Interannual, summer, and diel variability of CH 4 and CO 2 e ﬄ uxes from Toolik Lake, Alaska, during the ice-free periods 2010 – 2015 †

Accelerated warming in the Arctic has led to concern regarding the amount of carbon emission potential from Arctic water bodies. Yet, aquatic carbon dioxide (CO 2 ) and methane (CH 4 ) ﬂ ux measurements remain scarce, particularly at high resolution and over long periods of time. E ﬄ uxes of methane (CH 4 ) and carbon dioxide (CO 2 ) from Toolik Lake, a deep glacial lake in northern Alaska, were measured for the ﬁ rst time with the direct eddy covariance (EC) ﬂ ux technique during six ice-free lake periods (2010 – 2015). CO 2 ﬂ ux estimates from the lake (daily average e ﬄ ux of 16.7 (cid:1) 5.3 mmol m (cid:3) 2 d (cid:3) 1 ) were in good agreement with earlier estimates from 1975 – 1989 using di ﬀ erent methods. CH 4 e ﬄ uxes in 2010 – 2015 (averaging 0.13 (cid:1) 0.06 mmol m (cid:3) 2 d (cid:3) 1 ) showed an interannual variation that was 4.1 times greater than median diel variations, but mean ﬂ uxes were almost one order of magnitude lower than earlier estimates obtained from single water samples in 1990 and 2011 – 2012. The overall global warming potential (GWP) of Toolik Lake is thus governed mostly by CO 2 e ﬄ uxes, contributing 86 – 93% of the ice-free period GWP of 26 – 90 g CO 2,eq m (cid:3) 2 . Diel variation in ﬂ uxes was also important, with up to a 2-fold (CH 4 ) to 4-fold (CO 2 ) di ﬀ erence between the highest nighttime and lowest daytime e ﬄ uxes. Within the summer ice-free period, on average, CH 4 ﬂ uxes increased 2-fold during the ﬁ rst half of the summer, then remained almost constant, whereas CO 2 e ﬄ uxes remained almost constant over the entire summer, ending with a linear increase during the last 1 – 2 weeks of measurements. Due to the cold bottom temperatures of this 26 m deep lake, and the absence of ebullition and episodic ﬂ ux events, Toolik Lake and other deep glacial lakes are likely not hot spots for greenhouse gas emissions, but they still contribute to the overall GWP of the Arctic. Vast amounts of organic carbon are stored in Arctic permafrost soils. With climate warming it can be expected that an increasing amount of that carbon is freed aspermafrostthaws, and canescapeto theatmosphere via gase ﬄ uxfrom lakes.Withthe  rst continuous eddy covariance  uxmeasurements overadeepArctic lake in Alaska we provide evidence that during the ice-free period the e ﬄ uxes of both CH 4 and CO 2 show pronounced diel and summer variations which are important, but no signs of episodic events with extremely high e ﬄ uxes during the ice-free period could be found. This is in agreement with earlier estimates made for the Arctic and emphasizes the fact that deeper Arctic lakes are not the water bodies to be most concerned about regarding carbon emissions; however, better estimates of gas  uxes from the shallow lake-shore zones of such lakes are still needed.


Introduction
Arctic regions contain a vast reservoir of organic matter preserved in permafrost, the permanently frozen ground in northern high latitudes. 1 With climate warming, thawing of permafrost and the associated exposure of its organic matter to decomposition has become a great concern as a positive but unwanted feedback of the Arctic to climate change. [2][3][4] The role of open water bodies in the Arctic, which cover about 12-14 percent of the land surface area of the Alaskan North Slope 5, 6 and up to 48% in some regions of Alaska, 7,8 has thus taken a prominent place in the estimate of greenhouse gas uxes from Arctic ecosystems. 9 In this paper, we present eddy covariance (EC) ux measurements of the two primary greenhouse gases (CH 4 and CO 2 ) obtained during six ice-free lake periods (2010)(2011)(2012)(2013)(2014)(2015). Because CH 4 effluxes have a climatic effect that is z34 times that of CO 2 effluxes 10 (on a 100 year time-scale, including positive climatic feedbacks), our interest was in how continuous CH 4 ux measurements over Toolik Lake change previous estimates of Global Warming Potential (GWP) from Arctic lakes that were based only on CO 2 ux measurements (e.g., Eugster et al. 2003 (ref. 11)), but without an estimation of CH 4 effluxes.
Based on reports of huge amounts of CH 4 emitted from some Arctic water bodies, [12][13][14][15][16] expectations have become high that many or most Arctic lakes are or could be strong sources of CH 4 , but also not everywhere. 17,18 With discrete sampling, e.g., biweekly surveys of CH 4 and CO 2 concentrations in lake surface waters or discrete short-term deployments of oating chambers to measure gas efflux at specic times, episodic events that could dominate daily or summer emissions would easily be missed or under sampled, particularly for CH 4 . 19,20 Missing such events would lead to biased results and underestimates of emissions, but could be circumvented by using a higher resolution method, such as EC. For example, signicant efflux events were observed during fall turnover 21 and aer a substantial storm 22 in two Swiss lakes using EC. In addition to episodic events, strong diel patterns 20,23-26 could affect estimates of gas uxes depending on when in the day samples were taken. Continuous monitoring techniques are essential for resolving such events. Furthermore, repeated measurements over several years at the same site, required for climatological studies, are limited in the Arctic.
Based on the rst long-term EC ux measurements from a deep Arctic lake, this paper addresses the question: what cyclical processes and which episodic events are most relevant for obtaining a defensible ice-free period estimate of CH 4 and CO 2 effluxes from a deep Arctic lake? It also provides the foundation for follow-up investigations of the underlying mechanistic functional relationships between these uxes and environmental drivers.

