Permafrost-affected soils are a significant global carbon pool, storing more carbon than there currently is in the atmosphere . This permafrost is already beginning to thaw and large-scale future losses are projected due to climate change and the increased warming that is expected to occur in the Arctic . Thawing permafrost enables the microbial decomposition of the large amounts of carbon stored across the Arctic, potentially releasing considerable amounts of carbon to the atmosphere, thus creating a self-reinforcing carbon-climate feedback .

Of particular interest is the form in which the carbon will be released to the atmosphere, namely as either CO2 or CH4, due to the strong difference in climate forcing between the two gases, with methane being the much more potent one . Methane has contributed 11 % to the total radiative forcing since 1960, despite its relatively low concentration in the atmosphere . Furthermore, methane emissions have increased nearly 2-fold in the last two centuries and continue to grow persistently , thus garnering much research interest . The majority of emissions are expected to occur as CO2 but recent studies also highlight the importance of CH4 emissions from a thawing Arctic . This stresses the need for a more accurately constrained future methane budget, which presently remains uncertain . Methane production is tied to anoxic conditions in the soil, which usually occur when the soil becomes waterlogged . Since the future hydrology of the Arctic remains uncertain , so does the extent and timing of Arctic methane emissions . This is also the reason for the relative scarcity of model studies on the topic that involve Earth System Models (ESMs) . In fact, many ESMs do not explicitly model CH4 emissions at all . Those who do, often represent methane production in a highly simplified way, frequently via a certain CO2:CH4 production ratio factor . This is despite the fact that this ratio has been shown to be highly variable in both laboratory and in situ studies . showed in their long-term incubation study, that methanogenic communities in permafrost soils need time to establish themselves, resulting in a lag time of multiple years before eventually a CO2:CH4 ratio of 0.92±0.18 was reached . reported C-CO2:C-CH4 production ratios between 13–134, depending on soil depth, from their incubations. estimated in situ median CO2:CH4 emission ratios of 12 and 373, depending on the tundra type of polygonal tundra soils, though their values were affected by methanotrophy and, therefore, the actual production ratios are likely smaller . Another important factor, besides hydrology and soil properties, is vegetation. Due to the CO2 fertilization effect, the plant productivity will potentially increase, providing additional substrate for the methanogens . This aspect will especially be important in the Arctic, where large-scale vegetation changes can be expected upon warming .

The methane emission calculation does not stop at the methane production, however. For the methane to reach the atmosphere it needs to be first transported from its production point, through the soil column, to the surface. On its way to the surface, the methane can be oxidized by methanotrophic microbes in oxic soil layers, which affects the CO2:CH4 ratio at the surface . There exist three important transport mechanisms: diffusion, ebullition, and plant-mediated transport . Their relative share is important with regards to the potential methane oxidation, since plant-mediated transport, e.g., can enable methane to bypass the oxidative soil layers . Diffusion describes the methane transport along a concentration gradient and is the slowest way of transport, thus facilitating methane oxidation . Ebullition is a rather fast process, describing the rise of methane gas bubbles through water . Lastly, plant-mediated transport happens largely through vascular plants, which possess so called aerenchyma, a type of aerated tissue responsible for supplying O2 to the roots . That tissue enables methane and CO2 to be transported through the plant to the atmosphere . This connection between methane release and plants further hints at the fact that, aside from hydrological changes, future methane emissions are also influenced by vegetation changes . Many models account for these three transport ways, including large-scale land surface models . In fact, found that the majority of methane models in their meta-study represented these three pathways already, albeit to varying degrees of complexity. Considering all this, it is worth looking into the recent developments concerning methane modeling. In this study we will focus on the methanogenesis aspect in particular, since other methane-related processes, e.g., methane transport, have already been implemented into models in more detail over the years . It is also worth noting that we focus on terrestrial emissions in this study. Other methane sources, e.g., wildfires, lakes, and marine and geological sources, also make up a significant part of the Arctic methane budget, potentially contributing over 30 % to it . We will first recap the crucial processes and environmental factors that have been identified to govern methanogenesis and the CO2:CH4 ratio in the literature. We will then examine how methanogenesis is currently modeled in land surface models and state-of-the-art process-based methane models, and discuss efforts to bridge the divide between laboratory-scale and global-scale approaches. This will lead to a clear recommendation of a model structure for a methanogenesis module inside a land-surface model that can predict, process-based, the CO2:CH4 production ratio.

