Technical Note : A simple calculation algorithm to separate high-resolution CH 4 flux measurements into ebullition and di ff usion-derived components

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Introduction
Wetlands and freshwaters are among the main sources for methane (CH 4 ) emissions (Dengel et al., 2013;Bastviken et al., 2011;IPCC 2007).In open-water systems, CH 4 is released via three pathways: (i) diffusion, (ii) ebullition and (iii) plant mediated transport (e.g., Goodrich et al., 2011;Bastviken et al., 2004;Van der Nat and Middelburg, 2000;Whiting and Chanton, 1996), which are all subject to variable environmental drivers and conditions such as water level, atmospheric pressure, temperature gradients, and wind velocity as well as the presence of macrophytes (Lai et al., 2012;Introduction Conclusions References Tables Figures

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Full  Tokida et al., 2007;Chanton and Whiting, 1995).As the absolute and relative contributions of these pathway-associated flux components varies in time and space (Maeck et al., 2013;Walter et al., 2006), the resulting total CH 4 emissions feature an extremely high spatial and temporal variability at all scales (Koch et al., 2014;Repo et al., 2007;Bastviken et al., 2004).Hence, attempts to model CH 4 emissions based on individual environmental drivers are highly complex and complicated (Prairie and del Giorgio, 2013).The separation of measured CH 4 emissions into the individual pathwayassociated components is therefore crucial if aiming to identify relevant environmental drivers of CH 4 emissions (Bastviken et al., 2011(Bastviken et al., , 2004)).In consequence, the understanding of the complex processes determining the temporal as well as spatial patterns of CH 4 emissions is a prerequisite for upscaling field-measured CH 4 emissions to the regional or landscape scale, and thus for adequately quantifying the contribution of CH 4 emissions to global greenhouse gas (GHG) budgets (Walter et al., 2015;Koebsch et al., 2015;Lai et al., 2012;Limpens et al., 2008).However, field studies measuring emitted CH 4 above the water surface generally measure the total CH 4 emissions as a mixed signal of individual CH 4 emission components, released via all possible pathways (i.e.diffusion, ebullition and plant mediated transport).Studies directly measuring temporal and spatial patterns of CH 4 emissions resulting only from either ebullition or diffusion are rare.Measurements of CH 4 ebullition can be performed using manual or automatic gas traps, as well as optical and hydroacoustic methods (Wik et al., 2011(Wik et al., , 2013;;Maeck et al., 2013;Walter et al., 2008;Ostrovsky et al., 2008;Huttunen et al., 2001;Chanton and Whiting, 1995), often requiring a certain degree of manipulation of the studied system.Diffusive CH 4 fluxes are commonly either derived indirectly as the difference between total CH 4 emissions and measured ebullition, or directly obtained based on the use of bubble shields or gradient measurements of CH 4 concentration differences (DelSontro et al., 2011;Bastviken et al., 2010Bastviken et al., , 2004)).A graphical method to separate diffusion, steady ebullition and episodic ebullition fluxes from the total CH 4 flux was presented by Yu et al. ( 2014), using a flow-through chamber system.However, performed at the laboratory scale for Introduction

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Full a peat monolith, measurement results, as well as the applied method, were lacking direct field applicability.A first simple mathematical approach for field measurements to separate ebullition from the sum of diffusion and plant mediated transport was introduced by Miller and Oremland (1988), who used low resolution static chamber measurements.Goodrich et al. (2011) specified the approach using piecewise linear fits for single ebullition events.However, static thresholds determining ebullition events, as well as low-resolution measurements, limited the approach to estimates of medium and major ebullition events and prevent a clear flux separation.CH 4 flux separation approaches based on manual chamber measurements with rather low temporal resolution fail to capture the rapidly changing absolute and relative contributions of the pathway-associated flux components both in time and space (Maeck et al., 2013;Walter et al., 2006).Improvements in measurement techniques, particularly by using micrometeorological methods (e.g., Eddy Covariance (EC)), however, allowed for high temporal resolution records of CH 4 emissions (Juszczak and Augustin, 2013;Schrier-Uijl et al., 2011;Cole et al., 2010;Wille et al., 2008).Recently, a growing number of experimental GHG studies employ automatic chambers (AC) (Koskinen et al., 2014;Lai et al., 2014), which can also provide flux data with an enhanced temporal resolution capturing short-term temporal (e.g.diurnal) dynamics.In addition, AC measurements can also represent small-scale spatial variability, and thus, identify potential hot spots of CH 4 emissions (Koskinen et al., 2014;Lai et al., 2014).AC systems combine the advantages of chamber measurements and micrometeorological methods with respect to the quantification of spatial as well as temporal dynamics of CH 4 emissions (Savage et al., 2014;Lai et al., 2012).
Moreover, there is a need for a non-intrusive method for separating pathwayassociated CH 4 flux components both in time and space.Due to the combination high temporal measurement resolution and representation of small-scale spatial heterogeneity, AC measurements provide opportunities for (i) detecting even minor ebullition events and (ii) developing a statistically based flux separation approach.Based on high-resolution CH 4 flux data from an AC measurement system, this study presents Introduction