Study site
Measurements were made on Toolik Lake (68 37.830 0 N, 149 36.366 0 W, WGS84 datum) at 719 m asl, a relatively deep glacial lake (maximum depth z 26 m) with a surface area of 1.5 km 2 located on the tundra north of the Alaskan Brooks Range. Instruments were mounted on a oating platform that was moored at approximately the same location every year z 400 m from the nearest lake shore. Depth of the lake at this location was z12 m.
With the onset of snowmelt the ice on Toolik Lake begins to melt. Observations made in 2014 showed that the water arriving via overland ow and the main stream inlets initially ow over the thick ice sheet and gradually melt the ice from above along the shoreline, and then the ows move mainly under the ice and spread lakewide. 27 Once the ice sheet is sufficiently detached from the lake shores, stronger winds and associated waves can crack the ice, which then still covers most of the lake with oating chunks of ice that move around the lake as the wind shis between the two predominant wind directions from the south and the north. The physical forces at work are too strong for eddy covariance instrumentation to be out on the lake. Therefore, the placement of equipment on the lake was only possible when the largest ice chunks on the lake were less than a few square-meters and few in number, typically between mid to late June (Table 1).
Similar to the early-season conditions, the oat containing eddy covariance instrumentation had to be removed from the lake before any large ice areas had formed on the lake in the autumn. Ice-on aer the ice-free period was dened as the time when ice rst covered the entire lake until the following spring (i.e., temporary ice cover over night was not considered as the rst ice-on date). In this context it should be recalled that at this northern location the sun does not set from 23 May to 19 July, and thus "night" refers to the hours of day with lowest solar elevation angles. At the end of summers from 2010-2015, however, ice formation occurred later than observed in earlier years, and thus the platform was removed between 17 and 22 August for logistical reasons (Table 1).

Eddy covariance ux instrumentation
Flux measurements were made with a three-dimensional ultrasonic anemometer-thermometer (CSAT3, Campbell Scientic, Logan, UT, USA) in combination with a closed-path integrated off-axis cavity output spectrometer (ICOS) for CH 4 (FMA from Los Gatos Research, Inc., San Jose, CA, USA) and a nondispersive infra-red gas analyzer for CO 2 and H 2 O (Li-7000, Li-Cor Inc., Lincoln, NE, USA). The CSAT-3 was mounted horizontally on a tripod (Met One Instruments, Inc., Grants Pass, OR, USA) screwed to the oating platform in such a way that measurement height above the lake surface was between 1.29 m and 1.62 m above the water surface. Two intake hoses were placed next to the CSAT-3 sensor head to guide air to the FMA and Li-7000 analyzers. A TriScroll 300 vacuum pump (Agilent, Santa Clara, CA, USA) was used to reduce the cell pressure of the FMA to the nominal 137 Torr (183 hPa). The Li-7000 did not require a vacuum in the sample cell, which allowed use of a KNF Neuberger N920 pump. A 500 m submersible AC power cable was used to provide the instruments and pumps on the oat with mains power (120/240 V AC) from the power generator of Toolik Field Station (TFS). A step-up transformation of the voltage from 120 V AC to 600 V AC was necessary between lake shore and oat to satisfy the high power demand of the vacuum pump. The CH 4 ux measurements closely followed the technical setup described in detail by Eugster and Plüss. 28 The CO 2 ux measurements used the same data collection concept. This data collection system consisted of an embedded Linux computer system (MOXA UC7408 Plus; Moxa Americas, Brea, CA, USA) to which the CSAT-3, FMA, and Li-7000 were connected via RS-232 serial communication connections. The continuous data stream from the CSAT-3 was recorded at 20 Hz and was used as the master to which the data streams from the FMA and the Li-7000 were merged in near real-time as described by Eugster and Plüss. 28 The system clock of the Linux computer was synchronized daily with internet network time domain servers, whenever the wireless link from the oating platform to TFS was active.
Instruments were not disturbed during the measurements unless maintenance, troubleshooting or additional sampling of surface waters were necessary. Ancillary meteorological data and data from sensors in the lake water were operated during the eld seasons, but will be presented in a follow-up study where the response of uxes to environmental drivers will be addressed in detail; the aim of the current paper is to assess the relevant timescales of variations that must be addressed in such a follow-up study.

