Methane and carbon dioxide fluxes at high spatiotemporal resolution from a small temperate lake

A

• A new method for measuring CH 4 and CO 2 fluxes at high spatio-temporal resolution • Methane diffusion and ebullition showed extensive spatio-temporal variability.• 476 ebullitive events occurred among the 1.9 million CH 4 measurements.• Ebullitive CH 4 fluxes were highest from the deeper parts of the lake.• Methane ebullition was four times higher than diffusive CH 4 fluxes.

Introduction
Atmospheric concentrations of methane (CH 4 ) and carbon dioxide (CO 2 ) have increased profoundly over the past 100 years (European Environment Agency, 2019).Greenhouse gas fluxes from lakes and ponds have recently received more attention due to high fluxes of CH 4 and CO 2 .Rosentreter et al. (2021) found that aquatic ecosystems emit more than half of the global CH 4 emissions; lakes and reservoirs showing high median values of 35-72 μmol m −2 h −1 .Sieczko et al. (2020) found CH 4 fluxes reaching approximately 14 μmol m −2 h −1 in sub-arctic Sweden, while Bastviken et al. (2004) in temperate lakes found mean ebullitive and diffusive CH 4 fluxes of 85 and 27 μmol m −2 h −1 , respectively.The reported CH 4 effluxes are highly variable, resulting in large uncertainties in global flux estimates (Bastviken et al., 2004).The ambiguity in reported CH 4 fluxes can be attributed partly to the high expense associated with measuring CH 4 at high spatial and temporal resolution (Bastviken et al., 2004).Fortunately, newly developed cost-efficient sensors installed in floating chambers can measure CH 4 and CO 2 fluxes continuously (Bastviken et al., 2020).
Most attempts to measure CH 4 have been based on a small number of samples within lakes (n < 15), hampering evaluation of spatiotemporal variations and whole-lake fluxes, while a few comprehensive studies (e.g., Keller and Stallard (1994) (n = 362); Sieczko et al. (2020) (n = 134)) investigated depth patterns in CH 4 ebullition and diel changes of CH 4 fluxes.To our knowledge, no study to date has offered a comprehensive analysis of spatial differences in CH 4 fluxes within a lake, whereas spatial differences in CO 2 fluxes within lakes have received more attention (Andrade et al., 2016).Once these differences have been identified, it becomes possible to identify their controlling factors and ensure accurate determination of the flux for whole lakes.
Differences in CH 4 and CO 2 fluxes within and among lakes have mostly been attributed to nutrient status, dissolved organic carbon (DOC) concentrations, and lake size and morphometry (Bastviken et al., 2004;Keller and Stallard, 1994;Sieczko et al., 2020).Additionally, hydrothermal-magmatic flow and geogenic sources may also influence CH 4 and CO 2 fluxes, but this is only profound in volcanic areas (Tassi et al., 2018), while hydrothermalmagmatic flow does not exist in the lake and region studied here (Lake Lyng, Denmark).Furthermore, groundwater inputs to a lake can contain high concentrations of carbon (C), promoting increased CH 4 and CO 2 formation and thereby emissions (Striegl and Michmerhuizen, 1998).Additionally, stratification of lake water can reduce emission rates as bottom water with high concentrations of CH 4 and CO 2 does not reach the waterair interface, simultaneously, a buildup of CH 4 oxidizing bacteria at the oxic-anoxic layer is formed, causing reduced CH 4 concentrations reaching the water-air interface (Bastviken, 2009;Tassi et al., 2018).Higher lake trophic status and DOC concentration work as proxies for the productivity and external input to lakes, causing a positive relationship between lake productivity and CH 4 fluxes due to higher sedimentation and mineralization of organic matter in sediments with overlying anoxic waters (Bastviken et al., 2004).Furthermore, a positive relationship between lake productivity and the duration of summer stratification would increase the areal extent of anoxic sediments, thus promoting CH 4 formation (Bastviken et al., 2004).A high proportion of labile organic carbon increases the formation of acetate and hydrogen, fueling CH 4 production under anoxia (Fenchel et al., 2012).High input of allochthonous carbon is also known to increase CO 2 efflux due to stimulated heterotrophic degradation and respiration (Bastviken et al., 2004).Therefore, we expect that lake sediment's organic content links directly to CH 4 production.However, sediment organic matter content in lakes can be highly variable and time-consuming to measure.As an alternative, we used sonar imaging as a relatively fast assessment of sediment hardness usually correlated with sediment organic matter content (Kragh et al., 2017;Sø et al., 2021).
Lake morphometry and wind exposure affect both the ebullitive and diffusive CH 4 fluxes as well as CH 4 retention and oxidation in the water (Bastviken, 2009).CH4 flux has been shown to decrease with lake area, possibly due to a lower input of allochthonous organic carbon and nutrients relative to lake volume (Bastviken et al., 2004).Moreover, a greater lake size increases wind exposure and gas transfer velocity across the waterair interface (Vachon and Prairie, 2013).Wind-induced turbulence and water depth influence shear stress, oxygen influx to the sediment, and likely the CH 4 production and release (Bastviken et al., 2004).A deeper water column can also increase the loss of CH 4 from bubbles during the passage from the sediment to the water surface, thereby reducing the flux of CH 4 to the atmosphere (Langenegger et al., 2019).
It should be easier to quantify the CO 2 flux than the CH 4 flux because of the higher solubility of CO 2 compared to CH 4 , resulting in the vast majority of CO 2 exchange occurring by diffusion across the water surface (Enick and Klara, 1990) in contrast to CH 4 , which may show large effluxes by ebullition (Bastviken et al., 2004).Dissolved gases are distributed by advective and convective mixing, which tends to reduce spatial variations of concentrations (Boehrer and Schultze, 2008).Both CO 2 and CH 4 are exchanged across the water-air interface by diffusion according to the product of the partial pressure gradient and the gas transfer velocity (Rosentreter et al., 2021).Diel changes of the CO 2 partial pressure gradient may be substantial due to daytime CO 2 consumption in gross primary production, while CO 2 release by ecosystem respiration continues day and night (Natchimuthu et al., 2014;van Bergen et al., 2019).Diel variation of the gas transfer velocity may also be prominent, as near-surface turbulence is driven by wind shear and convection (Andersen et al., 2017).Moreover, local sheltering and differential heating and cooling may result in a spatial variation of the partial pressure gradients of both gases (Schilder et al., 2013) and the gas transfer velocity (Sand-Jensen et al., 2021).Thus, low horizontal mixing and different metabolic intensity between littoral and pelagic habitats may generate spatial variability of diffusive gas fluxes.The uncertainties in emissions are noticeable in reported values, Rosentreter et al. (2021) review estimated that more than half of global CH 4 emissions derives from aquatic systems, with lakes between 1-10 and 10-100 ha having average (± 95 % C.I.) CH 4 emissions of 255 ± 102 and 162 ± 98 μmol m −2 h −1 .However, CH 4 flux has been measured primarily during daytime, limiting the insight into diel variability (Sieczko et al., 2020).Existing studies show contradictory results regarding whether daytime or nighttime CH 4 fluxes are highest, and underlying drivers have not been identified with certainty (Podgrajsek et al., 2014;Sieczko et al., 2020).
Our overall objective was to measure CH 4 and CO 2 fluxes at high spatiotemporal resolution from a 10-ha eutrophic Danish lake and evaluate the environmental drivers explaining the variance in the fluxes.We measured environmental variables and applied CH 4 and CO 2 sensors mounted in floating chambers that automatically replenished headspace air.The chambers were deployed for five consecutive days and were moved to a new position every day, creating a spatial grid of one-day measurements.In addition, five chambers were kept in the same position to measure day-to day variations in gas fluxes.We hypothesized that: 1) spatial variability of ebullitive CH 4 fluxes is higher than for diffusive CH 4 and CO 2 fluxes due to the mixing of dissolved gases throughout the surface waters; 2) temporal variability of CH 4 emissions is low, though higher during daytime when wind and sediment shear stress may increase relative to nighttime; and 3) the main underlying drivers of variable CH 4 fluxes would be sediment hardness and oxygen availability at the sediment surface both being dependent on site location and water depth.

