INTRODUCTION

Interest in observations of the methane (CH4) content in the near-surface air layer stems from the effect of this compound on the radiative transfer and photochemical processes in the atmosphere [1], as well as from the importance of methane cycle in the dynamics of the Earth system as a whole [2]. For Northern Eurasia, the regional balance of tropospheric methane is urgent to study because of the high potential significance of the region as an emission source of greenhouse gases and climate changes occurring in this region. An important role of emissions from wetland and freshwater ecosystems of the region in global methane cycle was underlined in many model and experimental works (see, e.g., [3–8] and references therein).

Data from direct measurements of methane content in the near-surface air layer at background atmospheric monitoring stations are the necessary part of initial information on the Earth system when regional methane fluxes are estimated. The use of these data in the algorithms for retrieving the emission fields by the top-down method, which are based on the solution of the inverse atmospheric transfer problem [8], makes it possible to restrict the errors of reproducing the model fields of the atmospheric methane concentration when introducing corrections to a priori emission fields. The available quantitative estimates of the direct contribution of regional sources of methane to its content over continent are a few and very different because the emissions are uncertain against the background of their strong seasonal and interannual variations [8–11].

The purpose of this work is to estimate how natural and anthropogenic emissions of methane in Northern Eurasia influence its annual variations. The relevance of these estimates are dictated by the very limited methane monitoring data from Northern Eurasia and a need in analyzing the available observations in the framework of the most general formulation of the atmospheric transport problem taking into account the regional and remote emission sources.

1 DATA AND METHODS

In this paper, we analyze the measurements from the Zotino Tall Tower in Central Siberia (ZOTTO) [4] and from regional Arctic stations Teriberka and Tiksi (Fig. 1).

Fig. 1.
figure 1

Model domain “Northern Eurasia” (10° W–180° E, 40°–85° N). Gray shadings show territories with annual average wetland methane emissions ≥1.13 nmol/m2  s. Dark circles indicate the regions of nonzero anthropogenic methane emissions according to the EDGAR4.3.2 inventory.

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The data from multiyear observations at the Arctic stations are compared with the calculations using chemical transport model (CTM) GEOS-chem specifying all the main planetary-scale sources and sinks of methane. The contributions of anthropogenic and biogenic signals to the methane content at each station are estimated quantitatively by the method of reducing the emissions in the model domains specified. The beginning of the period analyzed roughly corresponds to the onset time of the new stage of the global growth of the methane content in the atmosphere after it slowed down in 1990s and in early 2000s [12, 13].

1.1 Station-Based Observations

In this paper, we used continuous time series of the methane concentration (mixing ratio, ppbv), obtained at the Tiksi station (January 2012–July 2018) from Picarro gas analyzers and in Teriberka (January 2007–December 2017).

The near-surface measurements of the methane concentration in Tiksi were carried out within the international Global Air Sampling Network of NOAA’s Global Monitoring Laboratory (GML). The initial one-minute data are provided for noncommercial use at the GML website (https://gml.noaa. gov/ccgg/ggrn.php). For the measurements of the methane concentration in Teriberka, air samples are taken regularly at the Voeikov Main Geophysical Observatory. The data are available at the WMO Global Atmosphere Watch Station Information System (GAWSIS at https://gawsis.meteoswiss.ch/GAWSIS).

Quantitative estimates of the annual and seasonal variations in the methane content within ZOTTO were obtained using Picarro gas analyzer measurements [4] over 2009–2012.

1.2 GEOS-Chem Model

The global GEOS-Chem CTM (Goddard Earth Observing System chemical model, https://geos-chem.seas.harvard.edu) [14] relies upon numerical integration of system of finite-difference Euler equations which describe the advection in a regular wind field, subgrid scale transport, and chemical conversions of trace gases and aerosol admixtures significant for the tropospheric photochemical system using MERRA2 reanalysis meteorological fields. The calculations were carried out on a baseline grid with the horizontal resolution 4° × 5°.

Anthropogenic methane sources were specified in accordance with the global inventory EDGAR4.3.2 with an initial resolution of 0.1° × 0.1° [15] (see Fig. 1). Methane emissions from biomass burning were calculated using the GFED4 data [16]; however, no systematic analysis of how wildfires influence the atmospheric methane content was performed because the model had limited spatial resolution and the emissions showed interannual and seasonal variations.

Methane fluxes from overwetted territories were specified using the WetCHARTs v1.0 model [17], which is based upon satellite data on the surface properties, temperature, and precipitation. The average flux (kg CH4/m2 s) was calculated using the empirical formula

$${{F}_{{{\text{C}}{{{\text{H}}}_{4}}}}}({{t}_{{\text{m}}}},{\mathbf{r}}) = sA({{t}_{{\text{m}}}},{\mathbf{r}})R({{t}_{{\text{m}}}},{\mathbf{r}}){\kern 1pt} Q_{{10}}^{{T({{{{t}_{{\text{m}}}},\,\,{\mathbf{r}})} \mathord{\left/ {\vphantom {{{{t}_{{\text{m}}}},\,\,{\mathbf{r}})} {10}}} \right. \kern-0em} {10}}}},$$
(1)