Flux calculations
Flux calculations and quality control procedures closely followed the recommendations given by Vesala et al. 29 Our in-house eddy covariance ux soware (eth-ux 30 ) was adapted to the specic datasets obtained from Toolik Lake, but closely corresponds to standard procedures used for long-term ux measurements over land. [31][32][33] The same calculation method was used in an earlier study using similar equipment. 22 In brief: calculations included (1) coordinate rotation of each 30 minute data segment to align the wind vector with the mean wind direction, thereby making (a) mean lateral wind speed v ¼ 0 m s À1 and (b) mean vertical wind speed w ¼ 0 m s À1 ; (2) screening out unrealistic CO 2 mole fractions > 3000 ppm or < 330 ppm, or when the Li-7000 cell pressure was >1000 hPa or <500 hPa; (3) screening out unrealistic CH 4 mole fractions when the FMA sample cell pressure was >149.7 Torr or <122.0 Torr, or ringdown time was <16.5 ms; (3) determination of time lag between vertical wind speed and CH 4 and CO 2 , respectively; (4) shiing the time series according to these lags within each 30 minute interval; (5) calculation of covariances; and (6) correction for density uctuations caused my moisture ux (WPL correction; 34 details of the specic approach used here were given by Hiller et al. 35 ).
Wave motion may affect the measurements obtained from an eddy covariance system. As investigated in detail by Eugster et al. (2003) 11 (see their Fig. 6), this mostly affects the variance of vertical wind speed with an increase on the order of 6%, but the effect is much small when reected in the uxes (or cospectrum 11 ). Thus, no special ux correction to eliminate the traces of this oscillation was applied. 11 The uncertainty of ux estimates was assessed based on statistical signicance of covariances. [36][37][38][39] For data of best and good quality (ags 0 and 1 according to Foken et al. 33 ), we obtained a median detection limit of 30 minute ux averages of AE1.12 nmol CH 4 m À2 s À1 and 0.12 mmol CO 2 m À2 s À1 . This translates to uncertainties of AE0.16 nmol CH 4 m À2 s À1 and 0.017mmol CO 2 m À2 s À1 for daily median uxes (average of 48 records), or better for median diel cycles at hourly resolution (average of up to 120 records per hour).

Gaplling of missing ux data
To obtain daily and ice-free summer totals of uxes, a procedure to ll data gaps is required. Here we only used measured and quality controlled data for the analysis, except for two special cases where gap lling was necessary: (i) the assessment of summer variations; and (ii) obtaining ice-free summer ux totals during the period of instrument deployment. The quality control procedure used here follows the agging procedure suggested by Foken et al. 33,40 Both an integral turbulence test (ITC) and a steady-state test (SST) were performed using the 9level agging system, from which a general overall ux ag (range 1-9) was deduced according to Foken et al. 33,40 Table 1 gives the percentages of records that remained for the analysis. Acceptable quality refers to ags 1-8, and best quality refers to ags 1-6, whereas uxes with ag 9 were not considered. Fluxes up to ag 8 were kept in the analysis to avoid potential erroneous removal of uxes during ebullition events. 41 Because no established procedure exists for lling ux data gaps in measurements carried out over a lake, we used the median diel cycle approach for short gaps up to 1.5 days. For each 30 minute gap in the dataset the available measurements from the same hour of day measured up to 3 days before and aer the date with the gap were considered to obtain the median ux for that hour of day in the period to ll the gap. In our dataset, 74-97% of the gaps observed in each summer season lled in this way were shorter than 3 hours, and 86-98% were shorter than 12 hours, except for 2011 (52% shorter than 3 hours). Compared to simple linear interpolation of short gaps, this procedure has the advantage that it is more robust when the longer-term ux signal is small compared to the variations from one available averaging interval to the next.
Gaps that were longer than 1.5 days were only lled for obtaining seasonal ux estimates using the daily average from the measured fraction of the respective season (see Section 4.5).

Lake surface temperature and stability measurements
Lake surface temperatures T s ( C) were measured with a downlooking CG3 pyrgeometer (Kipp & Zonen, Del, the Netherlands) of a four-way CNR1 net-radiometer using Stefan-Boltzmann's law, 42 with LW [ measured absolute outgoing long-wave radiation, s the Stefan-Boltzmann constant (5.67 Â 10 À8 W m À2 K À4 ), and an emissivity 3 ¼ 0.98 for water. 43 The Monin-Obukhov 44 stability parameter z/L was determined from EC ux measurements as with z measurement height above lake surface (m; see Section 2.2), k the von Kármán constant (0.40, dimensionless), w 0 T 0 v buoyancy ux (K m s À1 ), u * the friction velocity (m s À1 ), T v virtual (sonic) temperature (K), and g the gravitational acceleration (9.81 m s À2 ).

Statistical analyses
All statistical analyses were done with the open-source statistical soware R version 3.6.1. 45 Both CH 4 and CO 2 uxes measured over lakes tend to show a variability of 30 minute average uxes that is much larger than the longer-term mean ux itself. Hence, we mostly use robust statistics (median, quantiles, inter-quartile range) in our analysis. For comparability with other published values we also report arithmetic means and standard deviations, which are commonly used when sampling discretely with oating chambers. Spline smoothing was done with a local polynomial regression tting (loess function in R); the span parameter for smoothing set to 0.5 when smoothing diel cycles of data, and to 0.25 when smoothing ice-free period data.
2.6.1 Wavelet analysis. Morlet wavelet periodograms were calculated using the dplR package version 1.7.0 in R. Wavelet decomposition can be considered as a special kind of frequency analysis similar to the Fourier transformation, but with the difference that a Fourier transform analysis assumes that the time series under investigation is stationary and periodicity is constant over the time period of measurements. Contrastingly, a wavelet analysis also can resolve segments in a time series with higher or lower amplitude of a given periodicity or frequency, as it is normally required, for example, in seismic or dendrochronological analyses. Similar to episodic events in earthquake research, uxes measured over a lake may be primarily governed by ebullition or lake turnover (mixing) events (see e.g., Schubert et al. 21 ), which would be more easily identied with a wavelet analysis. Our approach closely follows standard procedures explained by Nason 46 using gaplled data. The term "Morlet wavelet" refers to the original work that is the foundation of the analysis. 47 For a quantitative assessment of the relevance of diel and weekly cycles we proceeded as follows: the ve wavelets with periods centered with the diel or weekly cycle were used to determine the fraction of measurements with a statistically signicant cyclicity (i.e., the wavelet power > the signicance threshold determined by the wavelet analysis). The ve wavelets used for this assessment have a bandwidth of 20 to 27 hours for the diel cycle, and 5.9 to 7.8 days for the weekly cycles that we report for each summer season.
2.6.2 Flux footprint analysis. We oriented the instruments to have the maximum fetch, undisturbed by the oat and tower itself, in the direction of the most common winds (Fig. 1). The overall ux footprint area for each summer was then calculated using the Kljun footprint model 48,49 using the 2-d integrated footprint for each 30 minute ux average, which was then aggregated for the seasonal maps. In all summers the typical extent of the footprint area was constrained to 100-150 m around the tower ( Fig. 2) with slightly larger areas in later years with a higher measurement height than in the earlier years with lower measurement heights. In all summers the dimension of the footprint was small enough to be entirely within the lake water surface (Fig. 2), given the distance to the nearest shoreline of z400 m and a lake area of 1.5 km 2 (see Section 2.1). It is well known that CH 4 and CO 2 concentrations are not constant in the surface waters of a lake. 50 Manual sampling of surface water CH 4 and CO 2 pressures in all summer seasons 2010-2015 showed a clear supersaturation of both gases with respect to the atmosphere (G. W. Kling, pers. comm.). This supersaturation might be somewhat stronger over shallower parts of the lake, and thus these measurements might underestimate the supersaturation for the entire lake. However, because of our analysis of the eddy ux footprint (see Fig. 2) we assume that our ux measurements are representative for the part of Toolik Lake that is deeper than 2 m (>85% of Toolike Lake; Fig. 2).

