4.1. Budget and Cycle for Organic Carbon
 A budget for organic C in Lake Superior (Table 2) makes several points immediately obvious. Photosynthesis represents the largest source of organic C to the lake, and respiration is the largest sink. Discharge of organic C from the lake is much smaller than the riverine input; apparently much of the terrigenous DOC supplied by rivers is degraded in the lake or lost to the sediments. Tabulated influxes (2.4–7.7 Tg/yr) are less than the sum of measured outputs (13–83 Tg/yr); either there are large errors in some measured fluxes or some inputs have as yet to be measured (e.g., photosynthesis in embayments, DOC in shallow subsurface flows, leaf and woody debris). Before examining this discrepancy further, it is useful to examine the pool sizes and other characteristics of C cycling in the lake.
 As do many oligotrophic aquatic systems [Gasol et al., 1997], Lake Superior has an “inverted pyramid” of biomass with heterotrophic biomass greater than that of autotrophs (Figure 7). Phytoplankton biomass may overestimate autotrophic biomass because some fraction of the cryptophytes and chrysophytes (together accounting for ∼50% of phytoplankton biomass [Barbiero and Tuchman, 2001; Fahnenstiel et al., 1998, 1986]) are undoubtedly mixotrophic [e.g., Sherr and Sherr, 2000; Turner and Roff, 1993]. Picoplankton represent nearly 50% of the phytoplankton biomass, but bacteria represent only 10–15% of the heterotrophic biomass [Fahnenstiel et al., 1998]. The total pool of particulate organic carbon (∼1 Tg) is only 5–7% as large as the pool of DOC (∼17 Tg), and biomass as reported by Fahnenstiel et al.  can account for 70–90% of the POC. It has been suggested [Zhou et al., 2001] that mortality and growth rates of large mesograzers in Lake Superior make possible the inverted pyramid (mesograzers represent ∼60% of total heterotrophic biomass [Fahnenstiel et al., 1998]), but an alternative hypothesis is that organic carbon inputs from the catchment support a significant portion of the heterotrophic biomass.
Figure 7. Carbon cycle in Lake Superior. Fluxes are in Tg C yr−1, pool sizes are in Tg C, and residence times (pool/total influx) are given in parentheses. Shaded arrows denote system-scale measurements, black arrows denote process rates measured in small discrete samples, and white arrows are fluxes calculated by difference or using efficiencies discussed in the text. Net heterotrophy is indicated by (1) an excess of inputs over outputs (system scale), (2) a net degassing of CO2, and (3) community respiration in excess of net primary production (NPP). There remains an imbalance between estimated rates of photosynthesis (GPP) and respiration (CR) that is not explained by system-scale inputs and outputs.
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 Autochthonous DOC production and organic carbon inputs from the catchment support the largest pool of organic C in the lake, the DOC (Figure 7). The specific absorbance (absorbance at 285 nm divided by DOC concentration) of the lake DOC (∼50 L/mole cm [Ma and Green, 2004]) is much lower than that of DOC in the inflowing Sturgeon River (300 L/mole cm) suggesting that lake DOC is not highly aromatic and may contain a substantial fraction of nonterrigenous origin [Chin et al., 1994]. The mass balance for organic carbon (Table 2, Figure 7) also points to autochthonous sources; the excretion rate of DOC by phytoplankton (0.9 Tg/yr) is comparable in magnitude to the estimated input of DOC in rivers (0.4–0.9 Tg/yr). Ultrafiltration and characterization of the colloidal organic carbon (i.e., 1 kDa < COC < 0.2 μm) also confirm that the DOC pool has both terrigenous and autochthonous components. The colloidal fraction (35–50% of bulk OC) in Lake Superior is intermediate in size between that of terrigenous material (40–80% [Guo et al., 2003; Hedges et al., 2000]) and the mixture of well-aged terrigenous DOC and autochthonous DOC found in the oceans (22–35% colloidal [Amon and Benner, 