where tm is the given month; r is a latitudinal-longitudinal grid cell; s is the global average scaling factor; A(t, r) = w(r)h(t, r) is the fraction of wetland area, w and h are the time-static and time-variable components; R is the intensity of heterotrophic respiration, being numerically equal to the total carbon (C) flux from unit surface area into the atmosphere during decomposition of organic substances; \(Q_{{10}}^{{{{T({{t}_{{\text{m}}}},\,\,{\mathbf{r}})} \mathord{\left/ {\vphantom {{T({{t}_{{\text{m}}}},\,\,{\mathbf{r}})} {10}}} \right. \kern-0em} {10}}}}\) determines the temperature dependence of the emission ratio CH4 : C, where Q10 is the ratio of methane to carbon mass at Т = 10°С, and T is the radiation temperature of skin layer. Formula (1) gives a first-order approximation in calculating the global field of methane emissions as a functional of the total carbon flux, temperature, and water balance [17].

The final value \({{F}_{{{\text{C}}{{{\text{H}}}_{4}}}}},\) specified on a grid with a resolution of 0.5° × 0.5° in space and 1 month in time, is a sum of methane fluxes from wetlands, waterlogged soils, and inland water bodies, in accordance with the GLOBCOVER classification of the Earth’s surface [18]. The last two classes were estimated in [17] to be capable of contributing up to 20% of the total area of model-calculated overwetted territories. Nonetheless, as applied to WetCHARTs, thereafter for brevity we use the term “wetland emissions” taking into account their determinant contribution to the total flux of methane from its natural sources.

The methane sources and sinks in the model were described comprehensively in [19].

For Russia, the average (2007–2018) annual methane emissions were indicated in EDGAR4.3.2 and WetCHARTs1.0 data to be 24.2 and 10.3 Tg, respectively. Dividing this latter quantity by the area of the territory of Russia (17.07 million km2), we obtain the methane flux from wetland and inland water ecosystems average over the same years \({{F}_{{{\text{C}}{{{\text{H}}}_{4}},{\kern 1pt} {\text{wet}}}}}\) = 1.81 × 10−11 kg CH4/m2  s (1.13 nmol/m2  s). The territories of Northern Eurasia with the annual average methane fluxes \( \geqslant {\kern 1pt} {{F}_{{{\text{C}}{{{\text{H}}}_{4}},{\kern 1pt} {\text{wet}}}}}\) are shown in Fig. 1.

1.3 Atmospheric Response to Regional Emissions

The GEOS_chem model calculations were carried out from January 1, 2007, to December 31, 2018, with results outputted once hourly. We analyzed the fields of the concentration [CH4] (ppbv) at the first calculational level; they corresponded to the average methane content in the 123-m thick near-surface layer.

The sensitivity of the surface methane field to anthropogenic and wetland emissions was estimated in the model domains (Ω) “Northern Eurasia” (a part of the continent poleward of 40° N) and “Russia” (mask of the territory on the 4° × 5° grid using data from naturalearthdata.com). The methane fluxes at the lower boundary were specified by considering a scenario with all planetary emissions in accordance with the basis model configuration (the А0 scenario), as well as the scenarios with switched-off anthropogenic or wetland emissions in Northern Eurasia (scenarios A1 and W1 respectively) and Russia (scenarios A2 and W2). The annual methane emissions \(({{E}_{{{\text{C}}{{{\text{H}}}_{4}}}}})\) in the model domains according to the EDGAR and WetCHARTs data are presented in Table 1.

Table 1.   The 2007–2018-average methane emissions \(({{E}_{{{\text{C}}{{{\text{H}}}_{4}}}}},\) Tg СН4/year) in different regions
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The model fields of atmospheric response in the methane content (χmod, ppbv) over each month in 2007–2018 were calculated by the method of reducing emissions. For the sources in the model domain, the value χmod in the cell r over the month tm was determined as the difference between the methane concentration obtained from the basis model calculation with all planetary emissions [CH4]0 (scenario А0) and the concentration [CH4](−) calculated according to either the scenario А or W:

$$\begin{gathered} {{\chi }_{{{\text{mod}}}}}({\mathbf{r}},t{}_{{\text{m}}};\Omega ) \\ = {{\left\langle {{{{[{\text{C}}{{{\text{H}}}_{4}}]}}_{0}}({\mathbf{r}},t) - {{{[{\text{C}}{{{\text{H}}}_{4}}]}}^{{( - )}}}({\mathbf{r}},t;\Omega )} \right\rangle }_{{\text{m}}}}, \\ \end{gathered} $$
(1b)

where \({{\left\langle {} \right\rangle }_{{\text{m}}}}\) means an average over the given month in the current year. Considering that the contribution of regional sources to the global methane emission is relatively minor (see Table 1), we can neglect the nonlinear effects caused by the effect of the atmospheric methane content on the global hydroxyl field. In this case, the χmod value will be equal to the contribution of the region of model domain to the global methane field calculated according to the scenario A0 for the current planetary sources of emissions and the state of the atmospheric photochemical system.

