Cold-Season Methane Fluxes Simulated by GCP-CH 4 Models

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et al., 2020) using contemporary atmospheric and ground observations and model-based analyses provide the most comprehensive estimate of methane sources and sinks to date.
Wetlands are the largest natural source of CH 4 to the atmosphere, contributing approximately 150 Tg CH 4 yr −1 globally (Saunois et al., 2020).Natural wetlands, ranging from tropical swamps to northern lowlands (e.g., Hudson Bay and West Siberia) and tundra, are distributed worldwide.CH 4 is mainly produced by microbial processes in wet soils, and its efflux is highly sensitive to environmental conditions such as temperature, water-table position, and substrate availability (Le Mer & Roger, 2001;Xu et al., 2016).These methanogenic processes and their environmental sensitivity are regulated in a complex manner, which creates a challenge for biogeochemical models to reproduce observed CH 4 emissions (Melton et al., 2013;Poulter et al., 2017).In terms of the global CH 4 budget and climatic change, the northern wetlands and permafrost are particularly important, both because of their vast area (about 3.5 × 10 6 km 2 ; Bubier & Moore, 1994), huge carbon stock (1,035 ± 150 Pg C; Hugelius et al., 2014), and faster climatic warming rates than the global average (IPCC, 2021).It is critical, therefore, to reduce model uncertainties associated with different model structures, parameterizations, and input data to better constrain the global CH 4 budget and to allow more reliable future projections of wetland emissions.
A growing number of in situ studies have revealed that the behavior of wetland CH 4 emissions at temperatures near or below freezing is both important and complex.Observations show that CH 4 emissions in the cold (non-summer) season (September to May) account for more than 50% of the annual CH 4 flux from Arctic tundra (Howard et al., 2020;Rößger et al., 2022;Zona et al., 2016).Observational studies also indicate that cold-season emission rates vary considerably; rates are high at the onset of freezing and thawing (Bao et al., 2021;Elberling et al., 2008;Mastepanov et al., 2008;Pirk et al., 2016) as well as during the "zero-curtain" period (when soil temperatures are near 0°C; Arndt et al., 2019).Particularly drastic variations in CH 4 fluxes such as burst emissions have been observed at soil temperatures close to 0°C (e.g., Mastepanov et al., 2008).Such findings have been made possible by recent technical advancements in measuring gas fluxes during the cold-season, but winter flux data are still sparse and insufficient (e.g., Pallandt et al., 2022).Recently, regional data have been provided by satellite remote sensing of atmospheric CH 4 (e.g., Qu et al., 2021), but it is difficult to apply this technique during the cold-season at high latitudes because of the low solar angle.
There remain large uncertainties in the estimation of wetland CH 4 emissions even by present state-of-the-art models.Model intercomparison studies (e.g., Bohn et al., 2015;Chang et al., 2023) imply that the wetland models can simulate different magnitudes of fluxes though using standardized input data and protocols.The uncertainty, likely coming from differences in model structure and parameterization of CH 4 processes such as methanotrophic production and transports, would be evident for cold-season fluxes.Using flux measurement and model-derived datasets (WETCHIMP and WetCHARTs), Treat et al. (2018) concluded that wetland models have underestimated cold-season CH 4 emissions.The models have estimated the cold-season flux to be negligible because microbial CH 4 production and consumption are strongly inhibited in cold and frozen soils (Bartlett & Harriss, 1993;Christensen, 1993;Ito, 2019).In addition, soil-freezing and snow cover are likely to reduce soil gas diffusivity by disrupting major CH 4 transport pathways (ebullition and plant aerenchyma), at least temporally, while vegetation dormancy reduces the belowground substrate supply (Olefeldt et al., 2013;Treat et al., 2018).
In this study, we analyze cold-season CH 4 fluxes from northern wetlands as simulated by 16 terrestrial biogeochemical models that participated in the GCP model intercomparison (Poulter et al., 2017(Poulter et al., , updated in 2022)).Using different definitions for the cold-season, we compare CH 4 emissions simulated by multiple models and examine the apparent temperature dependence of the CH 4 flux at freezing and thawing temperatures.Then, on the basis of this diagnosis of current modeling capabilities, we describe current challenges facing the modeling of cold-season CH 4 fluxes and propose key areas for future research.

