Methane flux measurements by the eddy-covariance technique are subject to large uncertainties, particularly linked to the partly highly intermittent nature of methane emissions. Outbursts of high methane emissions, termed event fluxes, hold the potential to introduce systematic biases into derived methane budgets, since under such conditions the assumption of stationarity of the flow is violated. In this study, we investigate the net impact of this effect by comparing eddy-covariance fluxes against a wavelet-derived reference that is not negatively influenced by non-stationarity. Our results demonstrate that methane emission events influenced 3 %–4 % of the flux measurements and did not lead to systematic biases in methane budgets for the analyzed summer season; however, the presence of events substantially increased uncertainties in short-term flux rates. The wavelet results provided an excellent reference to evaluate the performance of three different gap-filling approaches for eddy-covariance methane fluxes, and we show that none of them could reproduce the range of observed flux rates. The integrated performance of the gap-filling methods for the longer-term dataset varied between the two eddy-covariance towers involved in this study, and we show that gap-filling remains a large source of uncertainty linked to limited insights into the mechanisms governing the short-term variability in methane emissions. With the capability for broadening our observational methane flux database to a wider range of conditions, including the direct resolution of short-term variability on the order of minutes, wavelet-derived fluxes hold the potential to generate new insight into methane exchange processes with the atmosphere and therefore also improve our understanding of the underlying processes.

The eddy-covariance (EC) technique, a well-established method for the direct
quantification of turbulent surface–atmosphere exchange processes
(Aubinet et al., 2012), can provide valuable information on current

One potential mechanism for such high-methane-emission events is so-called ebullition (e.g., Kwon et al., 2017; Peltola et al., 2018; Männistö et al., 2019), i.e., periodic bubble outgassing with a typical length of seconds to minutes. Even though such emissions are part of the natural flux signal and should therefore be accounted for when accumulating longer-term budgets of methane exchange, in the context of EC data processing and quality assessment, these events are likely to be discarded during the quality screening of raw data, or they may be incorrectly handled by the data processing algorithms. In both cases, the natural high flux event would be incorrectly accounted for, potentially introducing systematic biases into methane fluxes and budgets (Baldocchi et al., 2012).

Spatial heterogeneity in the emission patterns of methane surrounding the
flux tower (e.g., Rey-Sanchez et al., 2019) may
also lead to pronounced variability in the observed

Since “outburst events” in methane fluxes are in many cases flagged as
non-stationary conditions, and are therefore discarded as low-quality data, the
assessment of the net impact of this effect needs to consider what will
happen to the resulting gaps in the quality-filtered EC time series. Gaps
are a common feature in eddy-covariance time series, resulting, for example, from
power failures, instrument malfunctioning or low data quality linked to the
violation of the above-mentioned theoretical assumptions (e.g.,
Foken et al., 2004). If they can be filled with a reliable, unbiased
algorithm, additional gaps would not pose a major problem. For

As an alternative to the regular eddy-covariance raw data processing, the flux calculations can also be performed based on the wavelet method by analyzing frequency patterns in the underlying time series of winds and scalars (Collineau and Brunet, 1993b, a). In contrast to the eddy-covariance method, the wavelet method is not restricted by the same set of theoretical assumptions, and in particular no steady-state conditions are required (e.g., Daubechies, 1990). Wavelets have been shown to be a powerful tool for quantifying turbulent fluxes (Mauder et al., 2007; Thomas and Foken, 2007). The ability to calculate turbulent fluxes for periods as short as 1 min has been proven to be very valuable for attributing flux variability to environmental controls, both being based on aircraft campaigns (Metzger et al., 2013) and stationary tower measurements within a heterogeneous landscape (Xu et al., 2017). Moreover, wavelet techniques have been applied to improve the frequency correction with the eddy-covariance method (Nordbo and Katul, 2013). A direct comparison between fluxes processed with the wavelet and eddy-covariance method found an excellent agreement between both methods for EC data of the highest quality (Schaller et al., 2017).