For a given emission field in the model domain, the long-term average methane concentration in r is determined totally by the probability distribution of transition of an air particle (carrying a certain mass of admixture) from this domain into r as a function of the advection time tadv (age spectrum). The FLEXTRA model calculations indicate [20] that, for European sources and an arbitrary point on the continent poleward of 30°–40° N, the predominant contribution to tracer concentration is introduced by air with age <10–20 days, corresponding to the upper boundary of synoptic-scale time interval Tsyn (= 20 days). The main portion of admixture on timescales ≤Tsyn remains trapped at altitudes lower than 2–3 km (see Figs. 5 and 11 in [20]) in view of relatively weak vertical exchange between the atmospheric boundary layer and the free troposphere during advection over continent. Poleward of 65°–70° N, the maximum of the spectral function shifts toward larger advection times, the main contribution to the total signal being observed at the transport time from 10 to 30 days. The upper boundary of this range is concluded in [20] to be close to the characteristic time Tmix (∼1 month) of zonal and meridional equalization of the tracer field in the Northern Hemisphere extratropical troposphere. At the same time, the Tmix turns out to be much shorter than the time of air exchange between midlatitudes and near-equatorial regions (∼0.4 years) and exponential time of inter-hemispheric exchange Tint (1.2–1.5 years) [21].

The above tendency of trapping the admixtures from European sources on timescales ≤Tsyn in the lower troposphere distinguishes the advection over the continent from large-scale admixture transport from the main climatically significant anthropogenic pollution regions, concentrating near eastern coasts of North America and Asia. The collocation of these latter with the high-altitude frontal zones determines the high speeds of the vertical advection with the subsequent trans-oceanic transport at the altitudes of the middle and high troposphere [20].

In our subsequent analysis, we neglect the possible multiyear trends of the wind and turbulence fields in the model domain, so that for the chosen month the transport of long-lived admixture in a synoptic time interval can be considered statistically stationary process. Owing to the inequality \({{T}_{{{\text{syn}}}}} \sim {{T}_{{{\text{mix}}}}} \ll {{T}_{{\operatorname{int} }}},\) which expresses the separation into fast and slow processes of atmospheric mixing, in this case the ensemble-average field of the atmospheric response χ(r, tm; Ω) from sources in the model domain can be represented as a superposition of the synoptic (χsyn) and global (χ′) components:

$$\begin{gathered} {{\chi }_{j}}({\mathbf{r}},t{}_{{\text{m}}}{\kern 1pt} ;\,\,\Omega ) = {{\chi }_{{{\text{syn}}({\text{m}})}}}({\mathbf{r}};\,\,\Omega ) + \chi _{j}^{{{'}}}(t{}_{{\text{m}}}{\kern 1pt} ;\,\,\Omega ) \\ (t{\kern 1pt} {}_{{\text{m}}}\, \gg {{T}_{{{\text{mix}}}}}), \\ \end{gathered} $$
(2)

where χsyn characterizes the direct contribution from sources for the transport time ≤Tsyn; \(\chi _{j}^{{{'}}}\) is the long-term effect of methane accumulation in the atmosphere (for tm ≥ Tint), j ≡ S and N stand for the Southern and Northern Hemispheres, respectively.

As in [22], we assume that \({{\chi }_{{{\text{syn}}({\text{m}})}}}({\mathbf{r}};\,\,\Omega ) = \) \({{\left\langle {\chi ({\mathbf{r}},\,\,t;\,\,\Omega )} \right\rangle }_{{{\text{m}},{\kern 1pt} y}}},\) where the operator \({{\left\langle {} \right\rangle }_{{{\text{m}},\;y}}}\) represents the arithmetic mean of the corresponding quantities over all days of the month “m” for all years from the time interval considered here.

In accordance with [21, 23], the explicit forms of the functions \(\chi _{{\text{S}}}^{{{'}}}\) and \(\chi _{{\text{N}}}^{{{'}}}\) will be found using two-box model of the atmosphere with a preset intensity r (=1/Tint) of the inter-hemispheric air exchange

$$\frac{{d\chi _{{\text{S}}}^{{{'}}}}}{{dt}} = r(\chi _{{\text{N}}}^{{{'}}} - \chi _{{\text{S}}}^{{{'}}}) - \lambda \chi _{{\text{S}}}^{{{'}}},$$
(3)
$$\frac{{d\chi _{{\text{N}}}^{{{'}}}}}{{dt}} = - r(\chi _{{\text{N}}}^{{{'}}} - \chi _{{\text{S}}}^{{{'}}}) - \lambda \chi _{{\text{N}}}^{{{'}}} + {{S}_{{\text{N}}}}$$
(4)

with the initial conditions \(\chi _{{\text{S}}}^{{{'}}}(0) = 0,\) \(\chi _{{\text{N}}}^{{{'}}}(0) = \chi _{{\text{N}}}^{0},\) where \(\lambda = {1 \mathord{\left/ {\vphantom {1 {{{\tau }_{{{\text{C}}{{{\text{H}}}_{4}}}}};}}} \right. \kern-0em} {{{\tau }_{{{\text{C}}{{{\text{H}}}_{4}}}}};}}\)

$${{S}_{{\text{N}}}} = \frac{{{{E}_{{{\text{C}}{{{\text{H}}}_{4}}}}}}}{{{{M}_{{{\text{NH}}}}}}}\frac{{{{\mu }_{{\text{a}}}}}}{{{{\mu }_{{{\text{C}}{{{\text{H}}}_{4}}}}}}}$$
(5)

is the total intensity of methane sources recalculated into mixing ratio units, ppb/year; MNH is the air mass in the troposphere of each Hemisphere (layer 1000–200 mbar thick), μa = 29 g/mol and \({{\mu }_{{{\text{C}}{{{\text{H}}}_{4}}}}}\) = 16.05 g/mol are the molar masses of air and methane respectively.

