Diel Variability of CO2 Emissions From Northern Lakes

Lakes are generally supersaturated in carbon dioxide (CO2) and emitters of CO2 to the atmosphere. However, estimates of CO2 flux ( FCO2 ) from lakes are seldom based on direct flux measurements and usually do not account for nighttime emissions, yielding risk of biased assessments. Here, we present direct FCO2 measurements from automated floating chambers collected every 2–3 hr and spanning 115 24 hr periods in three boreal lakes during summer stratification and before and after autumn mixing in the most eutrophic lake of these. We observed 40%–67% higher mean FCO2 in daytime during periods of surface water CO2 supersaturation in all lakes. Day‐night differences in wind speed were correlated with the day‐night FCO2 differences in the two larger lakes, but in the smallest and most wind‐sheltered lake peaks of FCO2 coincided with low‐winds at night. During stratification in the eutrophic lake, CO2 was near equilibrium and diel variability of FCO2 insignificant, but after autumn mixing FCO2 was high with distinct diel variability making this lake a net CO2 source on an annual basis. We found that extrapolating daytime measurements to 24 hr periods overestimated FCO2 by up to 30%, whereas extrapolating measurements from the stratified period to annual rates in the eutrophic lake underestimated FCO2 by 86%. This shows the importance of accounting for diel and seasonal variability in lake CO2 emission estimates.

, may lead to higher lake CO 2 emissions as more carbon is exported to and processed within these lakes. CO 2 fluxes across the water surface ( CO 2 E F ) in lakes is controlled by the difference in CO 2 concentration between the surface water (here expressed as partial pressure, pCO 2aq ) and atmosphere, and the gas transfer velocity (k) across the air-water boundary layer. Both pCO 2aq and k depend on processes that can have diel fluctuations. Primary production (PP) consumes CO 2 , reducing pCO 2aq during daytime, and respiration (R) at night can increase pCO 2aq ; Temperature declines, frequently occurring at night, facilitate convection which generates near-surface turbulence enhancing k and bringing CO 2 -rich water from depths to the surface (Czikowsky et al., 2018;Heiskanen et al., 2014;Liu et al., 2016;MacIntyre et al., 2010). Furthermore, winds may influence both k and pCO 2aq by influencing surface water turbulence, sediment pore water exchange or upwelling (Crill et al., 1988;Czikowsky et al., 2018;Heiskanen et al., 2014). When winds are similar both day and night, enhanced fluxes from the increased concentrations will usually occur at night (Liu et al., 2016); in contrast, when winds are higher in the day, the enhanced fluxes will usually occur in the day (Czikowsky et al., 2018).
Despite the many factors that have potential to influence diel variability of pCO 2aq and k and thereby also CO 2 E F , most estimates of CO 2 E F rely on daytime sampling of pCO 2aq or flux measurements, and it remains common to extrapolate such measurements to full 24 hr CO 2 E F . In cases where both daytime and nighttime fluxes have been estimated, observations have usually been made within one or a few 24 hr periods in single systems (Natchimuthu et al., 2014;Reis & Barbosa, 2014;Xiao et al., 2014), whereas studies covering diel variability over longer periods during seasonal stratification and mixing in lakes are rare (e.g., Amaral et al., 2020;Spafford & Risk, 2018). Hence, more extensive studies of diel variability in CO 2 E F are needed, where lakes are examined for multiple days across seasons.
Monitoring of direct CO 2 E F at high temporal resolution and for periods of weeks or months is almost exclusively made using eddy covariance (EC) (Franz et al., 2016;Jammet et al., 2017;Jonsson et al., 2008;Liu et al., 2016;Mammarella et al., 2015;Podgrajsek et al., 2015;Shao et al., 2015), which covers larger areas than flux chambers but depend on assumptions of homogeneous surface roughness and air movement (Aubinet et al., 2003). Additional challenges with EC remain for the large number of small boreal lakes. These lakes are often wind sheltered by surrounding trees, resulting in heterogeneous air movements across the lakes and in difficulties to separate CO 2 E F originating from the lakes with those originating from surrounding land (Kenny et al., 2017;Sahlée et al., 2013). Hence, supplementary studies of temporal variability using flux chambers would be beneficial to assess diel CO 2 E F variability of well-defined areas in boreal lakes.
Here, we present measurements of diel variability in CO 2 E F and the influence of potential factors influencing the fluxes in three contrasting boreal lakes, using high temporal resolution measurements with automated flux chambers (Thanh . We measured CO 2 E F at multiple locations in each lake, generating in total 3,361 CO 2 E F observations over 121 24-hr periods. Measurements were made during periods of stratification in all three lakes as well as during autumn mixing in the most eutrophic lake, where we investigated the role of diel variability before and after mixing. Additionally, we compare our results with previous research and assess the importance of diel variability and autumn mixing in estimates of annual CO 2 emission.