One of the most challenging aspects of studying and modeling CH4 production in soils is its high degree of complexity, encompassing various different processes, which are, in turn, affected by a multitude of environmental factors (). Methanogenesis is not one simple straight-forward process but rather an entanglement of various interacting microbial processes in the soil . The two main methanogenesis pathways are hydrogenotrophic and acetoclastic methanogenesis, during which hydrogen or acetate are being used as substrate by the microbes respectively, and methane is produced . A review performed by found that out of the 40 investigated models only 3 represented these two major pathways. This is significant because the two processes yield different products: acetoclastic methanogenesis results in CO2 and CH4 production, while hydrogenotrophic methanogenesis only produces CH4 . Furthermore, the contribution from each process to total methanogenesis varies strongly between different environments , soil depth , and active layer vs. permafrost layers , among others. Considering this, the need to distinctly represent these processes in models becomes evident if a realistic portrayal of the CO2:CH4 production ratio wants to be achieved.

The most important environmental factors that influence methanogenesis are temperature , soil pH , water table depth , and soil biogeochemical conditions . Especially temperature has a profound effect on not only microbial decomposition processes in general , but also on the CO2:CH4 ratio in particular . This is due to the different temperature sensitivities of the processes involved , though generally both CH4 and CO2 production experience an increase with rising temperature . showed in their meta-analysis that methanogenesis as a whole exhibits a higher average temperature dependence than general respiration (0.98 vs. 0.65 eV; measured as activation energy). In fact, such differences in temperature dependence persist even down to the finest scale, with temperature determining enzyme kinetics and thermodynamics of the individual methanogenesis sub-processes . Temperature-induced microbial community changes may lead to changes in the dominant methanogenesis pathway, moving from acetoclastic to hydrogenotrophic with increasing temperatures, thus affecting the CO2:CH4 ratio .

Naturally, this level of complexity can hardly be represented in global models. In methane modeling, there exist two common ways of representing the effect of temperature : the Q10 value and the Arrhenius-type functions . 1f(T)=Q10T-Tref102f(T)=exp⁡ΔER1T0-1T

In the Arrhenius equation, ΔE is the activation energy, R is the universal gas constant, and T0 is the reference temperature . The Q10 parameter expresses the factor by which the reaction rate increases upon a 10 °C change in temperature and it is ubiquitously used to express temperature dependency across models . Although, for microbial models in particular, found the Arrhenius functions to be more common. Despite its widespread use, however, the Q10 concept is very simple and not without criticism, owing in parts to the large span of reported values . Most models put the value for methanogenesis in the range of 1.5–4 – often a central value of around 2 is chosen – which lies in the range of values reported from many lab experiments . Despite that, a meta analysis by showed that the entire spectrum of reported Q10 values from lab and field studies has a large range from <2 to >300 . further criticized the use of constant Q10 parameters in models as overly simplistic, even finding that the decomposition rate behaved linearly rather than exponentially in the 5 to 30 °C range in their model experiment . They argue instead in favor of a more in-depth biogeochemical model approach that accounts for individual processes .

As for the second frequently used method, the idea behind Arrhenius functions is to express the temperature sensitivity through the activation energy of the process in question . This approach is based on fitting data to the Boltzmann–Arrhenius function, which, similar to the Q10 approach, assumes an exponential increase of the metabolic rate with increasing temperature . Here, reported values for methanogenesis lie between 0.62 and 0.98 eV . Both Q10 and activation energy values have been observed to decrease with increasing temperature and vice versa . In models, the Q10 parameter is usually chosen, with different processes sometimes having their own distinct Q10 values . This is still rare, however, with many models settling on a single Q10 value for methane production , despite the evidence for differences in the temperature response between the main pathways . Methanotrophy usually has its own Q10 value in models, which is typically assessed at a slightly lower value than the one for methanogenesis, lying between 1.2–2.4 . Since temperature is only a piece of the puzzle, the difficulty of how to accurately represent this factor in models alone hints at the overarching complexity of methane modeling.