The solution of Eqs. (3) and (4) has the form

$$\begin{gathered} \chi _{{\text{S}}}^{{{'}}} = \frac{1}{2}\left( {\chi _{{\text{N}}}^{{{{'}}0}} - \frac{{{{S}_{{\text{N}}}}}}{\lambda }} \right)\exp ( - \lambda t) \\ - \,\,\frac{1}{2}\left( {\chi _{{\text{N}}}^{{{{'}}0}} - \frac{{{{S}_{{\text{N}}}}}}{{2r + \lambda }}} \right)\exp \left( { - [2r + \lambda ]{\kern 1pt} t} \right) + \frac{{{{S}_{{\text{N}}}}r}}{{\lambda (2r + \lambda )}}, \\ \end{gathered} $$
(6a)
$$\begin{gathered} \chi _{{\text{N}}}^{{{'}}} = \frac{1}{2}\left( {\chi _{{\text{N}}}^{{{{'}}0}} - \frac{{{{S}_{{\text{N}}}}}}{\lambda }} \right)\exp ( - \lambda t) \\ + \,\,\frac{1}{2}\left( {\chi _{{\text{N}}}^{{{{'}}0}} - \frac{{{{S}_{{\text{N}}}}}}{{2r + \lambda }}} \right)\exp \left( { - [2r + \lambda ]{\kern 1pt} t} \right) + \frac{{{{S}_{{\text{N}}}}(r + \lambda )}}{{\lambda (2r + \lambda )}}. \\ \end{gathered} $$
(6b)

In the limit, as λ → 0, formulas (6a) and (6b) go into formulas (2) from [23], in accordance with which the tracer concentration linearly growths on large timescales:

$$\begin{gathered} {{\chi }_{j}}({\mathbf{r}},t;\Omega ) = {{\chi }_{{{\text{syn(m)}}}}}({\mathbf{r}};\Omega ) \\ \sim \frac{1}{2}\left( {\chi _{{\text{N}}}^{0} \mp \frac{{{{S}_{{\text{N}}}}}}{{2r}}} \right) + \frac{1}{2}{{S}_{{\text{N}}}}t\,\,\,\,(\lambda = 0,\,\,rt \gg 1), \\ \end{gathered} $$
(7)

where the signs “−” and “+” stand for j = S and j = N. In our calculational scenarios, \(\chi _{{\text{N}}}^{{{{'}}0}} \equiv 0,\) whence accounting for Eqs. (2) and (6b) yields

$$\begin{gathered} {{\chi }_{{\text{N}}}}({\mathbf{r}},t;\Omega ) = {{\chi }_{{{\text{syn(m)}}}}}({\mathbf{r}};\Omega ) \\ - \,\,\frac{{{{S}_{{\text{N}}}}}}{2}\left( {\frac{{\exp ( - \lambda t)}}{\lambda } + \frac{{\exp \left( { - [2r + \lambda ]t} \right)}}{{2r + \lambda }}} \right) + \frac{{{{S}_{{\text{N}}}}(r + \lambda )}}{{\lambda (2r + \lambda )}}. \\ \end{gathered} $$
(8)

At λ > 0 and \(\lambda t \gg 1\), the \(\chi _{j}^{{{'}}}\) values are determined by the last terms in the right-hand sides of Eqs. (6a) and (6b). The corresponding asymptote of the χ field for the Northern Hemisphere has the form

$${{\chi }_{{\lim }}}({\mathbf{r}};\,\,\Omega ) \sim {{\chi }_{{{\text{syn(m)}}}}}({\mathbf{r}};\,\,\Omega ) + \frac{{{{S}_{{\text{N}}}}(r + \lambda )}}{{\lambda (2r + \lambda )}}\,\,\,\,(\lambda t \gg 1).$$
(9)

For a chosen month, a comparison of model response χmod (1) with \(\chi _{{\text{N}}}^{{{'}}}\) (6b) for a known intensity of the source SN makes it possible to estimate the regional addition χsyn as the multiyear average difference between the total model response and its global component according to the model scenario:

$${{\chi }_{{{\text{syn(m)}}}}}({\mathbf{r}};\,\,\Omega ) = \left\langle {{{\chi }_{{{\text{mod}}}}}({\mathbf{r}},\,\,{{t}_{{\text{m}}}};\,\,\Omega ) - \chi _{{\text{N}}}^{{{'}}}({{t}_{{\text{m}}}};\,\,\Omega )} \right\rangle .$$
(10)

The calculations of time dependences χmod(t) (1) and χN(t) (8) are presented below as the final values for ZOTTO and Arctic stations. Multiyear average regional contribution χsyn(m) (10) and the corresponding asymptotic estimates for total atmospheric response χlim (9) are presented for January and July 2007–2018 (the central months of winter and summer).