Studied Lakes
Three lakes were studied ( Figure 1; Table S1). Venasjön (VEN; 58°27′22.61″N, 16°11′11.54″E) is a eutrophic lake [trophic state based on total phosphorous (Carlson, 1977)] situated in south-eastern Sweden in the transition between the temperate and boreal zones. It has mean and maximum depths of 5.4 and 10.5 m, respectively, and lake and catchment areas of ∼69 and ∼17,000 ha. The lake has a permanent inlet which drains farmland on its western side. Parsen (PRS; 58°20′25.7″N, 16°12′15.2″E) is a mesotrophic lake located in the same region as VEN, with mean and maximum depths of 3.4 and 8 m, respectively, and lake and catchment areas of ∼13 and ∼140  to Text S1. In LJU, sampling of CO 2 E F was done with AFCs during 2017 between July 11 and August 22. The AFCs were constructed as described by Thanh , and consisted of floating chambers made of round, plastic buckets (8.6 L volume, 31 cm diameter) covered with alumina tape to minimize internal heating, and attached to a control box. The control box regulated a pump maintaining ventilation of the chamber every second or third hour to restart measurements. By pumping air into a rubber bladder attached to the chamber, the bladder was inflated which lifted one side of the chamber from the water and allowed air to ventilate the chamber headspace. CO 2 concentration, temperature and humidity inside the chamber headspace were recorded each minute with a Senseair K33 ELG sensor located inside each chamber as described by Bastviken et al. (2015). Prior to being used in the AFCs, sensors were calibrated with nitrogen-gas according to manufacturer's instructions (zero calibration). Fluxes were based on relative changes in CO 2 concentration, and were therefore not sensitive to moderate sensor drift or differences in absolute values among sensors. The AFCs transmitted data to a server located at the lakes, allowing for data retrieval without the need to visit the chambers.
AFCs were distributed to cover off-shore and near-shore parts of the lakes (Figure 1). Six, five, and four AFCs were used in VEN, PRS, and LJU, respectively. In VEN, the AFCs were concentrated in the western bay, and in PRS they were located in the northern bay. In LJU, the AFCs were divided equally between the two basins. Additional AFCs were deployed to cover the off-shore pelagic zone in LJU (not shown in Figure 1), but CO 2 measurements in these AFCs were malfunctioning during the sampling campaign. As a result, CO 2 E F in LJU may not be representative of the pelagic zone.

Weather
Meteorological data (atmospheric pressure and temperature, relative humidity, precipitation, wind speed, wind gust speed, and wind direction) were retrieved from Swedish Meteorological and Hydrological Institute (SMHI), through their meteorological analysis model MESAN, which combines a meteorological model and interpolations from existing weather stations using a technique called optimal interpolation to determine meteorological variables on a 2.5 × 2.5 km grid for hourly intervals (Häggmark et al., 2016). The MESAN model uses data measured at 10 m above the surface, and the closest weather stations used in the interpolations are located around 15, 21, and 25 km from VEN, PRS, and LJU, respectively. Wind speed is sampled as 10 min averages, and wind gust speed is defined as the maximum wind speed within 2-s interval.
Hourly averages of wind speed and wind gust speed data compared reasonably well with measurements from anemometers located at the lake center in PRS (September 27-December 6, 2018; R 2 wind speed = 0.74-0.81, R 2 wind gust speed = 0.77-0.87; Figure S1) and at the lake center of the northern basin in LJU (September 2-October 27, 2019; R 2 wind speed = 0.65-0.78, R 2 wind gust speed = 0.77-0.87; Figure S1). We did not have measurements to compare at VEN. Due to differences in magnitude between wind speed at 10 m height and at lake level (slope wind speed = 0.45-0.67, slope wind gust speed = 0.39-0.46; Figure S1), wind speed measurements have been z-normalized in all figures, and we refer to relative differences in wind speed and wind gust speed in the text. Values of photosynthetically active radiation (PAR) were retrieved from SMHIs model STRÅNG, which uses input from MESAN to provide solar radiation estimates on a 2.5 × 2.5 km grid.