Materials and methods
This study was conducted in Lake Lyng, a small (10 ha) softwater (alkalinity 0.9 meq l −1 ) shallow lake (mean depth 2.4 m, max.7.6 m) located near the town of Silkeborg, Denmark (56.158668, 9.544308, Fig. 1).Lake Lyng has a small catchment of 0.56 km 2 of which 45 % are residential areas and a water residence time of approximately 1.4 years.The water entering the lake is primarily by surface runoff and probably groundwater input, as the lake has no distinct inlet and only a small outlet (Skovgaard and Carl, 2018).During the early autumn measuring period there was no surface water inlet or outlet.As the lake received untreated wastewater from 1889 until the mid-1950s, it became hypertrophic (> 200 μg total-P l −1 ; Bundgaard et al. (2002)).Nutrient concentrations decreased after sewage input stopped, and average summer concentrations in 2016 were 37 μmol total-N l −1 and 2 μmol total-P l −1 (Skovgaard and Carl, 2018).

Environmental conditions
We continuously measured GHG fluxes from floating chambers and multiple environmental variables for five days from 27 September -1 October 2021.From a buoy at the deepest point in the lake (7.6 m), we measured photosynthetically active radiation (PAR; HOBO S-LIA-M003, Onset, USA), wind speed, gust and direction (HOBO S-WSET-A), and temperature through the water column (HOBO UA-002-64) at 1 m intervals.Air temperature, barometric pressure, and relative humidity were measured every minute at a public weather station (Davis Vantage Pro2) located 3.5 km from the lake (Jessen, 2021).Oxygen was measured below each GHG chamber with a sensor (MiniDOT, PME, USA) suspended 0.5 m above the sediment surface.Alkalinity was measured on duplicate surface samples collected during the measurement period and analyzed by acidimetric titration (Gran, 1952).Water CO 2 concentration was calculated from measurements of pH, water temperature, and alkalinity (Hofmann et al., 2010).
Water depth, sediment hardness, and submerged aquatic plant coverage were determined across the lake using sonar (Lowrance HDS-16 Live equipped with a Lowrance Hybrid Dual Imaging (HDI) Skimmer Transducer and Active Imaging 3-in-1 Transducer).Sonar data were collected in September 2021 and analyzed as described in Kragh et al. (2017).In short, lake isobaths and maps of sediment hardness were calculated using Reefmaster 2.0 (Reefmaster Software Limited) with the bottom composition module and a maximum interpolation between paths of 15 m, while data points were recorded in one-meter intervals.Aquatic plant coverage and species separation were assessed using sidescan imagery, which was possible due to the low aquatic plant biodiversity and easily distinguishable signals of the species.When aquatic plants were present on the sidescan images a plant sample was collected for species identification.Two species of aquatic plants (Potamogeton crispus and Ceratophyllum demersum) and macroalgae were present and distinguishable on the sidescan imagery.Only P. crispus was rooted in the sediment and was included in the estimation of plant coverage.
CH 4 input via groundwater was estimated to explore whether input of CH 4 -rich groundwater could account for the observed CH 4 fluxes.The calculations were made using 395 mm of yearly groundwater input relative to surface area, representing the mean value of the region (Sand-Jensen et al., 2006), multiplied by the effective catchment area of the lake.Much of the catchment consists of residential areas which are sewered and do not contribute groundwater to the lake.Concentrations of CH 4 and CO 2 in groundwater wells in the vicinity of the lake from the period 2010-2023 were extracted from the Geological Survey of Denmark and Greenland (2023).

