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.
Figure 1. Half-hourly CO2 fluxes over open-water periods of 2003–2007. Positive values indicate upward transport (emission). Capital letters M and F represent times of ice melt and freeze-over, respectively. Upward arrows represent bursts of CO2 during summer stratification in June-July, as discussed in the text.
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Figure 2. Seasonality of CO2 fluxes. Spring and autumn periods are from ice melt until 31 May and from 1 October until freeze-over, respectively. Vertical bars represent standard deviation.
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 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.
Figure 3. (a) Relationship between CO2 flux and surface water partial pressure of CO2 (pCO2); CO2 flux = 0.3921 ln (pCO2) − 2.3944. The pCO2 explained 45% of the variation in CO2 flux (P = 0.000). (b) Linear relationship between pCO2 and Brunt-Väisälä stability frequency (Ns), which is a measure of the strength of stratification. The relationship is in the form of pCO2 = −16 783 Ns + 1944.7. Ns explained 77% of the variation in pCO2 (P = 0.000). Each point represents a monthly average (n = 30).
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 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].