DIC
DIC was sampled from vertical profiles, including near the surface (∼0.1 m depth), at monthly intervals during the open water season in all lakes. The samples were collected at the deepest spot in the lakes with a maximum distance of 2 m between each sample. In VEN and PRS, additional surface water DIC samples were collected at 12 locations 2-3 times during the same week as the profile samples were collected. Surface water DIC was sampled by transferring 4 or 5 mL of water from ∼0.1 m depth to a 22 mL and N 2 -filled vial holding 100 μL concentrated phosphoric acid, and samples were stored at 20°C until gas analysis. The sampling procedure for vertical profiles and surface water and the calculation of DIC concentration is described in Text S2.

CO 2 in Surface Water and Air
Samples of surface water CO 2 concentration (or its equivalent partial pressure; pCO 2aq ) were collected manually each month in the open water season at seven locations in VEN and PRS. A headspace equilibration method was used where 105 mL surface water was equilibrated with 35 mL of air, and the equilibrated headspace was transferred to a dry vial and stored at 20 C until analysis. pCO 2aq was then calculated by accounting for extraction volumes and temperature. The sampling procedure and calculation of pCO 2aq is described in Text S3.
In LJU, surface pCO 2aq was measured manually at monthly intervals with a CO 2 -sonde (Vaisala GMP222), calibrated for temperature and pressure according to Johnson et al. (2010) before the field campaign.
Automated sampling of surface pCO 2aq was made every minute using CO 2 sensors (Senseair K33 ELG, Sweden) in chambers that were closed at all time (in contrast to AFCs which were ventilated regularly) and allowed to equilibrate with the water, as described by Bastviken et al. (2015). The equilibration time in the closed chamber is subject to a delay, which depends on the air-water transfer rate of CO 2 . Due to the uncertainty of this delay, surface pCO 2aq measured this way was averaged for whole daytime and nighttime periods rather than for shorter time periods with awareness that the delayed response will lead to underestimation of day-night differences. This delay in equilibration time prevented us from calculating pCO 2aq from AFC concentration measurements, since equilibration was rarely reached within the 2-hr or 3-hr chamber closure times. Therefore, AFCs were only used for measuring CO 2 E F .

Surface Water pH
Surface water pH was derived indirectly from concentration of surface CO 2aq and DIC in VEN and PRS, as described in Text S3.

Surface Water O 2
Dissolved surface water O 2 (DO) was measured in PRS and LJU using PME MiniDot loggers at 0.2 and 0.25 m depths, respectively. In PRS, sampling was made close to the deepest point and in LJU sampling was made at the deepest point of each basin.

Water Temperature
Temperature was measured manually and continuously in the surface water and at depth. Manual temperature measurements were collected at the deepest spot in the lakes, and at the deepest spot of each basin in LJU, at least every second meter in the water column. Measurements were made with multimeter-sondes (AP-5000 Aquaprobe in VEN and PRS and YSI ProODO in LJU) and were done monthly in VEN and PRS. In LJU, measurements were done once before and twice during and after the CO 2 E F sampling campaign.
In VEN, continuous temperature measurements were made at ∼0.1 m and at four additional depths (1.5, 3, 4.5, and 5.5 m), in the middle of the western bay. HOBO U22-001 thermistors (Onset, USA) were used for all depth except at the water surface, where a light shielded RBRSolo 2 thermistor (RBR, Canada) was used. All thermistors were connected to a taut-line mooring. In PRS, continuous temperature measurements were made the same way as in VEN, but at different depths (0.1, 1, 2, 3, and 3.8 m) in the middle of the northern bay. In LJU, continuous temperature measurements were made at four depths (0.25, 2.5, 5, and 7.5 or 8 m) at the deepest point of the two respective basins, using PME MiniDot loggers.