Floating chambers for gas flux measurements
To obtain continuous measurements of CH 4 and CO 2 fluxes, we used the floating chamber design described by Bastviken et al. (2020), applied by Sieczko et al. (2020), and used in an automated version by Martinsen et al. (2018) Fig. S1).This design is a do-it-yourself and cost-efficient approach for measuring CH 4 (NGM2611-E13, Figaro, USA) and CO 2 (CO2 K33 ELG, SenseAir, Sweden) concentrations and auxiliary variables (humidity and temperature) at high resolution (every 2 s for CH 4 , humidity, and temperature and 20 s for CO 2 ) in the floating chamber's headspace.The sensors are connected to an Arduino (Arduino Uno Rev3, USA) that controls the sensors and records the signals.The floating chambers were made from PVC buckets (volume = 0.0135 m 3 ; surface area = 0.06 m 2 ) with a polystyrene floating collar.Each chamber was equipped with an air pump (DC radial blower, RS pro, flow capacity = 1.13 l s −1 ), replacing the floating chamber air headspace at regular intervals to enable automatic and continuous measurements of CH 4 and CO 2 fluxes as described in (Martinsen et al., 2018).Preparatory experiments confirmed that cycles with 20 min of air exchange (air pump on) followed by a 40-minute measurement period (air pump off) were appropriate.An air inlet and an outlet with a 1.5 m long PVC hose (diameter = 16 mm) were placed on each side of the bucket.The inlet hose was connected to the pump, while the outlet hose serves as a passive relief valve to prevent pressure build-up.The size, length, and type of the hose used were chosen to maximize exchange capacity of the chamber air headspace (100 times during a 20-minute pump cycle), while minimizing air pump power consumption and diffusive gas exchange between the chamber's air headspace and the atmosphere during measurements.Each floating chamber was powered by an 18 Ah 4S LiFePO 4 battery, placed in a polystyrene box next to the chamber.Floating chambers were tied to a sunk float which was held in place by an anchor, allowing the chamber to drift approximately 1 m to each side without disturbing the anchor and creating ebullition.
Calibration of the CH 4 sensors was done following the procedure outlined in Bastviken et al. (2020).The CO 2 sensors were pre-calibrated by the manufacturer.Methane sensors were calibrated in atmospheric air with injections of methane, measuring at a minimum of nine different CH 4 concentrations spanning 0-120 ppm.Furthermore, due to the measurement principle of metal oxide gas sensors, the sensor resistance increases with decreasing humidity.Thus, calibration was performed at three or more humidity levels to determine background resistance for each sensor at different CH 4 values (see Bastviken et al. (2020) for more details).A Gasmet DX4030 FTIR Gas Analyzer (Version E1.22, Finland) and a Los Gatos Microportable Greenhouse Gas Analyzer (GLA131-GPC ABB, Switzerland) were used to measure the CH 4 concentration within the calibration chamber.Each sensor was calibrated before and after deployment; we did not find any drift during the five-day measurement campaign.

Field measurements
In Lake Lyng, a total of 80 temporary stations (1-80) were distributed evenly across transects covering the entire lake (Fig. 1).Floating chambers measured CO 2 and CH 4 fluxes at each station for 16-21 h before being moved to the next station.For example, chamber number 1 measured at stations 1-4 over the five-day sampling campaign, chamber 2 measured at stations 5-8, and so on.Additionally, fluxes were measured at the five permanent stations throughout the five days, which were chosen to represent differences in depth and sediment conditions.Both temporary and permanent stations were used to ensure high spatial coverage on each day, as well as being able to obtain high number of replicate flux measurements that could correct for any possible differences between days.A total of 24 flux chambers were deployed throughout the sampling period, except for the first day, when only 23 were deployed.All chambers were placed within approx.0.5 m of the station using the GPS of the sonar (Lowrance HDS-12 Gen3 GPS;).Prior to deployment, all CO 2 and CH 4 sensors were switched on for 1 h or longer to enable the CH 4 sensor to warm up.We then confirmed that measurements were correct and calibrated the sensors with reference to the atmospheric concentration.