Wetland Models and Simulations
The wetland models used in this study are summarized in Table 1.In general, the models incorporate hydrological and biogeochemical schemes that simulate the water and carbon dynamics of wetlands to enable them to estimate wetland CH 4 fluxes (Table S1 in Supporting Information S1).Although several models can estimate wetland extent dynamically, in this study, the results of simulations based on prescribed wetland extent (i.e., diagnostic experiments) were used to focus on biogeochemical processes.
The experimental protocol was updated from WETCHIMP (Melton et al., 2013), such that each model is required to conduct prognostic and diagnostic runs using two climate forcing data.The prognostic run uses model-estimated wetland extent, while the diagnostic run uses the remotely sensed monthly wetland inundation data from the WAD2M data set (Zhang et al., 2021).The protocol requires the use of two climate datasets (surface air temperature, humidity, pressure, precipitation, wind speed, and incoming shortwave and longwave radiation): the Climate Research Unit 4.06 (Harris et al., 2020) and the Global Soil Wetness Project Phase three datasets.This study chose the former because it covers the longest period of the two, and we did not find a substantial difference between the results using the two climate datasets.In this study, we analyzed simulated monthly mean 0.5° × 0.5° gridded CH 4 flux data (kg CH 4 m −2 s −1 ).For composite model mapping, data of several models (Table 1) were regridded using the "remapbil" function from Climate Data Operators (https://code.mpimet.mpg.de/projects/cdo/).

Observational CH 4 Datasets
Observed CH 4 flux data were used only for evaluation of the simulation results.The field CH 4 flux observations were made by eddy covariance method, which generally have a local-scale footprint (on the order of m 2 to km 2 ).Therefore, we adopted the data set of Peltola et al. (2019), which comprised CH 4 flux data observed by the eddy covariance method at 25 northern wetlands sites scaled up with a machine learning algorithm to generate a continuous field for the land area north of 45°N at a spatial resolution comparable to that of the wetland models.This data set provides the monthly CH 4 fluxes during 2013-2014 for three different base wetland maps; we used the results for the Global Lakes and Wetlands Data set base map (Lehner & Döll, 2004).Additionally, to examine in situ CH 4 fluxes closely, we used the FLUXNET-CH 4 version 1.0 data set (Delwiche et al., 2021;Knox et al., 2019), which contains observational data from freshwater wetlands worldwide, including 16 northern wetland sites (wet tundra [inundated temporarily], bogs [ombrotrophic], and fens [minerotrophic]).Note that many sites provide data for only the summer growing season, which may affect the quality of the flux upscaling.For the sites used by Peltola et al. (2019), we found that 15 sites provided data for periods longer than 12 months and at least seven sites (FI-Sii, FI-Si2, US-Los, US-Bes, US-Ivo, Ru-Ch2, and SE-Deg) provided many CH 4 flux data at subzero air temperature conditions.

Analyses
There are several definitions of "cold-season," affecting the interpretation of observational data (Rafat et al., 2022).This study considered three definitions of the cold-season: (a) the subzero monthly-mean air

Model-Mean Annual Emissions
The 16 wetland models simulated annual CH 4 emissions during 2000-2020 from wetlands of 60°-90°N to be 10.0 ± 5.5 Tg CH 4 yr −1 and those of 45°-90°N as 26.7 ± 10.1 Tg CH 4 yr −1 (mean across models ± standard deviation).These values, which account for 6% and 16%, respectively, of the global total wetland emissions simulated by the models, are slightly lower than the corresponding upscaled flux data (Table S2 in Supporting Information S1).Particularly strong and spatially extensive CH 4 sources were located in the West Siberia and the Hudson Bay Lowlands, where land grids were dominated by wetlands including wet tundra (Figure S1 in Supporting Information S1).