Gas Analysis
Analysis of gas samples from VEN and PRS were made with a Agilent 7890A GC (Agilent Technologies, USA, equipped with a 1.8 m × 3.175 mm Porapak Q 80/100 column from Supelco, and a flame ionization detector) through automatic injection, with a 7697A headspace sampler (Agilent Technologies, USA) attached. Serially diluted certified high concentration standard (50,000 ± 1,000 ppm), and an independent certified standard of 1,985 ± 40 ppm were used for calibration. Before loading the GC for analysis, vial overpressure was removed by inserting a 0.5 mL hypodermic needle connected to a water-filled 60-mL syringe. This setup made it possible to account for potential gas leakage during storage. Analysis of samples in LJU was made with a Clarus 500 GC (Perkin Elmer, USA, equipped with a 30 m × 0.53 mm Elite-Q PLOT column from Perkin Elmer and a flame injection detector) through automatic injection, with a TurboMatrix 110 headspace sampler (Perkin Elmer, USA) attached. CO 2 standards of 410 and 9420 ppm were used for calibration.

Calculation of F CO 2
Following retrieval of CO 2 data from the AFCs (in ppm) and prior to calculating CO 2 E F , the data were filtered to account for humidity peaks, as described by Bastviken et al. (2015). Additional filtering was made to account for sensor issues related to unlikely concentration shifts and vapor condensation inside the measurement cell, as described in Text S4.
For each period when the AFCs were closed (i.e., between periods of ventilating), linear regressions were made for different subsets of the CO 2 data. Slopes were calculated from the regressions that had highest R 2 , as described in Text S4. Cases, when the R 2 of the highest slope was <0.9, were only considered if the RMSE was below 5 ppm in order to not discriminate against small fluxes, as R 2 decreases when the slope approaches zero. The slopes, corresponding to change in CO 2 mole fraction over time (ppm s −1 ), were converted to mmol m −2 h −1 by applying the ideal gas law, dividing with the area of the chamber, A (m 2 ), and multiplying with 3.6 × 10 3 as a conversion factor from second −1 to hour −1 , see Equation 1. The total barometric pressure, P (atm) was derived from the MESAN model, whereas air temperature, T (K), was measured directly with the CO 2 sensor. Volume, V (m 3 ), represents the chamber headspace, and R is the ideal gas constant, 8.21·10 −2 (L atm K −1 mol −1 ).
The concentration measurements that passed the filtering criteria mentioned above were used to derive 3,361 estimates of CO 2 E F . Of these estimates, 4.2% were discarded in VEN bef and <1% in VEN aft , PRS, and LJU due to low R 2 and high RMSE, resulting in a total of 3,303 CO 2 E F estimates that were used for analysis (n VENbef = 1,150; n VENaft = 446; n PRS = 402; n LJU = 1,305).

Diel Variability of F CO 2
We have defined daytime and nighttime from sunrise and sunset, where each 24 hr period started with a sunrise and ended with a sunrise the consecutive day. The length of daytime and nighttime varied between lakes due to differences in latitude and sampling times. In VEN, sunrise and sunset were (rounded to closest hour) between 04:00-07:00 and 19:00-22:00, in PRS between 07:00-08:00 and 17:00-19:00 and in LJU between 03:00-05:00 and 21:00-23:00, meaning that daytime periods made up 12-18, 10-12, and 16-20 hr for each 24 hr period in VEN, PRS, and LJU, respectively.

CO 2
We estimated annual CO 2 E F in VEN, where we sampled CO 2 E F during both the seasonally stratified period and the period of autumn mixing. Diel variability was first accounted for within the seasonally stratified and mixed periods, respectively. Measurements of 24 hr CO 2 E F made within each specific sampling period (seasonally stratified or mixed) were extrapolated to the full open-water season. The ice-covered periods were estimated from observations during fieldwork and air temperature measurements and were not considered in the annual estimate (details in Text S1). Our estimate of 24 hr mean CO 2 E F from measurements made during the seasonally stratified period was extrapolated to the whole period of seasonal stratification. Our estimate of 24 hr mean CO 2 E F measured within the period of autumn mixing was extrapolated according to two different scenarios-(a) to the period of full lake mixing in autumn alone and (b) to the period of full lake mixing in autumn and spring (assuming similar patterns of CO 2 E F in spring as in autumn), resulting in an estimate of minimum and maximum contribution of CO 2 E F during the period of seasonal lake mixing. These scenarios may be conservative, as the spring mixing period itself has been found to contribute to the highest annual CO 2 evasion rates in arctic lakes (Kling et al., 1991), contributing up to more than half of annual CO 2 E F (Karlsson et al., 2013).