2 RESULTS AND DISCUSSION

2.1 Comparison of Model- and Station-Based Data

The model-based and measured methane concentrations are compared in Fig. 2. The annual behaviors of the methane content in Teriberka and ZOTTO are characterized by a well-defined maximum in winter months and a minimum in late spring–early summer; the multiyear average differences between them (the amplitudes of variations) are 49.2 and 64.2 ppbv, respectively. The presence of a wintertime maximum reflects the general tendency toward accumulation of long-lived admixtures in the lower extratropical Northern Hemisphere troposphere in the cold period of the year and is associated with the seasonal decrease in the oxidation capacity of the atmosphere, the mixing layer height, and the intensity of the vertical air exchange between the boundary layer and the free troposphere [24]. An analogous (unimodal) annual behavior of methane is also found at other regional stations, located at the Northern Hemisphere middle and high latitudes [4, 24, 25]. On the whole, the annual behavior of methane at the Tiksi station is close to the above-described unimodal variations with the amplitude of 55.6 ppbv. In separate years, in late summer–early fall, there is the secondary maximum, the amplitude of which in October 2015 (as well as in August 2019 and November 2020, based on data published at the Voeikov Main Geophysical Observatory website) exceeds that of the winter maximum. As was indicated previously [6, 26], this maximum at the station Tiksi coincides in phase with the seasonal maximum of thaw depth of the near-surface soil layer on the continent and a minimum of the sea ice area in the ocean shelf, possibly indicating a marked contribution of regional natural methane sources to the observed seasonal growth of the near-surface methane concentration in anomalously warm years.

Fig. 2.
figure 2

Monthly average near-surface CH4 concentrations in (a) Teriberka and (b) Tiksi: \(\square \) indicate observations, and indicate the model; P10, P90 are the 10th and 90th percentiles of the daily average values over a given month in Tiksi; error bars indicate the scatter between minimal and maximal values for air samples.

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Figure 2 and Fig. 19 from [4] indicate that the scatter of the measured concentrations within a single month at all stations is comparable with the amplitude of the annual variation. This feature is manifested most strongly at the Teriberka and ZOTTO stations because of their proximity to the main methane source regions in the western part of the continent. A characteristic feature of observations in the near-surface layer is that “synoptic noise” contributes markedly to the total variations in the content of long-lived admixtures because of both meteorological factors and spatial inhomogeneity of the distribution of the corresponding emission sources.

As the criteria for the correspondence between observations and calculations at the Arctic stations, we used standard statistics: the bias \(\delta = \left\langle {O - C} \right\rangle ,\) the standard deviation \(\delta = {{\left[ {\left\langle {{{{(O - C)}}^{2}}} \right\rangle } \right]}^{{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}}}}\), and the Pearson correlation coefficient R, where О and С are the monthly average concentrations obtained from the observations and model calculations respectively. Based on Table 2, in December–February, the |δ| value is much smaller than 2σ (“model noise”) and than the amplitude of the annual variations in methane at both stations; together with high R, this indicates the success of the model prediction in the Arctic region during the winter. In June–August, there is a marked positive bias of the model concentrations amounting to about 25% of the amplitude of the annual variation, at lower correlation coefficients than during winter months.

Table 2.   Comparison of model-based and measured CH4 concentrations for separate stations
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Additional analysis showed that the poor general correspondence between calculations and experimental data in the summer period is probably because of the errors in the calculations of the subgrid-scale vertical transport due to overestimated intensity of the vertical turbulent exchange. Other causes for the observed discrepancy may be errors of reproducing high-frequency (synoptic-scale) fluctuations in the methane field due to limited spatial resolution of the model (which is indicated by relatively high σ), as well as the errors of reproducing methane emissions from local sources. On the whole, the model realistically reproduces both annual and long-term variations in the measured methane content, making it possible to use the calculation results for identifying the contributions from anthropogenic and biogenic signals taking into account the seasonal variations in the regional emission sources.

2.2 Atmospheric Response in Methane Field

The χN values calculated from formula (8) agree well with model responses χmod (1) for each of the stations within the \({{\tau }_{{{\text{C}}{{{\text{H}}}_{4}}}}}\) and Tmix uncertainty ranges, presented by different authors. The dependences χmod(t) and χN(t) at \({{\tau }_{{{\text{C}}{{{\text{H}}}_{4}}}}}\) = 10.6 years [19], Tmix = 1.4 years, and \({{E}_{{{\text{C}}{{{\text{H}}}_{4}}}}}\) values from Table 1 for the model scenarios A1 and W1 are presented in Figs. 3 and 4. (The results for the scenarios А2 and W2 look similar, with proportionally smaller absolute values of the signals.) In terms of the annual average values (Fig. 3), the discrepancies between χmod and χN in the second and next years do not exceed 1%. After comparing the χN(t) calculations by Eqs. (7) and (8) for ZOTTO (Fig. 3a), we can conclude that the finite methane lifetime in the atmosphere is important to take into account to estimate quantitatively the regional atmospheric responses on timescales larger than 1–2 years because of the long time of the response of the atmosphere to methane sources.