Here, we quantify the net impact of failing to resolve methane outburst events with the EC method, comparing both short-term emission patterns and longer-term flux budgets to a reference flux product derived with wavelet methods. The presented study is closely linked to two recently published papers (Schaller et al., 2017, 2019) that demonstrate that fluxes during such outburst events, with timescales on the order of only a few minutes, can be precisely quantified using the wavelet method, while the coarser temporal resolution of the EC method normally fails to resolve these details while aggregating over 30 min. In this follow-up study, we determine systematic offsets between both methods and the specific role that different types of short-term outburst events play in this context. Since many non-stationary events were leading to data gaps in the EC-flux time series, we placed a specific focus on evaluating the performance of different gap-filling algorithms to fill these gaps. Overall, our study aims at evaluating the effect of non-stationary conditions on the long-term methane flux budgets, with a special focus placed on systematic biases introduced by either flux processing approach or chosen gap-filling method.

The Ambolikha research site (Göckede et al., 2017),
located on a floodplain of the Kolyma River approximately 18 km south of the
town of Chersky, in northeastern Russia, is underlain by continuous permafrost and
characterized as wet tussock tundra dominated by tussock-forming

Data were collected from two eddy-covariance towers situated about 600 m
apart, both elevated

Both flux towers mentioned above in Sect. 2.1 were equipped with the same
instrumentation, including a sonic anemometer (uSonic-3 Scientific, 5 W
heating, METEK GmbH, Elmshorn, Germany) at the tower top (at heights of 4.9 and
5.1 m for the
drained and control tower, respectively) and a closed-path
greenhouse gas analyzer for

Ancillary meteorological data were collected at 10 s intervals from both towers and stored as 10 min averages on a data logger (CR3000, Campbell Scientific, UT, USA). Acquired parameters include, for example, air temperature and humidity, air pressure, precipitation or soil temperatures. Low-frequency meteorological data underwent a thorough data quality control screening and subsequently were averaged to 30 min (see Kittler et al., 2016, for details).

We based the raw data processing to obtain fluxes from the collected high-frequency data on two different methods:

The eddy-covariance raw data processing uses the software package TK3 (Mauder and Foken, 2015). When applied in stand-alone mode, this tool implements all required conversions, corrections and quality assessment procedures (Foken et al., 2012; Fratini and Mauder, 2014). Details on the TK3 implementation on the Ambolikha datasets are provided by Kittler et al. (2016, 2017a).

The second flux processing method (Schaller et al., 2017, 2019) is based on wavelet analysis and uses the sinusoidal and complex-valued Morlet wavelet transform for flux quantification. The Morlet wavelet provides an excellent resolution in the frequency domain and can be used to analyze atmospheric turbulence (e.g., Strunin and Hiyama, 2004; Thomas and Foken, 2005). Since this study focused on comparing eddy-covariance-derived and wavelet-derived fluxes, the temporal integration of the wavelet method was chosen to closely match the eddy-covariance method (30 min); however, due to the decomposition in time and frequency domain the averaging intervals could not match perfectly, and an averaging interval of 33 min for the wavelet method was used. A detailed description of the wavelet method, the wavelet transform and the corresponding flux data processing can be found in Appendix A1 and in Schaller et al. (2017).

In the context of the presented study, in a first processing step, both methods were applied to produce continuous time series of uncorrected half-hour fluxes of methane. In a subsequent processing stage, the results provided by both methods underwent the same flux correction procedure by the TK3 software package, including 2-D coordinate rotation of the wind field, cross-wind correction (Liu et al., 2001) and correction for losses in the high-frequency range (Moore, 1986).

The eddy-covariance post-processing quality control is commonly based on the
analysis of stationary and well-developed turbulence conditions (e.g.,
Foken et al., 2004, 2012). When applied for wavelet fluxes, the test for
stationarity can be dropped, since wavelet flux data quality is not
compromised by non-stationary conditions (see above). The development of the
turbulence is investigated based on the concept of flux-variance similarity
(Wyngaard et al., 1971) via the so-called integral
turbulence characteristics (ITC; Foken and Wichura, 1996). A low
data quality rating by the ITC can, for example, be caused by stable atmospheric
stratification that suppresses turbulent motions. Data stationarity is
tested by comparing signal covariance at different averaging intervals
(e.g., 5 min vs. 30 min; Foken and Wichura, 1996). In
this context, effects such as, for example, spikes in the signal, abrupt changes of
the signal level or intermittent turbulence may trigger low flux data
quality. We grouped eddy-covariance fluxes into different categories
(Table 1) based on their stationarity flag (SF)
ratings. Fluxes outside the range

Quality flag categories based on the stationarity rating of the eddy-covariance flux data. The definition of quality categories follows the scheme proposed by Sabbatini et al. (2018), which is based on stationarity tests developed by Foken et al. (2004, 2012) but uses stricter thresholds to separate categories.