1994; Benner et al., 1997, 1992]) or in shallow lakes with long residence times (27% colloidal [Waiser and Robarts, 2000]). Clearly, the DOC pool is not unaltered terrigenous material. Because the δ13C values of terrigenous DOC (−25.3 to −30.3‰ [Guo et al., 2003; Lara et al., 1998; Lobbes et al., 2000; Schiff et al., 1990, 1997]) and photochemically altered terrigenous DOC (−25.8 to −26.6‰ [Opsahl and Zepp, 2001]) overlap with that of autochthonous OM in Lake Superior (−26 to −27.8 [Keough et al., 1996; Lu, 2004; Ostrom et al., 1998]), the δ13C value for the colloidal OC (−27.1 ± 1.0) is not helpful in resolving its source. The molar C:N ratio of the colloidal fraction (25.7 ± 2.6, mean ± S.D.) is much lower than ratios for riverine colloidal OC (34–48 [Guo et al., 2003; Hedges et al., 2000]) but higher than in the surface oceans (C:N ∼ 16) where the colloidal pool is largely of algal origin [Amon and Benner, 1994; Benner et al., 1997]; evidently, a significant fraction of the colloidal organic carbon (COC) pool in Lake Superior is of autochthonous origin. The fraction of the COC that is of terrestrial origin may be calculated to be 55–85% for a range of C:N ratios for autochthonous COC of 8–16 and for terrigenous COC of 35–48. If all low-molecular-weight (LMW) DOC were of terrigenous origin, terrigenous OC would constitute 80–95% of the total DOC (i.e., LMW + COC) pool. This estimate agrees with our earlier estimate of autochthonous DOC in the summer epilimnion of 0.07–0.15 mg/L (5–15% of total DOC) based on seasonal DOC concentration changes (Figure 2a) and with the estimated terrigenous DOC concentration of 1.39 mg/L based on Figure 2b. Thus although the terrigenous DOC appears to have been altered in the lake, it nevertheless may be the major constituent of DOC in the lake.
 The dynamics of the DOC pool further suggest that the majority of the pool is only moderately reactive. The entire DOC pool (Figure 2a) undergoes only minor seasonal changes in concentration (≤0.2 mg/L), and those changes (Figure 2b) are consistent with enhanced production in surface waters and continued decay of the bulk DOC pool in the hypolimnion during summer stratification. Division of the terrigenous DOC pool size (80–95% of total DOC = 14.7–16.8 Tg) by the estimated DOC influx in rivers (0.4–0.9 Tg/yr) suggests a residence time of 16–42 years, much less than the lake's hydrologic residence time (170 years) but very long relative to turnover of the biota. If the terrigenous input has been underestimated, the residence time will be correspondingly lower.
 The relative importance of respiration, photolysis, and particle scavenging as sinks for DOC may be estimated from data collected in this study. Lower DOC concentrations in the summer hypolimnion as compared to the well-mixed lake in spring (Figure 2a) suggest that dark processes such as microbial respiration or particle scavenging must be capable of degrading terrigenous DOC. Low C:N ratios in the sediments (8–10 [Urban et al., 2004b]) indicate that particle scavenging is unimportant. A pseudo first-order rate constant (kresp) and turnover time (1/kresp) for microbial respiration may be estimated from measured bacterial production (1999 BP = 0.018 mg C/m3 hr), bacterial abundance (BA = 0.6 × 106/mL), bacterial C content (f = 20 fg C/cell [Bell, 1993; Fukuda et al., 1998]), and bacterial growth efficiency (BGE = 5–30%):
The calculated turnover times (1.5–8.3 days) are much too short; much higher input rates would be needed to sustain the measured DOC concentration at such a high rate of consumption. If the DOC concentration in the hypolimnion decreases only 0.1–0.2 mg/L (7–13%) over a 1–3 month period (Figure 2a), the turnover time for DOC would be 0.6–3.7 years (assuming negligible production in the hypolimnion). Although this rate is much slower than that calculated based on measured bacterial production, it is still much faster than the residence time estimated for terrigenous DOC in the lake (16–42 years).