Cold-Season Emissions
The simulated CH 4 fluxes show clear seasonality (Figure 1, for 60°-90°N; Figure S2 in Supporting Information S1 for 45°-90°N), with midsummer peaks that reflect higher temperatures, deeper soil thawing, enhanced vegetation activity, and wetland expansion under humid conditions.The simulated seasonal change, especially of the model-mean emissions, is consistent with the seasonal change in the eddy-covariance data upscaled with the machine learning model.As shown by Taylor diagrams (Taylor, 2001) for temporal variability, the simulated fluxes are strongly correlated with the upscaled flux (coefficient of determination R 2 of >0.9; Figure S3 in Supporting Information S1).However, the sixfold difference in peak CH 4 emissions among the models, as shown by the standard deviations, is striking.Because prescribed climate and inundation data were used, this difference can be attributed to differences in the parameterizations and assumed sensitivity of the models.In the non-summer months, emissions simulated by most models were lower than the observations.Only 0.7 ± 1.8% of the annual CH 4 emissions simulated by the models occurred during the midwinter months (December-February) in 60°-90°N wetlands, whereas 8.3% of the upscaled flux occurred in those months (Table S3 in Supporting Information S1).The emissions simulated during non-summer months (September-May) and subzero air temperature months accounted for 27 ± 9% (2.8 ± 1.9 Tg CH 4 yr −1 ) and 5.1 ± 4.7% (0.5 ± 0.6 Tg CH 4 yr −1 ) of annual emissions; by comparison, in the upscaled flux data, the non-summer months account for 45% of annual emissions.Cold-season CH 4 fluxes are difficult to evaluate with top-down approaches, but Tenkanen et al. (2021) recently used an atmospheric inversion system (CarbonTracker Europe) to estimate whole-year wetland fluxes.They estimated annual emissions from >50°N wetlands to be 23.1 Tg CH 4 yr −1 , of which 15% occurred in the cold-season (defined by satellite data by soil in the freeze/thaw state).
The contribution of cold-season emissions estimated by contemporary wetland models is notable but is still lower than that indicated by eddy covariance observations.This implies the necessity of model improvements not only in growing seasons but also in non-growing cold seasons.Simulated emissions in midwinter and subzero air temperature periods were generally low, whereas those in autumn and spring were substantial.We found that the model-simulated CH 4 fluxes differed widely during the "zero-curtain" periods in spring and autumn, although their contributions to annual flux were comparable to that of the observation-based flux (3%-5% in spring and 8%-11% in autumn, Table S4 in Supporting Information S1).The stronger autumn emissions are consistent with those observed in Alaskan wetlands due soil physical conditions (Bao et al., 2021).

Spatial Distribution of Fluxes
Model-mean maps of simulated CH 4 fluxes show that substantial emissions occurred during the cold-season in the West Siberian and Hudson Bay Lowlands, along the western coast of North America, and in northern Europe (Figure 2; see Figure S4 in Supporting Information S1 for individual model results).In most northern wetlands, emissions during midwinter (December-February) were low, and their contribution to the total annual flux was less than 20%.Instead, substantial contributions in these months come from temperate wetlands of Europe, where winter conditions are less frigid.Emissions during the non-summer period (September-May) were substantial across a broad area of northern wetlands (Figure 2d) and their contributions to the annual flux were also notable, except in major wetlands that have high summer emissions.Soil freezing in autumn and thawing in spring were accompanied by large CH 4 emissions, but in major wetlands, these contributions were still comparatively low.Emissions during the subzero temperature period (which varied spatially among grids) were higher than those in midwinter and lower than those in non-summer months (Figure 2c).In Central and East Siberia, as well as in Europe, the simulated emissions during the subzero temperature period were substantial (>30%).The simulated  et al. (2019) and data of an independent model study (WetCHARTs: Bloom et al., 2017).Light gray zones represent non-summer months (September-May), and pale blue zones represent midwinter months (December-February).See Figure S2 in Supporting Information S1 for the results for temperate to northern (>45°N) wetlands.same) clustering was found for emissions at subzero air temperatures and from >45°N wetlands.It looks that DLEM, which estimates CH 4 production from dissolved organic carbon, is relatively close to the reference data, although the model gave total cold-season emissions comparable to other models (Table S3 in Supporting Information S1).Apparently, results of the models adopting the same wetland schemes (e.g., ISAM and LPJ-GUESS implementing a scheme of Wania et al. ( 2010)) were close, but attributing the cluster formation to specific model attributes (Table S1 in Supporting Information S1) was, however, difficult, because they were related to many factors working at once.