Gaps of the eddy-covariance time series were filled with three different methods. A linear interpolation (LI) represents the simplest method. The mean of a 10 d moving window (MW) centered to the gap was used for a better representation of the seasonality. These two methods were chosen, since they do not require a sophisticated tool and can thus be easily applied. Finally, a neuronal network approach (NN; Dengel et al., 2013) represents a more sophisticated gap-filling algorithm, filling gaps based on prevailing environmental conditions.

To assess the agreement between EC and wavelet fluxes, a regression analysis
was applied. With flux data of both methods being subject to uncertainties,
no independent variable could be identified. Thus, in place of ordinary
least-square regression, an orthogonal regression (OR; linear model II
regression) was used with the R package “lmodel2” (Legendre, 2014),
and Pearson's correlation coefficients (

The characterization of high-methane-emission event types differentiated
within the context of this study is based on a wavelet approach using the
Mexican hat wavelet. In contrast to the Morlet wavelet, which we used to
precisely quantify flux rates due to its excellent localization in the
frequency domain, the Mexican hat wavelet has a very good localization in
the time domain, therefore facilitating an exact localization of single
events. Event periods resolved at minute intervals were identified by the
median absolute deviation (MAD; e.g., Hoaglin et al., 2000) test
followed by an additional manual adjustment. Events were separated into the
three categories introduced by Schaller et al. (2019):

Of the 5280 half-hourly flux values that would provide continuous data coverage within the study period 1 June to 18 September 2014, about 3.4 % or 6 % of the eddy fluxes were either missing or discarded as lowest data quality for tower 1 and tower 2, respectively (Table 2). For the wavelet datasets, missing flux values had a slightly higher percentage compared to the EC dataset, since a required 3 h window of continuous data focusing on the current timestamp broadened the window of missing fluxes around every gap in the raw data. From the remaining data, a further 11.8 % (tower 1) or 6.6 % (tower 2) were discarded during the EC quality control procedure as low quality, in all cases linked to non-stationary flow conditions. Since the wavelet method does not require stationarity, no additional gaps due to low data quality occurred. For both methods, the subsequent range test (see Sect. 2.3 for details) filtered out another 2 %–5 % of data that were assigned as having high to medium quality. Taken together, for each combination of the tower and processing method, more than 80 % of the fluxes remained after quality screening. Compared to the wavelets, this percentage is lower by about 7 % for the EC method, linked to the requirement of stationary flow conditions.

Gap fraction within the dataset used for this study, separated by flux processing method and tower position.

Regarding the distribution of gaps over time, no seasonal patterns were found for both towers and both flux processing methods, so each part of the study period received about equal data coverage. With respect to diurnal patterns in gap distribution, EC data display a higher gap fraction during the night compared to daytime data coverage. This imbalance is most pronounced for tower 1 (see also Appendix A2, Figs. A1 and A2). No such diurnal patterns in gap distribution were found within the wavelet flux time series, and also no systematic differences between both towers were found for this method. Taken together, wavelet flux data processing provides better overall data coverage, i.e., fewer data gaps have to be filled to replace unreliable measurements flagged as low quality. Also, the equal distribution of gaps between day and night supports an improved performance of gap-filling algorithms. Since gap-filled fluxes are associated with higher uncertainties than measured fluxes, this indicates that wavelet data processing holds the potential to produce more robust flux budgets.