Sonar surveys to detect ebullition
In 2012 an extensive sonar survey was carried out in a similar way as was done by DelSontro et al. 51 before using a 120 kHz (7 beam angle) split-beam scientic echosounder (Simrad EK60, Kongsberg Maritime, Norway), operating at 5 Hz. Surveys were carried out on 19, 23, and 24 July 2012, covering a total footprint area of 8100, 15 800, and 11 000 m 2 , respectively, of Toolik Lake. The average lake depth covered during the three campaigns was 11, 7, and 8.5 m. The total track length was 34.5 km in a regular pattern, providing a representative snapshot sample of the lake (see ESI †).

Inuences of instrumental failures on periodicities
A nearby lightning strike put the electronics of the serial port of the LGR FMA out of order on 2 July 2015, such that a temporary x was necessary to continue with measurements at this remote site where sending the instrument to the manufacturer for repair would have meant the end of measurements for that last year of the project. The temporary x was done by activating the second, unused serial port on the LGR FMA computer mother board, solder the wires to its open connectors, and then reroute the Linux device name (/dev/ttyS0) to that second port. The CSAT-3 also reported three error conditions: (1) unacceptably high differences in speed of sound measurements among the three measurement axes; (2) poor signal lock; and (3) too low amplitude of sonic signal. However aer hard power reset the CSAT-3 operated normally. The follow-up outages of data transfer from the FMA to the Linux data acquisition system thus were related to that defect on the instrument from the rst thunderstorm with lightning. Because we use fully digital data acquisition, 28 we could ascertain that the data that actually could be collected are of good quality and are not affected by the damage observed on the serial port of the FMA.
The CO 2 instrumentation was not affected in the same way by the same lightning strike near the oat. However, the Li-7000 was sensitive to the motions of the oat. The instrument uses a phaselock-loop system for the lter disk that has the three lters for CO 2 , H 2 O, and reference (neutral for both CO 2 and H 2 O). This lter disk had too low inertia to provide perfect phase lock when oat motions were increased. Because these conditions are well documented in the housekeeping variable of the Li-7000 (diagnostic ags), it was possible to screen out all CO 2 raw data values where the phase-lock-loop ag indicated an issue. Hence, the true sampling frequency from the Li-7000 was reduced to slightly below 20 Hz under conditions with phase-lock-loop problems.
Testing in the laboratory at Toolik Field Station in 2010 conrmed that no such issues occur when the same instrument is placed on a sturdy laboratory bench aer it had indicated an increased number of occurrences of phase-lock-loop issues. We thus deduced from this test that optical instruments with moving parts require additional attention and data treatment for reliable eddy covariance ux measurements on a moving platform. In reality, reducing the sampling rate below the nominal 20 Hz is no problem, and depending on measurement height above surface, even lower sampling frequencies can still produce ux measurements with acceptable quality. 28,52

Periodicities in CH 4 and CO 2 uxes of Toolik Lake
Eddy covariance greenhouse gas uxes from Toolik Lake tend to show a large temporal variability that is partly related to the measurement technique employing fast response sensors, but also to cyclical processes related to diel or longer-term variations in environmental conditions in the atmosphere above and the water below the lake surface. Wavelet decomposition thus is a powerful method to nd periodic patterns in time series.  and the corresponding cycle length in number of days is shown with the y-axis on the right. Horizontal white dashed lines show the diel and weekly cycles for reference. Only red areas with bold boundaries are statistically signicant at the 95% signicance level or better (corresponding to p < 0.05). During all summers the diel cycle is oen-but not alwayspronounced over several days and signicantly different from random variations. In years 2012, 2013, and 2014 the diel cycle in CH 4 uxes was more persistent in the second half of the icefree period than in the rst half. Contrastingly, years 2010 and 2015 have periods of several days with persistent diel cycles, which were interrupted by periods without diel cycles. In the special case of year 2015, several instrument failures in the CH 4 ux measurements (hashed areas in Fig. 3) make interpretation more difficult (see Section 2.8), but these failures were always related to thunderstorms at the end of fair weather periods; thus, it is not unlikely that the signicant diel cyclicity was restricted to the periods covered with data. CO 2 uxes were less affected by these storms than CH 4 , but the CO 2 uxes do not show a substantially different pattern in 2015 than the CH 4 uxes.
In the case of CO 2 uxes (Fig. 4) the diel cycles are even more pronounced than those of CH 4 uxes (Fig. 3). The fraction of the measurements with a signicant diel cycle is always higher in View Article Online a pairwise comparison of years (Fig. 5). Contrastingly, cycles on the order of the weekly cycle were clearly more pronounced in the CH 4 uxes than CO 2 uxes in all years. Given the short icefree period of Toolik Lake that typically only lasts for 1.5-2.5 months, these multi-week cycles are a major portion of the icefree summer period; therefore, we focus on the diel and ice-free summer cycles of gas effluxes from the lake.