Fig. 3.
figure 3

Dependences χmod(tm) (1) (dots) and χN(tm) (8) (solid lines) for (a) station ZOTTO and (b) for the Arctic stations Tiksi (TIXI) and Teriberka (TER) in 2007–2018, as well as χsyn (10) and χlim values (9) at ZOTTO and their averages over the Arctic stations; dashed lines indicate the linear approximations using formula (7) for ZOTTO. The scenarios A1 and W1 (model domain Northern Eurasia). Month number starting from January 2007 is plotted along the abscissa.

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Fig. 4.
figure 4

Dependences χmod(tm) (1) and χN(tm) (8) for ZOTTO and Arctic stations in scenarios (a, b) A1 and (c, d) W1 for (a, c) January and (b, d) July 2007–2018; χsyn (10) and χlim (9) for ZOTTO and averages over Arctic stations (ARCTIC, \(\left\langle {} \right\rangle \)).

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The vertical transects of χmod field (1) along 50° N in Figs. 5a and 5b and along 50° E in Figs. 5c and 5d for January and July 2015, taken as an example, clearly illustrate the conclusion that the atmospheric response in the methane field can reasonably be divided using fast and slow transport processes. It can be seen that the methane field from sources in Northern Eurasia is effectively divided into the domain of high absolute values and spatial gradients northward of 30° N in the longitudinal range 0–150° E and the other part of the atmosphere, where the methane concentration remains nearly constant (at a level of 125 ppbv). The main difference between the winter and summer χmod fields is due to relatively large mixing layer height in July (about 3–4 km versus 2 km in January) and proportionally smaller methane content near the lower boundary of the calculation domain. On the whole, there is a circumpolar equalization of the χmod field northward of 65°–70° N (figure is not presented) in accordance with the results in [20] (see discussion in section 1.3). This property of the numerical solution is manifested as the close correspondence of annual average (Fig. 3) and monthly average (see Fig. 4) χmod values for Tiksi and Teriberka. To simplify the quantitative analysis, the corresponding estimates for the Arctic region are given below as arithmetic means over both stations.

After the dependences χmod(tm) and χN(tm), presented in Figs. 3 and 4, are extrapolated into initial moment tm = −6 months (the moment when the model sources are switched on), the χsyn and χlim estimates can be obtained from formulas (9) and (10) (Tables 3 and 4). As follows from Table 3, the regional χsyn component of the total atmospheric response according to the scenarios А and W turns out to be 3–7 times less than the corresponding asymptotic quantity (χlim) for anthropogenic and biogenic signals. At the chosen methane lifetime \({{\tau }_{{{\text{C}}{{{\text{H}}}_{4}}}}}\) = 10.6 years in the atmosphere, function \(\chi _{{\text{N}}}^{{{'}}}({{t}_{m}})\) (6b), which determines the asymptote χN(tm), reaches 90% of its maximum for the time t * = 10.6 ln 0.2−1 ≈ 17 years, which is about a factor of 1.5 larger than the time interval analyzed here.

Table 3.   Annual average χsyn and χlim values for ZOTTO and Arctic stations, ppbv
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Table 4.   Monthly average χsyn values for ZOTTO and Arctic stations in January and July, ppbv
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In terms of the annual averages (Table 3), the anthropogenic signal at ZOTTO by scenarios А1 and А2 (56.3 and 38.6 ppbv, respectively) is about two times larger than that for the Arctic stations (31.9 and 19.5 ppbv). When the difference between the χsyn values in the scenarios А1 and А2 (W1 and W2) is considered an estimate of anthropogenic (biogenic) signal from the sources in Western Europe, it can be concluded that the anthropogenic methane emissions make the predominant contribution on the territory of Russia (38.6 ppbv) at ZOTTO as compared to European sources (17.7 ppbv); while for Arctic stations, the Russian and European sources make comparable contributions (19.5 and 12.4 ppbv, respectively). Both at ZOTTO and at the Arctic stations, the atmospheric responses in scenario W1 are only a little larger than their counterparts in the scenario W2. Thus, the contribution of wetland emissions on the territory of Russia in the total biogenic signal is absolutely larger than those from similar emissions from sources in Northern Eurasia: 34.2 and 19.7 ppbv for ZOTTO and Arctic stations (Russia) against 2.7 and 2.1 ppbv in Western Europe.

2.3 Seasonal Variations in Anthropogenic and Biogenic Signals

Similar estimates, but for January and July, are presented in Table 4. The decrease in the anthropogenic contribution and the increase in the biogenic contribution from winter toward summer observed at all stations reflect the total effect of seasonal variations in emission strengths, regimes of atmospheric circulation, and the depth and the rate of ventilation of the atmospheric boundary layer over the continent.

The strongest response in the methane content to the continental anthropogenic emissions throughout the year is observed at the station ZOTTO: 90.2 ppbv in January and 29.8 ppbv in July versus 51.5 and 22.5 ppbv in analogous months at the Arctic stations. As was already noted above, Central Siberia is in direct impact zone of anthropogenic sources of atmospheric pollution in Western Europe, European Russia, and southern Siberia [27] at characteristic time of atmospheric transport of 3–10 days from source regions to the region of the station. The decrease in the intensity of westerly transport and increase in the mixing layer height in the summer period are accompanied by decrease in the amplitude of anthropogenic signal in scenarios А1 and А2 by a factor of 2.5–3 at the station ZOTTO and by about a factor of 2 at the Arctic stations (see Table 4). The relative contribution of anthropogenic emissions in Western Europe when going from January toward July also decreases: from 35 to 31% at ZOTTO and from 57 to 48% at the Arctic stations.