Besides the two main methanogenesis pathways introduced earlier, there exist further processes that have an effect on methanogenesis. This can either be directly through processes like hydrolysis and fermentation, which break down the organic matter and provide the substrate for methanogenesis , or indirectly through other redox reactions such as Fe(III) reduction . Especially the interplay between methanogenesis and Fe(III) reduction has been the subject of recent studies and their interactions have started to be included in models . Additionally, some soil processes are in competition with methanogenesis for substrate, like other, energetically more favorable metabolic pathways . Another example is homoacetogenesis, through which acetate is being produced by the consumption of H2 and CO2. While acetate is the main substrate for methane production by acetoclastic methanogenesis, homoacetogenesis thereby reduces the substrates for hydrogenotrophic methanogens . Looking at this web of interconnected process , it becomes evident that by assuming a prescribed CO2:CH4 production ratio in process-based models, the reliability of future methane emission projections from warming Arctic soils and thawing permafrost is highly limited.

Despite recent efforts to integrate process-based methane production in LSMs , their representation of CH4 production largely remains overly simplified . This is also true for the land surface schemes that are a part of widely used ESMs, such as the ones partaking in the CMIP6 (Coupled Model Intercomparison Project Phase 6), though simulating the CH4 feedback was not part of this project . These models were featured in the latest IPCC AR6 report , so it would be desirable if they were able to simulate methane production from thawing permafrost landscapes in a more realistic fashion that reflects the seasonality and variability observed in studies . This dire need to more accurately portray permafrost carbon processes in ESMs has recently been reaffirmed by who concluded that methane emissions are only represented to an “intermediate” degree in ESMs. Tightly connected aspects such as wetland distribution remain “poorly” represented . The latter hints at a larger problem in regards to accurately modeling methanogenesis in soils. Methanogenesis occurs when soils become waterlogged and oxygen is eventually depleted . Predicting this in models, however, has been a persistent challenge . In models, this limitation of methanogenesis to anoxic conditions is usually realized through two different methods: (1) simulating the water-table in a given area and (2) explicitly modeling and tracking the O2 concentration in the soil layers . The former case is frequently realized via a TOPMODEL approach , which determines the inundated areas in a grid cell , thus representing horizontal heterogeneity while the latter method represents vertical heterogeneity. Although many models settle for one of the two methods, they are not mutually exclusive. Regardless of the chosen method(s), the problem remains that soil hydrology is subject to a high degree of sub-grid heterogeneity, especially in Arctic permafrost-affected regions .

In JSBACH, the land component of MPI-ESM (Max Planck Institute for Meteorology Earth System Model) featured in CMIP6 , methane production has been modeled through a temperature dependent partition factor which prescribes the fraction of carbon released as methane from total anaerobic decomposition – an approach based on the CLM(4Me) model by . The temperature dependence in their model is realized through a Q10 factor , which leads to an increased share of methane under warming conditions. The model uses the TOPMODEL approach to calculate the inundated fraction in the grid cells .

Another example is the UK Earth System Model's LSM JULES , which calculates methane production from substrate availability, temperature, and the wetland fraction of the gridbox through a multilayered scheme , using a tuned methane production scaling factor . The temperature sensitivity is modeled through an Arrhenius function and inundated areas are represented through the saturated grid cell fraction via TOPMODEL . Furthermore, showed an altered version of JULES called JULES-microbe, which features a much more detailed decomposition process including hydrolysis, methanogenic microbial biomass, and microbial activity, though they do not explicitly model the two main methanogenesis pathways either . Instead they partition the produced gases equally into CH4 and CO2, based on the theoretically assumed 1:1 production ratio of acetoclastic methanogenesis . Recently, the UKESM has further received an emission-driven fully coupled methane cycle , showing the ongoing research development towards more in-depth methane representation.