Diel cycles of CH 4 and CO 2 effluxes
The diel cycles of both CH 4 (Fig. 6) and CO 2 (Fig. 7) were pronounced in all years, with 2015 being an exception in case of CH 4 uxes (Fig. 6f). The diel peak of the hourly median ux (circles in Fig. 6 and 7) of CH 4 typically occurred between 2 and 6 hours in the morning (Alaska Daylight Time, AKDT) and 2 to 5 hours AKDT in case of CO 2 efflux; thus the peak uxes are synchronous with the lowest solar angle (around 2 hours AKDT) or the rst hour aer local solar minimum. Recall that the sun does not set at this northern location in the months of June and July, and only shortly disappears below the horizon in August. The highest daytime hourly median CH 4 effluxes tend to be around 50% of nighttime uxes (down to 20% in 2014; Fig. 6e), but only around 20% in the case of CO 2 effluxes (Fig. 7). The dayto-day variability, however, is substantial for both gases, as is indicated by the color bands showing the inter-quartile range for each hour of day in Fig. 6 and 7. While this day-to-day

View Article Online
variability within each hour of day only shows a weak relationship with the absolute CH 4 ux magnitude, this is not the case for CO 2 uxes, where nocturnal variability is clearly higher than daytime variability (Fig. 7).

Ice-free summer periodicities of CH 4 and CO 2 effluxes
The ice-free summer periodicities of both CH 4 and CO 2 uxes show a similar periodicity with timescales of about a week or longer ( Fig. 8 and 9; the spacing between date labels is two weeks), which is in agreement with the Morlet wavelet periodograms ( Fig. 3 and 4). There is, however, no consistent trend across all years. Only in the case of CO 2 uxes did the within-day variability (illustrated by the shading around each median ux) increase during some years (2012, 2013, Fig. 9c and d), but not so much in other years (2014, 2015, Fig. 9e and f). Daily median CH 4 effluxes started with low magnitudes at the beginning of the summer season in 2010 and ended with the highest efflux when the equipment had to be removed from the lake (Fig. 8a). Contrastingly, in 2015 the daily median CH 4 efflux started at a high level of around 2 nmol m À2 s À1 at the beginning of the ice-free period but ended almost neutral (Fig. 8f). In 2014, CH 4 effluxes were generally low with a slight increase towards the end of the ice-free period (Fig. 8e).
When all available ux measurements from all six summers 2010-2015 are combined (Fig. 10), the median diel cycle shows a 2-fold and a 4-fold difference between nighttime high and daytime low uxes for CH 4 and CO 2 , respectively. Contrastingly, the median summer cycle shows an increasing trend of CH 4 uxes in the rst half of the ice-free period followed by almost constant daily median uxes (Fig. 10b). A reversed pattern was observed in CO 2 uxes with daily median uxes being almost constant until the last week of the ice-free period when instruments were operated on the lake (Fig. 10d), during which an upward trend can be seen. In both cases, the early-season to late-season differences remained within a 2-fold range, similar to the diel cycle observed in CH 4 uxes, but clearly less pronounced than the observed diel cycle in CO 2 uxes. Also important to note is that median uxes for both gases at all scales were positive, indicating a persistent efflux from the lake over the ice-free period.

Ice-free mean uxes and interannual variations
For reference with earlier literature based on discrete chamber ux measurements from Toolik Lake, the daily aggregated uxes shown in Fig. 8 and 9 were averaged to daily means for each year (Fig. 11). Although robust statistics (using medians and quantiles) is helpful for interpreting noisy data such as eddy covariance ux estimates, most existing studies assume that such variations are normally distributed around a mean value and thus report arithmetic mean and standard deviation. In Fig. 11 the bar size corresponds to the arithmetic mean, and whiskers show AE1 SD. For comparison with the data presented in Fig. 8 and 9, the ice-free summer interquartile ranges and median uxes were added with a darker or brighter colored box and a white circle, respectively.
While variability during the ice-free period was quite comparable among years in both CH 4 and CO 2 uxes ( Fig. 11a and b), considerable interannual variation was found, with a 3 to 4-fold difference between the year with the highest and lowest uxes of both CH 4 and CO 2 . Yearly magnitude trends between CO 2 and CH 4 did not match, except for the fact that maximum emissions occurred in 2012 for both gases. The mismatch in overall trend thus indicates that CH 4 and CO 2 uxes were governed by different physical and chemical processes. In addition, all uxes observed over Toolik Lake were likely diffusive, as no ebullition was detected during a sonar eld campaign to detect bubbles that occurred in July 2012 (see ESI †) when CH 4 concentrations were highest ( Fig. 10b and 11a). Only a few features recorded during one of the three July 2012 sonar campaigns could potentially be bubble plumes, but the results are not conclusive (see ESI †). The features were not associated with any single bubble tracks, which is typically the case. 51,53 Because no single bubble tracks were observed, we could not make any estimations on the potential ux from these features if they were indeed plumes.
When converting both trace gas uxes to global warming potentials (GWP) in units of g CO 2,eq m À2 on a 100 year timescale ( Fig. 11c and Table 1), it becomes clear that it is primarily the CO 2 efflux from Toolik Lake that dominates the GWP, contributing 86-93% to the lake's GWP.
Plotting cumulative uxes for both trace gases over the icefree periods requires some interpolation of the larger data gaps. Fig. 12 shows that years with almost complete data coverage show no signs of special singular events, such as deep mixing from storms that might lead to short-term emission peaks. The changes in slope of each cumulative curve indicate the ice-free emission cycle with minor modications due to diel uctuations. In relation to the variation of median diel uxes the interannual variations were a factor 4.1 and 1.8 larger for CH 4 and CO 2 uxes, respectively. Hence, using the yearly averages presented in Fig. 11a and b for interpolating longer data gaps (shown with thin dashed lines in Fig. 12) can be considered a valid approach to obtain ice-free totals for each year.

