TM5 is an atmospheric chemistry transport model . Here, it was used as the observation operator to transform the methane fluxes to atmospheric mole fractions. In this study, its global horizontal resolution was 4°×6° with an intermediate zoom region of 2°×3° (14–82° N, 36° W–54° E) framing a 1°×1° zoom over Europe (24–74° N, 21° W–45° E). The model used preprocessed meteorological data from ECMWF ERA5 reanalysis data with a 3 h resolution . The vertical domain was divided into 25 hybrid sigma pressure levels from the surface to the upper atmosphere. The chemical loss of CH4 in the atmosphere to the sinks of OH, was based on monthly precalculated values by , and Cl and O(1D) sinks were based on the atmospheric chemistry general circulation model ECHAM5/MESSy1 . The variability of the atmospheric sinks between different years was not considered, but varied monthly, and the sinks were not optimized.

In addition to the observations from the ObsPack v4.0 , observations from two stations in Finland (Kumpula, Sodankylä) and from nine stations in Siberia were used. All stations are listed in the Appendix A1 and the location can be seen in Fig. A1. Globally, 183 stations had observations between 2011–2021, with some stations having two or three institutions contributing. The data included weekly discrete air samples and hourly continuous measurements of CH4, and the data was filtered according to the institutions' quality flags. Only data points that represented well-mixed conditions were included, which means that daily averages were calculated from 12 to 4 pm LT, except for high mountain sites where averages are calculated from 0 to 4 am LT, following .

Observational uncertainties, or “model–data mismatches”, were estimated for each site based on site-specific factors, measurement accuracy, and the capability of TM5 to simulate atmospheric CH4 mole fractions . These discrepancies arose from TM5’s resolution and transport errors, with e.g. better performance at remote marine sites compared to those affected by strong local emissions. Sites were categorized, for example, as marine boundary layer (4.5 ppb), terrestrial (25 ppb), mixed marine and terrestrial (15 ppb), and strong local influence (30 ppb). Uncertainties ranged from 4.5 to 75 ppb.

The prior anthropogenic emissions were taken from the Emission Database for Global Atmospheric Research (EDGAR v6.0) . The emissions from LPX-Bern DYPTOP v1.4 were used as the natural biospheric prior emissions. Methane emissions from other sources were: for ocean, the Global fire emission database (GFED v4.1s) for biomass burning, and VISIT for termites. Biospheric and anthropogenic fluxes were optimized globally. Other fluxes were not optimized. We only analyze the optimized biospheric fluxes in this study. The biospheric prior LPX-Bern DYPTOP represents ecosystem area fractions across several land-cover types: (i) peatlands suitable for peat growth as defined by DYPTOP ; (ii) rice paddies coinciding with croplands and the presence of rice paddies ; (iii) inundated wetlands other than peatlands or rice paddies; (iv) wet mineral soils, which are not wetlands, peatlands, rice paddies, permanent freshwater bodies, or ice/sea water covered areas, but are ocassionally wet; and (v) dry mineral soils, which are areas identical to wet mineral soils but are “dry” in general. Of these categories, we did not include rice paddies in our prior as they are not present in the northern high latitude region. Soilsink was included in the biospheric prior.

For both the anthropogenic and biospheric fluxes, we used the prior uncertainty of 80 % for terrestrial fluxes and 20 % for oceanic fluxes, assuming uncorrelated uncertainties, following previous studies e.g.,.

In this study, the melt period was defined as a season in the northern latitudes in spring, when the soil in a specific region turned from frozen to thawed based on the “thawed” state in the SMOS F/T data (see Sect. 2.1). The word “melt” is used here instead of “thaw” because the SMOS F/T data can indicate the melting of the snow instead of the soil, especially at the beginning of the melt period. This is because the microwave radiation signal from wet snow resembles the signal from thawed soil . However, methane emissions are possible even at the very beginning of the melt period because the air temperature rises above zero and melted or rain water can trickle into the soil and wintertime methane reserves are released . It is thus justified to start the melt period from the melting of the snow. The boundaries used in this study were similar to the ones used by to define different seasons in the northern high latitude wetlands, but instead of frozen or partially frozen state of the SMOS F/T data, we used the thawed soil state to define the melt period. The resolution of the SMOS F/T data was changed from 25km×25km to 1°×1° by calculating the fraction of the thawed 25km×25km pixels whose center was inside the 1°×1° grid cell.