The ORCHIDEE model is another commonly used LSM, which over the years has been updated to represent permafrost processes and high-latitude peatlands in ORCHIDEE-PEAT. It has recently received an updated methane module named ORCHIDEE-PCH4, based on the scheme described by , which uses the same temperature and soil moisture dependent function for methanogenesis as for aerobic respiration, albeit with a 10-times lower rate . Temperature dependence was modeled through a Q10 function, although the relationship is assumed to be linear instead of exponential at values below 0 °C, reaching zero at -1°C . While the base ORCHIDEE-PEAT uses the TOPMODEL approach to determine inundated grid cell fractions , ORCHIDEE-PCH4 explicitly uses the oxygen concentration in the soil for methanogenesis . The latter model has only been evaluated with data from peatlands . Peatlands, however, are a very specific environment with unique features and model requirements . This limits the model's application to these areas even though Arctic methane emissions from permafrost thaw will arise from other sources as well, such as thermokarst lakes or simply from thaw and inundation of non-peatland soils .

A land-surface model that has seen some recent progress in improving its methane representation is the Energy Exascale Earth System Model's (E3SM) land model (ELM) . Originally, its methane module was based on the CLM(4Me) , same as for JSBACH . Since then, there have been attempts to update the methane module and include a more process-based representation of many methane processes, for example in the ELM-SPRUCE version with acetoclastic and hydrogenotrophic methanogenesis, based in large parts on the process-based methane model developed by . This updated module, however, has yet to be incorporated into the ELM for global simulations as part of E3SM . The current version still uses the CO2:CH4 ratio partition factor as proposed by , as well as a Q10 parameter for modeling the temperature dependence of methane production . As for inundation, ELM uses a typical hydrological sub-model to calculate the spacial distribution of wetlands, however, it has recently received an updated version with a focus on wetlands called ELM-Wet, which introduces a distinct sub-grid wet-landunit that enables a more mechanistic portrayal of wetland processes .

In contrast to global LSMs, there exist smaller process-based methane models on the lab and site scale that represent many of the processes related to methane production in much more detail . The process-based methane models discussed in this section include both standalone models and methane-focused modules developed for larger models, such as LSMs. In contrast to the previously discussed LSMs, which are being used in global simulations, often as part of ESMs, the models in this section were developed for site-level or lab-scale applications, with an explicit focus on methane processes. Indeed, there has been an ongoing effort to refine the modeling of methane over the decades and a plethora of models with varying complexity have emerged, with models using process-based methanogenesis representation at the top . It is these process-based approaches that are needed to better understand the processes underlying methane dynamics in the soil, which will then enable more accurate predictions on how these processes and, by extension, the methane budget at large will react to future climate change . It should be noted, however, that many of the past in-depth methane models have been designed for environments other than permafrost landscapes, with much of the research being focused on (rice) paddy soils and general wetland areas . Although process-based models should ideally be applicable across different environments, permafrost-affected soils exhibit unique properties and microbial structures that are only comparable to the aforementioned ecosystems to a limited degree. have shown that the methane emission patterns of permafrost-affected areas differed significantly to those of non-permafrost areas, highlighting this issue. Nevertheless, since the thorough synthesis conducted by , this development has only continued further and in recent years some highly sophisticated methane models have been published. One such state-of-the-art model is the methane module developed by for the IBIS terrestrial ecosystem model . It is based on microbial functional groups, encompassing acetoclastic and hydrogenotrophic methanogenesis, fermentation, homoacetogenesis, and methane oxidation . Mathematically, these processes are largely realized through formulas based on Michaelis–Menten kinetics , while most of the parameter values stem from and . In the decomposition cascade, the model starts with dissolved organic carbon (DOC), which is calculated from the total soil organic carbon pool (SOC) via a temperature and moisture dependent DOC:SOC ratio factor . Acetate, CO2 and H2 are then produced through fermentation . In the next step, these fermentation products act as the substrate for the two main methanogenesis pathways and homoacetogenesis .