Flux calculations
CH 4 fluxes (F CH4-total ) were separated into ebullitive (F CH4-ebul ) and diffusive fluxes (F CH4-diff ).Only the diffusive flux of CO 2 (F CO2 ) was considered, as no ebullitive CO 2 flux occurred due to the high solubility of CO 2 in water.A 10-point moving average was repeated five times, as proposed by Kajiura and Tokida (2021), to minimize noise from the low-bit analogto-digital converter of the Arduino.Fluxes (μmol m −2 h −1 ) were calculated using the equation: where the first term (dC dt −1 ) is the rate of change (ppm h −1 ) of either CH 4 or CO 2 in the chamber's headspace, P amb is the ambient pressure (Pa), V is the chamber's headspace volume (m 3 ), R gas is the ideal gas constant (m 3 Pa K −1 mol −1 ), T is the ambient temperature (K), and A is the surface area of the flux chamber in contact with the water surface (m 2 ).A positive flux denotes transport from water (source) to the atmosphere and a negative flux denotes transport from the atmosphere to the water (sink).From the high-frequency time series collected for each flux measurement, we separated the CH 4 chamber headspace signal into F CH4-diff and F CH4-ebul by identifying ebullitive events that were characterized by a fast increase in CH 4 (Fig. S2).We used a 5-point running variance filter to identify any sudden increase in the time series caused by an ebullitive event and applied a threshold value (0.1-0.5) to distinguish ebullitive events from the running variance.We determined a threshold value in an iterative process for each station based on a visual inspection of the CH 4 concentration and the running variance time series.For each ebullitive event, we determined the minimum and maximum CH 4 concentrations including all CH 4 concentrations 1 min before and after the ebullitive event, to ensure the inclusion of the entire CH 4 concentration change.Events recorded as ebullitive but with a negative or low (< 2 ppm) change in concentration were removed, since these were most likely false detections of ebullitive events, and very low concentration changes might be due to diffusion.
Prior to the calculation of F CH4-diff , we discarded the first 200 measurements (6.5 min deadband) after replacement of the chamber headspace air to avoid any artifacts such as pressure changes due to deployment, and used up to 400 measuring points (13 min) to calculate a slope (dC dt −1 in Eq. ( 1)) using a linear regression model.The slopes of ebullitive events identified in this period were determined from the measurements leading up to this event.F CH4-diff was calculated based on at least 50 observations.F CO2 was calculated from chamber headspace CO 2 measurements.Similarly, for F CH4-diff , the slope of concentration over time was determined using a linear regression model.For both F CO2 and F CH4-diff , only regression models with R 2 > 0.5 were used for further analysis.The extensive sampling campaign in Lake Lyng resulted in 1475 CH 4 flux measurements for 87 'station days'.On average, 12 F CH4-diff and 14 F CH4-ebul measurements (minimum of 5) were available for each station.The CO 2 sensor malfunctioned over time in many of the floating chambers, most likely due to moisture accumulation in the sensing region.A total of 748 F CO2 measurements were available for 46 'station days' distributed randomly across the lake.

Statistical analysis
We used linear regression models to investigate drivers of F CH4-diff , F CH4- ebul , and F CO2 based on daily station averages.Prior to modeling, we assessed the correlation between the predictor variables using Spearman rank correlation.Variables with a Spearman ρ between −0.39 and 0.39 were kept, indicating no relationship between the two variables, while only one variable was kept if this threshold was exceeded based on correlation with the response variable.We fitted models with F CH4-diff , F CH4-ebul , and F CO2 as the response variables.For F CH4-diff , we used average oxygen concentration, sediment hardness, and aquatic plant coverage as the predictor variables.For F CH4-ebul , we used water depth, sediment hardness, aquatic plant coverage, and wind fetch (the unobstructed travel length of wind across the water surface from a given direction) as the predictor variables.For F CO2 , we used sediment hardness, wind gust, latitude, and longitude.For all models, we performed model selection using a stepwise backward elimination approach, in which predictor variables were removed until all remaining variables were either significant (p < 0.05) or showed a tendency (p < 0.1).A full list of all predictor variables can be found in the supplement (Table S1).
We performed a simple simulation to determine the number of daily flux measurements needed to measure representative lake levels for F CH4- diff , F CH4-ebul , and F CO2 .We randomly selected a number of daily fluxes 1000 times and compared these to the lake's actual average daily flux.The number of daily fluxes varied from 1 to 87 (87 being the maximum number of daily fluxes).For F CO2 only 46 daily fluxes were available.An arbitrary high precision boundary of the average daily flux of ±20 % was used, similar to Wik et al. (2016).When 95 % of the random draws reached this threshold, the number of daily fluxes was assumed to be sufficient.
We visualized whole lake fluxes by interpolating station measurements for the three fluxes and average oxygen concentration above the sediment.This was done using inverse distance weighted interpolation with an inverse distance power set to 1.

Environmental conditions
In autumn 2021, we carried out an intensive measurement campaign in Lake Lyng, quantifying CO 2 and CH 4 flux and a wide range of candidate predictor variables expected to be important for producing and exchanging these greenhouse gases.Wind speeds were generally low (mean 0.7 m s −1 ), with higher values during daytime (mean 0.9 m s −1 , range 0-3.1 m s −1 ) than nighttime (mean 0.6 m s −1 , range 0-3.3;Fig. 2) and daytime gust wind speeds approximately 4-times higher than nighttime gusts.Daily incoming irradiance as PAR (photosynthetically active radiation, 400-700 nm) averaged 11.4 mol m −2 d −1 , while air temperature was quite variable (7.8 to 18.6 °C) and atmospheric pressure very constant (1009 to 1022 hPa: Fig. 2).Water temperature profiles revealed a thermocline at approximately 5.5-m depth with epilimnion temperatures of 14-16 °C and hypolimnion temperatures of 10.5-11.5 °C (Fig. 2).Daily mean oxygen concentrations at 0.5 m above the sediment ranged between 0.02 and 3.8 mg O 2 l −1 below 5 m water depth (Fig. S3) and in the northern part (1.4-3.8 mg O 2 l −1 ), whereas levels were between 8 and 10 mg O 2 l −1 above 5 m water depth.
Alkalinity in Lake Lyng was 0.9 meq.l -1 , while pH in surface waters at the mid-lake station was 7.3 in the early mornings and 7.7 in the evenings, with a mean of 7.5 (Fig. S4).Depth profiles of pH were measured at the five permanent stations on one occasion and showed higher values (7.6) in surface waters than in bottom waters (6.7).Dissolved CO 2 concentrations were above the equilibrium concentration with the atmosphere (about 18 μmol CO 2 l −1 ) both during daytime and nighttime (Fig. S4; mean 52, range 24.8-72.2μmol CO 2 l −1 ¸Fig.S4).Daytime decrease in CO 2 concentrations correlated with higher wind speed (Fig. S4).
Submerged plants were present at 1-4 m water depth, while deeper and shallower areas had no plants.Shallow areas (< 1 m water depth) were dominated by the reed Typha angustifolia, while intermediate water depths (1-4 m) had submerged plants.The average plant coverage at the stations was low (mean 5.8 %), but the southern part of the lake had high coverage at some stations (mean 31 %, range 1-80 %).Submerged plant coverage was low in the western and northern parts of the lake (Fig. S4).
Sediment hardness showed high spatial variability across the lake bottom, particularly at water depths above 5 m (Fig. S5).Sediment hardness was generally lower (i.e., softer sediments) in the deeper parts (> 5 m) and in wind-sheltered, shallow water in the western and northern parts.Areas with steeper slopes showed higher sediment hardness.This was the case for depths of 4-6 m leading to the deepest part of the lake.In contrast, areas with a small slope or a plateau showed lower sediment hardness.This was mainly observed for depths of 2-4 m.