The melt period was defined for four permafrost zones: non-permafrost, sporadic, discontinuous and continuous permafrost (region-based approach), and separately for each 1°×1° grid cell (grid-based approach) in these zones. The region-based approach gives information about the permafrost areas constrained by their specific climatological conditions while the grid-based melt period was studied to illustrate the local variation in the melting of the soil.

With the region-based approach, the melt period was set to start (1) when the mean thawing fraction of a permafrost zone had surpassed the minimum thawing fraction of that year by 0.1 (thaw(%)≥thawmin,year(%)+10%), and (2) after the day when the zone reaches its minimum annual mean thawing fraction before mid July. During some years, the freezing of the soil continued past the turn of the year, which meant that the (1) boundary was reached before the maximum freezing of the soil. This meant that the additional (2) condition for the beginning of the melt period had to be defined. With the (2) condition, the melt period could be separated from the autumn freezing period. In regions with permafrost, the first (1) condition was surpassed later during the spring than the second (2) condition, but in the non-permafrost zone the second (2) condition was needed.

The season ended when the mean thawing fraction of the whole zone had surpassed 0.8 of the maximum thawing fraction of all years which was 1 for all zones (thaw(%)/thawmax,all(%)≥80%). The fraction of 0.8 was chosen because there was not as much variation in the thawing fraction that close to summer indicating a stable thaw state. The day when the melt period ended was included in the melt period. The melt period in each grid cell was defined from the amount of thawed pixels in a grid cell, emphasizing more the small grid cells in the north. The mean thawing fraction of all grid cells in a permafrost zone was then calculated. The selected thresholds were chosen to define a robust, zone-mean transition period rather than the exact timing of soil thaw at individual grid cells. In early spring, the SMOS F/T signal can respond to wet snow in addition to thawed soil, as liquid water in the snowpack produces a microwave signature similar to that of thawed soil (Rautiainen et al., 2025). Consequently, thawing fractions very close to 0 % or 100 % are more sensitive to short-term fluctuations in the microwave signal. Defining the season boundaries away from these extremes ensures that the melt period reflects a sustained, large-scale transition.

In the grid-based approach, the start of the melt period was defined differently. The season started when (1) one SMOS F/T pixel (25km×25km) in the 1°×1° grid cell had melted and (2) after the day when the grid cell reaches its minimum annual thawing fraction before the end of July. The second condition was needed for the same reason as in the region-based approach. There were a maximum of 18 SMOS F/T pixels and a minimum of 1 pixel in each 1°×1° grid cell depending on data availability and geographic location. For example, in a grid cell with 18 pixels, the season started when the thawing fraction was 1/18, meaning that 5.6 % of the area of that grid cell has melted. The season ended when the thawing fraction in the grid cell had surpassed 0.8 of the maximum thawing fraction of that year. To separate the spring melt period from the autumn freezing season, the melt period was defined to start and end before the 212th day of the year (end of July). Missing data in the grid cells was replaced by interpolating linearly between the previous and the coming day with an existing value. If none of the pixels melted in a grid cell, or if the thawing fraction never was below 0.8 of the maximum thawing fraction of that year before the end of July, meaning that the grid cell did not freeze, the grid cell did not have a melt period. In some of the grid cells, the condition for the end of the melt period was never surpassed before the 212th day of the year even though the season had a beginning. For those grid cells, the end of the melt period was defined as a day when the soil had thawed the maximum amount during the melt period. However, this only happened in 2 grid cells in 2017. Additionally, in a few grid cells, the minimum thaw fraction occurred after the maximum had already been reached. In these cases, the onset of the season was defined to occur prior to the maximum. Excluding the first three years, fewer than 1 % of grid cells in the study area did not have a melt period annually. In the first three years, this percentage ranged from 6.5 % in 2011 to 1.1 % in 2013.

