the spring melt, and thus, could cause high pCO2 and a CO2 efflux.
 Here we include river supplies of carbon (DIC, DOC), alkalinity, and soluble reactive phosphorus (SRP). We do not aim to include all biogeochemical active components in runoff, but rather to simulate the impact of large river flows on Lake Superior carbon cycling and the resulting near to offshore gradients. Daily river flows from the nine largest tributaries (flow) to Lake Superior are included and comprise about 56% of the annual flow [Thompson, 1978] (see Text S1 in the auxiliary materials). River mouth locations and river names are shown in Figure 1. There are insufficient observations of river flow, river nutrient concentrations, or shoreline erosion to include all carbon inputs to the lake. Here we aim to determine whether these inputs have the potential to explain the perceived imbalance in the lake's carbon budget, not to simulate all of them. The impacts of river momentum and vorticity on lake momentum are assumed negligible to the whole lake flow and are ignored here.
 We use the USGS program LOADEST [Runkel et al., 2004] via the LoadRunner interface [Booth et al., 2007] to determine the most likely relationship between tracer concentration and flow. LOADEST uses point measurements of DIC (estimated from pH, temp, alkalinity), alkalinity, SRP (Model 1 only) [EPA STORET], and daily historical river flows to solve for the most likely relationship between flow and tracer concentrations, including the impacts of season, for each river. These relationships are applied to daily flows for the model run period to determine daily tracer concentrations reaching the river mouths and are shown in Figure 4. In general, there is an inverse relationship between alkalinity and flow and DIC and flow. Soluble reactive phosphorus concentrations tend to increase under high flow conditions. River flow rates were retrieved from USGS, Environment Canada, and Ontario Power Generation at gauges nearest the river mouths. We assume a mixing of river and lake water of inorganic matter at the river mouth's local grid cell, with a mixing time equal to the time it would take the river to replace the entire grid cell volume if the flow rate were constant at that day's rate.
Riverine supply of organic and inorganic carbon varies by year according to river flow. During 1998, a year of little river flow, only 0.18 Tg DOC and 0.02 Tg DIC are added to the lake by the rivers. Riverine DOC supply was 0.32, 0.31, 0.30, and 0.31 Tg C in 1997, 1999, 2000, and 2001, respectively. For DIC, rivers added 0.06, 0.05, 0.05, and 0.05 Tg C to the lake in 1997, 1999, 2000, and 2001 respectively.
 Although riverine DOC is no longer believed completely recalcitrant, it is unlikely that DOC entering the lake via the rivers is as labile as autochthonous carbon, and in fact, consists of multiple DOC pools of varying lability [Zigah et al., 2011]. We make a crude assumption that 15% of the organic carbon from the rivers has a remineralization time scale equal to that of autochthonous carbon, 80% decomposes to DIC with a time scale equal to the estimated DOC residence time of 30 years [Cotner et al., 2004], and 5% returns to an inorganic form within the residence time of the water, 180 years. This is roughly consistent with Zigah et al.  who find the oldest carbon to be several decades old and the mean residence time of carbon to be less than 60 years and consistent with supply and the observed concentrations of DOC in the lake. Based on the work of D. M. Dolan and S. C. Chapra (D. M. Dolan, personal communication, 2012), we assume that riverine supply of dissolved organic phosphorus is three times as high as the supply of dissolved inorganic phosphorus.
 The lability of riverine carbon may vary by season. DOC supplied to the Arctic Ocean via river inputs was believed to be refractory during its residence time in the Beaufort Gyre [Cooper et al., 2005]. However, recent work has suggested that during the spring melt, when there were no previous observations, highly labile carbon is transported to the ocean where it is decomposed. During the spring melt, cold temperatures, the scouring of surface terrain, and rapid river flows allow for labile DOC to reach the ocean before being remineralized [Holmes et al., 2008]. Lake Superior is also situated in a very cold environment where the maximum river flows occur during the spring melt; thus we expect labile carbon to reach the lake before decomposition. As we do not vary the percentages of highly labile, semi-labile, and refractory carbon over the year, we assume a relatively high percentage of highly labile DOC in the rivers at all times. We are consistent withHolmes et al. who show a 15–25% loss in DOC over a 1-month period from three Arctic rivers during the snowmelt period. We purposely err on the side of too labile, because previous carbon budgets have suggested the lake to be a significant source of carbon dioxide to the atmosphere.