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Full canary grass (Phalaris arundinacea), which disappeared after rewetting due to the higher ground water level.At present, the water surface is partially covered with duckweed (Lemna), while bulrush (Typha) and swamp grass (Glyceria) are present next to the shoreline.However, below chambers, no emergent macrophytes were present throughout the study period.

Automatic chamber system
In April 2013, the measurement site was equipped with an AC system and a nearby climate station (Fig. 1).The AC system consists of four transparent chambers, installed along a transect directed from the shoreline into the lake.Chambers are made of Lexan Polycarbonate with a thickness of 2 mm and reinforced by an aluminium frame.Each chamber (volume of 1.5 m 3 ; base area 1 m 2 ) is mounted in a steel profile, secured by wires, and lifted/lowered by an electronically controlled cable winch, located at the top of the steel profile.All chambers are equipped with a water sensor (capacitive limit switch KB 5004, efector150) at the bottom, which allows steady immersion (5 cm) of the chambers into the variable water surface.Hence, airtight sealing, as well as constant chamber volume are ensured during the study period.Chambers are connected by two tubes and a multiplexer to a single Los Gatos Fast Greenhouse Gas Analyser (911-0010, Los Gatos), measuring the air concentration of carbon dioxide (CO 2 ), methane (CH 4 ), and water vapor (H 2 O).To ensure consistent air pressure and mixture during measurements, chambers are ventilated by a fan and sampled air is transferred back into the chamber headspace.However, due to the big chamber volume, mixture of the chamber headspace needed up to 30 s, wherefore most peaks due to ebullition events showed overcompensation (Fig. 3).Concentration measurements are performed in sequence, sampling each chamber for 10 min with a 15 s frequency once an hour.A wooden boardwalk north of the measurement site allows for maintenance access, while avoiding disturbances of the water body and peat surface.Introduction

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Ancillary field measurements
Temperatures were recorded in different water (5 cm above soil surface) and soil/sediment depths (2, 5, 10 cm below sediment-water interface), using thermocouples (T107, Campbell Scientific).Additionally, air temperature in 20 and 200 cm height, as well as wind speed, wind direction, precipitation, relative humidity, and air pressure were measured by a nearby climate station (WXT52C, Vaisala).Information about the water table depth was gained by a pressure probe (PDCR1830, Campbell Scientific).All parameters were continuously recorded at 30 min intervals and stored by a data logger (CR 1000, Campbell Scientific) connected to a GPRS radio modem.

Flux calculation and separation algorithm
CH 4 flux calculation was performed using a standardized R-script presented in detail by Hoffmann et al. (2015).Measured fluxes were determined using Eq. ( 1), where M is the molar mass of CH 4 , δν is the linear concentration change over time (t), A and V denote the basal area and chamber volume, respectively, and T and P represent the inside air temperature and air pressure.R is a constant (8.3143 m 3 Pa K −1 mol −1 ).
To estimate the relative contribution of diffusion and ebullition to total CH 4 emissions, flux calculation was performed twice, adjusting selected user-defined parameter setups of the used R-script (Hoffmann et al., 2015) (Fig. 3).was calculated as the difference between the start and end CH 4 concentration, using an enlarged MW with a minimum length of 7.5 min.To avoid measurement artefacts (e.g.overcompensation), being taken into account as start or end concentration, measurement points representing an inherent concentration change lower or bigger than the upper and lower quartile ±0.25 times IQR, were discarded prior to calculation of the total CH 4 flux.Third, the proportion of the total CH 4 emission, released via ebullition, was estimated following Eq.( 2).
Since no emergent macrophytes were present below the automatic chambers, plant mediated transport of CH 4 was assumed to be zero.In case of negative estimates, CH 4 emission, due to ebullition, was assumed to be zero.To exclude measurement artefacts, triggered by the process of closing the chamber, a death band of 25 % was applied to the beginning of each measurement prior to all flux calculation steps.The used R-script is available at www.carbozalf.org.