After defining the melt period, the methane emissions were calculated from the CTE-CH4 inverse model biospheric posterior emission estimates. The methane emissions were optimized weekly, and to calculate the daily emissions, the model data was interpolated linearly from one optimized weekly value to the next weekly value. From these daily values, the posterior methane emissions were analysed during the melt period. Similarly to the melt period, the regional emissions were calculated separately for the four permafrost zones: non-permafrost, sporadic, discontinuous and continuous permafrost zones.

The total melt period CH4 emissions in a region or grid cell in teragrams of methane (Tg CH4 per region per season, hereafter denoted simply as Tg) were calculated from the daily methane emission estimate. The daily values of all grid cells were added together in each permafrost zone during the melt period. The average emissions were calculated in the unit of µgCH4m-2s-1 by dividing the average daily emissions during the melt period in a permafrost zone by the area of the specific permafrost zone. The emissions were studied against the land area of the permafrost zones instead of the actual area of wetlands or permafrost in each zone. This was done because the exact area of wetlands is uncertain , and using the estimated wetland area extent would have added another source of uncertainty.

As the melt period was defined separately for each 1°×1° grid cell, the melt period emissions were calculated separately as well. The sum of the emissions per grid cell per melt period was calculated in each grid from the first day of the melt period to the last. To calculate average of the methane emissions in the unit of µgCH4m-2s-1, the average daily emissions during the melt period in a grid cell were divided by the respective area of the grid cell. To compare with the other method, we divided the grid-based emissions to the four permafrost regions as well.

With the region-based melt period, the start and end of the season varied from year to year in each permafrost zone (Table A2). The range of variation of the starting days was 21 d in the non-permafrost and sporadic zones, 15 d in the discontinuous permafrost zone, and 18 d in the continuous permafrost zone. The range of variation of the ending days was shorter, only 6 d in the non-permafrost zone, 14 d in the sporadic zone, and 8 d in the discontinuous and continuous permafrost zones. Between different grid cells, the start and end of the melt period varied more within a year than the averages from year to year. However, even inside one grid cell, there was more inter-annual variation that was not seen from the average (Fig. A4b and c). On average, the region-based melt period started earlier and ended later than the grid-based melt period. However, in some grid cells, the melt period started much earlier and ended later than the region-based season, as expected since at least 10 % of the grid cells had to be thawed for the region-based melt period to start and 80 % had to be melted for it to end.

With both methods, the season typically started and ended the earliest in the southernmost regions and the latest in the northernmost regions, with the season starting later in some of the southernmost grid cells (mostly mountainous regions). Using the grid-based approach, the melt period in the southernmost regions began as early as January. However, the average onset occurred in April in the non-permafrost zone and in May in the continuous permafrost zone, although the earliest onset in the latter was already observed in February. Similarly, the melt period ended earliest in January in the non-permafrost zone and in March in the continuous permafrost zone. On average, the season ended in April in the non-permafrost zone and in June in the continuous permafrost zone. Using the region-based approach, the melt period in the non-permafrost zone extended from mid-March to early May. In the sporadic permafrost zone, it lasted from mid-April to mid-May. In the discontinuous permafrost zone, the season began in the second half of April and ended in late May. In the continuous permafrost zone, the melt period occurred from early May to mid-June. In the Eurasian continent, the melt period started earlier in the west and later in the east. The regions with the most permafrost are located in the eastern part of Eurasia which means that the regions with less permafrost started to melt first. In the American continent, an east–west thawing gradient is not apparent. However, the melt period started and ended the latest where the most permafrost is located. Our region-based melt period started on average 10–20 d earlier in all the zones compared to the start of the thaw season defined by . With our grid-based approach the melt period started on average 1–10 d later than the thaw season.