 The model includes no outflows or sedimentation. Sedimentation is estimated to be small and located primarily offshore, where sediment re-suspension is less frequent [McManus et al., 2003]. Yet, since river inputs are included, we must find a way to remove these inputs if we wish to have a long-term steady state solution. To prevent a positive trend in phosphorus and net primary production, phosphorus tracers return to their initial state on December 31 every year, similar to below thermocline restoring of nutrients in OCMIP [Najjar et al., 2001]. We do not include precipitation or erosion and their effects on alkalinity or carbon. Therefore, we apply a relaxation of alkalinity to the mean lake concentration of 838 mmol m−3with a time scale of 60 days, allowing for local impacts but preventing the model from drifting. We do not relax or re-initialize carbon concentrations, as the air-lake exchange creates a pathway for excess carbon to leave the lake.
2.5. Model Respiration
 For comparison with observations, we use the term respiration to refer to the sum of autotrophic respiration and the decomposition of all organic matter. Thus, at any time,
Where R is respiration, AR is autotrophic respiration, here defined as 0.75*NPP, and organic matter decomposition (DEOM) includes the decomposition of POC, autochthonous DOC (DOC), allochthonous DOC (TDOC), and refractory DOC (RDOC):
Rates of decomposition are determined by base rates of remineralization for each type of organic matter (Table 1) multiplied by the temperature function given in equation (4).
2.6. Model Initial Conditions
 Due to computational costs, the coupled hydrodynamic-ecosystem models were spun up for five years at 10 km horizontal resolution. The ecosystem states at the end of this spin up were interpolated to the 2 km model grid for final model runs. For the 10 km spin up, alkalinity was initialized everywhere at 838 meq/mol in both models. Phytoplankton, particulate organic matter, and autochthonous organic carbon are initialized at negligible levels and allowed to grow in time. The models were then run for 1996–2001 at 2-km resolution, and we consider 1996 to be a spin-up year. The semi-labile (TDOC) and the recalcitrant carbons pool (RDOC) are initialized in 1996 at 115 and 10 mmol/m3 everywhere, respectively, for a total DOC pool of 17 TgC [Urban et al., 2005]. Soluble reactive phosphorus is initialized at 0.1 mmol/m3 everywhere in Model 1, consistent with total phosphorus pools in EPA and Environment Canada observations.
2.7. Model Similarities and Differences
 Model chlorophyll is calculated from phytoplankton biomass in both models. Rates of decomposition and partitioning of river carbon are identical in the two models. Both receive the same inputs (except no P for Model 2). The major model difference is in how phytoplankton growth rates are determined. Model 2 uses an empirical equation to calculate growth rates from local light and temperature conditions [Sterner, 2010]. Changes in nutrient conditions do not impact growth in Model 2, and mixing and upwelling events can only impact growth according to the changes in light and water temperature the phytoplankton experience. This model is unable to simulate local effects of changing nutrients and always produces higher rates of primary production during warm, cloud-free years. Model 2 is suitable for constraining the seasonal cycle of primary production in Lake Superior and the biological impact on lake-widepCO2. In contrast, phytoplankton growth in Model 1 is co-limited by nutrients, light, and temperature, and biomass can respond to changing nutrient conditions caused by mixing or upwelling events. This model is suitable for investigating how changes/trends in dynamics may impact the ecosystem and carbon cycle of the lake.