In this section, we compare measured methane flux rates between EC and wavelet methods, with the intention of deriving the dependence of differences between methods on the stationarity of the underlying flow conditions. This analysis excludes gap-filled results. A comparison between methods focusing on the derivation of long-term flux budgets, which include also the gap-filled values, will be presented in the following section (Sect. 3.2.2). For both flux processing methods, higher methane emissions under all quality and stationarity conditions are observed at tower 2 (see also Fig. 1), which features a higher fraction of inundated areas in its footprint in comparison to tower 1. At tower 2, for both flux processing methods, flux rates display a pronounced increase in mid-July, leading to a peak in August and a subsequent decrease at the beginning of September, a pattern that follows the general seasonal trends in soil temperatures. During these times of increased methane emissions, a diurnal cycle with higher flux rates during daytime is observed (see also Fig. A1), while at tower 1, for both flux processing methods, no seasonal or diurnal cycle was observed.

Under highly stationary
flow conditions, we found an excellent agreement between half-hourly flux
rates derived with EC and wavelet flux processing, respectively. A direct
comparison shows that both methods produce highly correlated

Median and variability of non-gap-filled methane fluxes based on
the EC (pink) and wavelet (green) flux processing methods for different
stationarity classes at tower 1

Statistical coefficients of an orthogonal regression analysis
(wavelet

The correlation between half-hourly flux rates derived with both processing methods is reduced under medium-stationary flow conditions compared to the high stationarity. This observation is confirmed by the OR analysis, which produces coefficients that deviate stronger from the ideal targets, as shown above for high stationarity (Table 3). Mean flux rates are reduced in comparison to highly stationary conditions, and positive offsets between fluxes derived by the EC method and the wavelet method are higher for both towers (Table 3; Fig. 1).

For this evaluation of fluxes under low-stationarity conditions, measured EC fluxes with low-quality flags had to be used. Please note that such data would normally have been filtered out during the EC quality control procedure, leaving gaps that would subsequently be filled by gap-filling algorithms. A comparison of methods including such gap-filled data will be presented in the following section, while here the low EC data quality influences the findings. As to be expected, under these circumstances the flux processing methods agree less than under medium- or high-stationarity conditions, with both the slopes and intercepts derived through the OR analysis increasing considerably (Table 3). Also averaged flux rates for the entire study period deviate strongly between methods, with the EC fluxes strongly underestimating the wavelet reference. In comparison to high- and medium-stationarity conditions, also a wider range of wavelet-based fluxes is found at both towers. These results indicate that non-stationarity flow conditions cause a low bias in the EC-derived methane fluxes in comparison to the wavelet method (Table 3; Fig. 1).

To evaluate the impact of discarding portions of an EC dataset due to low
stationarity (SF

Frequency distribution of flux rates (

When integrating the entire dataset, the direct intercomparison of
half-hourly fluxes between EC and wavelet methods based on OR analyses
yields good agreement for tower 2 across gap-filling methods (slope:
1.01–1.05;

For the calculation of long-term methane budgets, the above-mentioned biases
in gap-filling results become more important at tower 1, in part also because
of the overall higher percentage of gaps compared to tower 2
(Table 2). This is reflected in the fraction of the
cumulative methane budget contributed by gap-filled values, which makes up
12 %–15 % at tower 1 but only 6 %–8 % at tower 2
(Table 4). In spite of these deviations,
accumulated fluxes for the entire study period are in very good agreement
between flux processing methods and also between gap-filling methods: flux
budgets based on wavelets sum up to 1.96 and 4.56 g C m

Stationarity flag frequency distribution of half-hourly
timestamps, separating between fluxes that were influenced by events

We restricted this analysis to flux data from tower 2, since here the
overall higher methane fluxes were measured (see also Sect. 3.2.1).
Similar patterns were found at tower 1 (not shown). The vast majority of
30 min flux values (5123 cases, or 97 %) were categorized as “no
events”; i.e., none of the three event types could be detected
(Fig. 3). This category differs substantially
from the event categories regarding the frequency distribution of
stability filter (SF) classes: 76 % of cases fell into the high-stationarity range (classes 1 and 2), and only 12 % were labeled as low
stationarity. The “detected event” statistics combine 26 half-hourly fluxes
from the category “peak events”, 9 “up–down/down–up events” and 123 “cluster
events”. Across these categories, the percentage of high-stationarity data
only makes up about 17 % of the dataset, while the percentage of low-stationarity data has been more than doubled to 32 % compared to the no-event category. The majority of cases (

