Significant amounts of terrestrial carbon are processed in lakes and emitted into the atmosphere as CO2. However, due to lack of appropriate measurements the absolute role of lakes in the landscape as sinks or sources of CO2 is still uncertain. We conducted the first long-term, ecosystem-level CO2 flux measurements with eddy covariance technique in a boreal lake within a natural-state catchment covering 5 years. The aim was to reveal the natural level of CO2 flux between a lake and the atmosphere and its role in regional carbon cycling. On average, the lake emitted ca 10% of the terrestrial net ecosystem production of the surrounding old-growth forest and the main immediate drivers behind the fluxes were physical rather than biological. Our results suggest that lakes are an integral part of terrestrial carbon cycling.
 The importance of inland waters in carbon cycling has only recently been recognized [Cole et al., 2007; Battin et al., 2008; Tranvik et al., 2009]. Globally the majority of lakes have surface water CO2 concentrations higher than the equilibrium with the atmosphere and thus they are net sources of CO2 [Cole et al., 1994]. Generally, this surplus CO2 is attributed to in-lake heterotrophic respiration fuelled by organic carbon of terrestrial origin [Jonsson et al., 2003; Sobek et al., 2003]. Lakes also store carbon effectively in their sediments, but in the boreal zone the annual CO2 emissions are 17–43 times higher than the net sedimentation of carbon [Kortelainen et al., 2006]. A distinct feature of the majority of boreal lakes is the brown water color, implying high loads of allochthonous dissolved organic carbon (DOC). Carbon enters lakes also in inorganic form (DIC), but the transport of DIC from the catchment to lakes is largely unknown. These lateral transport processes from the terrestrial to aquatic ecosystems are not yet routinely included in network of micrometeorological EC (eddy covariance) flux towers, which are becoming the standard of CO2 flux studies [Baldocchi et al., 2001] and there are only a few lakes equipped with EC towers. However, reliable assessment of the total terrestrial net ecosystem production (NEP) and calculation of terrestrial carbon balance requires information on the lateral transport processes of DIC and DOC. Thus, accurate knowledge of CO2 fluxes to the atmosphere from inland waters is a prerequisite for precise estimates of terrestrial carbon sinks.
 In aquatic sciences, flux estimates are usually based on discrete samples and indirect models heavily relying on wind-based gas transfer coefficients [Wanninkhof et al., 1985; Cole and Caraco, 1998], or chamber measurements that are very labor-intensive when high temporal resolution is needed. Hence, the natural dynamics and level of CO2 exchange in lakes have thus far been somewhat uncertain. Here we present unique data on CO2 exchange at ecosystem scale measured with the most reliable and accurate method available, namely the direct EC measurement technique, over five consecutive ice-free periods (2003–2007) in a small, stratifying polyhumic headwater lake (Valkea-Kotinen) and relate the flux dynamics to the possible drivers. Lake Valkea-Kotinen represents the lakes in natural-state areas within the boreal part of the Precambrian Shield in Northern Europe and North America, where as a result of the latest glacial period, numerous lakes with low alkalinity and hence low pH were formed in the ancient bedrock. The lake is surrounded by an old-growth forest, and hence the study demonstrates the truly natural dynamics and level of lacustrine CO2 flux.