The melt period was additionally studied in the Hudson Bay lowlands (land area in 50–60° N latitudes and 75–96° W longitudes) and the Western Siberian lowlands (land area in 52–74° N latitudes and 60–94.5° E longitudes). Hudson Bay lowlands and Western Siberian lowlands are some of the largest methane emitting wetlands in the northern high latitudes . They consist of the four permafrost zones, except the Hudson Bay lowlands where there is no continuous permafrost. On average, the grid-based melt period was slightly shorter in the Western Siberian lowlands (∼9d than in the Hudson Bay lowlands (∼10 d). The season started and ended a few days earlier on average in the Western Siberian lowlands than in the Hudson Bay lowlands. The region-based melt period length was not defined separately for these wetland regions, but the original region-based lengths in the four permafrost zones were used.

Overall, in the Hudson Bay lowlands, there was a negative correlation between the mean temperature and mean length of the melt period (p<0.05 in all zones) with the grid-based approach. In the Western Siberian lowlands, there was also a negative correlation in all of the permafrost zones but it was statistically significant only in the non-permafrost and sporadic zones (p<0.05). This means that the season was shorter when the mean temperature was higher at least with the grid-based approach.

With the region-based approach, there was not as clear negative correlation between the length of the melt period and the mean temperature of the melt period especially in the Western Siberian lowlands (p<0.05 only in the sporadic zone). In the Hudson Bay lowlands, there was a statistically significant negative correlation in the sporadic and discontinuous zones (p<0.05). If the melt period was defined with the region-based approach separately in the Hudson Bay and the Western Siberian lowlands areas, then the correlations might have been more significant.

The total prior emissions during the melt period were 1.81±0.29Tg with the region based approach and 0.447±0.11Tg with the grid-based approach. This means that the inversion increased the total melt period emissions from the prior to the posterior. In the permafrost zones the inversion increased emissions from the prior in areas with less permafrost (Fig. 6a) and decreased in areas with more permafrost (Fig. 6d). This was more evident with the region-based approach and was seen the most distinctly in the non-permafrost and continuous permafrost zones. In the non-permafrost zone the posterior was almost always larger than the prior with both methods, despite already having the highest emissions. In the continuous permafrost zone the posterior emissions were always smaller than the prior emissions with both methods.

To see where the differences between prior and posterior emissions were most noticeable, we plotted a map of the total difference of the grid-based emissions during the melt period (Fig. A7) including the same years as in Fig. 8 and an average of all the years. The region-based figure was very similar to the grid-based, thereby only the grid-based figure is shown in the Appendix. Grid cells with no prior emissions during the melt period were masked out in the figure, though there were only a few. During these years, we can see spatial variation throughout the years. The most notable differences appear in the Western Siberian Lowlands and the Hudson Bay Lowlands region. The average region-based biospheric prior CH4 emissions during the melt period in the Western Siberian lowlands were 0.45±0.11Tg and in the Hudson Bay lowlands they were 0.09±0.026Tg. The corresponding grid-based emissions in the Western Siberian lowlands were 0.11±0.03Tg and in the Hudson Bay lowlands 0.03±0.01Tg. The change from the prior to posterior is percentage wise larger in the Hudson Bay lowlands and Western Siberian lowlands than it is in the total northern high latitude region used in our study. In the total northern high latitude region, the posterior is about 1 % larger than the prior with both methods. In the Hudson Bay lowlands the posterior is about 6 % larger than the prior with both methods and in the Western Siberian lowlands it is about 3 % (grid-based) to 4 % (region-based) larger. In the four permafrost zones, the posterior emissions were 0.4 % (discontinuous permafrost) to 3 % larger (non-permafrost) or 6 % smaller (continuous permafrost) than the prior on average with the region-based approach. With the grid-based approach the posterior emissions were about 2 % larger (non-permafrost and sporadic zones) or 2 % (discontinuous) to 8.6 % (continuous permafrost) smaller than the prior on average.

We further examined the relationship between the difference in posterior and prior emissions and the length of the melt period (Fig. A8). Using the region-based approach, a significant positive correlation was found in the continuous permafrost zone between the difference in emission rate and melt-period length (p<0.05; Fig. A8b). In contrast, the grid-based approach revealed a negative correlation in the sporadic permafrost zone between melt-period length and both the emission difference (p<0.05) and the emission rate difference (p<0.01). Although differences between posterior and prior emissions were also observed in the other zones, no statistically significant correlations were detected between posterior-prior emission differences (or emission rate differences) and melt-period length. Overall, these results suggest that the inversion only marginally altered the relationship between emissions and melt-period duration.

