The data presented in this study were collected on board a National Aeronautics and Space Agency (NASA) C23-B aircraft during the Alaskan growing seasons of 2012–2014. In 2012, flights occurred in the last 2 weeks of each month from May to September for a total of 31 flight days and 212 flight hours. In 2013 and 2014, flights occurred in the first 2 weeks of each month from April to October and May to November, resulting in 290 and 300 flight hours over 42 and 48 flight days, respectively. All flights analyzed in this study originated from Fairbanks, AK, and stayed within Alaska. Not all regions and altitudes were sampled every month since the flight routes were limited by icing concerns and weather conditions. Data were typically acquired at 150 m above ground level (a.g.l.) to maximize sensitivity to local surface–atmosphere fluxes; however, periodic profiling of the atmosphere to 5–6 km a.g.l. occurred throughout the flights to characterize planetary boundary layer height and mole fractions in the free troposphere.

Mole fractions of CH4, CO2, carbon monoxide (CO), and water vapour (H2O) were measured in situ every ∼ 2.5 s using two independent cavity ring-down spectrometers. Each system had an individual rear-facing inlet on the port side of the aircraft. Sample flow from the inlets passed through a length of Synflex tubing with an approximate transit time of 30 ± 2 s. The first system (Picarro; G1301-m in 2012, G2401-m in 2013 and 2014) directly sampled the air without any pre-treatment and alternately sampled from one of two on-board calibration cylinders every 30 min. These on-board calibration cylinders were changed throughout the campaigns as the pressure approached 3.4 MPa (500 psi). They were calibrated by NOAA before and after each deployment. Calibration for the water vapour correction was conducted on the flight instrument before and after each year's campaign according to . Further details of this system can be found in .

The sample flow in the second system first passed through a 0.2 µm Teflon filter before passing through a Nafion dryer followed by a dry ice trap which effectively lowered the dew-point temperature of the sample flow to ∼ 195 K before entering the spectrometer (Picarro; G2401-m). This reduced the water vapour of the sample flow to <0.001 % and allowed dry mole fractions of CH4, CO2, and CO to be directly measured. Two onboard 8 L calibration cylinders (independent of the first system's) were sampled at the beginning and end of every flight as well as every 30 min during flight. These in-flight calibrations were linearly interpolated between calibration times to generate time-varying calibration curves. In-flight calibrations that were greater than 2.5 standard deviations away from the mean of the calibrations for a given flight were excluded.

Before each year's campaign, the onboard calibration cylinders for the second system were flushed twice and then filled from 30 L fill tanks (Scott Marrin, Inc., Riverside, CA). Due to the longer sampling seasons in 2013 and 2014, the onboard calibration tanks were topped up once in each of those years with the original fill tanks before the pressure dropped below 3.4 MPa. Both the original fill tanks from Scott Marrin and the onboard calibration cylinders were calibrated in the laboratory with the spectrometer used in-flight before and after each year's campaign using tanks with known mole fractions obtained from NOAA, tying our measurements to the WMO scales . The differences in mole fractions before and after each year's flight campaigns in both the onboard calibration cylinder and the fill tanks were less than 0.15 ppm for CO2, 0.8 ppb for CH4 and 7 ppb for CO, all of which were within the precision of the system. The mole fraction in the on-board calibration cylinders was therefore treated as constant throughout each year's study and assumed to be unaffected by the addition of gas. It was also assumed that any changes within any of the tanks were negligible throughout each year's campaign.

The one deviation was that the onboard calibration cylinders were not calibrated before the 2012 deployment due to time constraints. However, these cylinders were calibrated after the 2012 campaign and compared to the fill tanks calibrated before and after that year's campaign. Except for CO2 in one of the onboard calibration cylinders, which was 0.29 ppm lower than the fill tank, the comparison with the fill tanks for the other gases all fell into the ranges given above. In the case of this exception, the post-mission calibration of the onboard calibration cylinder was used since the tank was not topped up during that year's mission.

Comparison of the two systems showed a mean difference of 0.8, 0.3, and 0.4 ppb for CH4 for 2012, 2013, and 2014, respectively, with no dependence on water vapour levels (r2=0.008). The mole fractions presented in this study merges those measured by both systems, to fill in times when one of the systems was calibrating or functioning imperfectly. The system used to gap-fill is offset by the mean difference between the two systems for a given flight. Since our analysis is based on the difference between mole fractions in the free troposphere and the mixed layer (see below), this treatment does not bias our analysis. The greenhouse gas measurements were merged to a common 5 s timescale along with the location data, measured using a global positioning unit (GPS) (Crossbow; NAV420); outside air pressure (Parascientific; 745-15A); outside air temperature (Harco; 100366-18), dew-point temperature (Edgetech; Vigilant); and ozone (2B Technologies; 205).