Figure 5 shows the mean seasonal cycles of pCO2 resulting from both model runs. Seasonal cycles in both models show the same shape and relative levels of under and super saturation at the lake surface, relative to the atmosphere. The main difference begins in August, when the pCO2 in Model 1 begins to increase and Model 2 pCO2 continues to decline. Model 1 experiences nutrient limitation during the end of the summer (Figure 3). In October and November, Model 2 more rapidly returns to super-saturation, as the higher level of summer productivity in this model (Figure 6) lead to elevated levels of decomposing carbon in the mixed layer during fall. Despite the significant difference in primary production formulation, the lake pCO2 cycle is approximately the same from both models (Figure 5), indicating the significance of lake thermodynamics in determining the shape of the cycle. The main conclusions about the lake's carbon cycle are the same from both models, and thus, In the following sections, we discuss only Model 1, with phosphorus cycling, and return to the implications of Model 1 – Model 2 similarity in the Discussion.
3. Model Evaluation
 The physical model is evaluated in Bennington et al. , but important physical model characteristics will be reiterated here. The model captures the observed current structure and locations of upwelling and downwelling. The model adequately simulates near to offshore gradients in temperature, as well as temperature variability caused by the passing of synoptic weather systems. The model has a warm bias during cold years due to a forcing deficiency, which causes a premature spring overturn and over-prediction of summer temperatures during cold years. The model does not have a bias during warm years, and thus, the model dampens inter-annual variability caused by changes in atmospheric temperature.
3.1. Chlorophyll and Primary Production
 Although chlorophyll is not a direct measure of biomass or primary production, it is a commonly observed characteristic of Lake Superior's ecosystem. The Environmental Protection Agency (EPA) conducts biannual cruises to 19 open lake stations on Lake Superior (Figure 1), generally once in April or May and again in August or September. Among the suite of biological parameters measured, the EPA measures chlorophyll at several depths throughout the water column. Figures 7a and 7bshow all EPA measurements of chlorophyll-a taken between 1997 and 2001 and the daily mean modeled chlorophyll on the same date and location. Modeled chlorophyll profiles are daily averages from the 4 km2grid cell and day containing the snapshot observation. The model tends to under- predict spring chlorophyll with a root mean square error of 0.358 mg/m3 in spring. Figures 7c–7gshows a subset of modeled and observed chlorophyll profiles in Lake Superior during spring, including both good and poor model-data fits. The model adequately captures the shape of the chlorophyll profile, as well as the magnitude and depth of the deep chlorophyll maxima during summer, as observed by the EPA during August (Figures 7h–7l). EPA observations suggest greater variability in depth and magnitude of the deep chlorophyll maxima, although this is expected given the large areal extent of model grid cells and the comparison of an instantaneous snapshot to a daily mean value. The modeled root mean square error (RMSE) during summer is 0.453, though it is important to note that a small model error in the depth of the chlorophyll maximum leads to a large RMSE. The RMSE between maximum chlorophyll concentrations at any depth and model and in the observations is 0.25 during summer. The model simulates the seasonal progression of both the magnitude and the shape of the vertical profile of chlorophyll adequately.
 Estimated rates of primary production in Lake Superior ranged from 5.3 to 8.2 TgC/yr [Cotner et al., 2004; Urban et al., 2005], and until recently, the lake was thought of as ultra-oligotrophic. However, recent in situ measurements of open lake primary production suggest that gross primary production creates ∼10 Tg organic carbon each year and is driven by light and temperature [Sterner, 2010]. Model 1 net primary production is 2.8 TgC/yr and gross primary production is 4.9 TgC/yr, within the low end of previous estimates. Sterner [2010, 2011] estimates of summer net primary production would suggest a significant influx of carbon dioxide into the lake during summer and fall, currently not supported by the work of Atilla et al.  (section 3.2).