Ebullitive CH 4 fluxes
F CH4-ebul was highest in the deepest parts and less in the shallower parts of the lake (Fig. 3).F CH4-ebul showed no diel pattern over the five-day sampling period and no difference between daytime and nighttime values (Fig. 4, diel mean 54.8 μmol CH 4 m −2 h −1 ; paired t-test, t = 0.06, df = 72, p = 0.95).F CH4-ebul increased towards the end of the campaign, while the probability of ebullition events did not change systematically (Fig. 4).Only a few ebullitive events occurred during the first two days while higher flux rates occurred on days three and four, followed by a further increase on day five (Fig. 4).F CH4-ebul for the entire lake averaged at 54.8 μmol CH 4 m −2 h −1 , which was determined by interpolation between sites (Fig. 3).

Diffusive CH 4 fluxes
The spatial variability of F CH4-diff was generally lower than for F CH4-ebul (Fig. 3).Average F CH4-diff showed small diel variations but were significantly higher during daytime compared to nighttime (Fig. 4, daytime mean 19.5 and nighttime mean 15.0 μmol CH 4 m −2 h −1 ; paired t-test, t = 2.9, df = 69, p = 0.005).F CH4-diff increased towards the end of the campaign but was of low magnitude.F CH4-diff and F CH4-ebul were significantly positively related but the proportion of explained variation was very low (linear regression model, n = 1409, t-value = 5, p < 0.001, R 2 = 0.02).F CH4-diff for the entire lake averaged 13.6 μmol CH 4 m −2 h −1 , which was determined by interpolation between sites (Fig. 3).Some stations had negative F CH4-diff , but most negative values were low (mean − 18 μmol CH 4 m −2 h −1 ) and close to the detection limit of the setup (Bastviken et al., 2020).

CO 2 fluxes
F CO2 exhibited substantial temporal variability both within and between days which was characterized by few CO 2 influxes and large CO 2 effluxes (mean 919, range − 3941 to 5667 μmol CO 2 m −2 h −1 ; Fig. 4).F CO2 tended to be higher during daytime than nighttime, but this difference was not significant (daytime mean 935, nighttime mean 778 μmol CO 2 m −2 h −1 ; paired t-test, t = 0.8, df = 36, p = 0.43).F CO2-diff for the entire lake averaged at 1127 μmol CO 2 m −2 h −1 , which was determined by Fig. 2. Environmental conditions during the five-day measuring period.A) Air temperature (black) and atmospheric pressure (blue, secondary y-axis).B) Wind speed (solid line) and gust wind speed (dotted line).C) Isopleth of water temperature from the deepest part of the lake.Grey dots denote the depth of water temperature sensors.interpolation between sites (Fig. 3).There was no systematic spatial pattern in F CO2 , though higher fluxes occurred from mid-lake deeper waters.An area above a depression in the lake bottom with hypoxic water (station '20', Fig. 1 + S2) had the highest F CO2 and released almost twice the amount as the station with the second-largest flux.
Six groundwater wells, located within 2 km from Lake Lyng, contained 0.31-0.62μmol CH 4 l −1 and 659.1-1091 μmol CO 2 l −1 .Applying the expected groundwater flow multiplied by the and dissolved gas concentration within Lake Lyng's catchment, we calculate that the lake relative to its surface area receives only 0.43-0.86nmol CH 4 m −2 h −1 and 0.92-1.5 μmol CO 2 m −2 h −1 .

Sampling intensity for accurate measurement of whole-lake CH 4 and CO 2 fluxes
Simulation of the number of daily fluxes measured across the lake surface, to determine the average whole-lake daily F CH4-ebul , F CH4-diff , and F CO2 with high certainty, revealed large differences (Fig. 5).Especially F CH4-ebul required a high number of daily flux measurements (> 70) to be within 20 % of the average daily flux.For F CH4-diff , approx.39 daily flux measurements were needed to be within the 20 % range of the average daily flux, and for F CO2 , approx.27 daily flux measurements were required.Too few measurements (≤ 10) of daily ebullitive fluxes could lead to an overestimation of average daily fluxes by a factor of 3-12 or, alternatively, an underestimation, resulting in values as low as 0-4 % of the average daily ebullitive fluxes.