To identify the contribution by upwind surface processes to observed mole fractions of CH4, source–receptor relationships (“footprints”), that represent the adjoint of the transport model, were computed using a Lagrangian particle dispersion model (LPDM) driven by three-dimensional winds from a regional high-resolution numerical weather prediction model. Specifically, the Weather Research and Forecasting (WRF; ) regional numerical weather prediction model was coupled offline to the Stochastic Time-Inverted Lagrangian Transport Model (STILT; ). The coupling of the STILT model with WRF meteorological fields, hereafter WRF–STILT, is described by . The polar variant of WRF coupled with STILT was configured for the Arctic CARVE domain by , who provide a detailed description and meteorological validation of the high-resolution simulations performed on a 3.3 km grid suitable for simulating particle transport on regional scales in mountainous terrain. Their initial STILT footprints from WRF v3.4.1 were used in the analysis of . The current investigation uses WRF v3.5.1 and incorporates recently available PIOMAS cryosphere fields and footprints on an expanded circumpolar domain north of 30∘ N.

To avoid unnecessary computational costs, measurement locations that occurred below 1 km a.g.l. were placed into discrete bins on a grid of 5 km in the horizontal and 50 m in the vertical, while locations above 1 km a.g.l. were similarly binned 5 km in the horizontal and 100 m in the vertical . These spatial bins were then used as receptor points for each STILT simulation. Measurement times were also truncated to the hour to match the time resolution of the meteorological fields. The use of WRF at high resolution to drive the STILT model results in higher-fidelity meteorological fields and subsequent transport calculations than afforded by most global reanalysis .

To derive source–receptor relationships, each STILT simulation launched 500 particles into the atmosphere at the location of each receptor point and traced their dispersion through the atmosphere in reverse time over 10 days via three-dimensional advective winds and stochastic (i.e. random, probabilistic) processes determined from the underlying meteorology . Every hour, particles that were in the lower half of the boundary layer were assumed to be influenced by the surface see the Supplement for further discussion about this assumption and are gridded to generate a footprint sensitivity plot for that hour. The footprint used in this analysis was calculated on a 0.5∘×0.5∘ latitude–longitude grid, with a unit of abundance flux-1 (e.g. ppb (nmol m-2 s-1)-1, where ppb is parts per billion) , and allows us to relate upwind surface influence to an observation at a given time and location. These footprints are therefore species-independent. The original STILT runs simulated transport 10 days backward in time . However, as discussed in the next section, our analysis only uses the first 5 days. Past studies that have used WRF–STILT footprint sensitivities for this region have been successful in attributing fluxes of CO2 , a much harder problem due to its bi-directional flux and strong diurnal cycle. These studies were therefore much more reliant on WRF–STILT generating accurate footprints during both day and night compared to our study. The success of these past CO2 studies gives us confidence in the footprint sensitivities used in this analysis.

This analysis focuses on the influence of surface emissions from Alaska and Yukon on observed CH4 mole fractions. To this end, we restricted our region of interest to 50–75∘ N and 130–170∘ W (Fig. ) and only consider footprint sensitivity derived from WRF–STILT during the first 5 days preceding each receptor point. The timescale of 5 days was chosen because sources outside the domain are expected to have transport timescales roughly equal to that of free-tropospheric mixing and therefore only contribute to background values of CH4. Figure  shows the cumulative 5-day footprint of our analyzed times for each year averaged over the number of profiles in each year and shows that our observations are mostly influenced by the boreal interior of Alaska as well as tundra regions. It should be noted that although our mean footprints were more sensitive in the North Slope of Alaska in 2012, our absolute sensitivity was comparable in all 3 years due to the increased number of flights in 2013 and 2014.

Our choice of the spatial domain was determined by the distribution of 5-day footprints. As will be defined in the subsequent section concerning the mixed layer, footprint sensitivity simulations that had less than 1.0 ppb (nmol m-2 s-1)-1 total land sensitivity were identified as being in the free troposphere, following . For an idealized homogeneous distribution of sensitivity, where an air parcel is equally sensitive to all land areas within the domain, this threshold would translate to ∼ 1 ×10-4 ppb (nmol m-2 s-1)-1 in any given grid cell. It was assumed that areas of the globe with sensitivities smaller than this threshold did not significantly contribute to CH4 enhancements, since, even at extreme fluxes of 1000 mg m-2 d-1, they would contribute < 0.1 ppb to the observed enhancement. In the cumulative 5-day footprints shown in Fig. , 71 % of the footprint that exceeded the grid-cell threshold was from land in the chosen domain, while 29 % could be sourced to oceans. It is worth noting that the previous study of restricted its domain to 135∘ W. While the May–September footprints showed that < 2 % of the footprint originated in regions east of 135∘ W, it was found that at least 5 % of the total land sensitivity in April, October, and November came from the Canadian Yukon. Of all the land surface influence on our observations, only 0.3 % originated from land outside of our study region, suggesting that our sampling strategy and choice of domain allowed our observations to be most sensitive to surface emissions from the study region.