Methane fluxes (

Methane fluxes based on the EC (pink) and wavelet (green) flux
processing method for three stationarity flag (SF) categories during
different event types at tower 2. For SF

Our dataset from tower 2 demonstrates that mean methane flux rates differed
between event types (see also Fig. 4; similar
trends observed at tower 1). Across stationarity categories, average fluxes,
where wavelet fluxes were available, were highest during cluster events
(wavelet: 52.8 nmol m

Comparing the three different stationarity classes, similar patterns emerge
across event types, confirming the overall results displayed in
Fig. 1: during high stationarity, the highest
median (Fig. 4) and mean flux rates were found
across event categories, with wavelet flux rates during peak events being the
single exception. Results agree well between processing methods, with no
systematic difference observed in either median or mean flux rates. At
medium stationarity, mean flux rates are consistently lower than at high
stationarity, and the differences in medians as shown in
Fig. 4 indicate a minor positive offset in flux
rates between EC and wavelet methods. At low stationarity, wavelet-derived
flux rates are slightly higher again, compared to medium stationarity.
EC-based mean fluxes severely underestimate this reference by fractions
ranging between

Methane fluxes summed up for the wavelet and EC methods (mg C m

As to be expected from the low fraction of half-hourly timestamps containing
detected events (

Regarding the role of flow stationarity, the budgets reflect the distribution of stationarity flags shown above in Fig. 3 well; for the fluxes during “events”, 44 %–51 % of the budget was emitted during medium stationarity, with the remaining flux portions being about equally distributed between high and low stationarity. For the no-event cases, on the other hand, about 85 % of the total methane emissions can be attributed to high-stationarity cases, and only 9 % of the fluxes belong into the medium-stationarity category.

Regarding the intercomparison of wavelet and EC-based flux budgets,
including the influence of the gap-filling approaches, it needs to be
considered that the range test filtered out values at different timestamps
between flux processing methods, and the resulting gaps can occur within any
stationarity category. Accordingly, the performance of the gap-filling
algorithm slightly influenced also the flux budgets for high and medium
stationarity, while the biggest impact is found under low stationarity, where
results are exclusively based on gap-filling output. Sorting by event type,
gap-filled EC flux sums tend to be slightly higher than the wavelet
reference, with the exception of NN budgets for peak and cluster events.
Sorting events by stationarity, results summarized in
Table 5 indicate that events at high stationarity
tend to be underestimated by

Mean absolute methane flux rates showed a uniform pattern with respect to
the stationarity of the flow (e.g., Fig. 1), with
fluxes within the highest stationarity class (SF

Diurnal variability in flux rates, as, for example, observed at tower 2 within the
peak summer season, may particularly alter the comparison of mean flux rates
between events and no events. With the majority of events being detected
during nighttime (Schaller et al., 2019), higher overall
flux rates during the day would mostly raise the no-event flux rates.
Accordingly, the slightly lower averaged fluxes during peak events
(wavelet: 39.0 nmol m

Excluding gap-filled values from the analysis, we achieved an excellent correlation between wavelet- and EC-derived methane flux rates at high stationarity of the flow. This agreement across processing methods under well-developed atmospheric turbulence, which has been reported before by Schaller et al. (2017, 2019), applies to both the regression analysis of half-hourly fluxes (Table 3) and the statistics on averaged flux rates integrated over the study period (see, e.g., Fig. 1). Given that the assumptions for the application of wavelet flux processing are more relaxed compared to the EC method, mainly because there is no requirement for stationarity of the flow, wavelet-derived fluxes therefore provide a solid reference for constraining potential biases in EC fluxes under non-ideal conditions.

Under medium stationarity, mean EC-flux rates are slightly higher than the
wavelet reference fluxes at both towers (tower 1:

Our flux processing method intercomparison under low stationarity clearly indicates that EC-derived methane fluxes under such conditions are unreliable and should be sorted out to ensure plausible results. Mean flux rates for both towers only amounted to slightly more than 50 % of the wavelet reference fluxes; therefore the inclusion of such data into the computation of long-term methane flux budgets would lead to a systematic and potentially severe underestimation of the actual emissions. Since a reliable direct measurement with the EC method is not reliable, and also gap filling is associated with considerable uncertainties (see below), wavelet processing holds the potential to provide novel insights into methane exchange processes also under difficult measurement conditions.