One process that has recently started to be included in methane models more frequently is iron reduction . It is an energetically more favorable metabolic pathway for microbes, during which Fe(III) is being reduced to Fe(II) under anoxic conditions . Although these processes are in competition with each other , they have been observed to occur concurrently in soils , thus hinting at a more complicated interplay . A recent model that includes this process is the model developed by . It features largely the same microbial (methane) processes as the model, minus the homoacetogenesis, in a comparable level of detail. Their model, however, adds another level of complexity by explicitly modeling the Fe(III) reduction alongside the methane processes . The methane production is modeled via Monod-type equations and the interactions with Fe(III) reduction as well as the dependence of the methanogenic pathway on pH was represented . They found the inclusion of other terminal electron acceptors to be important for accurate methane predictions, since Fe(III) reduction either increased or decreased CH4 production, depending on how much substrate was available to the microbes . These findings complement the results from , who also used a process-based methane model, and found that Fe(III) reduction positively impacted methanogenesis, by means of raising the pH, when substrate was not limiting . Their model is an augmented version of the CLM-CN model , which has been expanded by incorporating additional biogeochemical process from, e.g., ecosys and the model from .

Similarly, developed a process-based methane model that uses Monod-type equations to model methanogenesis (acetoclastic and hydrogenotrophic) and features Fe(III)-reduction and fermentation . They further included a thermodynamic factor to simulate the dynamic between the different redox processes . In their model, hydrolysis of polysaccharides was assumed to be the rate limiting process for methanogenesis under anaerobic conditions , which aligns with the importance of substrate availability for the methanogenesis-iron-reduction-system found by . This connection has further been supported by incubation study results that also found a correlation between iron reduction, acetate production and methanogenesis . Fermenters prefer organic carbon compounds with low-molecular weight and the fermentation products (e.g., acetate) are required for methanogenesis . Consequently, this early stage of the anaerobic decomposition appears to have significant impact on the final methane production rate . The designation of hydrolysis as the rate-limiting step has, however, been called into question by , who instead argued in favor of the final steps in the methanogenesis process as being rate limiting .

The methane model developed by as a module for the ISBA LSM is another interesting approach. They model methanogenesis with the same 10-times lower decomposition rate, compared to aerobic decomposition, from that is also used in the recent ORCHIDEE module . Aside from the usual temperature and substrate availability dependence, their model also factors in the limitation by oxygen concentration in each respective soil layer . Their approach of explicitly modeling O2 concentration in the soil layers and its impact on methanogenesis differs from the more common approach of determining the water table level and strictly limiting methanogenesis to layers below that level – an approach that has previously been criticized . Their model, however, does not have a representation of the two main methanogenesis pathways , thus reducing its complexity.

The data-constrained process-based methane model from is another example for a methane module incorporated in a terrestrial ecosystem model (TECO) . Even though methanogenesis itself is not modeled in as much detail as other models discussed here – they used an ecosystem-specific CH4-release ratio parameter with no distinction between pathways – their warming experiment resulted in an increased CH4:CO2 emission ratio . This makes the study one of the few who put a focus on the changes of this ratio.

Looking at the discussed small-scale process-based methane models and global LSMs side by side, it becomes clear that they differ profoundly with regard to how detailed methane processes, especially methanogenesis, are being represented. Bridging this gap and using the process understanding gained in smaller scale process-based models have been identified as major remaining challenges for making ESMs more reliable and grounded in reality . This development is needed, if models want to capture the highly variable CO2:CH4 ratios observed in the field and lab . At this point, it is important to clearly distinguish between methane production and emission ratios. The high variability of CO2:CH4 emission ratios measured in the field is the result of many different processes , beyond methanogenesis. The methane has to be transported to the surface and, depending on the dominant transport mechanism, may be oxidized almost completely by methanotrophs before it can reach the atmosphere . Additionally, CO2 emissions from other processes that happen concurrently with methanogenesis at sites with anaerobic conditions, such as Fe(III) or sulfate reduction , and respiration in oxic layers also affect the CO2:CH4 emission ratio . Refining the methanogenesis process alone will consequently not be sufficient for greatly reducing the uncertainty of the emission ratio between CO2 and methane at the surface. However, the modeling of methanogenesis, and by extension the CO2:CH4 production ratio, in the soil is already a source of uncertainty. Looking at the production ratios obtained under controlled lab conditions from , who reported values between 0.2–0.8, in contrast to the fixed ratio factors used in many LSMs (see Table 1), it becomes evident that using these fixed ratios directly leads to an increase of the uncertainty of methane release, already in the initial step. To quantify this uncertainty, especially in relation to the other processes affecting the methane budget, a dynamic process-based methane models is needed, giving further agency to its development.