The melt period occurring during springtime was defined for the northern high latitude wetlands for the first time based on the SMOS F/T data. As the SMOS F/T algorithm cannot distinguish between thawed soil and wet snow, it likely extended the season beyond the duration of true soil thawing. E.g. found that the SMOS F/T data showed later soil freezing but earlier soil thawing than a process-based ecosystem model. However, it is justified to define the melt period to start from the melting of the snow (see Sect. 2.5.1). In addition, including either snow depth data from in-situ measurements or fractional snow cover data from satellites could have helped our algorithm to detect the starting of the soil thawing.

The amount of SMOS F/T pixels in a 1°×1° grid cell made the definition of melt period spatially inconsistent. The number of pixels decreased towards the north, requiring a higher fraction of thawed soil in northern grid cells before the melt period began. However, with our definition, the absolute area, which had to be thawed before the season could start, was similar across the study area, though it also meant that the estimated thawing state of the soil was more uncertain if there were missing SMOS F/T datapoints. The difference in the amount of pixels in a grid cell might have introduced systematic biases, causing longer melt periods in south and shorter in north.

With both methods, the melt period generally started the earliest in the southern regions. However, there were some mountainous regions in the south, for example, the mountains in Mongolia, and the Rocky Mountains in the western coast of North America (Fig. 3), where the season started and ended later, causing long melt periods. This is likely due to higher altitude and lower temperatures. The SMOS F/T data is not as reliable in the mountainous regions as it is elsewhere, mainly because there is less soil substance, especially at higher elevations. Since the SMOS satellite measures the soil freezing through the permittivity difference between ice and water, it does not measure the soil freezing correctly in areas with less absorbent soil. Thus, the melting of snow or ice on solid rock does not significantly affect what is measured. A sufficient difference between thawed and frozen states requires soil that has absorbed water. Additionally, the topography affects the remote sensing measurements: the measurement angle varies a lot in the mountains, which means that with different measurement angles, the measured thawing state of the soil also changes.

The region-based melt period was on average about 4 times as long as the grid-based melt period. The region-based approach does not represent the local melt period accurately because of the substantial area of the permafrost zones and the difference between the start and end days inside one zone was large. In other words, the melt period in the southern grid cells might have already ended, while soil was still frozen in northern parts of the zone. However, with this method, the thawing fraction varied less during the melt period, and the beginning and end of the melt period were more consistent, making it easier to compare the different permafrost zones' melt periods and methane emissions with each other on a larger climatological scale.

The grid-based melt period was on average almost twice as long in the southernmost zone: non-permafrost (12 d) compared to the northernmost permafrost zone: continuous permafrost (7 d). This suggests that the season was shorter when there was more permafrost and the further north the region was, except for the mountainous permafrost regions in the south (Fig. 3). In a small area, the soil melts almost simultaneously leading to a shorter melt period. Additionally, because the grid-based period could not begin before the minimum thaw fraction was exceeded for the final time in spring, some grid cells may have experienced fluctuations in thaw fraction prior to this date. This variability could therefore have been included within the defined melt period. However, with this method the melt period was separated from the autumn freezing season if it continued past the turn of the year.

Each of the four permafrost zones consisted of areas in the North American and the Eurasian continents. Especially the region-based melt period could have been more precise if it was defined separately for the two continents due to their different year-to-year variability of climates.

Different methods used to study the timing of snowmelt and spring thawing season have produced varying results. According to the definitions of the Finnish Meteorological Institute (FMI) based on temperature data, spring starts approximately in the middle of March in southern Finland and in April in northern Finland and lasts for two to four weeks during which snow melts and the growing season starts. Our estimated melt periods in Finland, which is located mostly in the non-permafrost area, coincide with this: on average, the melt period started in March–April using both the grid-based and the region-based methods.