Interannual Variability
This study first revealed that emissions during the cold periods showed substantial interannual variability (Figure 3), although previous studies focused on annual emissions dominated by growing-season emissions (e.g., Poulter et al., 2017;Thompson et al., 2017).Because variability of the simulated flux was caused mainly by inundation and temperature variabilities of the prescribed input data, most models showed coherent year-on-year variation.Higher non-summer emissions were simulated in 2005, 2011, 2016, and 2020, when the mean air temperature was higher than the long-term average (Figure 3a).As a result of interannual variability in emissions, the contribution of the cold-season to the annual flux also varied from 18 ± 9% in 2002 to 24 ± 9% in 2005 (16 model-mean).During the study period, the simulated flux increased gradually with time (on average, +0.4 ± 0.8% decade −1 : from −0.004 to +0.025 Tg CH 4 yr −2 , depending on the model).Rößger et al. (2022) have reported that, at one wet tundra site in Siberia, CH 4 emissions in June and July have been increasing substantially, and the results of the present study imply that cold-season emissions are also increasing, though long-term observation data supporting the trend are still insufficient (e.g., Masyagina & Menyailo, 2020).The simulated widths of interannual variability of fluxes during the subzero air temperature period were smaller than those during the cold-season (Figure 3b), mainly by a methodological reason.Namely, because the length of the subzero temperature period varies inversely with average temperature (i.e., the subzero period is shorter in warm years), cumulative emissions during the subzero temperature period in individual years may be relatively stable when averaged over all models.As a result, interannual variability of the non-summer flux was strongly correlated (R 2 = 0.70 for the model-mean) with the variability of annual emissions, while that of the subzero temperature period was correlated only poorly (R 2 = 0.04).