We use the term “mixed layer” to refer to the combination of both the residual layer and the boundary layer throughout the remainder of this paper. As our footprints predict the sensitivity to surface influences 5 days prior to a measurement, both local and regional sources need to be considered. As a general approximation, CH4 enhancements in the boundary and residual layers reflect local and regional surface emissions, while the portion of a vertical profile above the mixed layer can be used to represent background levels. In practice, the footprint sensitivity maps attribute the spatial distribution of sources that influence a particular receptor, whether it is in the boundary layer or residual layer. It should be noted that particles in the residual layer do not contribute to the footprint at that specific time but carry surface influence from earlier time spent in the boundary layer and therefore may have elevated surface influence compared to background values.

We estimate the bottom of the free troposphere (h) by calculating the refractivity (N) using parameters measured at different altitudes on the aircraft : N=77.6PT+3.77×105PwT2, where P and Pw (hPa) are the atmospheric pressure of air and water, respectively, and T (K) is the atmospheric temperature. The height at the minimum of the gradient in N is the top of the mixed layer.

Tables S1–S3 in the Supplement list every time the aircraft flew between 200 m and at least 2.7 km as an individual profile. In analyzing these profiles, it was often found that this method overestimated the mixed layer height compared to profiles of CH4, O3, and the total land surface sensitivity calculated by WRF–STILT; as a secondary calculation, the height at which WRF–STILT sensitivities dropped below 1.0 ppb (nmol m-2 s-1)-1 was used to approximate h . Upon individual inspection of profiles, it was found that in 25 % of cases (i.e. 68 profiles) neither method captured an h which correctly separated the free troposphere and mixed layer. After removing these profiles, a further 25 % of profiles within the remaining set (i.e. 50) had h differing by > 750 m between the two methods (paired t test; p<0.005). In these cases, either the boundary layer dynamics within WRF–STILT were not representative of local meteorology or there was too much variance about the minimum of the gradient in N. Therefore, these profiles were not included in the analysis. In the final set of profiles used for analysis, a paired t test found that the two methods did not statistically differ from each other (p>0.1) and both agreed to within 500 m ∼ 90 % (r2=0.6) of the time. We attempted to use other variables such as virtual potential temperature to define the mixed layer but the methods described above gave the most consistent results.

Across all years, h was found to occur between 1.1 and 1.8 km with a median of 1.5 km above Alaska, consistent with estimates derived from satellite retrievals . On average, h in May–September was 30 % higher than in April, October, or November. These findings are consistent with lower solar zenith angles and shorter solar days in colder months, both of which reduce the strength of convective forces which form the boundary layer .

In this analysis, we use column enhancements of CH4 (ΔCH4) to estimate net surface fluxes . This method assumes that CH4 enhancements below h that are above background levels are a result of interactions with the local surface that are not well mixed with the free troposphere. Net surface fluxes are determined by calculating the corresponding surface influence at each height in the column using the footprint sensitivities determined from WRF–STILT. This method of calculating ΔCH4 is less reliant on the accurate simulation of the vertical structure of the atmosphere as well as turbulent transport in the lower atmosphere. Instead, we rely on the integrated model simulation to match the integrated observations. The majority of the measurements from the aircraft flights were in the surface layer. As such, this method also reduces bias in regional emission estimates by focussing on measurements throughout the atmosphere.

To calculate ΔCH4, measurements in a vertical profile were first block-averaged by altitude into 250 m bins. A sample of such a profile observed during the CARVE campaign is shown in Fig.  and shows median, minimum, and maximum [CH4] observed in each 250 m bin up to 3 km along with the estimated CH4 flux from the WRF–STILT footprint influence according to Eq. . In this sample profile, the calculation of the refractive index (N) properly captured the transition from the mixed layer to the free troposphere and WRF–STILT adequately modelled the mixed layer, leading to a reasonable estimate of CH4 flux. Using h as the upper bound on the section of the profile affected by local sources and sinks, ΔCH4=∫0h([CH4](z)-[CH4]0)Pd(z)R*T(z)dz, where ΔCH4 (nmol CH4 m-2) is the column integrated mixed layer enhancement of CH4, [CH4]0 is the background CH4 estimated by averaging the lowest 1 km in the free troposphere, Pd is the calculated atmospheric pressure of dry air using measurements of P and Pw, R* is the universal gas constant, and z is the height a.g.l. as calculated from the height above sea level measured by the GPS and an underlying digital elevation map within the input meteorology of WRF. As an entrainment zone between the free troposphere and mixed layer was usually evident in profiles of CH4, 500 m was added to h for our estimate of [CH4]0. Since [CH4]0 is typically stable with altitude in the free troposphere, this should not affect the integral in Eq. ().