As demonstrated by the frequency distributions of methane flux rates derived by wavelet processing and three different gap-filling methods (Fig. 2), all EC gap-filling approaches tested here cannot capture the full range of natural variability of the methane emissions observed by the reference wavelet fluxes. The wavelet flux distribution indicates that the occurrence of high flux rates, or emission outbursts that may be related to events as further discussed below, are an important element of the methane release dynamics at our study site. These high flux rates, which cause the positive skewness and the long positive tail in the wavelet flux frequency distribution, are at best coarsely approximated by the gap-filling algorithms. The fact that the simplest gap-filling algorithm, linear interpolation, gets closest to a positively skewed flux distribution as provided by the wavelet reference indicates that even sophisticated algorithms such as neural networks have limitations when it comes to capturing the mechanisms that control episodic high methane emissions from wetland ecosystems.

While the uncertainty associated with methane gap filling produces partly
large offsets when comparing individual 30 min flux rates to the wavelet
results, we found that the integrated flux over a longer-term study period is
rather stable across gap-filling approaches and that mean flux rates still
agree well with the reference for parts of the dataset. At our tower 2, the
gap-filled mean fluxes ranging between 37.2 and 41.3 nmol m

As any other type of model, gap-filling approaches need to be based on reliable statistical and/or process-based algorithms, and in addition they need representative training data to produce reliable results. In the tests conducted within the context of this study, none of the three gap-filling algorithms could fully hold up to these standards. For the two simple approaches, linear interpolation and moving window averaging, with no mechanisms available that link fluxes to controls these methods can only rely on the available range of measured fluxes under high to medium stationarity to base their output on. As a consequence, in the absence of process-based algorithms all gap-filling methods are dependent on the distribution of gaps to be filled, and therefore their performance is subject to a certain level of randomness. Regarding the neural network approach, since our example at tower 1 demonstrates that this sophisticated algorithm can produce offsets as large as found for the MW method, the established links between environmental controls and methane fluxes, which again are based on observations during high or medium stationarity, are not necessarily representative under poorly developed turbulence. This caveat can only be improved through reliable, process-based gap-filling algorithms that do not exclusively focus on biogeochemical aspects but also incorporate biogeophysical elements such as atmospheric pressure or turbulence conditions into the calculations.

With only up to 11 % of flux values to be filled as gaps resulting from
low data quality during our study (Table 2), even a
systematic underestimation of reference fluxes by the gap-filling methods of

Our datasets demonstrate that event emissions make up a small but noticeable part of the methane flux time series observed at our Ambolikha observation sites in northeastern Siberia. At tower 2, summed up over the study period of 108 d in summer 2014, about 3 % (158 cases) of half-hourly flux values were affected by events, contributing 2.5 %–2.8 % of the total methane budget emitted during this period. At tower 1 (data not shown), the event fraction was slightly higher (3.7 %; 193 cases), and also the fraction of the total flux affected by events increased in comparison to tower 2 (3.7 %–5.3 %). Differences between towers are associated with the higher fraction of extreme outliers, as detected by the MAD test at tower 1 (Schaller et al., 2019), which may be linked to the fact that mean flux rates at this site are lower so that emission peaks differ more strongly from the baseline emissions. Overall, these results indicate that, even when completely ignoring the potential presence of such events, regular EC data processing and gap-filling algorithms on average can produce flux rates that are reasonably close to the wavelet fluxes that resolve events (see detailed discussion below). Consequently, for the case study presented herein, the presence of non-stationary methane outburst events did not lead to systematic biases in the EC-based long-term methane budget that go beyond the regular measurement uncertainty.

At tower 2, at times without event occurrence, the EC-derived fluxes overestimated the wavelet reference by 1.2 % under high stationarity and 5.8 % under medium stationarity. Similar offsets were observed at tower 1 (not shown). During events, the overestimation of fluxes under medium stationarity (11 %) approximately matched these biases, while under high stationarity, fluxes tended to be underestimated by 18 %. At tower 1, on the other hand, event fluxes under both stationarity categories were underestimated by 9 %–13 %. With the contributions of total fluxes per stationarity category ranging between 0.7 % and 2.8 % across towers, this minor tendency towards underestimating event fluxes did not influence the EC-computed flux budgets considerably.