Comparison With Other Studies
We compared our estimates with other studies that included measurements of CO 2 E F during both days and nights (Table S2). Daytime and nighttime were defined differently between studies but were often based on sunrise and sunset, or metrics that followed diel patterns. In studies where multiple methods (floating chambers, eddy-covariance, or k-models) were used (Czikowsky et al., 2018;Erkkilä et al., 2018), we averaged daytime and nighttime results separately for each method and considered whether the lake was seasonally stratified or mixed.

Statistical Analysis
All calculations, data handling, plotting and statistical testing was made using Python 3.7. Reported R 2 -values are modified according to the number of predictors in the model (adjusted R 2 ). P-values below 0.05 have been considered statistically significant to reject null-hypotheses.
To test for significant day to night differences, the two-tailed non-parametric Wilcoxon ranked-sum test was applied. Bi-variate and multiple regression analyses were made to distinguish factors related to diel variability of CO 2 E F and were carried out using Python package sklearn (sklearn. linear_model.LinearRegression), and p-values for regressions were derived using the two-tailed Spearman rank-order correlation (scipy.stats. spearmanr).

CO 2 Exchange
CO 2 E F was continuously monitored for 1-2 months in each lake (Figure 2) together with additional measurements (DIC, pCO 2aq , pH, DO and temperature; measured the whole open-water season. See Section 2, Figures S2 and S3 for details). Autumn mixing occurred in VEN from September 11 to 13, resulting in an increase in CO 2 E F (Figure 2a), whereas PRS and LJU were partly stratified for the full sampling period and are regarded as stratified lakes.
All lakes were net sources of CO 2 to the atmosphere during the sampling campaigns based on the areal cumulative flux (Figure 3a), and mean (±1 SD) 24 hr CO 2 E F was estimated as 5.3 ± 17.1, 76 ± 26.2, 24.3 ± 11.4, and 9.9 ± 3.2 mmol m −2 d −1 in VEN bef , VEN aft , PRS, and LJU, respectively. The rates are within the range of estimates from 96 inland waters (lakes, reservoirs, ponds) in Sweden, Norway and Finland, compiled by Natchimuthu et al. (2017) (range: 0.4 and 71.8 mmol m −2 d −1 , mean: 21.7 mmol m −2 d −1 ). VEN bef was a sink if only considering measurements made in July and onwards, where net uptake of CO 2 was observed in more than half of the 24 hr periods (Figure 2). This is similar to what has been observed elsewhere, where CO 2 uptake occurred in the growth period in eutrophic lakes with high photosynthetic rates Natchimuthu et al., 2014;Shao et al., 2015). Apart from VEN bef , we only observed occasional uptake of CO 2 E F during daytime from individual measurements (Figure 2). CO 2 E F was most variable in VEN, where we observed five-fold greater  during the 13 days after autumn mixing than during 38 days of the stratification period (Figure 3a).

Diel Variability of F CO 2
CO 2 E F during daytime (between sunrise and sunset) was higher than during nighttime (between sunset and sunrise) in VEN aft , PRS, and LJU (Table 1; Wilcoxon signed-rank test, p < 0.05), but no corresponding difference was observed in VEN bef (p = 0.15). The lack of diel variability in VEN bef was likely due to its near-equilibrium levels of surface pCO 2aq ( Figure S2a) Note. Daytime and nighttime CO 2 E F mean (±1 standard deviation), median (med) and range for the studied lakes including before and after autumn mixing in VEN, statistical difference (Stat.diff) between daytime and nighttime CO 2 E F (Wilcoxon signed-rank test; * = p < 0.05, ** = p < 0.01, *** = p < 0.001), total number of 24 hr periods with diel CO 2 E F measurements (n 24 hr ), and total number of CO 2 E F measurements (n obs ).