Discussion
These are the rst eddy covariance ux measurements from multiple ice-free summers of a deep lake in the low Arctic. They are a follow-up to the pioneering EC measurements made over Toolik Lake in years 1994 and 1995, 11 which only quantied short-term CO 2 uxes and not CH 4 emissions.

Short-term periodicities in CH 4 and CO 2 uxes
As described in Section 2.8, instrument failures and wave motion did not contribute to periodicities in the EC ux data. Both CH 4 and CO 2 showed signicant periodicities at shorter time scales than the diel timescale as seen in Fig. 3 and 4, namely in the lowest part of the Morlet periodograms with periods <8 that correspond to cycle lengths of <4 hours at 30 minute resolution. We consider these periods to be related to the artefact that eddy covariance ux measurements are typically averaged over xed clock-based intervals of 30 minutes. In reality, eddies of any size do not respect these articial boundaries between averaging time intervals, and thus oen a strong deviation in one direction is counterbalanced at least in part by a deviation in the other direction in the following averaging interval. Such variations are not noise and not random variations, hence they are correctly identied as signicant variations, but they basically indicate that depending on atmospheric conditions the turbulent time scale in the atmosphere is on the order of 1 h during daytime to 4 h during the night. This problem is well known from EC ux measurements above tall canopies. 54,55 This is also the reason why individual 30 minute periods of EC measurement can show a ux < 0 mmol m À2 s À1 due to such artefacts. For example, Fig. 6b shows a relevant share of negative CH 4 uxes in 2011, although on average CH 4 evades from the water body to the atmosphere.

Diel cycles of CH 4 and CO 2 uxes
In contrast to land surfaces, a lake surface is warmer than the atmosphere at night during the ice-free period, and thus convective conditions dominate at night but much less so during the day (Fig. 13b) when the lake surface oen is colder than the atmosphere above. 29 Thus, in contrast to EC ux measurements over land, there is rarely an issue with stagnant air and stable stratication of the atmosphere at night. 29 Therefore, nocturnal EC ux measurements can be considered at least as reliable as daytime measurements when measurement instruments are placed on the lake such that the measurement footprint lies entirely over the lake surface and inuence from land is minimal. Peak effluxes of CH 4 (Fig. 6) and CO 2 (Fig. 7) tended to occur during the night in most years. Night in this context means the period with low solar elevation angle, but it does not mean that it was very dark. The diel cycles of CO 2 uxes, which have also been observed elsewhere, 56,57 are in agreement with the interpretation presented in Eugster et al. (2003) 11 that the enhanced nocturnal CO 2 effluxes may at least in part be related to the mixing of CO 2 -rich waters from the deeper layers to the lake surface, although a decrease in photosynthetic uptake at night may also be important. The enhancement of nocturnal CO 2 effluxes is most prominently seen in the 2012 ice-free period View Article Online (Fig. 7c), but occurs in most years. A diel cycle of CO 2 ux with nocturnal ux peaks was also observed in a long-term study from Lake Valkea-Kotinen, a boreal lake in southern Finland, 58 but contrasts with observations from another boreal lake in Finland, where EC measurements did not show a diel cycle in CO 2 ux, but only in the CH 4 uxes. 25 A diel cycle of CH 4 uxes is also seen at Toolik Lake, but it was clearly less pronounced than that of CO 2 , even in 2012 (Fig. 6c) with the highest median and peak CH 4 effluxes of all six ice-free periods investigated. The daily range of median uxes is typically on the order of 2Â for CH 4 uxes (Fig. 6) but on the order of 4Â for CO 2 uxes (Fig. 7). The timing of the peak effluxes coincides with the hours of day when the surface cooling of the water is strongest and promotes convection 59 (Fig. 13). The relative contributions of both processes will need an in-depth assessment that would go beyond the scope of this paper.
The evidence of a pronounced diel cycle of CH 4 and CO 2 effluxes (summarized for all summers in Fig. 10a and c) indicates that when discrete sampling with other techniques is done over such lakes, careful considerations about time of day when measurements are taken are required; for example, if sampling is always done during the day then efflux estimates may be conservative (i.e., Kling et al. 5,60 ). Alternatively, measurements carried out at a consistent time of day would allow to scale up to daily values. This approach is complicated by the fact that not all summers showed pronounced diel cycles as were observed in 2012; e.g., the diel cycle of CH 4 uxes was almost nonexistent in 2015. In contrast, the diel cycle of CO 2 uxes showed similar View Article Online ratios of the maximum vs. minimum median uxes (indicated by the factor given on the right-hand axis in Fig. 7), but with year-specic absolute amplitudes.