 Similarly, the potential role for photolysis may be estimated by extrapolation from in situ incubations. In situ incubations (4–8 hours) of DOC in quartz tubes yielded a half-life of 144 hours (6 days) of daylight at the lake surface [Ma and Green, 2004]. Dividing the measured half-life by the photoperiod at the time of measurement accounts for the period of darkness, but the rate is probably still an overestimate because it spanned the period of maximum solar intensity rather than the whole period of daylight. Measured extinction coefficients for UVA light (324–380 nm) ranged from 0.4–0.9/m in offshore waters (S. Green, unpublished data, 2003). Accounting for seasonal variations in solar irradiation at the lake surface as well as for seasonal changes in photoperiod and integrating over the mixed layer (25–150 m depending on season [Assel, 1986; Bennett, 1978]) the turnover time (1/first-order rate constant) of DOC by photolysis is estimated to be between 4 and 8 years. Because the more energetic wavelengths are attenuated more rapidly in water and because wavelengths of ∼320 nm are most effective at photolyzing DOC [Gao and Zepp, 1998], the turnover time is likely to be at the long end of this range. These calculations suggest that respiration is 1.1–13 times faster than photolysis. However, because these turnover times are still shorter than the estimated residence time for terrigenous DOC in the lake (16–42 years), the entire pool of terrigenous DOC must not be susceptible to either photolysis or microbial decomposition at the rates calculated above. Rather, some fraction of the DOC pool must be less reactive or recalcitrant to both processes. In the study of Ma and Green , rate constants decreased with increasing incubation time due to preferential loss of chromophoric DOC, and other studies have also reported that photobleaching is more rapid than photolytic mineralization of DOC [e.g., Gao and Zepp, 1998]. An upper limit for the labile fraction (flabile) of terrigenous DOC is calculated to be 15% using the rate constants for photolysis and microbial respiration given above and the estimated residence time of terrigenous DOC in the lake (16–42 years) in equation (2):
 The high respiration rate constant calculated above from bacterial production points to a large bacterial carbon demand that must be met by a small pool of labile DOC that is cycled rapidly. Bacterial regrowth bioassays indicated the existence of a labile fraction (15–50% of DOC) that had a turnover time of a few days under the bioassay conditions [Apul, 2000; Elenbaas, 2001]. The calculated carbon demand of the bacteria (BP/BGE = 6–38 Tg C/yr in 1999 assuming BGE of 5–30%) is much larger than the estimated rate of carbon fixation (2.5 Tg/yr). There is at least a factor of 2 uncertainty in the thymidine:bacterial cell conversion factor [Ducklow et al., 2002], but this uncertainty is not enough to account for the discrepancy between bacterial carbon demand and photosynthesis rates. For a growth efficiency of 5%, the bacterial production measurements predict a microbial respiration rate of 36 Tg/yr in 1999, close to the measured rate of community respiration (42 Tg C/yr). The discrepancy between the estimated rate of bacterial carbon uptake (6–38 Tg/yr) and the supply rate of DOC to the lake (1.8 Tg/yr) reflects in part the unmeasured DOC production via viral lysis of cells, sloppy feeding by zooplankton, DOC release from fecal pellets and microbial breakdown of particulate organic carbon [e.g., Sondergaard et al., 1995; Strom et al., 1997]. However, estimated rates of microbial respiration require an additional input to the lake of up to 35 Tg/yr of organic carbon. Thus the apparent imbalance of the organic carbon budget (Table 2) points to a need to understand the constraints on microbial growth efficiencies. The respiration and bacterial production rates are consistent with a bacterial growth efficiency of ∼5%, a value in line with recent literature [Biddanda et al., 2001; del Giorgio and Cole, 1998] while the measured rates of photosynthesis and bacterial production are consistent with a BGE slightly above 20%. In other words, either the measured rates of respiration or photosynthesis must be in error.