Influence of Environmental Factors on Diel F CO 2 Variability
CO 2 E F and incident PAR, wind speed, wind gusts, air temperature (T), and air:water temperature ratio (T r ) were all higher during daytime, except for in VEN bef where CO 2 E F did not have clear diel patterns ( Figure 5).
Continuous measurements of pCO 2aq , which were limited to LJU, did not show significant differences between daytime and nighttime (p = 0.16). Furthermore, we did not observe correlation between CO 2 E F and surface water DO in PRS and LJU. The mean day-night differences in surface water DO were low (0.05 and 0.07 mg L −1 ) and corresponded to only 0.6% and 0.8% of variation from the 24 hr mean DO in PRS and LJU, respectively ( Figure S6). In VEN, only occasional manual DO measurements were available, preventing direct comparisons between variability of diel CO 2 E F and diel DO. However, we observed that surface water DO in VEN went from being supersaturated 14 days before autumn mixing (105%; 9.8 mg L −1 ) to unsaturated 16 days after autumn mixing (83%; 8.7 mg L −1 ).
Bivariate linear regressions with the day-night differences for CO 2 E F (Δ CO 2 E F ) and other variables measured at high enough resolution to resolve day-night differences, had strongest relationships with day-night differences in wind gust speed (ΔWGS) and in wind speed (ΔWS), particularly in wind-exposed VEN aft , where they explained 82% and 77% of Δ CO 2 E F variability ( Figure S5). In PRS, the contribution from ΔWGS and ΔWS was lower, explaining 31% and 39% of Δ CO 2 E F variability. In LJU, only ΔWGS was significant, explaining 28% of Δ CO 2 E F variability. Adding additional variables to ΔWS and ΔWGS did not increase model performance except for in PRS, where addition of wind direction to the ΔWS model increased the degree of explanation of Δ CO 2 E F variability by 10%. The fact that wind gust speed was more relevant than wind speed for explaining diel CO 2 E F patterns in VEN aft and LJU is interesting, since CO 2 E F is usually modeled from wind speed rather than wind gust speed (Cole & Caraco, 1998;Heiskanen et al., 2014;Wanninkhof, 1992). Possibly, wind gusts were important for transferring kinetic energy to the water, thereby influencing water turbulence, and consequently k and CO 2 E F , more than average wind speed.For 24 hr periods where the day:night CO 2 E F ratio ( CO 2 F E R ) was above 1 (i.e., higher during day), this coincided with periods of day:night WS ratio (R WS ) above 1 in 100%, 84% and 88% (or 12 of 12, 16 of 19, and 30 of 34) of the cases in VEN aft , PRS and LJU, respectively. The same analysis but for CO 2 F E R below 1 showed a degree of coincidence with R WS below 1 in 100%, 75% and 50% (or 1 of 1, 3 of 4, and 4 of 8) of the cases. This may imply a smaller influence from direct wind effects to drive CO 2 E F during nights than during days in stratified PRS and LJU, but the few 24 hr periods observed where R WS was below 1 makes it difficult to draw clear conclusions.
Although fluxes were typically higher in the daytime in agreement with wind speeds being, on average, higher in the day (Figure 5), in LJU we found several peaks in CO 2 E F during nighttime. These peaks were limited to local sampling locations and thereby more likely caused by upwelling of CO 2 than by convection, which would cause mixed layer deepening over much of the lake. One of these peaks (July 19 and 20; A1 in Figure 6) may have been caused by upwelling following changing wind directions from north-western to southern winds, and the enhanced mixing to at least 3 m depth. Two other peaks (July 25-27; A2 in Figure 6) coincided with a shift in nighttime wind direction from northern to southern winds, that is, shifting winds at nighttime from opposite to similar direction as winds during daytime. CO 2 E F increases were distinct in A2 even though daytime winds were below the measurement period average, and temperature stratification was less pronounced than during A1. Observed peaks in A1 and A2 resulted in a 5%-15% increase in sampling location mean CO 2 E F . It is noteworthy that such a small lake displays pronounced and local spatial variability in near-shore CO 2 E F . Our observations at LJU also correspond to observations in a similar lake under light to moderate winds (MacIntyre et al., 2021). That relations between Δ CO 2 E F and day-night differences of other environmental factors was less clear in LJU than in VEN, and PRS is compatible with the hypothesis that upwelling events may blur, otherwise, wind-driven patterns of diel CO 2 E F in small and wind-sheltered boreal lakes.
Changes in DO and pCO 2aq can be used to interpret alterations in the balance between respiration (R) and primary productivity (PP), where the former consumes O 2 and produces CO 2 and the latter consumes CO 2 and produces O 2 . The unsaturated surface water DO observed in VEN aft and the small day-night DO variability in PRS and LJU indicate higher R than PP, and the higher daytime than nighttime CO 2 E F in these lakes implies that PP had limited influence on CO 2 E F . However, the observed DO supersaturation in VEN bef is in accordance with the near-equilibrium pCO 2aq levels, showing that PP was higher and could explain the low or even negative daytime CO 2 E F observed there. Decreased PP relative to R may also lead to lower pH, and mean pH did decline from 7.9 to 7.5 between sampling occasions half a month before and after mixing, respectively (n = 28; Figure S2a). Decreased PP following lake mixing is logical due to shorter daylight time and deeper mixing, reducing the mean light exposure in the mixed surface water layer. The lack of clear diel CO 2 E F variability in VEN bef may imply that PP, when being large enough to deplete pCO 2aq to levels of near-atmospheric equilibrium, can reduce diel variability in CO 2 E F compared to situations when surface waters are highly supersaturated with CO 2 .