First efforts in this direction are being done, with one example being the inclusion of the aforementioned model by into a terrestrial ecosystem model. Another case is the model by , which has been included in the ELM and features a process-based methanogenesis scheme . Their model reproduced the observed distinct seasonality of the two main methanogenesis pathways , showing the advantages of such a detailed representation, though their model has so far only been run on a site level scale . These models are focused on natural wetland and peatland emissions respectively, meaning that the distinct features of permafrost-affected areas are largely not considered in their model composition and subsequent evaluation with site data . Still, the ELM has recently received an improved wetland scheme in ELM-Wet and there are plans to implement the already discussed in-depth methane model by in the future to further improve methanogenesis representation .

have recently performed a similar inclusion of an in-depth biogeochemical model into a LSM, featuring methanogenesis and methanotrophy among others, but their model study was concerned with and evaluated against data from coastal wetlands, which are distinct in their own right with, e.g., sulfate dynamics . Modeling efforts like these are direly needed for permafrost-affected soils as well , since estimations of the permafrost-carbon-climate feedback remain uncertain in both their spatiotemporal extent and magnitude . Indeed, the future ratio of CO2:CH4 emissions is one of the key open questions in that endeavor . Even though the emission ratio is affected by many other processes, as discussed above, the production ratio is an important initial step. Additionally, the representation of permafrost processes in ESMs is generally still severely lacking , with many of the models informing the most recent IPCC report still not having permafrost processes included .

More complexity or realism, in regards to how certain processes are modeled, might not always be the optimal way however. argued in their meta study, for example, that the ever increasing complexity and amount of processes in SOC-focused models may in fact add to the already large uncertainty of projections, due to an increase in modeling possibilities to choose from . A more concrete example would be the JULES LSM, which had in the past been enhanced with a more detailed methane soil-transport and oxidation scheme . This scheme was later-on abandoned due to the overall negligible improvement in terms of making the results more accurate . In light of many other processes being underrepresented or all out missing in global models, the adequate complexity of each included process needs to be considered. Abrupt thaw processes, e.g., could lead to an increase in permafrost thaw emissions by up to 40 % if accounted for, yet they are not featured in global models . Naturally, numerical resources are not endless and current ESMs already struggle with their ever-increasing complexity . Considering this, it might be necessary to find a middle ground between the current state of methane representation in most LSMs and the state-of-the-art smaller scale process-based methane models. Furthermore, it will be important to quantify the uncertainty and importance of the various processes contributing to the total methane budget, to see which processes require more attention, numerical resources and further refinement.

In conclusion, when modeling methane production in soils, the essential processes determining the CO2:CH4 production ratio appear to be (1) fermentation, which has been identified as a potential rate-limiting step in multiple studies , (2) acetoclastic and (3) hydrogenotrophic methanogenesis and the variable share between the two . LSMs need to feature at least these three core-processes (see Fig. 1) if the dynamics of the CO2:CH4 production ratio wants to be represented.

Additionally, these core-processes may be complemented by closely connected processes that either enhance or stand in competition with methanogenesis, most importantly Fe(III) reduction and homoacetogenesis (see Fig. 2), something that has already been achieved in some smaller scale process-based models . Though it would undoubtedly be preferable to have these ancillary processes featured in LSMs as well, this would make the task all the more difficult. Previous studies found, for example, Fe(III) reduction to impact methanogenesis indirectly through changes to the pH , meaning that LSMs would have to both model global soil Fe concentrations and soil pH levels. When considering the current, highly simplified state of methanogenesis modeling in LSMs, it would be a more realistic first step to focus on the three aforementioned core-processes, before tackling further connected processes.