A similar calculation was undertaken for the corresponding footprint sensitivity, with the cumulative 5-day footprint at each height replacing ([CH4](z) - [CH4]0) in Eq. (), to calculate the sensitivity of the entire mixed layer to the surface (ΔI with units of nmol CH4 m-2 (nmol m-2 s-1)-1). As a first estimate, our a priori CH4 flux is assumed to be uniformly emitting from our entire domain. Surface contributions outside of the study domain were excluded, as were seas and mountains, which we assume to be neither sources nor sinks of atmospheric CH4 and therefore to not contribute to ΔCH4. The total mixed layer sensitivity, ΔI, is then scaled to match ΔCH4 to estimate CH4 flux, E^: E^=ΔCH4ΔI, with appropriate unit conversion to mg CH4 m-2 d-1. The estimation of uncertainties in CH4 flux using Eq. () will be discussed in Sect. .

Monthly-mean CH4 flux (E‾) was estimated by weighting individual flux estimates by the total footprint sensitivity of each profile , so that E‾=(∑E^×ΔI)∑ΔI=∑ΔCH4∑ΔI.

This biased the average towards profiles with larger spatial coverage and helped normalize profiles with lower ΔI, which sometimes resulted in high estimates of E^. The residuals of individual estimates against these monthly means are shown in Fig. S2 of the Supplement. Their normal distribution about the trend in the monthly mean suggests that this method of weighted averaging was successful in mitigating biases in CH4 flux stemming from differences in footprint sensitivity.

Growing-season budgets were calculated by integrating the monthly emissions from May through September and over our study domain (excluding mountains). The surface area of our domain was estimated using a digital elevation map from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) to estimate the enhancement of surface area in sloped terrain . A land–ocean mask at 0.1∘ × 0.1∘ was then used to approximate the fraction of land cover at 0.5∘ × 0.5∘ to estimate surface area in coastal grid cells (i.e. Aland=A*fland). The total land surface area of our domain is estimated to be 2.1 million km2 including mountains and 1.04 million km2 without.

Since the goal of this study is to understand biogenic CH4 emissions, observations influenced by combustion were excluded. Measurements of CO were used as an atmospheric tracer for air influenced by biomass burning events or oil development off-gassing, which co-emit CO and CH4. Any profile which had measurements of CO exceeding 150 ppb within the mixed layer was not used in the analysis. This threshold was determined by observing that the annual distribution of CO deviates from normal above 150 ppb . It should be noted that our calculations only estimate net CH4 emissions from non-mountainous land surfaces. These estimates include all processes such as biogenic, thermogenic, and non-combustion-related anthropogenic sources and sinks. We assume that the latter two processes are small compared to biogenic sources over the study domain; however, were this not true, our values could still be considered upper estimates for net biogenic emissions.

After CO screening, each individual vertical profile was assessed on a case-by-case basis to ensure that the WRF–STILT model adequately captured a mixed layer (i.e. the footprint sensitivity attenuated to zero as altitude increased) and that the estimated h from WRF–STILT clearly separated the mixed layer from the free troposphere. Of the 273 profiles identified, 9 were rejected due to excessive CO mole fractions. In addition, 118 were rejected using the two methods described in Sect. . The remaining 146 profiles, just under half of all the profiles, were kept for analysis. While this is a severe reduction in data, footprint sensitivity plots comparing the total footprint sensitivity of all the receptor points within all profiles against the total footprint sensitivity of those within the profiles kept for analysis showed no significant bias. As a result, this subset is thought to be both representative of the CARVE sampling campaign and free from errors in integration limits.