Temperature Response Functions
The simulated relationship between temperature and the CH 4 flux differed among the models; therefore, to compare results among the models, we standardized all fluxes by the annual flux (Figure 4, see Figure S7 in Supporting Information S1 for bulk fluxes).Several models showed an exponential relationship between flux rate and air temperature, reflecting their parameterizations (e.g., CLASSIC, ISAM, JULES, TRIPLEX-GHG, and VISIT).Several models estimated substantial CH 4 emissions from subzero-temperature grid points (e.g., DLEM, ELM-ECA, and JSBACH), whereas a few models discretely suppressed emissions under subzero temperatures (e.g., LPJ-GUESS and SDGVM).Other models exhibited complicated patterns with multiple modes (e.g., CH4MOD wetland , DLEM, LPX-Bern, TEM-MDM).Differences in simulated fluxes under subzero temperatures may be attributable to model-specific parameterizations of biogeochemical factors such as the threshold temperature of microbial activity, the impact of vegetation activity, the spatial representativeness stemming from the data used, and the snow insulation effect (Table S1 in Supporting Information S1).For example, several models set a clear temperature threshold for CH 4 production (e.g., LPJ-GUESS, TEM-MDM, TRIPLEX-GHG, and VISIT), whereas other models assume that production continues at subzero temperatures in parallel to heterotrophic respiration (e.g., CH4MOD wetland , CLASSIC, JSBACH, LPJ-MPI, and LPX-Bern).
Adjusting the simulated cold-season flux to better reproduce field evidence will result in higher winter and then annual simulated emissions (e.g., Treat et al., 2018) and increase the region's contribution more to the global CH 4 budget.Although the models captured the seasonal cycle of emissions seen in observations, their quantitative accuracy was low, as revealed by the model intercomparison analyses.The models differed in the temperature responsiveness of emissions at temperatures around freezing, likely because of their different soil ITO ET AL. 10.1029/2023GL103037 9 of 12 structure and physical and biogeochemical parameterizations (Ueyama et al., 2023).For example, several models assumed threshold temperatures for CH 4 production and emission, but it should be examined against the observed temperature-flux relationships (Figure S8 and Text S1 in Supporting Information S1).Also, explicit soil-layer schemes are required to capture the processes during the zero-curtain periods, and observation-based tuning of key parameters such as temperature sensitivity of CH 4 production is required.
A revised parameterization specifically for capturing cold-season CH 4 emissions may be required, although it has been proposed that growing-period CH 4 production shows a consistent temperature dependence (Yvon-Durocher et al., 2014).Note that wetland models account also for methane oxidation in aerobic layers, which responds to temperature and affects local fluxes (e.g., Juutinen et al., 2022;Virkkala et al., 2023) but was differently parameterized in the models.Differences in the CH 4 transport pathways assumed in the models also partly account for the differences in fluxes at subzero temperatures.Diffusive emission likely dominates cold-season fluxes, but models differ in how gas diffusivity is treated in subzero-temperature soils as well as assumptions about other (i.e., plant-mediated and ebullition) pathways.Moreover, ice wedge and permafrost parameterizations, which were not examined in this study, would cause additional differences among the models.Masyagina and Menyailo (2020) showed that CH 4 emission characteristics differ between permafrost and non-permafrost areas in northern high latitudes, and Wickland et al. (2020) reported that ice wedge degradation enhances CH 4 emissions at landscape scale.Observations showed high heterogeneity of northern wetlands (e.g., ice wedge, polygon, hammock), which cannot be directly retrieved by broad-scale models, and therefore appropriate scaling schemes should be developed and introduced into wetland models.For model improvements and validation, our findings strongly encourage correcting year-round CH 4 flux data from more sites in high-latitude regions.

Concluding Remarks
Global CH 4 budget would be more important in terms of climatic projection and mitigation (e.g., Kleinen et al., 2021;Zhang et al., 2017).Ongoing global warming, especially at high latitudes with Arctic amplification (Dai et al., 2019;Previdi et al., 2021) will increase the importance of CH 4 emissions from northern wetlands to the CH 4 budget.This study confirmed the importance of cold-season emissions as suggested by field observations, and further studies are needed to estimate the future CH 4 emissions.Future projection of wetland CH 4 budget would be more difficult by including direct human impacts such as land-use conversion (e.g., Qiu et al., 2021;Strack et al., 2019) and indirect impacts through changes in disturbance regimes accompanied with permafrost degradation (e.g., Miner et al., 2022).This study used outputs of the "diagnostic" experience in which inundation area was prescribed, and using of model-estimated inundation extent may introduce additional model specificities in hydrological dynamics.These aspects of wetland CH 4 models are being examined at global scales by comparing with atmospheric data (e.g., Chang et al., 2023), but specific analyses as done here are effective to specify important areas, periods, and processes.