 The most likely sources of error in estimation of photosynthesis rates are methodological issues with 14C fixation and assumptions made in extrapolation from point measurements to the entire lake. The ranges of volumetric rates of photosynthesis reported for five studies made over a 30 year period in Lake Superior agree well with one another (2.2–8.8 mg C/m3 hr [Vollenweider et al., 1974], 0.5–3.5 mg C/m3 hr [El-Shaarawi and Munawar, 1978], 0.5–3 mg C/m3 hr [Fee et al., 1992], <0.05–5 mg C/m3 hr [Bub, 2001]). Consequently, the extrapolated annual rates of primary production also agree within a factor of about two (30–65 g C/m2 yr) but they are at the low end of the range reported for both lakes and oceans. This is not reassuring given that an awareness of the importance of trace metal clean techniques [e.g., Fitzwater et al., 1982] was developed during this 30 year period. Until ultraclean techniques are shown to yield identical results with less rigorous techniques, the possibility for metal inhibition cannot be excluded. Trace metal contamination may cause photosynthesis rates to be underestimated by up to a factor of 2.5 [Fitzwater et al., 1982], but this is still less than the discrepancy between respiration and measured photosynthesis rates. All estimated lake-wide rates have been based on rates measured under light-saturated conditions and then extrapolated to the entire water column based on P-I curves. It is well known that parameters in P-I curves change with depth and season [e.g., Fahnenstiel et al., 1989, 1984]. In situ incubations would remove some uncertainty in extrapolations based on P-I models [Ondrusek et al., 2001]. Additional uncertainties arise in attempting to partition the lake spatially into nearshore and offshore areas; while photosynthesis rates were found to vary between these two zones, the differences changed seasonally. The contribution of embayment areas to the lake-wide rate of photosynthesis is unknown; remote sensing shows that these areas have higher chlorophyll concentrations [Budd, 2004]. Rates of DOC excretion by phytoplankton (Figure 7) may have been underestimated because they were not corrected for bacterial C uptake [Baines and Pace, 1991] and may have been underestimated for the same reasons just discussed for photosynthesis. We suggest that it is important (1) to prove that trace metal clean techniques do not result in higher rates than the protocols followed in the KITES study, (2) to conduct in situ incubations to verify that vertical distributions of chlorophyll and photosynthetic parameters are accurately incorporated into integrated areal rates of photosynthesis, and (3) to measure more accurately photosynthetic contributions of embayments and nearshore regions to the entire lake.
 Another critical research need is to conduct measurements during winter. The organic carbon budget for the lake has been extrapolated based on measurements made between April and October. If the average bacterial production value during the 5 month period of November–March is substantially less than during April–October, the respiration rate may have been overestimated by about a factor of two. We did not use a temperature coefficient to reduce the estimated bacterial activity in winter because respiration rates showed no seasonal response to temperature [Urban et al., 2004a] and recent work has shown that enhanced nutrient supplies compensate for reduced temperatures in winter months in Lake Michigan [Cotner et al., 2000]. While it does not seem inconceivable that primary production may have been underestimated by even a factor of 5 and may be as large as 200 g C/m2 yr, it is difficult to believe that it could be as high as 500 g C/m2 yr, the estimated rate of respiration.
 Lakes play a dual role in regional carbon cycling. On the one hand, lake sediments sequester organic carbon at globally significant rates [Dean and Gorham, 1998]. This fact is consistent with the classic view that lakes are carbon sinks with autotrophic production balanced by respiration and burial in sediments [e.g., Eadie and Robertson, 1976]. However, recent studies have clearly shown that many if not most lakes are sources of CO2 to the atmosphere [Anderson et al., 1999; Cole et al., 1994; del Giorgio et al., 1999; Dillon and Molot, 1997; Kling et al., 1991; Striegl et al., 2001; Wachniew and Rozanski, 1997]. Measurements of δ13C have indicated that the evolved CO2 comes, in most cases, from respiration [Striegl et al., 2001]. The view that has evolved is that lakes receive organic carbon subsidies from their catchments (or from macrophytes in littoral areas and adjacent wetlands [Wetzel, 1990]) in the form of DOC, and that some fraction of this DOC is respired within the lake. As a result, heterotrophic bacteria (and potentially lake food webs) are not solely dependent on pelagic photoautotrophs for their carbon supply. In oligotrophic systems, the allochthonous organic carbon that is respired is greater than the autochthonous organic carbon that is buried. As a consequence, oligotrophic lakes tend to be net heterotrophic with rates of respiration in excess of rates of photosynthesis [del Giorgio and Peters, 1994, 1993].
 On the basis of observations in other lakes, ultraoligotrophic Lake Superior would be expected to be net heterotrophic (P/R < 1). However, Lake Superior also has a small ratio (1.55) of catchment area to lake surface area. This small catchment size might limit the organic carbon subsidy available from the watershed.