The previous assumption that the study region emits CH4 uniformly is correct only to the zeroth order. It serves as the best estimate for the total magnitude of net flux and provides the most robust regional budget calculations. However, this assumption misses much of the spatiotemporal heterogeneity observed in emissions across and even within different biological and hydrological regimes as summarized by. At regional scales, such as in this study, it is useful to separate the domain into eco-regions which group regions with similar vegetation, elevation, soil type, and soil moisture dynamics. One can then use the different eco-regions as a basis set of independent sources and sinks in a linear inversion. The eco-regions used within this study were taken from the Environmental Protection Agency's Level II map of eco-regions and grouped into the three following land types: tundra, which includes “Alaska Tundra”; boreal, which includes “Alaska Boreal Interior” and “Taiga Cordillera”; and mountains, which includes “Brooks Range Tundra”, “Marine West Coast Forest”, and “Boreal Cordillera” (see Fig. ). While “Marine West Coast Forests” are not mountainous by definition, a study of CH4 fluxes north of 50∘ N identified heavily forested areas as being negligible sinks of CH4 . Therefore these forests are suitably grouped with mountains under the assumption that footprint sensitivity from these areas did not affect observed ΔCH4. By using these predefined maps, we are attributing all net emissions to biogenic sources.

By calculating the mean fraction of the influence of each eco-region on our measurements using the footprint sensitivity maps, it is possible to estimate the net CH4 flux from each eco-region using multiple linear least-squares regression according to the following: E^=∑ifiEi, where fi are the fractions of influence from different eco-regions, E^ are the uniform CH4 flux estimates, and Ei are the CH4 fluxes from each eco-region. These estimates were grouped by month across all 3 years to maintain a sufficient sample size. To test the assumption that emissions from the mountain land type negligibly affected ΔCH4, CH4 flux was estimated with and without the mountain land type and presented in Sect. .

To explore how the variability in CH4 flux estimates is related to ecological, biological, and hydrological parameters, the footprint sensitivity functions were also used to calculate weighted means of different variables common in process-based models of CH4 flux. Maps that were included in this analysis were surface, 10 and 40 cm daily soil temperature (Tx, where x is the depth, K), and liquid soil moisture content (Sx, no unit) from the North American Regional Reanalysis (NARR) project ; digital elevation (z, m) from ASTER; days since thaw (DST), derived from passive microwave satellite observations of surface thaw ; wetlands (%) ; 30 and 100 cm soil organic carbon content (Cx, kg m-2) from the Northern Circumpolar Soil Carbon Database (NCSCD) ; and percent of soils classed as turbels, histels, gelisols, or non-soils from NCSCD .

Previous correlation analyses have suggested that CH4 flux varies non-linearly with variables such as soil temperature and elevation . As such, the following functional forms were used to characterize variability in CH4 flux: E=ef(x)f(x)=Ea(1kx‾-1kx),Boltzmann–Arrhenius type(1x+x‾),Inverse type(x-x‾),Linear type where E is CH4 flux, x is a hypothesized predictor variable, eV is the value of an electron volt in Joules (1.602×10-19 J), k is the Boltzmann constant (1.38×10-23 J K-1), and x‾ represents the mean sampled value of x. This transformation of units is performed such that when the predictor variable is soil temperature, the fitted parameter optimizes the activation energy (Ea) in units of eV .

Multi-variable fits were also performed using an equation of the following form: E^=ef(Z)β, where E^ is an N⋅1 vector of modelled CH4 flux estimates, Z is an N⋅(M+1) matrix with M columns of predictor variables transformed by f(x) and one column of ones, and β^ is an (M+1)⋅1 vector of estimated parameters. We searched through all possible combinations of functional forms by allowing the M columns of Z to take either the Boltzmann–Arrhenius, inverse, or linear forms written in Eq. (), leaving the column of ones to fit a constant. The parameter vector β^ is then constrained using the Levenberg–Marquardt algorithm for non-linear least-squares regression. Subsets of the data (n<N) were also fit to explore behaviour in limiting spatial and temporal cases. The best fit for each subset was chosen if it minimized the Aikake information criterion (AIC) .

The footprint sensitivities are cumulative over 5 days, causing CH4 flux estimates from individual profiles to represent 5-day averages (see Sect.  and ). Regression analysis using the CH4 fluxes estimated from individual profiles resulted in a lot of noise, and the majority of the environmental drivers could not explain the variability in these estimated CH4 fluxes. To compensate for this, CH4 flux estimates were first averaged into 5-day bins before fitting to reduce issues of autocorrelation and to generate independent estimates of CH4 flux. As with the monthly-mean estimates, these were weighted by the total footprint influence. This temporal averaging reduced the total number of independent estimates used in the regression from 146 to 68, thus reducing the reliability of these results. It should be emphasized that the regression analyses are only reflective of seasonal variations on timescales of 5 days.