Data Availability Statement
temperature period irrespective of calendar month, determined at each grid; (b) the non-summer months approximating the non-growing period in northern high latitudes, from September to May (the same months as those used byZona et al., 2016); and (c) the midwinter months from December to February, when soils are assumed to be entirely frozen.The second and third ones are defined simply by calendar and then can contain warm spells.In contrast, cold-season defined by the first one focuses on cold periods only but can vary year-by-year.When focusing on the "zero-curtain" period, we extracted data at air temperatures between −5° and 5°C in spring (March to May) and autumn (September to November), assuming that soil temperature is at around 0°C.Note that this study used air temperature for analyses, primarily due to data availability of model-simulated soil temperatures, but it has several justifications.Rafat et al. (2022) showed that air temperature well represented the non-growing season of CO 2 emissions, andKnox et al. (2019) showed that the responsiveness of the observed CH 4 flux to air temperature (R 2 = 0.65) is comparable to its responsiveness to soil temperature (R 2 = 0.66).Simulated wetland CH 4 emissions by the models were split into two regions: arctic to boreal (60°-90°N) and arctic to cool-temperate (45°-90°N) regions.These regions were examined for their seasonal and interannual variability, spatial distribution, and relationship with temperature, especially around the freezing point.The temperature-emission relationship is useful for clarifying model-specific behavior, but a large inter-model discrepancy in the flux magnitude can obscure individual model characteristics.Therefore, we used standardized monthly CH 4 fluxes (= monthly flux/annual flux) in each grid cell to scale the simulated flux magnitudes from the different models.

Figure 1 .
Figure 1.CH 4 fluxes from northern (>60°N) wetlands as simulated by each of the 16 models during 2013 and 2014.(a) Annual emissions during summer (June-August) and non-summer months and (b) monthly fluxes.The results were compared with eddy-covariance flux data upscaled with a machine learning model by Peltola et al. (2019) and data of an independent model study (WetCHARTs:Bloom et al., 2017).Light gray zones represent non-summer months (September-May), and pale blue zones represent midwinter months (December-February).See FigureS2in Supporting Information S1 for the results for temperate to northern (>45°N) wetlands.
19448007, 2023, 14, Downloaded from https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103037by MPI 348 Meteorology, Wiley Online Library on [03/08/2023].See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions)on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons Licensecold-season emission patterns appear comparable to those of the upscaled flux data but differ in the magnitude of their contributions to annual flux (FigureS5in Supporting Information S1).In the upscaled flux data, the contributions of emissions at subzero air temperatures were substantial in far East Siberia and Alaska, and non-summer emissions were substantial across a wide area of Central and East Siberia and northern North America.We used dendrograms to identify clusters in the spatial patterns simulated by the different models and the upscaled observations (FigureS6in Supporting Information S1).For non-summer emissions from >60°N wetlands, three small groups of models were identified: (a) CH4MODwetland and CLASSIC; (b) LPJ-wsl, LPX-Bern, and ORCHIDEE; and (c) ISAM, JULES, LPJ-GUESS, LPJ-MPI, SDGVM, TEM-MDM, TRIPLES-GHG, and VISIT.Several models (DLEM, JSBACH, and ELM-ECA) showed model-specific patterns.Similar (but not the

Figure 2 .
Figure 2. Model-composite maps of averaged CH 4 emissions during 2000-2020 simulated by 16 models.Mean fluxes during (a) subzero air temperature periods, (b) the non-summer season (September-May) and (c, d) contributions of (a) and (b), respectively, to the annual CH 4 budget (Figure S1 in Supporting Information S1).See Figure S4 in Supporting Information S1 for the results of each model.

Figure 3 .
Figure 3. Interannual variability of wetland CH 4 fluxes for (a, b) >45°N and (c, d) >60°N simulated by 16 models, shown by deviations from the long-term mean, in (a, c) subzero air temperature months and (b, d) non-summer months (September-May).

Figure 4 .
Figure 4. Relationship between monthly mean air temperature and monthly CH 4 fluxes normalized by the annual total flux from northern (>45°N) wetlands simulated in each model grid.Color shows point density, from low (blue) to high (red).See Figure S7 in Supporting Information S1 for absolute fluxes (in kg CH 4 m −2 month −1 ).