 Using the empirical equation derived by Sterner  (updated by Sterner ) relating light and temperature to rates of primary production, we plot estimated vertically integrated lake-wide rates of primary production for the modeled physical conditions (light, temp) inFigure 6 in black. Sterner  used 14C measurements to estimate primary production, and thus, observations lie somewhere between gross (GPP) and net primary production (NPP) [Peterson, 1980]. Integrated modeled rates of net primary production are shown in red for Model 1. Winter rates of primary production are lower in the model than suggested by the empirical fit of Sterner [2010; updated 2011]. Model 1 primary production includes two local maxima, one occurring in spring and another in June and July. Figure 3illustrates the progression of temperature, phosphorus concentrations, and phytoplankton biomass for shallow (<100 m) and deep (100+m) portions of the lake during 1997. With sufficient cooling, weak stratification occurs during Mar-Apr and April for shallow and deep lake locations, respectively (Figure 3, top). Weaker growth occurs during these periods, resulting in decreases in phosphorus (Figure 3, middle) and increases in phytoplankton biomass (Figure 3, bottom). The spring mixing brings phytoplankton out of the well-lit surface, productivity decreases, and biomass remains relatively constant (shallow regions) or decreases (deep). With the onset of summer stratification, production rates increase again in June (July) for the shallow (deep) regions. Phytoplankton biomass increases as phosphorus is rapidly depleted in the surface waters. Only unrealistic remineralization and mortality rates could sustain high levels of modeled net primary production through late through summer.
3.2. Partial Pressure of Carbon Dioxide (pCO2)
 The exchange of carbon dioxide (CO2) between the lake and overlying atmosphere is driven by the difference in partial pressure of carbon dioxide (pCO2) across the air-lake interface and wind speed. Estimates of lake surfacepCO2 in the open lake for spring and summer by Atilla et al.  are shown against modeled pCO2 at the same EPA stations in Figure 8. The black whisker plots show the median (solid line), range, and outliers (red crosses) of pCO2 estimated from pH, temperature, and alkalinity at the 19 open lake stations in spring and summer. The EPA is unable to reach all stations on the same day or night, and we plot daily average model pCO2 at each station within the month of sampling. For spring and summer sampling months between 1997 and 2001, whisker box plots show the spread in estimated and modeled pCO2values at the 19 lake-wide stations (Figure 6).
Atilla et al. find a super-saturation of carbon dioxide in the surface waters during April or May, and the lake in near equilibrium with the overlying atmosphere during August. The model captures the seasonal trend of elevated concentrations of carbon dioxide during spring and a reduction during summer. Summer modeledpCO2 is indistinguishable from Atilla et al.  estimates of summer pCO2, using a two-tailed t-test at 95% confidence level. However, modeled springpCO2 is lower than observed at the 95% confidence level with a mean bias of −48 μatm, assuming measured pH is the true pH. Observations suggest a much larger spatial heterogeneity (vertical extent of box plots) in spring pCO2 than the model, although this may in part be due to the difficulty of obtaining accurate pH data and the comparison of instantaneous data to a daily averaged model grid of 4km2. Nonetheless, the model does a reasonable job capturing seasonal variation, and to some degree, year-to-year variation inpCO2. These comparisons also agree support the suggestion by Atilla et al.  that observations during the spring of 1999 are erroneous.
 Two time series of direct measurements of pCO2 are known to exist for Lake Superior, but only one set of data was available for direct comparison. A mooring was deployed at 12 m depth in the western arm of Lake Superior from June to September in 2001, 7.5 km offshore from the Split Rock Light House near Duluth (47.19°N, 91.34°W, Figure 1). The mooring was equipped with a Submersible Autonomous Moored Instrument for CO2(SAMI-CO2) [DeGrandpre et al., 1995; Baehr and DeGrandpre, 2002, 2004] and a temperature sensor. The SAMI collected half hourly data from 6 June 2001 through 11 September 2001.