Uncertainties in the estimated CH4 flux from individual profiles were determined through bootstrapping both observational measurements and the integrated model footprints involved in its calculation by sampling each variable with replacement 500 times. Explicit variables included were as follows: (1) matching observations of CH4, T, P, and Pw at each 250 m altitude bin to estimate uncertainties associated with the observations and spatial variability; (2) the footprint sensitivity at each 250 m altitude bin, approximating the uncertainty of releasing particles within neighbouring grid cells – it should be emphasized that this is not a true posterior variability and may underestimate full modelling uncertainties, although it is still a useful approximation of a type of model uncertainty; (3) the mixed layer height, which we varied by ±250 m and propagated through our calculations of E^ by either adding or removing another 250 m bin to the integration in Eq. () but not changing [CH4]0, representing the uncertainty due to h; (4) same as (3) but changing [CH4]0 and representing the uncertainty due to [CH4]0; and (5) all of the above propagated through the entire calculation, representing the total methodological uncertainty in our calculations of CH4. The 95 % confidence interval (CI) of the last step was used to estimate the uncertainty associated with the estimated CH4 flux from individual profiles. The mean, minimum, and maximum 95 % CI (2.5–97.5 percentile) for each of these steps is shown in Table S4. They reveal that the largest methodological uncertainty associated with the results is the combined uncertainty in identifying both the mixed layer height and the [CH4] background.

Uncertainties in the monthly-mean CH4 flux were estimated in four ways: average uncertainty, the 95 % CI for each individual estimate is averaged for each month with no weighting; weighted average uncertainty, the 95 % CI for each individual estimate is averaged for each month and weighted by the column-integrated total surface influence (ΔI); standard deviation, the normal standard deviation is calculated from the residuals of the weighted monthly mean; and weighted standard deviation, the standard deviation of all CH4 flux estimates within a given month is calculated, weighting each residual by ΔI and the inverse of the square of the 95 % CI. We present uncertainties calculated using the weighted standard deviation, because it accounts for both monthly variability and the uncertainty in the flux estimated from each profile. Results estimated using the average uncertainty were slightly lower, likely because they do not account for the variability in a given month. Uncertainties in the budget are propagated from the average monthly flux uncertainty by quadrature. For reference, uncertainties in the budget and monthly-mean estimates calculated using all four methods are shown in Table S4.

Using the methods described in Sect. , monthly-mean net CH4 fluxes for 2012–2014 were estimated from individual aircraft profiles of the atmosphere (Fig. ). As will be shown in Sect. , we found that footprint sensitivity from oceans and mountains was poorly correlated with observations of ΔCH4. Therefore, the estimated fluxes presented in this subsection only attributed CH4 flux to the boreal and tundra eco-regions defined in Sect. . These estimates ranged from 2 to 36 mg CH4 m-2 d-1 (2.5–97.5 % percentile) for individual profiles and showed a distinct seasonal cycle that peaked in late July or early August across all years (Fig. S1). Figure S2 illustrates that the residuals of the estimated net flux from individual profiles from the monthly mean are normally distributed, suggesting that our monthly-mean estimates are not strongly biased. Overall, our results are consistent with tall and eddy-covariance tower studies e.g. and provide observational evidence that region-wide CH4 flux may be, on average, as high as 5 mg m-2 d-1 in the colder months of April and November, also consistent with previous studies on the North Slope and interior of Alaska.

Monthly-mean flux estimates were found to be higher than those inferred from the CARVE tall tower near Fairbanks for the same months (3–9 mg CH4 m-2 d-1) , although the ranges from the two studies overlap. As discussed by , the tower observations likely underestimate CH4 flux compared to the aircraft observations because of the aircraft's increased sensitivity to the North Slope and southwestern Alaska, regions that are known to be seasonal wetlands (and therefore a significant CH4 source, ), compared to the interior sites which were more sensitive to upland regions that are thought to emit less CH4 .

Integrating over the months sampled every year (May–September), we estimate CH4 emissions from our study region to be 2.2 ± 0.5 Tg, 1.9 ± 0.4 Tg, and 2.3 ± 0.6 Tg for 2012, 2013, and 2014, respectively, with the assumption that all non-mountainous land surfaces emit at a uniform rate over the entire month. As our observations do not extend throughout the colder months, we do not provide annual budget estimates since other studies have found that significant emissions of CH4 are observed in the shoulder and cold seasons .

Previous estimates of emissions from Alaska during the growing season include the study by , who used a similar method to estimate the May–September 2012 emissions to be 2.1 ± 0.5 Tg, as well as the geostatistical inversion of the CARVE observations by , who estimated May–October CH4 emissions of 1.80 ± 0.45, 1.65 ± 0.43, and 1.77 ± 0.45 Tg CH4 for 2012, 2013, and 2014, respectively. Our mean estimates are within the uncertainties of these other studies, especially when we account for the ∼ 20 % greater area in our study domain. It is promising that our relatively simple method for calculating budgets using selected profiles from the CARVE aircraft observations arrives at similar estimates to values derived from the much more complex geostatistical inverse model used by , particularly as their study was constrained by all the aircraft observations as well as hourly-averaged observations from the CRV tower.