Change in DIC After Autumn Mixing
The onset of autumn mixing in VEN mixed DIC from deeper to shallower waters ( Figure S3a) and can explain higher CO 2 E F in VEN aft , in line with previous findings López Bellido et al., 2009;Riera et al., 1999;Striegl & Michmerhuizen, 1998). The increase in CO 2 E F after mixing implies loss of DIC in terms of CO 2 release to the atmosphere, but we found that total amount of lake DIC increased by 3% half a month after compared to before autumn mixing ( Figure S7). This was unexpected, especially as we calculated (according to Text S5) this half month of post-mixing CO 2 E F to amount to 25% of the total DIC amount. The DIC necessary to support both losses through emission and the increased DIC amount after autumn mixing seems to have been compensated by either DIC formation from in-lake net R, DIC input from the catchment or lateral exchange of DIC from littoral regions of the lake. We did observe increased precipitation during late summer and autumn in VEN (Figure 2), which may have resulted in DIC input from the catchment . It is also known that mixing can reduce light for primary producers, favoring R over PP (Rõõm et al., 2014;Staehr & Sand-Jensen, 2007), which could contribute to the increase in DIC. The effect of this shift in metabolism on surface pCO 2aq is usually difficult to separate from the effect of deep water CO 2 mixing to surface waters, as they occur simultaneously Hanson et al. (2016). Nevertheless, here we find that DIC alterations after autumn mixing cannot be explained by autumn mixing alone, and that shifts in metabolism or DIC export from catchments to lakes may increase CO 2 E F on an annual basis despite summertime surface water CO 2 depletion by primary productivity (Maberly et al., 2013).The increase in DIC amount after autumn mixing in VEN and the supersaturation of pCO2 aq during most of the measurement periods thereafter ( Figure S2a), implies that CO 2 E F may be elevated for weeks to months after autumn mixing in eutrophic systems. Such systems often have high alkalinity and a pH above 6.5 (Balmer & Downing, 2011), resulting in a large pool of HCO 3 − serving as a reservoir from which CO 2 is formed following losses by emission (Stumm & Morgan, 1996). In eutrophic lakes, upwelling of DIC-rich deep water may therefore contribute to a disproportionally high share of the annual CO 2 E F (Riera et al., 1999;Striegl & Michmerhuizen, 1998), as in VEN illustrated by the larger cumulative CO 2 E F after than before autumn mixing (Figure 3e).