Discussion
CH 4 and CO 2 fluxes are expected to display different spatiotemporal patterns depending on the specific gas and the type of gas flux, either diffusion from the water surface or ebullition due to bubble release from sediments.Logically, the observed patterns should reflect differences in biological processes and physical regulations underlying diffusive fluxes and ebullition.Methane mainly is produced by anaerobic respiration in the sediments and oxidized by anaerobic and aerobic processes in sediments and water (Bastviken, 2009;Fenchel et al., 2012), whereas CO 2 is formed by aerobic and anaerobic respiration in sediments and water and consumed by photosynthesis in illuminated sediments and water layers (Fenchel et al., 2012).Moreover, CH 4 and CO 2 effluxes may derive from an external input of soil water with high concentrations of these gases (McDonald et al., 2013).Lake Lyng receives water from surface runoff and groundwater input, the latter containing elevated CH 4 and CO 2 concentrations.However, due to the small effective catchment area and low concentrations, the groundwater inputs CH 4 or CO 2 were negligible compared to the in-lake carbon conversion processes and gas effluxes from the lake.

Ebullitive CH 4 fluxes
CH 4 release by ebullition is a highly stochastic process, occurring when production rates of CH 4 exceed losses by anaerobic and aerobic CH 4 oxidation and diffusion from the sediment surface (Bastviken, 2009).Bubbles rich in CH 4 may form, grow, and obtain a buoyancy that overcomes the combined atmospheric and hydrostatic pressure and the physical resistance to release from the sediment matrix (Boudreau, 2012;Katsman et al., 2013).An initial bubble release, with or without physical disturbance by water flow above the sediment, may weaken sediment resistance and give rise to a stream of bubbles (Delwiche et al., 2015).Subsequently, it may take a while before the sediment site has produced sufficient CH 4 to release bubbles again.The temporal variability of bubble release from one site compared to another may reflect temporal variations in the interactions of physical and biological processes at the sites (Bastviken, 2009;Bastviken et al., 2004).
We recorded 476 ebullitive events in 1.9 million measurements during five days with 24 floating chambers.The recorded events are probably a small underestimation of bubble release because it is difficult to distinguish between bubbles that enter a floating chamber within two seconds of each other.Nonetheless, considering the small surface area covered by the floating chambers relative to the lake surface area, the daily mean number of bubbles is 7.9 per m 2 of surface area, but almost 800,000 for the entire 10-ha lake.These values stress that CH 4 ebullition can be intense in eutrophic lakes like Lake Lyng, even outside the warm summer period when ebullition is expected to peak (Langenegger et al., 2019).
While a few permanent stations recorded an above-average number of ebullitive events during the last two days of the study period, this spatiotemporal variation was not apparent when considering all stations together.Previous studies have attributed episodic ebullitive events to a sudden drop in atmospheric pressure and an increase in wind speed (Joyce and Jewell, 2003;Varadharajan and Hemond, 2012).Although these effects were not specifically tested in our study, we did record a drop in atmospheric pressure on 29 September, the day with the most ebullitive events and highest F CH4-ebul .Although wind speed varied through the measuring period, the frequency of ebullitive events, or the magnitude of fluxes did not correlate with wind speed.In fact, the highest wind speed was recorded on 1 October, yet F CH4-ebul decreased.Furthermore, wind speeds showed large diel variations but did not correlate with the frequency of ebullitive events or the magnitude of F CH4-ebul .However, we acknowledge that the study period was short, and the magnitude and variability of wind speed on the small, sheltered Lake Lyng was probably too low to generate substantial changes of wind-induced shear on sediments and, thereby, potentially influence CH 4 ebullition.
Methane ebullition in Lake Lyng increased towards areas deeper than 3 m, while areas shallower than 2 m had little or no release.Ebullition has previously been found to change with water depth, but some studies report a decrease with depth (Bastviken, 2009;Bastviken et al., 2004), while others report an increase (Schilder et al., 2016).We found a significantly higher F CH4-ebul in deep water, which also had significantly lower oxygen concentrations caused by stratification and only slightly lower temperature above the sediments.Stratification of lake water promotes the presence and most likely a greater abundance of active methanogenic bacteria (Lyautey et al., 2021), while also inhibiting the oxidation of CH 4 due to anoxic conditions in the deeper water.Sediments in the deeper water of Lake Lyng were softer and thereby possibly richer in organic matter, which is likely promoted by sediment focusing as a consequence of the lake's bathymetry (Håkanson and Jansson, 1983).The input of labile organic matter from primary production in the surface waters to deep, anoxic hypolimnion sediments has been shown in other studies to fuel methane formation (Grasset et al., 2018).However, we found no significant relationship between F CH4-ebul and sediment hardness, indicating that the methane formation caused by an input of organic matter does not emit as bubbles, but rather by diffusion.Although no significant relationship was present, we do believe that variation of sediment organic matter content influences the magnitude of CH 4 formation and emission.Some authors have suggested that greater hydrostatic pressure in deeper water prevents bubbles from being released from the sediment (Bastviken et al., 2004).However, an increase of water depth from 2 m to 7 m only increases the combined air and hydrostatic pressure from 1.2 to 1.7 atm.This small difference cannot explain the 40 % higher net release rate of CH 4 from water depths of 7 m relative to 2 m in Lake Lyng.Furthermore, the amount of CH 4 in the bubbles that gets dissolved during the passage from 7 m depth to the surface is expected to be small: Estimates from a similar type of lake show that only 14 % of the CH 4 content was dissolved from a 6 mm diameter bubble traveling 6 m, from the sediment surface at 10 m depth to a CH 4 trap positioned 4 m below the water surface (Langenegger et al., 2019).As long as the depth range is modest (e.g., 0-20 m), CH 4 ebullition should not markedly decrease with water depth as bubbles may still reach the required size and positive buoyancy to being released.When bubble release from sediments at modest water depth does not occur, it is more likely due to a combination of lower temperature, low sedimentation rates, and predominance of old, recalcitrant organic matter in the sediment lowering CH 4 production rates (Grasset et al., 2018).Accordingly, we propose that patterns of ebullition in shallow lakes should change with lake trophy and bathymetry influencing the settling rate and quality of organic particles as well as temperatures and oxygen concentrations in bottom waters influencing CH 4 production.