Our estimates of May–September net CH4 flux have a mean of 2.1 ± 0.5 Tg and show no significant difference over the 3 years. These results are consistent with the findings reported by , who suggest that regional CH4 emissions would require decades to respond to changes in surface conditions. Similarly, a recent analysis of long-term measurements of CH4 flux on the North Slope in Alaska observed little change in boundary layer CH4 enhancement over the past 29 years, despite increases in air temperature . This lack of trend could potentially be related to methanogen community structure in the Arctic, as recent microbiological research has found that communities from Arctic soils that were incubated at lower temperatures were insensitive to substrate manipulations, indicating that Arctic methanogens may not be sensitive to the addition of new labile carbon from thawing permafrost . While it is true that local-scale permafrost degradation patterns such as thermokarsts can result in local CH4 fluxes of > 100 mg m-2 d-1 , multi-decadal studies such as suggest that at a regional scale, CH4 fluxes in Alaska have been stable.

The results of the regression analysis described in Sect.  are listed in Table  and indicate the r2 of the best model, the driving variables, and the functional type for each subset (see Eq. ). Overall, net CH4 flux was seen to most strongly correlate to variance in a Boltzmann–Arrhenius function of T40 and the inverse of elevation (r2=0.36). While these relationships have been observed in our study region in the past, primarily at the smaller scales of chambers and eddy-covariance towers e.g., far fewer studies have reported them at a regional scale . These latter analyses also identified the inverse elevation and subsurface temperatures to be important in explaining the variance of observed CH4. As in the work of , we used a relatively simple analysis method to arrive at similar explanatory variables than the more sophisticated geostatistical inversion model used by but with only a subset of the data. Although the r2 from our analysis may seem low, they are comparable to values derived from regression analysis conducted for chamber studies . Our results suggest that soil conditions that affect CH4 flux at the more local scale are also relevant at regional scales.

Since both CH4 production and flux can be much stronger in wetlands, e.g., the profiles were subdivided into two groups based on the sensitivity of the profiles to wetlands in the domain. When a profile's footprint sensitivity was ≥ 20 % wetland by area, the profile was categorized as “Wetland Present”. Conversely, profiles which had sensitivities ≤ 10 % to wetlands by area were categorized as “Wetland Absent”. The percent of wetland per area sampled by a profile was calculated by averaging a map of wetland fraction weighted by the footprint sensitivity. It was found that for profiles in the Wetlands Absent category, soil temperature and soil moisture at 40 cm soil depth were the key predictors in understanding the variability in net CH4 flux (r2=0.48), suggesting that CH4 was being formed deeper in the soil column. By contrast, net CH4 flux was best correlated with T10 and S10 (r2=0.40) for profiles in the Wetland Present category.

These two regressions highlight the importance of understanding the depth at which methanogenesis (and methanotrophy) occurs. For instance, in non-wetlands, the water table is deeper than in wetlands. As a result, the onset of CH4 production in non-wetland regions can significantly lag wetland areas, as the lower section of the soil column will take much longer to thaw. In fact, maps of soil temperature from NARR estimate that, on average, soil at 10 cm in the Wetland Present region thawed nearly 3 weeks before soil at 40 cm in the Wetland Absent regions . In addition, soils at these depths and in these regions warmed very differently: T10 in the Wetland Present regions increased at an average rate of 0.10 K day-1 from point of thaw to the point of annual maximum, while T40 in the Wetland Absent regions increased by only 0.06 K day-1. While CH4 production may occur at any depth within an inundated soil column, CH4 produced at lower soil depths can be transport limited (depending on bubble formation or aerenchyma); it is, therefore, intuitive that CH4 produced in wetlands will be more directly correlated to differences in temperature near the surface. Similarly, the dependence of CH4 production (and ultimately, CH4 flux) on soil moisture will be most pronounced just beneath the water table, where soil moisture is more susceptible to variability than at lower depths.