 Regardless of what measures are used, Lake Superior appears to be net heterotrophic. Small-scale, point measurements of photosynthesis, respiration, and bacterial growth made in this study all indicated a condition of net heterotrophy. In 14 of 16 cases where photosynthesis and community respiration were measured simultaneously in surface waters, volumetric respiration rates were higher than rates of 14C fixation into particulate matter [Urban et al., 2004a]. This comparison does not account for excretion of photosynthate by autotrophs, and autotrophic respiration is included in measurement of both particulate OC fixation and community respiration. However, if bacterial respiration represents ∼98% of community respiration in Lake Superior [Biddanda et al., 2001], the latter error is small. Integration of profiles of point measurements into areal rates of respiration and photosynthesis always revealed P:R ratios less than one [Urban et al., 2004a]. More frequently, photosynthesis and bacterial production (rather than respiration) were measured simultaneously; these measurements show that, for the range of bacterial growth efficiencies of 5–30%, areal rates (integrated over the entire water column) of bacterial respiration exceeded areal photosynthesis rates 40–80% of the time (Figure 8). This comparison is compromised by the uncertainty in the conversion factor between thymidine uptake and bacterial growth [e.g., Ducklow et al., 2002]. When the areal rates are extrapolated to the entire lake for an annual period (Figure 7, Table 2), the P:R ratio (0.02–0.38) is much below one.
Figure 8. Comparison of areal rates of photosynthesis (NPP), bacterial production (BP), and bacterial respiration (BR). Bacterial respiration rates were calculated from bacterial production for the range of bacterial growth efficiencies of 5–30%; vertical lines between solid circles indicate the range of possible bacterial respiration rates. Values represent integrated profiles through the entire water column at station HN210 (21 km from shore, 180 m water depth).
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 Measurements made at the ecosystem scale agree well with the magnitude of rates measured at the point scale and also point to a condition of net heterotrophy in Lake Superior (Table 2, Figure 7). From the mass balance equation, the difference between respiration (R) and photosynthesis (P) should equal the difference between nonphotosynthetic inputs (I) and nonrespiratory outputs (O):
From Table 2, the terms on the right hand side of equation (3) total −1.66 to 0.76 Tg C/yr; only if river inputs are at the low end of the estimated range or if rates of OC burial are at the high end of the estimated range is NEP (P-R) positive. If inflows and outflows of DIC are balanced (see above), the annual exchange of CO2 across the lake surface should equal the difference between photosynthesis and respiration. The values (>360 μatm) calculated from measured pH and alkalinity [Urban et al., 2004a] indicated that the lake was supersaturated with respect to atmospheric CO2 for most months between April and November. Gas fluxes calculated with the wind speed–dependent transfer velocities of Wanninkhof et al.  or Cole and Caraco  averaged ∼3 Tg C/yr out of the lake. This CO2 efflux is of the same order of magnitude as NEP predicted by other inputs and outputs. The estimate of CO2 efflux also is in good agreement with CO2 production rates estimated with bottle incubations and hypolimnetic mass balances [Urban et al., 2004a]. The estimated CO2 efflux is an order of magnitude larger than the annual degassing predicted (0.2–0.3 Tg/yr) from river DIC loadings but about equal to the seasonal CO2 uptake and degassing expected due to temperature changes in the lake. Accurate determination of NEP from gas flux measurements would require either year-round measurements or accurate corrections for temperature-induced fluxes.
 Other independent measurements also point to the net heterotrophic status of the lake. If respiration exceeds photosynthesis, there must be a net influx of oxygen into the lake. Indeed, PO2 values did indicate an oxygen flux into the lake from April–October 2000 except from late July through late August [Russ et al., 2004]. Measurements of δ18O in dissolved oxygen profiles led to a similar conclusion; P:R ratios calculated from the stable isotope ratios were consistently below one except during summer stratification when ratios above one were observed in the epilimnion [Russ et al., 2004]. An earlier study [Kelly et al., 2001] had reported undersaturation of epilimnetic waters with CO2 and predicted a net influx of CO2; however, that study reported measurements only for the months of August to early October, a period slightly longer than the period of oxygen evolution from the epilimnion in 2000 [Russ et al., 2004]. The CO2 influx (0.09 g C/m2d) reported by Kelly et al.  is fivefold to 20-fold smaller than the rate of hypolimnetic oxygen consumption (0.4–1.8 g C/m2d) reported in this study and that of McManus et al.  and is, therefore, still consistent with a state of net heterotrophy even during summer. Although each individual approach has considerable uncertainty in the estimation of the small net flux of CO2, the consistency among all of the approaches in estimation of the direction of the net flux (out of the lake) leads us to conclude that Lake Superior is net heterotrophic on an annual basis and during each season of the year.