According to regional studies in northern Alaska, underlain by continuous permafrost, the spring thawing season in the tundra region was approximately 20 d long , which is shorter than the region-based melt period defined here (45 d on average, Table A2) and longer than the average grid-based melt period (10 d). With our grid-based method, the average length of the melt period during our study period in the grid cells closest to the coordinates of the measurement stations used by and varied between 4–19 d. Overall, in many grid cells in the whole northern high latitude domain, the length of the melt period was ∼20 d. Both and used soil temperature data to define the thawing of the soil. We did not use in-situ soil temperature data in this study as in-situ measurements of frozen soil are rare, and thus not suitable for our larger region study. Other option would have been to use reanalysis soil temperature data such as ERA5, which has shown higher skills than other products and a significant improvement over its predecessor . However, it is not well-suited for permafrost research . Thus, SMOS F/T data is a good proxy for the soil thawing.

The SMOS F/T data starting the melt period already from the melting of the snow instead of the soil is likely the reason for the longer region-based melt period. According to our prior LPX–Bern DYPTOP v1.4 (Fig. A9), the soil temperature rose to 0 °C during the region-based melt period on all permafrost zones. This means that the SMOS F/T melt period started earlier than the process-based ecosystem model melt period. However, the prior had a monthly temporal resolution compared to the daily resolution of the SMOS F/T data, and so the soil temperature rising above 0 °C in the middle of the melt period is a good indicator for the correct timing of our melt period.

According to the prior emissions used in this study (LPX–Bern DYPTOP v1.4), peat emissions were relatively high during the melt period compared to emissions from inundation for all other permafrost zones but continuous permafrost (Fig. A9). However, even in the continuous permafrost zone, the peat emissions are higher than those from inundation in April, and are rising during the melt period. At the beginning of spring, extensive snow melt inundation causes a large part of methane emissions, and after the end of the melt period, the methane emissions are dominated by peat emissions. Even though methane emissions from peat dominated over emissions caused by inundation for a large part of the year, there were evident peaks in inundation emissions in every permafrost zone during and/or right after the melt period. This indicates that the melt period timing we defined is reasonable.

Multiple previous studies have shown higher emission rates to our results with many of them showing large bursts of CH4 from wetlands during the spring thawing season . These events typically last for a short time, from few hours to a few days . Such emission bursts could have caused large emissions even during a shorter melt period, causing the relationship between the length and the emissions of the melt period to be non-linear. However, we found a positive correlation between the total melt period methane emissions and length, which was observed with both the grid-based and the region-based methods in permafrost zones and Western Siberian and Hudson Bay lowlands. This indicates that the bursts were not large enough to be detected with our model resolution (1°×1°) and weekly temporal optimization of the fluxes. The emission rates were also estimated from the whole area of the 1°×1° grid cell instead of the wetland area, which made the emission rates smaller compared to the local studies. Another reason for the positive correlation between the values could be that in our study, we focused on emissions within larger permafrost zones. In individual grid cells, some emission peaks could have been detected but that was not explicitly studied here. Above mentioned studies reporting large CH4 bursts during the spring thaw used field measurements to define the emission rate which have sensitivity for smaller areas compared to our inverse model. Emission rates defined from the eddy covariance measurement measure the local methane bursts rather than the average rates from a larger permafrost zone.

Using a process-based model showed an emission rate closer to what we found in this study. The atmospheric inverse model used here used atmospheric CH4 measurements to inform and “re-evaluate” the process-based estimates. In most years, our inversion showed an increase from the prior emission estimates which were based on the process model LPX-Bern DYPTOP. This means that there might have been short-lived emission bursts during the melt period, which the process model was not able to produce due to the poor spatial and temporal resolution or missing processes, or that the process model emission estimates were overall too low during this period.

With our inverse model, the grid-based emission rates were higher in some grid cells (Fig. A5), and on average, the grid-based emission rates were higher than the region-based (Fig. 7). The grid-based melt period likely represents local emission bursts during soil thawing better than the region-based approach. Within a single permafrost region, fluxes vary widely because the area does not consist entirely of permafrost or wetlands. This lowers the CH4 emission rate. The local measurement studies might be more comparable to the melt period emissions in the Hudson Bay lowlands and Western Siberian lowlands in grid cells, where the total area of the cell is mostly wetland. However, the focus of this study was to estimate the total melt period emissions rather than occasional hotspots.