The freeze–thaw processes and soil microphysics discussed above can be extended to explain the seasonal cycles presented in both Figs.  and . First, as remarked in Sect. , the tundra eco-region possesses more wetland extent than the boreal. As a result, the delayed thaw of the 40 cm soil in combination with slower warming likely explains the delay in boreal eco-region CH4 flux. Second, while maps of footprint sensitivity across all years showed relatively consistent sensitivity to the tundra in the west and southwest of Alaska (see Figs.  and ), they showed that our 2012 measurements were more sensitive to the North Slope of Alaska relative to the boreal eco-region than in other years. On average, ∼ 30, 20, and 20 % of the footprint sensitivity was from regions classified as tundra in 2012, 2013, and 2014, respectively. Since the tundra region possesses more seasonal wetlands, it is therefore not surprising that the 2012 seasonal cycle of net CH4 flux in Fig.  closely resembles the tundra eco-region in Fig. . However, as the tundra only represents 18 % of the total area of interest, it is likely that the sampling in 2013 and 2014 sampled the eco-regions more evenly with respect to their total area, while the sampling in 2012 may have been over-sensitive to the tundra. In particular, if we consider that early season flux in 2014 is identical to that in 2012, it is obvious that soil moisture is not the only variable at play. In fact, seasonal cycles of domain-average subsurface temperature from NARR are very nearly identical in timing to the seasonal cycles observed in CH4 flux. To highlight this timing, the start of the warm season shown in Fig.  was defined as the day when domain-averaged soil temperatures at 40 cm exceeded 273 K. In this respect, the early season of 2012 and 2014 may be more similar than previously thought. Since we postulate that CH4 flux is occurring at 40 cm within the boreal eco-region, which is larger by area and more heavily sampled by the campaign, it is not surprising that domain-average CH4 flux rises at the same rate in the spring of 2012 and 2014, while showing significant delay in 2013.

Overall, subsurface soil temperature was seen to be the single best explanatory variable throughout the regression analysis. Following the work of , the seasonal cycles of CH4 flux are plotted versus soil temperature and coloured by days since the thaw in Fig. . In this figure, CH4 flux estimates from individual profiles are shown in black points. To highlight the average seasonal trend, these individual estimates were block-averaged into 5-day bins of DST based on satellite retrievals of thaw state (coloured points), before being smoothed by a lowess filter which locally averaged 35 %, or 80 days, of the seasonal cycle (coloured line) . Flux estimates from May 2014 were suspected of being overestimated (Sect. ) and were thus excluded from this analysis.

Of the three depths presented in Fig. , the seasonal cycle of CH4 flux has the most consistent, monotonic relationship with T40 throughout the study, while the other depths, especially the individual profiles (small black points) show more scatter. We conjecture that the monotonicity of the relationship between T40 and CH4 we observe for our study region is reflective of the fact that CH4 production is, on average, taking place near this soil level. Evidence for the production of CH4 at soil depths well below the surface have been reported at the eddy-covariance scale before. In particular, the counterclockwise hysteresis loop in our observations of T10 and CH4 flux is very similar to the relationship observed by eddy-covariance towers at Ivotuk between CH4 and T15 . Whereas observations of CH4 flux in wetland sites exhibited a clockwise hysteresis loop, the Ivotuk site itself was much drier than other eddy-covariance sites compared in the study, leading the authors to conclude that the direction of the loop was related to whether CH4 production was occurring above (clockwise) or below (counterclockwise) the soil depth at which temperature was measured . Similarly, an eddy-covariance tower near Fairbanks, AK, also observed a counterclockwise hysteresis loop when CH4 flux was plotted against T20 . It is, therefore, reasonable to believe that CH4 production is occurring at depths of ∼ 40 cm in the broader Wetland Absent regions as a result of a lower water table. In particular, these drier regions play a large role in the late season (September–December) budget, as the production of CH4 at soil depths well beneath the surface enables CH4 flux to continue even after the surface soil has begun to freeze . In the specific case of Ivotuk, CH4 emitted after the surface had frozen represented nearly 30 % of the total annual budget . Since Wetland Absent regions make up 50 % of the surface area of the tundra and boreal eco-regions, it is important that these regions are not overlooked when modelling CH4 emissions at a regional scale.

From Fig. , we fit the mean CH4 flux and T40 from the 5-day means to a Boltzmann–Arrhenius equation and determined an activation energy of 0.75 ± 0.20 eV. This value is slightly lower than, but still within uncertainties of, the global mean activation energy of 0.96 eV (0.86–1.07 eV, 95 % CI), calculated using CH4 flux measurements from static chambers . Using T40 from NARR in this parameterization, we estimate May–September emissions from our study region to be 2.1 ± 0.3 Tg, 1.8 ± 0.3 Tg and 2.0 ± 0.3 Tg for 2012, 2013, and 2014, respectively (only integrating over non-mountainous areas). This simple model does a remarkable job of capturing the growing season budget estimated from the aircraft observations as well as the timing of the peak in CH4 emissions. As more winter-time measurements would be necessary to properly constrain cold season fluxes, estimates of total annual budgets based on this model are not reported.