Verification of applied flux separation algorithm
A laboratory experiment under reasonable controlled conditions was performed, to verify the used flux separation algorithm.Therefore, distinct amounts (5, 10, 20, 30 and 50 mL) of a gaseous mixture (25 000 ppm CH 4 in artificial air; Linde, Germany) were inserted by a syringe through a pipe into a water filled tub, covered with a closed chamber (V = 0.114 m 3 ; A = 0.145 m 2 ).Airtight sealing was ensured by a water filled frame, connecting tub and chamber.The chamber was ventilated by a fan and connected via pipes to a Los Gatos Greenhouse Gas Analyser (911-0010, Los Gatos), measuring CH 4 concentrations inside the chamber with a 1 Hz frequency (Fig. 2).In terms of comparability between in vitro and in situ measurements, data processing was performed based on 0.066 Hz records.Expected concentration changes within chamber headspace as the Introduction

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Full result of methane injections were calculated as mixing ratio between the amount of inserted gaseous mixture (25 000 ppm) and air filled chamber volume (2 ppm).

Results and discussion
The assumption of using sudden changes in chamber based CH 4 concentrations measurements for detecting ebullition events was verified by the conducted lab experiment.
Calculations of simulated ebullition events and the amount of injected CH 4 showed a well overall agreement, which indicates the accuracy of the calculation algorithm (Fig. 4).However, flux separation might be hampered due to a steady flux originating from other processes than diffusion through peat and water layers, such as steady ebullition of micro bubbles (Goodrich et al., 2011).A resulting potential impact on estimates of diffusive CH 4 emissions can be minimized by an enhanced frequency of concentration measurements during chamber closure.Based on a high temporal resolution small-scale differences within measured concentration changes can be identified and filtered by the variable IQR-criterion, which thereby reduces the detection limit of ebullition events.Compared to direct measurements of either diffusion or ebullition, as reported by e.g.Bastviken et al. (2010), the presented calculation algorithm prevents an interfering influence of spatial heterogeneity on separated ebullition and diffusion CH 4 fluxes, since both flux components are derived during the same measurement.Moreover, the integration of the ebullition component over measurements rather than the calculation of single ebullition events are ensuring a reliable flux separation despite of potential measurement artefacts such as overcompensation or incomplete ebullition records (Goodrich et al., 2011;Miller and Oremland, 1988).In case of a low water level, such as within the presented study (< 35 cm) or parallel measurements of different trace gases (e.g.CO 2 and CH 4 ), the use of direct measurement systems for either ebullition (gas traps, funnels) or diffusion (bubble shields) might be limited.Hence, the presented simple and robust calculation algorithm as purely data processing based Introduction

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Full seems to be applicable for a broader range of different manual and automatic closed chamber systems, setups and ecosystems.Due to the performed flux separation, the accuracy of certain spatial and temporal tendencies within the exemplary field data set was improved (Fig. 4 and Table 1) and explanatory approaches could be addressed.Total CH 4 emissions spatially integrated over the study period, as well as the respective contributions of ebullition and diffusion are shown in Fig. 4. Apart from short-term measurement gaps, a considerable loss of data occurred between the 27 July and 7 August 2013, due to malfunction of the measurement equipment.In general, biochemical processes driving CH 4 production are closely related to temperature regimes (Christensen et al., 2005), determining the CH 4 production within the sediment (Bastviken et al., 2004).Hence, measured total CH 4 emissions showed clear seasonal patterns, following the temperature regime at 10 cm soil depth.In addition to seasonality, total CH 4 emissions also featured diurnal dynamics, with lower fluxes during daytime and higher fluxes during nighttime, which were most pronounced during July and early September.Especially during August, the diurnal variability was superimposed by short-term emission events and high amplitudes in recorded total CH 4 emissions.Similar to the total CH 4 emissions, also diffusive fluxes showed a distinct temperature-driven seasonality, as well as clear diurnal patterns throughout the entire study period.However, compared to diurnal variability of the total CH 4 fluxes, a pronounced shift of maximum CH 4 emissions from night-to daytime was revealed for the diffusive flux component (Fig. 5).While maximum diffusive fluxes during July were recorded at nighttime hours (approx.19:00 to 7:00 LT), a shift to the daytime started in August, with maximum fluxes in September occurring between 2:00 and 14:00 LT.This might be explained by differences in turbulent mixing, due to certain water temperature gradients.During daytime, the surface water is warmed, preventing an exchange with the CH 4 enriched water next to the sediment, which results in lower diffusive CH 4 emissions.During nighttime, when the upper water layer cools down and intermix is undisturbed, enhanced diffusive CH 4 emissions can be detected.This dynamics are more pronounced during warm days, explaining the Introduction