 In Figure 9, we show modeled temperature and pCO2at the grid cell containing the SAMI instrument. The SAMI data suggests a subsurface super-saturation with respect to the atmospheric value of 364μatm during spring and a substantial decrease in pCO2during summer. The observed decrease begins in June, but is dynamic and increases again in July until a substantial local decrease in DIC causes a large under-saturation in August. Modeled temperatures are too warm in spring due to a forcing bias [Bennington et al., 2010]; thus, a decrease in modeled pCO2 begins in May as model productivity begins with stratification. The model suggests that waters in the region of the SAMI are impacted by cool upwelled waters from the coastline to the west and from warmer waters coming from St. Louis Bay, depending on wind direction. Dramatic decreases in modeled lake surface temperatures at the SAMI location begin on Julian day 208, or July 27, 2001. This decrease is caused by a change in wind direction that causes water at the SAMI site to come from the upwelling coastline to the west, while local water was impacted by the warm waters from St. Louis Bay just prior (see Movie S1 in the auxiliary materials). Wind direction shifts again mid-August, and warmer waters return from southwestern Lake Superior. At the end of August, the upwelling coastal waters return to the SAMI site. Modeled temperatures capture the synoptic scale changes in temperature at the SAMI site well.
 Modeled pCO2 in June is lower than observed, likely due to the warm bias causing biological production to start earlier, but the gradual increase in pCO2 observed by the SAMI in June is present in the model. Both the model and observations show a decrease in pCO2during July and increase from mid-July to the start of August. The model does not capture the large drawdown of DIC during August that causes a dramatic reduction inpCO2 at the SAMI site. This may be due to a very localized bloom that a model with 4 km2 resolution cannot capture. SAMI observations show that temperature does not control summertime pCO2 in Lake Superior [Atilla et al., 2011], as warmer waters at the SAMI site generally have lower pCO2, and the model captures the dominance of the biological control of pCO2 during summer in Lake Superior.
 During the Keweenaw Interdisciplinary Transport Experiments (KITES), respiration rates were measured west of the Keweenaw Peninsula near the mouth of the Ontonagon River and near the middle of the peninsula (site HN, Figure 1). Water samples were gathered along transects, and respiration rates were immediately estimated from measured rates of oxygen consumption [Urban et al., 2004]. In Figure 10a, we compare observed rates of respiration at site HN to the model and find that it captures the magnitude of spring and summer respiration nicely, as well as the sporadic nature of the rates. At site Ontonagon (Figure 10b), we find the model again captures observed respiration rates. We are confident that modeled respiration rates are reasonable along the Keweenaw Peninsula.
 The model captures observations of near-shore respiration and simulates primary production within the lower observational estimates. Model 2, which directly incorporatesSterner's  equation for primary production, results in a similar seasonal cycle of pCO2and air-lake carbon fluxes for the lake, so we believe the current model is a reasonable for understanding the carbon cycle of the lake. Further, this model may be updated as more observations become available to realistically simulate alterations to the ecosystem as a result of changing nutrient conditions in the lake. Modeled chlorophyll is reasonable compared to snap shot observations taken by the EPA at the 19 lake stations, and the model captures the vertical profile and relative magnitude of chlorophyll during both spring and summer. The model captures the elevated concentration of carbon dioxide in the surface waters during spring relative to summer, in agreement with calculations of spring and summerpCO2 made by Atilla et al. . Modeled pCO2 is reasonable compared to direct measurements taken near Split Rock Lighthouse during 2001, although the model is unable to simulate what may have been a very localized bloom that led to a strong DIC drawdown in August. Overall, we believe the model adequately simulates the physics and ecosystem of Lake Superior, with the observations currently available, so that it may be utilized to understand the carbon cycle of Lake Superior.
4.1. Respiration in Lake Superior
Figure 10cshows the five-year mean column average respiration rates modeled for Lake Superior. Volumetric rates of respiration are two orders of magnitude larger near shore than in the open lake. Integrating over the entire water column, the great depths of the open lake in part compensate for low volumetric rates (Figure 10d), and open lake areal rates of respiration are about half of near-shore rates. Integrating over the entire lake,Figure 10e depicts the seasonal cycle of the mass of inorganic carbon created by respiration in Lake Superior. Modeled respiration peaks in late July, as autotrophic respiration is high, and the decomposition of both terrestrial and allochthonous carbon is fastest in the warm, sunlit water. Respiration rates are lowest in the cold, dark, and unproductive month of February. The model respires only 5.45 TgC/yr (autotrophic respiration + respiration of organic matter), significantly lower than the 13–81 TgC/yr suggested by previous carbon budgets for the lake [Cotner et al., 2004; Urban et al., 2005].