 The study lake, Valkea-Kotinen (61°14′ N, 25°04′ E) is situated within a nature reserve area in Evo, Southern Finland. Surface area of the lake is 0.041 km2 and maximum and mean depths are 6.5 m and 2.5 m, respectively. Details of the lake are given by Kankaala et al. , Vesala et al. , and Huotari et al. . The CO2 fluxes were measured with EC, as described by Vesala et al. , with some modifications in data postprocessing introduced by Nordbo et al. . Upward fluxes were defined to be positive representing net CO2 emission into atmosphere. Footprint modeling and data quality selection ensured that the measurements were representative of lake-atmosphere exchange [Vesala et al., 2006; Nordbo et al., 2011]. Due to advances in data postprocessing and quality control the flux estimates presented here for 2003 diverge slightly from those by Vesala et al. , and are regarded more reliable. Quality selection retained 10% of all measured CO2 fluxes in analysis. The percentage is quite low since we kept the quality criteria strict for this micrometeorologically non-ideal site [Vesala et al., 2006]. However, the amount of collected data is much larger than using traditional methods instead of the EC technique. The partial pressure of surface water CO2 (pCO2) was calculated from weekly samples of DIC and pH, using Henry's law. Temperature stratification in the lake was measured at least at hourly intervals at different depths and the strength of stratification was calculated as the Brunt-Väisälä stability frequency (Ns) between the surface water (0.2 m) and the depth of 1.5 m [see Huotari et al., 2009]. The precipitation data were provided by the Finnish Meteorological Institute and the DOC, DIC and pH was taken from the sampling of International Cooperative Programme on Integrated Monitoring of Air Pollution Effects on Ecosystems (ICP IM) [Keskitalo and Salonen, 1994]. All data were averaged over full calendar months from June to September, and from ice melt until 31 May (spring) and from 1 October until freeze over (autumn). The annual CO2 flux estimates were further integrated by multiplying the daily averages of the monthly periods by the number of days in the corresponding period and summing the periods during the year. The relationships between the pCO2 or CO2 fluxes and the chemical and physical variables measured by ICP IM were studied graphically, and using Pearson's correlation analysis. The dependences of the pCO2 and the CO2 flux on Ns and CO2 flux on pCO2 were studied, using monthly averaged values with curve estimation regression analysis. PASW Statistics 18.0.0 software (SPSS Inc., Chicago, IL, USA) was used for all the analyses.
3. Results and Discussion
3.1. Temporal Dynamics of CO2 Flux
 Lake Valkea-Kotinen was a source of CO2 to the atmosphere with a clear annual pattern in CO2 flux dynamics. Most of the CO2 was emitted to the atmosphere in late summer, when the thermocline was deepening, and during the autumn turnover in September-October (Figure 1). The mean daily CO2 fluxes (±SD) during these time periods were from 0.52 (±0.18) to 0.56 (±0.22) g C m−2d−1 (Figure 2), and they contributed together up to 77% of the annual fluxes. The time of ice melt and the following spring turnover, which was often incomplete and short, was also distinct in the annual pattern (Figure 1). As a consequence of the rapid vernal development of strong stratification, the contribution of spring turnover to annual fluxes was small. The mean daily CO2 flux in spring, averaged over the period from ice melt until 31 May, was 0.31 (±0.16) g C m−2d−1 (Figure 2), and the spring period contributed 13.4% (±6.3%) to the annual flux.
 The midsummer CO2 fluxes were usually small and were affected by sporadic physical events (Figure 1). In June and July, the fluxes were only 0.08 (±0.17) and 0.19 (±0.10) g C m−2d−1, respectively (Figure 2), and the surface water CO2 concentration was sometimes under atmospheric equilibrium, presumably as a consequence of vigorous primary production [Huotari et al., 2009]. Thus, during the summer months the lake acted occasionally as a CO2 sink, which is hardly ever reported for boreal polyhumic lake before. However, sporadic bursts of CO2, comparable to fluxes during turnover, were also detected. They were associated with event-type deepenings of the epilimnion due to convection [cf. Eugster et al., 2003] after cooling of the air and sometimes a simultaneous increase in wind speed or precipitation. The summer bursts of CO2 in 2004 may also have resulted from extreme rain events flushing CO2 from the catchment, as reported from a nearby larger lake [Ojala et al., 2011]. Due to differences in data quality screening night time influx into the lake in summer evidenced by Vesala et al.  could not be detected in this study. In general, the fluxes in June and July had only a small annual contribution (2.5% ± 5.7% and 7.5% ± 4.0%, respectively).