According to , the annual global methane emissions estimated from atmospheric inversions were 575 [553–586] TgCH4yr-1, in 2010–2019. Of these emissions, 165 [145–214] TgCH4yr-1 were from wetlands. The average global biospheric emissions using the CTE-CH4 data from this study for the years 2011–2021 were 124 TgCH4yr-1, including also soil sink (LPX-Bern DYPTOP prior soil sink 33 TgCH4yr-1). In the northern high latitudes (defined in the chapter 2.3), the average annual methane emission were 23 TgCH4yr-1. The region-based melt period posterior emissions were 1.83 Tg (8.1 % of the annual northern high latitude emissions) and grid-based were 0.45 Tg (2 % of the annual northern high latitude emissions), only a small portion of the annual total global emissions. The length of the melt period with the grid-based method was 3 %, and with the region-based method 12 %, of the total length of a year.

Methane emissions during other seasons and the high northern latitudes have been studied previously. According to , the winter cold season (November to April) emissions were 3.3 Tg in the northern high latitudes (above 50° N), which included partly emissions from both the autumn freezing and spring thaw seasons. The autumn freezing season methane emissions from the same model with a different setup were 1 Tg . estimated the autumn freezing, winter cold season and summer thaw season emissions in the northern high latitudes with the same inverse model but a different setup to ours. They found emissions to be 1.2 Tg in winter, 0.73 Tg in the freezing period, and 16.2 Tg in the thaw (summer) period. In both studies, winter and freezing season emissions were smaller than our region-based melt period emissions but larger than the grid-based emissions.

According to a study which used upscaled flux measurements, the methane emissions during the melting of the soil in wetlands in a northern high latitude permafrost region were 0.5–0.97 Tg in 2011 . In a study by , the spring season (March–May) methane emissions were calculated with multiple process-based ecosystem models for the northern wetlands (>45°), and their mean value was 0.80±1.89TgCH4yr-1 (3.07%±9.61% of the annual emissions), where the error is the variation between the maximum and minimum model result. These estimates are closer to the grid-based emissions estimated in this study.

Defined from the inverse model used in this study, the mean annual emissions in the Hudson Bay lowlands and Western Siberian lowlands were the size of 2.9 and 5.0 Tg, respectively. This is close to the values defined in other studies . The average region-based melt period emission in the Hudson Bay lowlands and the Western Siberian lowlands were the size of 0.1 and 0.47 Tg, respectively. The grid-based emission were smaller with the magnitude of 0.03 and 0.11 Tg, respectively. This means that together they produced approximately 31 % of the total melt period emissions from the northern high latitude wetlands with both methods. This is a significant part of the total melt period emissions when their areas only represent a portion of the total study region (Hudson Bay lowlands is 2.5 % and Western Siberian lowlands is 9.6 % of the total study region land area). The region-based melt period emissions were 7 % and grid-based emissions were 1.7 % of the annual emissions from the Hudson Bay lowlands and the Western Siberian lowlands. The increase in emissions from prior to posterior estimates was also more pronounced in these two regions than across the northern high-latitude domain as a whole. This may be attributed to the greater extent of continuous wetlands in these regions and/or the higher density of the observational network (Fig. A1), which likely influenced the prior estimates. Additionally, there are large areas in the high northern latitudes, where the difference between the posterior and prior emissions was close to zero during the melt period (Fig. A7). In grid cells where prior emissions were zero, posterior emissions during the melt period were also zero. This likely contributed to the minimal differences observed between prior and posterior estimates in those areas. However, the emissions in the Western Siberian lowlands could have been overestimated, because the NIES observation sites, which we did not adjust before using the measurements in the inversion, had a different calibration scale (3.0 to 5.5 ppb higher) than WMO CH4 X2004A scale as in the ObsPack . The NIES observations are now included in the newer version of ObsPack, with scale corrected. A higher density of observations in the northern high latitudes could have improved our inverse method estimates.