 Modeled annual respiration rates vary from 5.04 TgC/yr during 2000 to 5.70 TgC/yr in 1997. Annual average volumetric rates of respiration are 7.89, 2.09, 1.02, and 0.67 ug/L/day for depths < 50 m, 50 < depth < 150 m, 150 < depth < 250, and depth > 250, respectively. In contrast to the findings of Urban et al. , who find a threefold decrease in respiration rates offshore relative to near shore, when we include the entire lake, respiration rates are 11.8 times greater in the open lake then in shallow areas. Within the Keweenaw Peninsula region sampled by Urban et al. , however, the model indicates that a threefold decrease in volumetric rates is reasonable along the transects and for the months sampled. Thus, the whole lake does not appear to behave like the waters impacted by the Keweenaw Current.
4.2. Seasonal Cycle of pCO2 and CO2 fluxes
Figure 6depicts the mean seasonal cycle of atmospheric and lake-wide surfacepCO2 in Lake Superior from 1997 to 2001, as simulated by the models. The seasonal cycle of pCO2 in Lake Superior is similar to a double sinusoidal curve during the simulated period, in contrast to the single sine curve seasonal cycle of oceanic regions at similar latitude [Sarmiento and Gruber, 2006]. The lake surface is super-saturated with carbon dioxide in winter and for a period during spring and early summer. The lake is under-saturated during cold springs and summer. The minimumpCO2occurs during July in the model and the maximum during January. The climatological mean air-lake CO2 flux (positive to the atmosphere) is shown in Figure 11a. Note that a positive flux is a flux of carbon dioxide from the lake into the atmosphere.
 Winter is a period of cold, super saturated water and strong wind (Figures 11b and 11c), and therefore, the largest efflux of carbon dioxide to the atmosphere. Although cold winter temperatures work to reduce the partial pressure of carbon dioxide in the lake, the deep mixing allows dissolved inorganic carbon from below the summer thermocline to reach the surface waters. Weak stratification is possible during this period but the mixed layer is significantly deeper than in summer and can be more easily broken up during strong winter mixing events [Austin and Allen, 2011; Bennington et al., 2010]. This increase in DIC is responsible for the super-saturation of carbon dioxide beginning in late fall (start of December) and continuing until the start of March. The maximum super-saturation occurs during January, and as the lake effluxes excess carbon to the atmosphere from the mixed layer (Figure 6) and continues to cool, the pCO2 decreases through March. Ice can impede efflux (Figure 11b). From mid-March through much of April, the lake may become under-saturated (Figures 11c and 11d) until spring warming increases the temperature.. Spring is the period of greatest interannual variability in the model (Figures 11d and 11e), as both temperature and ice impact the lake's carbon cycle. The continued increase in temperature and spring mixing (Figures 11a and 11b) that brings up any decomposed carbon from the lake bottom causes an efflux before primary production (Figure 11b) is able to overcome the impact of temperature on pCO2. Thus, the lake is super-saturated from mid-April through June. During summer, biological production is able to reduce surface DIC enough such that significant increases in lake surface temperature do not cause super-saturation, and the lake acts as sink of atmospheric carbon from July throughfall. Although primary production is decreased during fall, cooling allows the lake to remain under-saturated until the beginning of December (Figure 11b).
 There is a small mean annual carbon dioxide efflux from Lake Superior (0.19 TgC/yr here).