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Full seasonal shift and concealed during periods with a high wind velocity.The obtained diurnal trend is in accordance with findings of Sahlée et al. (2014) and Lai et al. (2012), who reported higher nighttime and lower daytime CH 4 emissions for a lake site in Sweden and an ombrothropic bog in Canada, respectively.However, an opposing tendency was found by Deshmukh et al. (2014), who reported higher daytime and lower nighttime CH 4 emissions from a newly flooded subtropical freshwater hydroelectric reservoir within the Lam Theun river valley, Laos.In contrast to diurnal trends obtained for the total as well as diffusive CH 4 emissions, estimated ebullition events occurred erratically and neither showed clear seasonal nor diurnal dynamics.Nonetheless, periods characterized by more pronounced ebullition, seemed to roughly follow soil temperaturedriven CH 4 production within the sediment as e.g. reported by Bastviken et al., 2004 (Fig. 5).This is confirmed by a distinct correlation between daily mean soil temperatures and corresponding sums of measured ebullition fluxes.Moreover, fewer and smaller ebullition events were detected in times of reduced wind velocity and high relative humidity (RH), for example from 10-11 September and 18-19 September 2013.
However, on the level of single flux measurement, no significant dependency between recorded environmental drivers and CH 4 release by ebullition events was found.The relative contribution of diffusion and ebullition was 55 % (min.33 to max.70 %) and 46 % (min.30 to max.67 %), respectively.This is in accordance with values, reported by Bastviken et al. (2011), who compiled CH 4 emission estimates from 474 freshwater ecosystems with clearly defined emission pathways.A similar ratio was also found by Tokida et al. (2007), who investigated the role of decreasing atmospheric pressure as a trigger for CH 4 ebullition events in peatlands.
Comparison of flux data among the four chambers, reveals considerable spatial heterogeneity within the measured transect (data not shown).Monthly averages of diffusive, ebullative and total CH 4 emissions for all four chambers of the established transect, as well as statistics, showing the explanatory power of different environmental variables, are summarized in Table 1.Separated into diffusion and ebullition, different tendencies along the transect, as well as dependencies from different environmental Introduction

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Full drivers, were revealed.With respect to total CH 4 emissions, neighboring chambers generally featured high differences in CH 4 fluxes, with no obvious trend along the transect.However, the spatial variability of diffusive CH 4 fluxes was characterized by lower emission rates near the shoreline and elevated fluxes at longer distances.These trends might be a result of the increasing water column further from the shore, causing a reduced gas transfer across the air-water interface as a result of e.g. higher hydrostatic pressure to be overcome by gas bubbles on the one hand and an increased diffusive CH 4 flux based on enhanced CH 4 gradients on the other hand (Bastviken et al., 2004).In contrast, ebullative CH 4 emissions showed no gradient and were highly variable.Thus, the detected spatial variability of total CH 4 emissions was dominated by highly variable ebullition events rather than by systematic differences in diffusive CH 4 emissions (Wik et al., 2011;Walter et al., 2008).