During low-stationarity conditions, all fluxes based on EC processing will
be sorted out and will subsequently be replaced by gap-filling values,
independent of whether or not an event was contained in the specific
half-hourly window. Therefore, the correspondence between gap-filling results
and wavelet reference fluxes was largely identical between event and no-event cases at both towers. The influence of events under such
circumstances is therefore restricted to the question whether or not event
occurrences increase the fraction of detected low-stationarity cases, which
will be filtered out during quality screening and therefore create gaps.
Data summarized in Table 5 show that, for our
dataset from tower 2, the relative fraction of cases with low stationarity
was

Regarding the impact of events on the short-term variability of fluxes, the
range of differences between wavelet- and EC-derived 30 min flux rates is
similar for event and no-event cases (see Appendix A4, Fig. A3);
however, while during no-event cases a large number of values still show
good correspondence; those cases with substantial deviations from the 1 : 1
line dominate the method intercomparison for fluxes influenced by events.
This is clearly indicated by the root-mean-square errors (Table A2), which
under all stability categories are higher for the events cases. Under high
to medium stationarity, the offsets produced by EC processing appear to be
random; therefore the number of events does not seem to introduce a
systematic bias into the long-term budget. Still, Fig. A3 demonstrates
that, particularly for medium stationarity, the EC-derived flux rates
influenced by events have poor quality overall, with RMSE values

Our findings demonstrate that regular eddy-covariance flux processing yields highly reliable results under high-stationarity conditions, while for medium to low stationarity, the half-hourly averaged flux rates by the wavelet method should be preferred instead when investigating methane emission dynamics at high temporal resolution. Particularly in the presence of events, individual EC-flux rates are associated with a very high uncertainty and should only be used for the computation of long-term flux budgets. With events often occurring at timescales of only a few minutes, the wavelet flux processing holds the potential to provide new insights into the characteristics of these important elements of the methane cycle, since it facilitates flux computation down to time steps of 1 min without violating underlying theoretical assumptions. As demonstrated already for the decomposition of flux signals from spatially varying source areas (Metzger et al., 2013; Xu et al., 2017), wavelets provide a valuable tool for investigating the statistics of highly irregular emissions and how they can be correlated with environmental conditions and potentially be resolved by process-based algorithms for gap filling and/or extrapolation purposes.

Our study investigated the impact of short-term episodic emission outbursts, so-called event fluxes, on the overall data quality of methane fluxes observed by eddy-covariance towers over a wet tussock tundra ecosystem in northeastern Siberia. We evaluated the EC-flux dataset against reference fluxes based on wavelet processing, which are not restricted to stationary flow conditions and can resolve flux patterns down to time steps of 1 min. The wavelet analysis demonstrates that high-methane-emission events influenced 3 %–4 % of the flux observations during our study period, with integrated event emissions contributing 3 %–6 % to the net methane budget. EC-flux data processing tended towards slightly underestimating the wavelet fluxes while events were present, but the net impact on long-term flux budgets is minor in relation to other uncertainties associated with eddy-covariance measurements. For the intercomparison of flux rates at 30 min time steps, however, our results demonstrate that the presence of events substantially increases the scatter between wavelet- and EC-derived fluxes, indicating that events introduce additional uncertainty into the EC results.

A second focus of this study was placed on the evaluation of common gap-filling approaches for EC-derived methane fluxes. Our wavelet-derived fluxes provided an observation-based reference for the fraction of gaps in the EC time series that was created because measurements under low stationarity were filtered out by the data quality assessment protocol. None of the three gap-filling approaches tested herein could reproduce the range of values provided by the wavelet reference, but resulting biases in long-term flux budgets were still minor because of the comparatively small fraction of gaps that needed to be filled in our datasets. The performance of the gap-filling methods appeared to be dependent on the gap distribution and the ratio of flux rates between the gaps and the remaining dataset. With a profound mechanistic understanding on processes and controls that govern the short-term variability in methane emissions still lacking, the quality of gap-filling products retains a certain level of randomness; therefore systematic biases even over longer timeframes cannot be ruled out, particularly for datasets that contain a higher gap fraction than the ones used in our study.