4.3. Mechanisms of CO2 Flux Variability
 The seasonal cycle of pCO2 and CO2fluxes of Lake Superior are driven by a combination of lake temperature, biological drawdown of DIC, decomposition, and mixing. The forces often counteract one another as discussed above, but inter-annual variability is determined by changes in lake temperature and the subsequent impacts on lake physics and biology. InFigures 11d and 11e we show the pCO2gradient across the air-lake interface and the resulting CO2 fluxes for all modeled years. Both 1998 and 2001 stand out. During 1998, a strong El Niño year, there is a dramatic change in the seasonal cycle. Instead of a double sinusoidal curve, 1998 exhibits a single sinusoidal curve in CO2 fluxes. The winter and spring of 1998 never cools enough to cause an influx at the end of winter, and the lack of ice allows a late winter efflux. Thus, the influx only occurs during the summer of 1998. This influx occurs earlier than during a cold year, as lake stratification and production start earlier during 1998 in the model. The total efflux in 1998 is 0.33 TgC/yr, the largest of simulated years. In contrast, a large influx of carbon dioxide occurs during the spring of 2001. The winter and spring of 2001 were cold, but with far less ice cover than 1997, a year with similar winter and spring temperatures (see Figure S1 in the auxiliary materials). The timing of maximum spring under-saturation corresponds to the timing of minimum lake-wide temperatures (Figure S1). The annual efflux during 2001 was 0.22 Tg C.
 The mean seasonal cycle of fluxes is more similar to the cycle during 1997, but the winter efflux during January exceeds the mean. The presence of ice during February–April of 1997 blocks air-lake carbon dioxide exchange, and the annual efflux is 0.24 TgC/yr.
5. Discussion and Conclusions
 We have coupled two separate ecosystem models to an eddy resolving, three-dimensional physical model of Lake Superior at 2km horizontal resolution and simulated 1997–2001. Both models result in a similar seasonal cycle ofpCO2for Lake Superior, suggesting a physical dominance in the annual cycle. We utilize Model 1, with explicit phosphorus cycling, for our analysis of lake-widepCO2and air-lake CO2flux. The lake-wide seasonal cycle of surfacepCO2 resembles a double sinusoidal curve, with two peaks and troughs in all modeled years except the extremely warm El Niño year of 1998. The modeled cycle is in agreement with both direct and indirect observations during spring and summer [Kelly et al., 2001; Atilla et al., 2011]. The seasonal cycles of pCO2 and CO2 fluxes are physically and biologically driven. Winter mixing brings inorganic carbon to the lake surface, and high winds allow for a large efflux before extreme cooling and ice reduce this flux. With sufficient cooling, the lake may act as a sink of carbon dioxide during the late winter/early spring before warming, mixing, and fluxing carbon to the atmosphere during spring. Although warming would act to increase pCO2 at the lake surface, biological productivity reduces DIC and pCO2, allowing the lake to act as a small sink or neutral during summer. The lake remains a sink until winter mixing returns.
 The simulated primary production is on the lower end of observational studies. If actual rates of net primary production are significantly higher during winter than modeled (Model 1), both the late winter influx and spring efflux would be greater. Sterner  used 14C to measure rates of primary production, which may yield results somewhere between net and gross primary production [Peterson, 1980], overestimating NPP. Although Sterner [2010; 2011] suggests higher rates of net primary production during summer, such a DIC drawdown would lead to lower pCO2 in the lake surface during summer, a large summer influx, and summer pCO2 closer to that observed by Kelly et al.  than estimated by Atilla et al.  during summer. As Model 2 primary production has the same shape in its seasonal cycle as Sterner , such a change in primary production would result in a slight shift in the pCO2 seasonal cycle but would not likely alter its shape (Figure 6). A larger summer drawdown would cause an even larger modeled winter efflux, because sediment burial is not considered within the model.
 We assume a quadratic relationship between wind speed and carbon dioxide fluxes, but a cubic relationship may be possible for lower wind speeds. This would cause more rapid winter and spring effluxes (late winter and summer influxes), resulting in a more rapid decline (increase) in lake pCO2 during periods of super (under) saturation. Certainly more direct measurements of pCO2 and CO2 fluxes throughout the lake and during more seasons, as currently being done by Bootsma et al.  on Lake Michigan, would be a valuable addition to this research.