Ice-free summer periodicities of CH 4 and CO 2 effluxes
While the diel cycles of both CH 4 and CO 2 effluxes showed a relatively clear and simple pattern, the yearly ice-free cycles observed are more difficult to generalize. The years with almost complete data coverage (2010, 2012-2015; Fig. 8 and 9) as well as the Morlet periodograms ( Fig. 3 and 4) indicate that the entire ice-free uxes for each year can be estimated well even if there are breaks in the continuous EC measurements. In other words, the variation over the ice-free period is low enough that weekly sampling that accounted for the diel cycles could provide a defensible ice-free summer ux estimate. Based on our direct ux measurements we estimated that 86-93% of the lake's GWP is due to CO 2 uxes, thus only 7-14% originating from CH 4 . A recent study by Sepulveda-Jauregui et al. 61 estimated that roughly 65% of typical non-yedoma lakes' GWP stems from CH 4 uxes. This discrepancy indicates that future studies should address why direct ux measurements (via EC) differ so strongly from ux calculations (i.e., piston velocity modeling) based on discrete sampling, which may have better spatial coverage but always a lower temporal resolution than EC ux measurements.

Estimating uxes from summer measurements
In general, ebullition could be a signicant emission pathway during ice-melt or freeze-up considering bubbles have been observed in iced-over lakes of the north. 62 A previous study of 40 Alaskan lakes 61 reported an ebullition estimate for Toolik Lake based on ice surveys, but no other specics on location or degree of ebullition was given. We, on the other hand, did not observe any ebullition via our 2012 sonar survey in Toolik and have no evidence that ebullition is a signicant CH 4 emission pathway in this lake, even during ice-melt or freeze-up (T. Del-Sontro, pers. comm.). Ebullition is typically most prevalent during the warmest part of the summer as production rates are temperature-dependent and emissions scale with temperature. 63 Lake depth and sediment temperature of Toolik are however not independent variables due to the presence of permafrost that helps keep lake bottom temperatures below 5-  6 C throughout the summer, which thereby limits the decomposition of organic matter in sediments in deeper locations. 64 The continuous EC measurements during multiple icefree periods at Toolik, however, did not reveal any CH 4 emission events (detected by our 30 minute averaging period) that would suggest ebullition occurred, as has been observed elsewhere. 21 However, if ebullition is occurring frequently via small bubbles, then the wavelet-based method suggested by Iwata et al. (2018) 65 might help to quantify the ebullition contribution aer a thorough validation of the applicability of this method to lakes where ebullition is very obvious; however, this might be challenging for Toolik Lake data where ebullition is not obvious.
In the case of CO 2 ux, however, using the available data to extrapolate to summer totals might be an underestimate Fig. 12 Cumulative fluxes of (a) CH 4 and (b) CO 2 during the ice-free periods 2010-2015 when flux instruments were active on the lake. Ice-off and refreezing were typically one to two weeks before and after instruments could be operated on the lake. A AE30% uncertainty range was added to the 2011 data due to the large data gap. Fig. 13 Diel course of (a) lake surface temperature, and (b) atmospheric stability z/L (Monin-Obukhov stability parameter 44 ). Measurements from all seasons 2010-2015 were aggregated by hour of day. The range between the 10th and 90th percentile (80% confidence interval, CI) and the inter-quartile range (50% CI) are shown with color bands, and the bold line shows the median value. Stability values in the range À0.0625 < z/L < 0.0625 show near-neutral stability, 75 whereas positive z/L indicate stable stratification of the atmosphere, and negative z/L unstable and convective conditions. Free convection exists if z/L ¼ À1, forced convection is found under unstable conditions but with z/L $ À1.
because we missed the few days aer removal of EC instrumentation but before the onset of ice cover (see Table 1). Within these limitations, which are the same as those of all other studies of ux measurements in the Arctic, it can be assumed that the available data provide a sound basis for estimating total gas losses from Toolik Lake, and to quantify its global warming potential during the ice-free summers.