 The CO2 flux was best explained by pCO2 (Figure 3). The pCO2 and consequently the CO2 flux were clearly dependent on the strength of stratification in the water column, i.e., the more stable the stratification the lower the pCO2 (Figure 3) and the flux (R2 = 0.341, P = 0.001, n = 30). Due to the high DOC concentration and rapid light attenuation, the euphotic zone and the mixing depth were restricted during stratification within the top 1-m layer, below which there was a large storage of CO2 [Vesala et al., 2006; Huotari et al., 2009]. Hence, when the mixing depth increased, resulting from a decreasing Brunt-Väisälä frequency, CO2 was supplied from the metalimnion to the surface. Simultaneously, the planktonic primary producers were mixed deeper in the water column, which deteriorated their light climate and hence productivity, i.e., uptake of inorganic carbon decreased. Stratification determined how the biological activity was reflected in the surface water CO2 concentration and thus, physical rather than biological processes had the immediate control over the surface water CO2 concentration in Lake Valkea-Kotinen [Huotari et al., 2009] and, further, over the flux to the atmosphere.
 The annual fluxes were 97, 74, 74, 74 and 68 g C m−2yr−1 in 2003, 2004, 2005, 2006 and 2007, respectively. The differences between the annual fluxes in Lake Valkea-Kotinen were small and only the efflux in 2003 was slightly higher. This may have been due to the longer winter in 2002–2003, since in autumn 2002 the lake froze over 1 month earlier than normally, and the ice melt occurred rather late in spring 2003. Thus, a month's efflux from autumn 2002 was trapped below the ice cover and evaded in 2003. The date of freeze-over was more variable than the time of ice melt, and thus the length of the ice-covered period determined how large an efflux was transferred to the next year, i.e., there was a positive correlation between the annual fluxes and the length of the preceding ice-covered period (R = 0.994, P = 0.001, n = 5). The lake water DOC concentration or precipitation did not explain the fluxes, although summer 2004 was very wet as a consequence of which the DOC concentration increased by one third, i.e., monthly averages were 12.6 in 16.9 mg L−1 in June and August, respectively. However, mineralization of the DOC of allochthonous origin is slow [e.g., Wetzel, 2001] and the stratification dynamics determined when the CO2 produced was released. The highest daily flux (0.96 g C m−2d−1) was recorded in August 2005 and probably resulted from mineralization of the DOC already flushed to the lake in 2004.
3.2. Direct Flux Measurements Versus Modeled Flux
 The mean annual flux over the 5-year measuring period was 77 (±11 SD) g C m−2yr−1. This value is lower than estimated with the gas flux model [Cole and Caraco, 1998] for a large sample of statistically selected lakes in Finland, where the CO2 flux from small lakes (<0.1 km2) was 102 g C m−2yr−1 [Kortelainen et al., 2006]. Those estimates were based on only four samples of surface water CO2 per year, whereas the continuous measurements from Lake Valkea-Kotinen show that the annual course of CO2 flux is dynamic and partly behind sporadic events (Figure 1). On the other hand, our directly measured CO2 fluxes were higher than the values of 44 and 30 g C m−2yr−1 for Lake Valkea-Kotinen in 2005 and 2006, respectively [Huotari et al., 2009], which are based on continuous surface water CO2 measurements and calculated with the wind-based gas flux model [Cole and Caraco, 1998]. MacIntyre et al.  have suggested divergent wind-based gas transfer equations for times when lakes are cooling and when they are heating. We determined times of cooling and heating from the change in heat storage [Nordbo et al., 2011] and applied those equations to hourly averages of continuous surface water CO2 measurements for 2006 [Huotari et al., 2009]. This resulted in annual flux estimate of 60 g C m−2yr−1, i.e., much closer to EC values than attained with flux model of Cole and Caraco . Gas transfer coefficient (k600), computed according to Jonsson et al.  from the EC and the continuous surface water CO2 concentration data for the year 2006 [Huotari et al., 2009], was 1.5 times higher than obtained with the wind-based equation of Cole and Caraco  from Huotari et al. , i.e., 3.8 ± 0.8 cm h−1 vs. 2.5 ± 0.05 cm h−1 (±95% CI), respectively. Since the relationship between k600 and wind speed is nonlinear the wind-based models where the regressions are derived from data over longer periods of time, underestimate the importance of short-term changes in wind speed captured by the EC method [Cole et al., 2010]. Also other sources of turbulence besides wind shear, such as heat loss, enhance gas transfer across the air-water interface [MacIntyre et al., 2010] and most likely affected the results in the steeply stratifying Lake Valkea-Kotinen. Wind-based flux models may not adequately describe the gas transfer across the air-water interface and perhaps other models, such as surface renewal models would be better [MacIntyre et al., 2010]. However, these discrepancies emphasize the need of high-frequency flux measurements with EC to reveal the true flux dynamics and to accurately estimate annual CO2 fluxes.