Fig. 5.
figure 5

Vertical transect of the field χmod (1) along (a, b) 50° N and (c, d) 50° E over January and July 2015; contour interval is 25 ppbv. The EOS-chem calculations using the scenario А1.

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In July, the biogenic signal at the ZOTTO station is a factor of 2 larger than the anthropogenic signal; while at the Arctic stations, signals due to emissions from Northern Eurasia turn out to be nearly equal (22.0 and 22.5 ppbv; see Table 4). The biogenic signal calculated using the scenarios W1 and W2 also turns out to be a factor 1.5–2 larger at ZOTTO than at the Arctic stations. This difference is because the ZOTTO region is affected directly by methane emissions from overwetted territories of Western Siberia [4], characterized by one of the highest methane fluxes into the atmosphere of Northern Eurasia [9, 11].

It should be noted that in winter period, the biogenic signal at both ZOTTO and Arctic stations is still quite high, at a level of 10–20 ppbv. The presence of significant methane fluxes into the atmosphere during high-latitude winter was found previously from results of numerous experimental works for different types of wetland landscapes (see [10, 11] and references therein). Based on the methane measurements in wetland ecosystems in the northeast of European Russia (Bolshezemelskaya Tundra) and Western Siberia, positive methane fluxes (from soil into the atmosphere) in fall and winter were from 0.03 to 2 mg С/m2  h (0.7–46 nmol СН4/m2  s) [11]. In the Alaskan Arctic tundra [10], the winter (January–May) methane flux was about 0.1 mg С/m2  h (2.3 nmol СН4/m2  s), or ∼0.1 of the analogous value in summer months; at the same time, the total СН4 emissions for September–May from soil poleward of polar circle in the study region are estimated in [10] to be about 40% of the annual emissions.

On the same considerations as in derivation of Eq. (2), we represent the measured methane content [CH4]obs as the sum [CH4]obs = χsyn + χ(+) + \(\chi _{{\text{N}}}^{{{'}}},\) where χ(+) is the contribution of long-range transport from sources outside the model domain. Assuming the long-term average difference between the corresponding values in January and July as an estimate of the amplitude of annual variation (denoted below as Δ) yields

$$\Delta {\kern 1pt} {{[{\text{C}}{{{\text{H}}}_{4}}]}_{{{\text{obs}}}}} = \Delta {{\chi }_{{{\text{syn}}}}} + \Delta {{\chi }^{{( + )}}}.$$
(11)

Substituting χsyn from Table 4 gives us an estimate of the contribution of Δχsyn from sources in Northern Eurasia to the observed annual variations in methane content at the stations:

$$\begin{gathered} \Delta {{\chi }_{{{\text{syn}}}}} = \left[ {{{\chi }_{{{\text{syn}}}}}({\text{A}}1) + {{\chi }_{{{\text{syn}}}}}({\text{W}}1)} \right]\left( {{\text{January}}} \right)~ \\ - \,\,~\left[ {{{\chi }_{{{\text{syn}}}}}({\text{A}}1) + {{\chi }_{{{\text{syn}}}}}({\text{W}}1)} \right]\left( {{\text{July}}} \right), \\ \end{gathered} $$
(12)

whence accounting for Eq. (11) yields: Δχsyn = 38.9 ppbv, Δχ(+) = 25.3 ppbv (ZOTTO) and Δχsyn = 22.9 ppbv, Δχ(+) = 32.1 ppbv (Arctic stations).

These Δχsyn values turn out to be a factor of 1.5–2 smaller than the amplitudes of annual variation in the methane content, averaged over the period under study at ZOTTO (64.2 ppbv) and at the Arctic stations (∼55 ppbv). Analogous calculations for emissions on the territory of Russia (scenarios A2 and W2) give Δχsyn = 16.0 ppbv and Δχ(+) = 48.2 ppbv, Δχsyn = 5.6 ppbv and Δχ(+) = 49.4 ppbv at ZOTTO and at the Arctic stations, respectively. It can be concluded that, on the whole, the emissions in Russia and in Northern Eurasia have a limited effect on these stations as compared to long-range transport from its planetary-scale sources. This tendency is manifested most strongly at the Arctic stations, for which the annual variations in the total signal from anthropogenic and wetland emissions on the territory of Russia is about 10% of the amplitude of annual variation in the near-surface methane content.