Conclusions
The results of the laboratory experiment, as well as the estimated relative contributions of ebullition and diffusion during the field study, indicates that the presented algorithm for CH 4 flux calculation and separation into diffusion and ebullition delivers reasonable and robust results.Temporal dynamics, spatial patterns and relations with environmental parameters, well established in the scientific literature, such as soil temperature, water temperature gradients and wind velocity, became more pronounced when analyzed separately for diffusive CH 4 emissions and ebullition.However, not all ebullition events (e.g.micro bubbles) seemed to be filtered correctly, as detected in case of enhanced CH 4 emissions during the beginning of August and the thereby superimposed diurnal cycling.Hence, further adaptation of measurement frequency and/or the applied data processing algorithm is required.In a next step, the flux separation algorithm should be systematically tested against flux estimates generated with methods for measuring either ebullition or diffusion, such as bubble traps or bubble barriers.Moreover, the algorithm needs to be tested and evaluated with regards to generalizability and appli-Introduction

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Full cability to other freshwaters and wetland ecosystems.Despite the mentioned shortcomings, the presented calculation approach for separating CH 4 emissions increases the amount of information about the periodicity of CH 4 release and may help to reveal the influence of potential drivers as well as to explain temporal and spatial variability within both separated flux components.Introduction

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Full  −2 h −1 ) for the chamber transect (from chamber I-IV, starting next to the shoreline).The median of standardized (beta) coefficients as well as of the Nash-Sutcliff's efficiency (NSE) based on daily linear and multiple linear regressions between different environmental drivers and calculated CH 4 emissions throughout the study period is shown below.Monthly averages as well as statistics are separated according to diffusion, ebullition and total CH 4 flux.Superscript numbers indicates significant differences between chambers.p values of applied linear and multiple linear regressions are indicated via asterisks.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |a new calculation algorithm for separating open-water CH 4 fluxes into its ebullitionand diffusion-derived components based on ebullition-related sudden concentration changes during chamber closure.A variable ebullition filter is applied, using the lower and upper quartile and the interquartile range (IQR).Data processing is based on the R-script developed byHoffmann et al. (2015), modified for the purpose of CH 4 flux calculation and separation, thus including the advantages of automated and standardized flux estimation.We hypothesize that the presented flux calculation and separation algorithm can reveal concealed spatial and temporal dynamics in ebullition and diffusion-associated CH 4 fluxes, thus, facilitating the identification of relevant environwas measured at a rewetted former fen grassland site, located within the Peene river valley in Mecklenburg-Western Pomerania, northeast Germany (53• 52 N, 12• 52 E).The long-term annual precipitation is 570 mm.The mean annual air temperature is 8.7• C (DWD, Anklam).The study site was particularly influenced by a complex melioration and drainage program between 1960 and 1990, characterized by intensive agriculture.As a consequence, the peat layer was degraded and the soil surface was lowered by subsidence.Being included in the Mecklenburg-Western Pomerania Mire Restoration Program, the study site was rewetted at the beginning of 2005, resulting in a water level permanently above the soil surface, thus, transforming the site into a shallow lake.Exceptionally high CH 4 emissions at the measurement site are reported by Hahn-Schöffl et al. (2011), who investigated sediments formed during inundation.Prior to rewetting, the vegetation was dominated by reed Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | First, the diffusive component of the flux rate (CH 4diffusion ) was calculated, based on a variable moving window (MW) with a minimum size of 5 consecutive data points.Abrupt concentration changes within the MW were identified by means of a rigid outliner test, discarding fluxes with an inherent concentration change bigger or lower than the upper and lower quartile ±0.25 times the interquartile range (IQR).Tests of variance homogeneity and normal distribution were applied with α = 0.1.Second, the total CH 4 flux (CH 4total ) for each measurement Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Wille, C., Kutzbach, L., Sachs, T., Wagner, D., and Pfeiffer, E.-M.: Methane emissions from Siberian artic polygonal tundra: eddy covariance measurements and modeling, Glob.
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Figure 1 .Figure 2 .
Figure 1.Transect of automatic chambers (AC) established at the measurement site.The arrow indicates the position of the climate station near chamber II.

Figure 4 .Figure 5 .
Figure 4. Scatterplot of amount of injected CH 4 and calculated corresponding CH 4 ebullition event.The solid black line indictes the 1 : 1 agreement.Linear fit between displayed values is represented by the black dashed line, and surrounded by the 95 % confidence interval (grey shaded area).

Table 1 .
Monthly averages ±1 standard deviation of hourly CH 4 emissions (mg m