Comparison With Other Studies
We compared our results on diel variability with 29 published estimates of diel CO 2 E F within 16 studies, covering 11 lakes, 1 reservoir and 4 ponds (  (Figure 7), allowing for comparisons between methods and seasonally stratified and mixed systems. For easier interpretation, only estimates where daytime and nighttime CO 2 E F were of the same direction have been compared (i.e., data from all systems except one).
Day:night CO 2 E F ratios were higher for measurements made using floating chambers (FCs) or models compared to when EC was used (1.26 ± 1.18; range 0.042-3.2, and 0.89 ± 0.4; range 0.34-1.57, respectively). For estimates derived using FCs and models (n = 17), higher mean day:night CO 2 E F ratio have been reported in 10 cases (five mixed system, four stratified systems, and one full-year estimate). In contrast, estimates made using EC (n = 12) report higher nighttime mean CO 2 E F in all but two cases (one mixed system and one full-year estimate). This difference implies there may be systematic methodological differences that need to be accounted for. Disagreements between methods have been observed previously (Anderson et al., 1999;Czikowsky et al., 2018;Erkkilä et al., 2018;Eugster, 2003), and EC results may have been affected by differences in footprint size and location and/or in lateral air transport patterns between daytime and nighttime (Kenny et al., 2017;Sahlée et al., 2013). Nevertheless, studies reporting diel CO 2 E F variability are relatively rare, and it is possible that differences reported here reflect natural variability. More studies on diel flux variability are needed to evaluate potential methodological differences.
We found lower mean day:night CO 2 E F ratios for stratified (n = 8) than mixed (n = 7) systems (1.08 ± 0.59; range 0.34-2.14, and 1.43 ± 0.35; range 0.75-1.91). This compares well with day:night CO 2 E F ratios in seasonally stratified VEN bef and mixed VEN aft (1.08 and 1.67). Day:night CO 2 E F ratios in PRS and LJU (1.5 and 1.4) were also within the range of other studies (Figure 7). It should be noted that eutrophic systems are overrepresented in these studies, and few may have the high DOC and pCO 2aq levels that are common in northern lakes globally (see Table S2). The difference in diel variability between mixed and stratified systems demonstrates the importance of sampling both before and after seasonal mixing events to account for  (Balmer & Downing, 2011;Lazzarino et al., 2009) accounting for seasonally stratified and mixed periods as above, but only using daytime measurements (between sunrise and sunset) or measurements made between the morning and late afternoon (08:00-16:00), overestimates total fluxes by 21%-22% and 28%-30%, respectively. Hence, it may be crucial to account for both seasonal mixing and the diel patterns when estimating long-term CO 2 E F .
From our results of diel variability in CO 2 E F in VEN aft , PRS, and LJU (Table 1), we suggest a 1.5 times higher mean CO 2 E F from 0800 to 1600 than over the rest of the 24 hr period. From this, we derived a conversion factor (CF 24 hr ) of 0.83 to convert CO 2 E F obtained from morning to late afternoon hours to full 24 hr estimates: Figure 7. Comparison of estimated mean day:night CO 2 E F ratios among studies. Classification is by trophic state, method used eddy covariance (EC), floating chambers (FC), models from pCO 2aq measurements, and modeled gas transfer (MOD) (Cole & Caraco, 1998;Heiskanen et al., 2014;Tedford et al., 2014), coverage of stratification and mixing (sampling during seasonally stratified periods, mixed periods or both) and number of 24 hr periods measured. Estimates are sorted by latitude. The black line denotes the 1:  (Franz et al., 2016;Jammet et al., 2017;Jonsson et al., 2008;Podgrajsek et al., 2015;Reis & Barbosa, 2014;Shao et al., 2015) are displayed in Table S2.

CF
The large variability in diel CO 2 E F across studies (Figure 7) means that this conversion factor is not applicable for the full spectrum of boreal lakes. Instead, it can serve as way to facilitate comparisons with future studies. Such a conversion factor was recently proposed for methane (Sieczko et al., 2020) and represents an attempt to account for diel variability if diel data are missing.

Conclusions
Our results indicate that diel CO 2 E F variability can be expected in boreal lakes except when surface pCO 2aq is close to equilibrium with the atmosphere and generates small fluxes. In all cases where we observed daynight differences in CO 2 E F the pattern was similar, with daytime exceeding nighttime CO 2 E F with 40%-67% and with peaks in CO 2 E F observed between mornings and late afternoons (08:00-16:00), when sampling campaigns are generally conducted. We found that extrapolating such peak measurements to open-water periods may overestimate CO 2 E F with 28%-30%, demonstrating the importance of accounting for diel variability when calculating annual CO 2 E F .
Day-night variability in wind speed explained 77% and 39% of the day-night CO 2 E F variability in two of our lakes. In the smallest and most wind-sheltered lake, individual local peaks of CO 2 E F were observed at nighttime when winds were low indicating complex and local CO 2 E F variability, possibly induced by convection or upwelling. Additional work is needed to address such within-lake spatial variability of CO 2 E F .
In the eutrophic lake, an increase in diel CO 2 E F variability coincided with high and sustained CO 2 E F following post-autumn mixing which represented a more important part of the open-water CO 2 E F than the lower and variable fluxes observed during the longer stratified period. This raises concerns that CO 2 E F measurements in eutrophic lakes may not be representative of the annual flux and that eutrophic lakes, despite being net CO 2 sinks during summer, may in fact be considerable CO 2 sources over the whole open-water period.
For future sampling campaigns, we suggest that measurements are conducted during multiple days and nights in ways that include both seasonal stratification and mixing periods and different wind conditions to properly estimate CO 2 E F from lakes.