Diffusive CH 4 fluxes
As expected, the diffusive CH 4 flux in Lake Lyng showed higher diel variation than the ebullitive CH 4 flux.Diffusive fluxes of CH 4 were higher during daytime than nighttime and were positively correlated with higher wind speeds, which increase the gas transfer velocity (Heiskanen et al., 2014).Other studies have reported different diel patterns; e.g., Zhang et al. (2019) found the highest diffusive fluxes of CH 4 in the spring during nighttime, while Podgrajsek et al. (2014) observed the highest diffusive CH 4 fluxes after sunrise and in the evening, but found no correlation to wind speed.
The relationship between sediment hardness and F CH4-diff suggested that sediment characteristics influence CH 4 formation in Lake Lyng, with softer sediments causing higher methane formation compared to harder sediments.Lakes with sediments rich in organic matter have previously been shown to have high CH 4 flux compared with lakes of lower organic content (Bastviken et al., 2004).However, variations within lakes have not been studied in detail.We found no significant relationship between sediment density and sediment organic matter, likely due to difficulties related to locating the exact sampling site of sediment cores.Moreover, when CH 4 is released from the sediment it disperses both vertically and horizontally through the water column, F CH4-diff observed using floating chambers is proportional to the CH 4 concentration gradient and transfer velocity and therefore only weakly related to sediment characteristics below the floating chamber.Finally, the lability of the sediment organic matter likely has a stronger effect on CH 4 formation than the bulk content of organic matter per se (Grasset et al., 2018).
The effect of vegetation on CH 4 fluxes has focused mostly on emergent plants working as methane release vents (Desrosiers et al., 2022).Only a few studies have looked at the role of submerged aquatic plants in CH 4 fluxes.Aquatic plants may increase the input of organic litter to the lake floor, which in turn could be degraded and form CH 4 (Mille-Lindblom and Tranvik, 2003), but in contrast rooted aquatic plants may reduce CH 4 concentrations in sediments due to root oxygen release into the sediment (Sand-Jensen et al., 1982).Furthermore, root surfaces and above-ground shoots create habitats for CH 4 oxidizing methanotrophs (Mille-Lindblom and Tranvik, 2003;Sorrell et al., 2002).In fact, plant coverage negatively correlated with F CH4-diff , and a CH 4 influx from the atmosphere to water was observed in areas with the highest plant coverage, which may be due to methanotrophs attached to leaf surfaces.

Diffusive CO 2 fluxes
CO 2 flux from lakes is often lower during daytime compared to nighttime due to photosynthesis (Kling et al., 1992).Calculations of surface water CO 2 concentration from pH and alkalinity sampled at the center of Lake Lyng showed permanent supersaturation of CO 2 relative to the atmosphere throughout the entire period, with modest daytime reduction of CO 2 concentrations (Fig. S4).Decreasing CO 2 concentrations occurred simultaneously with the occurrence of increasing wind, which further points to the importance of wind speed and its influence on the gas transfer velocity as the main predictor of CO 2 fluxes and thereby surface water CO 2 concentration in Lake Lyng.We a priori expected a diel effect of plant coverage on CO 2 fluxes due to higher photosynthesis and CO 2 utilization during daytime, whereas higher CO 2 fluxes were expected during nighttime due to ongoing respiration and possibly higher rates in areas with submerged plants.Furthermore, litter from the aquatic plants could supply organic matter to decomposing bacteria, thereby increasing the nighttime CO 2 flux.However, no diel, nor plant, relationship was found in our models.We speculate that the lack of significant impact in our model may be due to low plant coverage or low irradiance during the measuring period in Lake Lyng.Conversely, diffusive CO 2 efflux in Lake Lyng was higher during daytime than nighttime which may be due to the higher daytime wind speed and resulting higher gas transfer velocity.