4.3. Factors Regulating Bacterial Production
 It is generally accepted that, over long timescales and across systems, heterotrophic activity is limited by production of labile carbon substrates by autotrophs. Thus across a wide range of ecosystems, Pace and Cole  demonstrated that bacterial activity is proportional to autotrophic production (chlorophyll-a used as a surrogate). Similarly, in a survey of lakes, epilimnetic bacterial production was best explained by trophic status (i.e., nutrient concentrations), the regulator of autochthonous organic carbon production [Cimbleris and Kalff, 2003]. However, over short timescales within individual systems, heterotrophic activity may be limited by other factors including temperature [Pomeroy and Wiebe, 1988], inorganic nutrients [e.g., Chrzanowski and Grover, 2001; Skoog et al., 2002], or more proximal sources of DOC [Ducklow et al., 2002; Sondergaard et al., 1995].
 Rates of bacterial production within Lake Superior are not well predicted by the empirical relationships observed for other aquatic systems. The empirical relationship between total P and BP observed by Cimbleris and Kalff  in 14 Canadian lakes overpredicts BP in Lake Superior by over a factor of 10; the deeper mixed layer depth in Lake Superior may result in lower photosynthetic production per unit of nutrient because of light limitation and concomitantly lower production of carbon substrates for bacterial use. In contrast, the empirical relationship between chlorophyll-a and BP observed by Cole et al.  for lake and marine systems underestimates the BP measured in Lake Superior; this discrepancy could point to low bacterial mortality in Lake Superior [Pace and Cole, 1996] or to allochthonous sources of labile organic C.
 The few data available to evaluate factors regulating BP on an annual timescale suggest that temperature and P availability may be important. Within this limited data set (Figure 9), several observations stand out. The highest lake temperatures on record were measured in 1998, a strong El Niño year. This year also witnessed much higher rates of community metabolism and significantly higher TP concentrations [Siew, 2003] than in 1999. Chlorophyll concentrations increased each year of the study, and DOC concentrations in 1999 were higher than in 1998. Only TDP concentrations show decreases between years that exhibit decreases in community respiration rates and BP rates. Clearly, the significance of these observations will require a longer period of measurements to evaluate.
Figure 9. Annual mean values for total dissolved P (TDP), chlorophyll-a, DOC, bacterial production (BP), and respiration rates. Values of DOC, BP, and respiration rates were discussed above; values for TDP are from Siew , and chlorophyll means represent all KITES data. Concentrations of DOC and chlorophyll-a increased during the study, while rates of respiration and bacterial production declined, as did concentrations of TDP.
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 On shorter timescales, KITES data point to interactions between BP, DOC concentrations, temperature, and P concentrations but little dependence on either chlorophyll concentrations or rates of 14C fixation. Volumetric rates of 14C fixation and BP in surface waters measured in 1999 showed no significant correlation when all data were pooled; segregating data into near- and offshore samples on each transect and analyzing each month separately (ANOVA indicated significant interactions between transect, distance from shore and month), only 2 of 20 subsets showed significant correlations with slopes of 0.3–0.4. Areal rates of BP and 14C fixation (adjusted for light attenuation) showed disparate patterns in both near- and offshore waters (Figures 4, 5, and 8). Statistically, there were significant correlations between BP and temperature, DOC concentrations, and TDP concentrations (Table 1) but not between BP and chlorophyll concentrations. Although the bacteria are indirectly dependent on phytoplankton for fixation of the carbon that ultimately ends up in the labile DOC pool, either the bacteria are more limited by temperature and availability of phosphorus than by availability of labile DOC, or phytoplankton excretion is not the major mechanism for generation of labile DOC.