3.3. Regional Importance
 The mean annual CO2 flux of 77 g C m−2yr−1 is almost 30 times higher than the long-term (postglacial) carbon accumulation rate of 2.8 g m−2yr−1 determined from sediment core samples of Lake Valkea-Kotinen [Pajunen, 2004]. The flux per unit area of the catchment, which can be used when assessing the importance of a lake as a site for remineralization of terrestrial carbon, is 11 (±1.4 SD) g C m−2yr−1. The published values of NEP for the unmanaged boreal forests corresponding to the annual temperature and precipitation regime of Lake Valkea-Kotinen range from −50 to 200 g C m−2 yr−1 [Luyssaert et al., 2007] the mean value being around 100 g C m−2yr−1. This means that on average the CO2 flux from the lakes decreases the carbon sink of natural forests by 10%. This being valid for the whole boreal zone, the carbon sink in boreal forests [Hari et al., 2008] would be in order of magnitude of 100 Tg C yr−1 smaller than assumed. However, in the managed forested catchments in the boreal zone the carbon loss to the atmosphere through lakes is estimated to be considerably less, i.e., 1–4% of terrestrial net ecosystem exchange [Jonsson et al., 2007; Ojala et al., 2011].
 The long-term record of direct ecosystem-scale CO2 flux measurements in a lake illustrates a substantial natural leakage of terrestrially fixed carbon back to the atmosphere through aquatic conduits. Global change in terms of higher temperatures and precipitation [Intergovernmental Panel on Climate Change, 2007] will increase lateral carbon transport and, e.g., the total organic carbon flux in the outlet brook of Lake Valkea-Kotinen is predicted to increase up to 26% by the 2050s [Holmberg et al., 2006]. Thus, the importance of inland waters as conduits of terrestrial carbon to the atmosphere will increase. Global change also alters the stability of the water column, which was shown here to be crucial for gas fluxes. Increased DOC together with higher temperatures strengthens the stratification in lakes, which results in lower summertime fluxes, but since total carbon loadings will be higher, the annual CO2 efflux presumably increases.
 Warmer autumns already increase CO2 loss from terrestrial ecosystems in northern latitudes [Piao et al., 2008; Vesala et al., 2010]. Supposedly, the loss of terrestrial carbon through lakes is also enhanced, due to warmer autumns, which emphasizes the role of autumns in the annual pattern of the CO2 flux. Nevertheless, these results based on the most reliable and direct measuring technique available suggest that natural inland waters are an integral part of terrestrial carbon cycling and hence must be taken into account in balance calculations and when considering the strength of regional as well as global terrestrial carbon sinks [Hope et al., 2001; Luyssaert et al., 2007; Battin et al., 2008]. Besides the importance of autumn for the fluxes, the results also highlight physical phenomena rather than biological processes as the drivers. The flux model must be chosen with great care in situations when direct flux measurements cannot be made. The obtained results can also be used in representations and parameterizations of the lake-atmosphere CO2 exchange in Earth system models.
 This study was funded by the Academy of Finland, projects TRANSCARBO (1116347), FASTCARBON (130984), 213093 and the Centre of Excellence programme (project 1118615) and ICOS (projects 137352 and 141518); EU projects GHG-Europe, IMECC and ICOS; TEKES and Vaisala Oyj through project CO2EKO. We thank the Finnish Meteorological Institute for providing the precipitation data. Rob Striegl and two anonymous reviewers are acknowledged for their valuable comments that improved the paper. Pasi Ala-Opas is acknowledged for his help in the field.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.