Influence of spatiotemporal variability on whole-lake flux estimates
We applied automated floating chambers to collect hourly measurements of diffusive and ebullitive fluxes of CO 2 and CH 4 .Changes in CH 4 concentrations were measured at high time resolution in the chambers' headspace air, enabling us to separate between diffusive and ebullitive fluxes by identifying individual bubble events when they were separated by more than just a few seconds.In comparison, traditional deployment of floating chambers followed by withdrawal of chamber headspace air for analysis cannot distinguish diffusive from ebullitive fluxes, and shortterm measurements are cumbersome.Bubble traps such as inverted funnels (Keller and Stallard, 1994) cannot assess the size and content of individual bubbles, and the temporal resolution is modest, though relatively short, repeated incubation periods are possible.These shortcomings are probably the main reasons why studies of gas fluxes with a high spatiotemporal resolution are that few.
One disadvantage of our setup was the sub-optimal resolution of the analog-to-digital converter, making it hard to distinguish between small changes in CH 4 concentrations.Furthermore, separation of ebullitive and diffusive fluxes was sometimes difficult, and there may have been cases where ebullitive events were missed, though they represent a small and insignificant fraction of the total.Future studies should attempt to improve methods for identifying short-term ebullitive events (e.g., Delwiche et al. (2015)).
In situ measurements of CH 4 and CO 2 fluxes have long been timeconsuming, as numerous measurements are needed due to the large heterogeneity of fluxes, particularly for ebullition.Compromises are needed when selecting a number of sites and frequency of measurements.Wik et al. (2016) estimated the minimum number of measurement sites needed to determine the average whole-lake flux.Our study is, to our knowledge, the first with the sufficient spatial resolution of CH 4 and CO 2 fluxes from a whole lake, ensuring high-accuracy determination of mean whole-lake fluxes for a selected period.
Measurements showed extensive spatiotemporal variability of all fluxes but particularly high variability of CH 4 ebullition.Thus, the 72 daily fluxes for 10-ha Lake Lyng to attain a reliable mean whole-lake value of CH 4 ebullition was close to the 88 daily flux measurements conducted.An additional simulation was made considering the water depth (not shown), in which the lake was divided into two depth intervals (0-3 m and > 3 m) to investigate if this would reduce the number of daily flux measurements needed to attain a better mean estimate of the entire lake fluxes.However, this procedure did not change previous simulations suggesting no effect of depth.Nonetheless, water depth did show significant effect on the ebullitive flux, while the simulation with and without depth included showed no difference.Use of more than two depth intervals was not tested.The temporal and spatial resolution is much lower in contemporary studies, stressing that finer temporal and spatial resolution is required in the future by the traditional use of floating chambers to attain reliable whole-lake mean values.Lakes with complex bathymetry will increase the required spatial coverage even further to obtain reliable whole-lake estimates compared with the small Lake Lyng.Thus, we see three future directions for quantification of whole-lake CH 4 fluxes: 1) use a high number of floating chambers with a high temporal resolution; 2) apply an eddy covariance method to cover the entire lake (Aubinet et al., 2012); and 3) apply a mass balance approach directed at quantifying CH 4 production and release from the sediment and loss in the water column (e.g., Langenegger et al. (2019)).Our approach (1) has the potential to determine underlying drivers of spatial and temporal variability of CH 4 and CO 2 fluxes.

Conclusions
During five days intensive measurements in Lake Lyng, we estimated 800,000 bubble events, which were the primary source to CH 4 flux from the lake (mean 68.4 μmol CH 4 m −2 h −1 ).Concurrently, the mean diffusive CO 2 efflux was 1127 μmol CO 2 m −2 h −1 .Our results are in the lower end of values for other small lakes (Rosentreter et al., 2021), which is likely due to our autumn sampling period.The automatic floating chambers collected numerous measurements of CH 4 and CO 2 fluxes revealing spatiotemporal patterns and offering accurate whole-lake estimates of CH 4 and CO 2 emissions.The low cost of the automated floating chambers also solves the earlier problem of GHG measurements being very expensive.We identified several factors having a significant effect on CH 4 and CO 2 fluxes, although a large proportion of the variance was still unaccounted for in the statistical models.F CH4-ebul was mainly influenced by water depth, F CH4-diff by plant coverage and sediment hardness, and F CO2 by wind gust and position during the five-days period.Despite sediment hardness only showed a significant correlation with F CH4-diff , we suggest that sediment organic matter and its lability influence the formation rate of CH 4 and CO 2 (Grasset et al., 2018;McDonald et al., 2013).The low explanatory power, particularly regarding ebullitive CH 4 fluxes, suggests that the underlying mechanisms are still not well understood or, alternatively, that they are so complex, intricately regulated, and stochastic that accurate evaluation of drivers of fluxes may be difficult to obtain.In eutrophic, shallow Lake Lyng, CH 4 ebullition is responsible for the main CH 4 loss and future measurements during summer, including better sediment analyses, may improve analysis of drivers.

CRediT author contribution statement
All authors contributed to the conceptualization of the project, with Jonas Stage Sø (JSS), Theis Kragh (TK) and Kaj Sand-Jensen (KSJ) developing the idea of this project.Development of equipment was done by JSS and TK.Formal analysis was performed by JSS and Kenneth Thorø Martinsen (KTM), while investigation was done by JSS, TK, EP and JEK.Visualization was done by JSS and KTM.Writing the original draft was done by JSS, while reviewing and editing was done by all authors.Funding acquisition was done by TK, KSJ and Kasper Reitzel (KR).

Fig. 1 .
Fig. 1.Bathymetric map of Lake Lyng and stations where environmental variables and gas fluxes were measured.Temporary stations are shown as numbers (1-80) and permanent stations as letters (A-E).The inset map shows the location of Lake Lyng in Denmark.

Fig. 3 .
Fig. 3. Interpolated maps of (A) ebullitive methane flux, (B) diffusive methane flux, and (C) diffusive CO 2 flux over five days in Lake Lyng.The magnitude of rates is shown by the colour bars.

Fig. 4 .
Fig. 4. Temporal variability of fluxes of F CH4-ebul , F CH4-diff , and F CO2 both during the entire measuring campaign (A, C, E, G) and throughout the day (B, D, F, H).Grey points are flux measurements, and solid lines are generalized additive models where different distributions are assumed (A-D are Gaussian, E-F are Binomial, and G-H are Gamma).The black line indicates all measurements, while the others indicate the permanent stations.

Fig. 5 .
Fig. 5. Simulation of the number of daily fluxes required to attain mean values within + − 20 % of the overall lake average of ebullitive (purple) and diffusive (green)) CH 4 flux and diffusive CO 2 flux (yellow) over five days in Lake Lyng.