Our findings demonstrate that wavelet analyses hold the potential to enhance our understanding in methane exchange processes between terrestrial ecosystems and the atmosphere. With excellent agreement between wavelet- and EC-derived fluxes demonstrated under ideal turbulence conditions, wavelet fluxes facilitate quantifying biases in EC datasets linked to non-ideal conditions, for example, medium to low stationarity of the flow. Moreover, the provision of observationally based reference fluxes at times when the EC method produces data gaps can support the development of novel process-based modeling algorithms that are representative for a wider range of environmental conditions, which can be employed, for example, in the improvement of gap-filling algorithms. Finally, the option to resolve fluxes down to temporal resolutions of 1 min facilitates new insights into the intermittent nature of methane emissions and its impact on the quality of methane flux observations.

The software scripts that execute the wavelet-based flux data processing can be made available by the authors upon request.

The following description of the wavelet method is a slightly shortened version of the description provided by Schaller et al. (2017), which is the companion paper introducing the methodology that the presented study is based upon. It has been included here again to facilitate an easier overview on the procedure without having to read other papers. For more details, please refer to Schaller et al. (2017).

A continuous wavelet transform of a discrete time series

The wavelet

As mentioned in the main text above, this study used the complex-valued
Morlet wavelet for quantification of flux rates and the Mexican hat wavelet
for the exactly localization of

For two simultaneously recorded time series

Fingerprint plots showing the diurnal distribution of flux rates and gaps (white) for both towers and processing methods.

Seasonal

Mean methane fluxes for the wavelet method and EC method, split into three stationarity categories. For the lowest stationarity, in addition to measured EC values, model results by the three different gap-filling approaches, linear interpolation (LI), moving window (MW) and neuronal network (NN), are given. Absolute flux values are given in usual font, while italic font indicates flux differences between EC and wavelet processing; numbers in brackets give the percentage deviation. NA stands for not available.

Impact of events on the direct intercomparison of half-hourly flux rates between wavelet and eddy-covariance processing methods, sorted by tower and stationarity flag (SF) category. The displayed dataset includes gap-filled data, where linear interpolation was used to fill gaps for the EC method under low stationarity. Fluxes influenced by events are plotted in red, while no-event cases are black. The thin grey line gives the 1 : 1 line, and the black line gives the fit of the orthogonal regression (OR) analysis.

Deviations between 30 min averaged fluxes based on wavelet and
EC processing, expressed as the root-mean-square error (nmol m

MG was responsible for study conception and supervision. All authors contributed to development of the methodology and formal data analysis, with computation largely carried out by FK (eddy covariance) and CS (wavelets). All authors contributed to underlying fieldwork. MG wrote the initial paper, with contributions by FK. All authors contributed to reviewing the paper text and editing the final paper version.

The authors declare that they have no conflict of interest.

The authors would like to thank Thomas Foken (University of Bayreuth) for his comments to an earlier version of the paper. The German Academic Exchange Service (DAAD) provided financial support for the travel expenses. The authors appreciate the contribution of staff members of the Northeast Scientific Station in Chersky for facilitating the field experiments.

This work was supported through funding by the European Commission (PAGE21 project, FP7-ENV-2011, grant agreement no. 282700; PerCCOM project, FP7-PEOPLE-2012-CIG, grant agreement no. PCIG12-GA-201-333796; INTAROS project, H2020-BG-09-2016, grant agreement no. 727890; Nunataryuk project, H2020-BG-11-2016/17, grant agreement no. 773421), the German Ministry of Education and Research (CarboPerm project, grant no. 03G0836G; KoPf project, grant no. 03F0764D), and the AXA Research Fund (PDOC_2012_W2 campaign, ARF fellowship for Mathias Göckede).The article processing charges for this open-access publication were covered by the Max Planck Society.

This paper was edited by Paul Stoy and reviewed by Gil Bohrer and one anonymous referee.