Considering that semianalytical and numerical solutions agree well, we use the box model to estimate the atmospheric response in methane content to the observed trend of anthropogenic emissions on the territory of Russia, the average value of which over 2007–2017 \(\left( {\left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}} \right\rangle } \right)\) is shown to be about 0.34 Tg СН4/yr using the EDGAR6.0 data. The solution of Eqs. (3) and (4) at \(\chi _{{\text{S}}}^{{{'}}}(0) = 0,\) \(\chi _{{\text{N}}}^{{{'}}}(0) = 0,\) \({{S}_{{\text{N}}}}(t) = \left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}{\kern 1pt} } \right\rangle t\) for rt ≥ 1 is given to an accuracy of better than 2% by the asymptotic formula

$$\chi _{{\text{N}}}^{*}(t) \sim \frac{{\left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}} \right\rangle }}{{{{\lambda }^{2}}}}\left( {\lambda t - \frac{{r + \lambda }}{{2r + \lambda }} + \frac{{\exp ( - \lambda t)}}{2}} \right).$$
(13)

In accordance with Eq. (13) and initial conditions, the curve \(\chi _{{\text{N}}}^{*}(t)\) slopes to the abscissa at an angle monotonically increasing from 0 at t = 0 to \({\kern 1pt} {{\left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}} \right\rangle } \mathord{\left/ {\vphantom {{\left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}} \right\rangle } \lambda }} \right. \kern-0em} \lambda }\) as λt → +∞. The linear trend of methane concentration averaged (±1 standard deviation) over the Arctic stations in January 2007–2018 had been 6.6 ± 1.0 ppbv/yr (R2 = 0.78) versus the asymptote \({\kern 1pt} {{\left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}} \right\rangle } \mathord{\left/ {\vphantom {{\left\langle {{{d{{S}_{{\text{N}}}}} \mathord{\left/ {\vphantom {{d{{S}_{{\text{N}}}}} {dt}}} \right. \kern-0em} {dt}}} \right\rangle } {{\kern 1pt} \lambda }}} \right. \kern-0em} {{\kern 1pt} \lambda }}\) = 3.05 ppbv/yr (Fig. 6).

Fig. 6.
figure 6

Average СН4 concentrations at the stations Tiksi and Teriberka in January 2007–2018, linear trend y = Ax + B (thick line), and \(\chi _{{\text{N}}}^{*}(t)\) (13) (dashed line); solid line indicates an angle at which \(\chi _{{\text{N}}}^{*}\) slopes to the abscissa axis in the limit as λt → +∞. The dependence \(\chi _{{\text{N}}}^{*}(t)\) is shifted 1900 ppb upward along the ordinate axis.

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Over the period under study, the average methane growth according to station-based data had been about 73 ppbv in January; while the methane growth caused by the trend of emissions addressed here had been only 21.8 ppbv, i.e., about 30% of the total contribution from regional and planetary processes.

CONCLUSIONS

Many researchers note that the strong spatial and time inhomogeneity of the fields of atmospheric emissions and near-surface concentrations of methane leads to significant uncertainties in the calculations of regional methane fluxes by the top-down method (see recent work [8] and references therein to more recent studies) and proportional to the strong effect of a priori information on final estimates. However, our calculations demonstrate another potentially significant source of uncertainties in estimates of regional fluxes. Relatively minor contribution of emissions from sources on the territory of Russia (∼10–25%) to the amplitude of annual methane variations, observed at the stations, is one of the factors determining the overall low useful signal-to-noise ratio in retrieval algorithms. This data property can be offset in the sense of decreasing final error of estimates only by increasing the total number of high-latitude measurement sites and/or by additional a priori information on the emission sources. At present, the amount of data on near-surface methane content, obtained from the relatively sparse network of background stations of the atmospheric monitoring in Northern Eurasia, is insufficient to obtain reliable estimates of the methane fluxes from high-latitude ecosystems and, in particular, during studies of long-term changes and seasonal variations in emissions, consistent with findings of recent paper [8].

A significant feature of the atmospheric response to the regional methane emissions is that the equilibrium concentration field is reached for a time as long as 20 years (for the case where a source is switched on “instantaneously”). The seasonal variations in synoptic-scale component of the total response, caused by the direct effect of windward sources during advection in the mixing layer, is in phase with the annual variation in near-surface methane content at extratropical latitudes with the maximum in winter months and minimum in summer months. The numerical experiments carried out in this work show that the amplitude of the annual variation in the methane content, obtained directly from station-based measurements cannot be considered equivalent to the absolute contribution of regional anthropogenic emissions, which was erroneously done by a number of the authors before.

In terms of the annual average, the synoptic component of anthropogenic signal at ZOTTO from the sources on the territory of Russia (38.6 ppbv) is more than a factor of 2 larger than the contribution from sources in Western Europe (17.7 ppbv); while for Arctic stations the contributions from Russian and European sources turn out to be comparable in value (19.5 and 12.4 ppbv, respectively). For natural sources of methane in Northern Eurasia, the contribution of wetland emissions on the territory of Russia is absolutely predominant at all considered stations: 34.2 and 19.7 ppbv for ZOTTO and Arctic stations, respectively, versus 2.7 and 2.1 ppbv for wetland emissions in Western Europe.

Our model estimates obtained using the scenarios W1 and W2 confirm the conclusion in work [10] that the contribution of wetland emissions to the measured methane content at high-latitude stations should be taken into consideration not only in the warm season but also in winter. In the latter case, the effect from regional emissions will intensify against the background of a seasonal decrease in the mixing layer depth and reduction in intensity of air exchange between the atmospheric boundary layer and the free troposphere.