Ice-free mean uxes and interannual variations
Earlier estimates of CO 2 efflux from Toolik Lake (red range in Fig. 11b) and open waters globally 5,66 (blue range in Fig. 11b) provide a reference for EC uxes measured during the 2010-2015 ice-free summers. A statistically more elaborate recent estimate by Hastie et al. 66 for boreal lakes of various sizes provides similar estimates for CO 2 uxes (Fig. 11b), of which Toolik falls into the 1-10 km 2 size range. While 2012 was almost reaching earlier estimates for Toolik Lake and 2013 matched the range given for all lakes by Kling et al. (1991), 5 ve out of six years clearly showed lower CO 2 effluxes than earlier estimates for Toolik Lake. Few CH 4 ux estimates for Toolik exist for comparison with our CH 4 results. One estimate from 1990 (ref. 60) (1.02 mmol m À2 d À1 ; Fig. 11a), and a 2011-2012 estimate from another study 61 (1.25 and 0.56 mmol CH 4 m À2 d À1 for total and diffusive uxes, respectively, assuming 100 days of ice-free conditions in summer; Fig. 11a) were much higher than what we observed with continuous EC measurements, although it should be noted that substantial differences between direct (EC) and indirect (headspace, chamber) ux measurement methods still exist. Contrastingly, the CO 2 ux estimates from the same studies were of the same order of magnitude as ours (35.0 AE 5.3 and 9.1 mmol CO 2 m À2 d À1 , respectively; Fig. 11b). These previous studies, however, were based on only one or a few measurements of the headspace equilibration method using dissolved gas concentrations combined with a surface ux model (e.g., Kling et al. 60 ) and thus lack the temporal and spatial resolution that a summer of EC measurements provides.
A comparison of the ice-free ux density estimates from 2010-2015 with similar estimates obtained from 1977-1989 (ref. 60) but with a very low number of samples (N ¼ 2 to 11 per summer from 1975 to 1989, Fig. 14) shows a broad overlap of two rather different methods: (1) EC for the 2010-2015 data and (2) headspace equilibration in combination with a gradient-ux model for the 1975-1989 data. 60 Only the exceptional years 1977 and 1978 indicate much higher CO 2 effluxes than those observed in any of the EC years 2010-2015. However, in early August 2012 and 2013 the 3rd quartile of EC ux measurements of several days (Fig. 9c and d) was of the same order of magnitude as CO 2 uxes reported from 1977 and 1978, 60 indicating that some of the earlier reported interannual variability may be an artefact of the lack of continuous observations when discrete sampling is used. In other words, the main advantage of EC ux measurements is the better temporal coverage of dynamic processes that show diel, weekly, and interannual variations as compared to random sampling with low numbers of samples.
When the additional global warming potential of CH 4 uxes from Toolik Lake are added to CO 2 ux measurements (Fig. 11c) the overall interpretation changes little as CO 2 remains the dominant climate-relevant gas ux from Toolik Lake to the atmosphere. In other words, while summer CH 4 emissions did vary annually by a factor of 4 (Fig. 11a), they were too low to rival CO 2 emissions when converted to CO 2 -equivalents. Other studies in boreal and Arctic regions have found, however, that aquatic CH 4 emissions can signicantly change the overall global warming potential of a system. 9,67 These studies found that CH 4 uxes were driven by sediment temperature, depth and oxygen 67 or soil organic matter (SOM) erosion. 9 Sediment temperatures, however, remain below 5-6 C throughout the summer, which is the typical temperature observed at the bottom of the lake. Thus, the role of lake temperature, oxygen or depth controlling the interannual variability in CH 4 ux may be limited at Toolik Lake because little change in lake temperature or oxygen has been observed from 2010 to 2015, 68 if we assume that conditions in 2010-2015 were similar to the earlier observations reported by Hobbie and Kling. 68 However, recent studies have suggested that inputs from the active layer water may be more important than internal production. 69,70 As for SOM, Toolik Lake is a glacial lake with negligible amounts of SOM erosion observed around the lake shore (Hobbie and Kling, 68 and pers. observation), and thus the comparatively low CH 4 effluxes from Toolik would be expected. Seeing as CH 4 ebullition tends to be stochastic and higher in emission than diffusion when it does occur, its presence could cause annual variability in overall uxes. However, we found no evidence for CH 4 ebullition via the sonar survey and the EC method that would capture ebullition events adequately, as in Schubert et al. 21 In Toolik Lake, our placement of the EC platform in 12 m of water was assumed to be representative of average lake conditions of the >85% of the lake with depth > 2 m (see Fig. 2), and thus on the basis of a lack of clear ebullition events and a lack of CH 4 bubbles observed in the water column, we suggest that ebullition plays a negligible role in the variability of CH 4 and overall GHG effluxes at any frequency in Toolik Lake. However, potential ux peaks during the disappearance of the ice 71 or related to vernal or autumnal lake turnover 72 might be underestimated in our ice-free ux estimate in Table 1, and thus future studies should try to extend the measurements beyond the period when an EC system can safely be operated on a seasonally ice-free Arctic lake. It should also be noted that if episodic events were not detected during six years of seasonal deployment of our EC system, this does not imply that such events never occur. Our measurements represent lake depths > 2 m, and thus if such episodic events such as ebullition with much stronger uxes should occur in the shallower areas of the lake (<2 m, 11.3% of the total lake surface; Fig. 2), then our ice-free estimates presented in Table 1 would be conservative with respect to the overall ux magnitude.

Conclusions
Six summers of eddy covariance CH 4 and CO 2 ux measurements on Toolik Lake indicated that earlier estimates of CO 2 efflux based on other techniques (oating chambers, gas concentration gradients) were mostly yielding the correct order of magnitude, despite the small number of samples that were taken. We found that interannual variability in gas uxes was larger than the median diel variability of uxes, by on average factor 4.1 for CH 4 and factor 1.8 for CO 2 .
Due to lack of ebullition and the absence of large effluxes from episodic events during the ice-free periods, 86-93% of the global warming potential of Toolik Lake is due to CO 2 effluxes from the lake, with CH 4 effluxes only playing a minor role. To improve our understanding of how deep glacial lakes in the Arctic might respond to climate change, future studies should carefully investigate the drivers of the diel cycle of CH 4 and CO 2 uxes, the trends during the ice-free period, and what drives the large interannual differences. Moreover, new approaches should be found to measure uxes also during the critical period of ice-off and ice-on, when technical constraints limit direct measurements on the lake.

Data availability
The data used in this study can be downloaded from the Environmental Data Initiative (EDI) portal via DOI: 10.6073/pasta/ 919cd028d73ef4f8427d951148f974ec.

Conflicts of interest
The author declare no conicts of interest.