 Here we include the inorganic and organic carbon of nine of more than 200 tributaries into Lake Superior, although more than half of the riverine carbon reaching the lake is included. We expect that all coastal regions near all river mouths experience a local increase in respiration rates caused by the decomposition of organic matter and increased rates of autotrophic respiration; the larger the tributary, the greater the magnitude and footprint of the inflow. The influx of DIC, alkalinity, and phosphorus can also lead to a reduction in local pCO2, driven by high biological productivity or low concentrations of inorganic carbon reaching the lake. We estimate that model flux would double with the inclusion of all rivers, for a total modeled efflux of approximately 0.5–0.7 TgC/yr. The annual flux to the atmosphere suggested by the model (order of tenths of Tg C) is an order of magnitude lower than suggested by previous studies (∼3 Tg C) [Urban et al., 2005]. Still, the model is able to capture the elevated rates of respiration observed near shore but suggests that open lake volumetric rates of respiration are significantly smaller than previously estimated. Findings with respect to the annual cycles of lake-widepCO2 did not differ substantially when remineralization occurred twice as rapidly or with alternative sets of model parameters [Bennington, 2010]. Thus, we believe our findings to be robust. Lake Superior need not be a significant source of carbon dioxide to the atmosphere in order to allow for known inputs and observations.
 The model can only respire and efflux as much carbon as is supplied to it, so it is no surprise that modeled CO2 fluxes are small over the course of the year. The model suggests, however, that a large efflux is not required to account for previous observations of respiration. Spatial heterogeneity is likely the cause for large discrepancies in previous attempts to create a carbon budget for the lake [Cotner et al., 2004; Urban et al., 2005]. Both the model and observations show high respiration rates close to shore (within 5km) and near river mouths, and lower rates further from the coast. The model, however, suggests extremely low respiration rates in the open lake, where no observations were available.
 The surface circulation moves with a current speed of a few cm/sec or less [Bennington et al., 2010], although flow along the Keweenaw Peninsula can be on the order of tens of cm/sec. Sub-surface current speeds are significantly weaker. Even if all coastal surface speeds are 2 cm/sec and directed perpendicular to the shoreline, 50% of the highly labile terrestrial (river) carbon would be respired before moving 40 km offshore. The spring runoff event occurs during a period of significant near to offshore temperature gradients, further inhibiting transport to the open lake. Summer, the period of most sampling, is also a time of year when the surface circulation is counterclockwise along the coastline [Bennington et al., 2010]. Eddy-induced mixing should be the primary mechanism for which terrestrial carbon moves into the open, deep waters of Lake Superior. Thus, it is reasonable for such large near to offshore gradients in respiration rates to exist.
 Although it is unlikely that Lake Superior effluxes large amounts of carbon to the atmosphere each year, recent work by Vasys et al.  suggests that the western arm of Lake Superior influences observations of the terrestrial carbon budget at the tall tower in Park Falls, WI. Assuming a zero flux from the lake may cause an overestimate of terrestrial wintertime respiration and overestimate of fall terrestrial respiration, when the lake's impact is larger than measurement uncertainty.
 The developed model is a useful tool for investigating the mechanisms and spatial heterogeneity of the carbon cycle in Lake Superior. It is, however, limited by the observations, simulation length, and inputs to the system. The model alone cannot provide a carbon budget for the lake, but can provide a framework from which to interpret and extrapolate observations and should be useful for locating ideal future observation stations. In the future, the model will be used for evaluating long-term variability in the lake's carbon cycle and the mechanisms that cause particular regions of the lake to be areas of high respiration.
 We thank NSF for funding this work (OCE-0628560). NARR Reanalysis data provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their website athttp://www.esrl.noaa.gov/psd/. We acknowledge NOAA ESRL Carbon Cycle Greenhouse Gases Group for the GLOBALVIEW-CO2 data product and USGS for LOADEST. The authors would like to acknowledge David Dolan at UW-Green Bay for nutrient loading data, Robert Sterner at UMN for help with model primary production in both ecosystem models, and Nazan Atilla at UW-Madison for assistance with ecosystem Model 1. We thank the reviewers, whose thoughtful comments improved this manuscript.