These processes are influenced by multiple environmental factors, the most important of which are: temperature , pH , and oxygen availability or water table depth . Soil biogeochemical conditions, especially the discussed interplay with Fe(III) reduction, is another important, albeit more complicated factor that has relatively recently emerged as a focus point in modeling studies on methane . Despite their importance, many of these factors are poorly quantified across the Arctic . This is largely due to the scarcity of observational field data in the vast and remote Arctic areas like Northern Russia . ESMs, however, require spatial maps of these soil parameters to accurately portray the soil biogeochemical processes in the Arctic regions. Besides the obvious need for more field data, there are some recent publications which provide spatial datasets derived from the few data we already have. . extrapolated sampling data to create a Pan-Arctic map of bioavailable soil elements, including Fe, based on lithology. Another interesting approach is shown in who used machine learning algorithms to digitally map soil properties, like soil pH, in Arctic areas with scarce data availability. These techniques may prove to be important tools to bridge the large gaps in the spatial data. Both still depend on field data, however, which means that more extensive field studies remain crucial . The same is true for methanogenesis measurement data required to benchmark models at large scales, something that is difficult to attain for the same reasons. In fact, have shown the importance of constraining models with in situ observational data, since CH4 and CO2 emissions show distinct responses to climate change . Even though lab incubations only offer limited insights into in situ conditions , they can nevertheless be useful to isolate and study single processes that are hard to disentangle in the field.

Concerning the temperature dependence, the Q10 function is arguably the most commonly used method for describing the temperature sensitivity of methane production in models , likely due to its simplicity . At the same time, the Q10 value has been repeatedly identified as a highly sensitive model parameter , making its accurate assessment paramount. Parameter estimations, however, vary strongly between different models , owing in large part to the wide range of reported values from experiments . Furthermore, the different temperature sensitivities of the processes involved in fermentation and methanogenesis need to be considered and should be represented in future models. Reducing the uncertainty introduced through the modeling of temperature dependence will be a crucial step towards improving the overall predictive abilities of methane models.

For predicting future methane emissions from soils, further processes are required. First, the transport of methane to the surface through the main three transport ways and, second, methanotrophy, which has the possibility to drastically reduce methane emissions before they reach the atmosphere . These processes are, however, already more broadly represented in models , including LSMs , compared to methanogenesis. Here it could be interesting to explore, e.g., the kinetic differences between low-affinity and high-affinity methanogens, the former requiring high methane concentrations while the latter can function even under atmospheric methane concentrations , which is rarely explored in models. One model study that did include high-affinity methanogens into a biogeochemical model is the one by . They used the Terrestrial Ecosystem Model (TEM) as a basis and found that the addition of high-affinity methanogens to the model led to a doubling of the Arctic upland methane sink, reducing net CH4 emissions by ca. 5.5 Tg CH4 per year . This significant reduction shows that further refining methanotrophy in models will also be crucial for reducing the uncertainty of CO2:CH4 emission ratios, and more studies focused on the inclusion of high-affinity methanogens in models are needed .

There are other important uncertainty sources concerning the methane budget, one of which are cold season methane fluxes, which can make up more than half of the total annual Arctic methane flux . In models, however, these emissions are commonly underestimated and poorly constrained . showed that constraining a process-based model ensemble with measured data from the non-growing season (September–May) could increase the annual wetland methane flux by 25 % when compared to the unconstrained approach. These findings have been corroborated by , who compared the cold season (September–May) methane flux outputs of 16 models to in situ observational data and found that the models underestimated methane emissions during that period, with the discrepancy being especially pronounced in months that exhibited air temperatures under 0 °C. This underestimation is due to insufficient cold season process representation and parametrization . Models fail to capture, for example, the observed burst of methane emissions during the freeze-in period in late-autumn . This period falls into the “zero curtain” period, during which the soil stays unfrozen, while temperatures stay at around 0 °C, due to latent heat of fusion of soil water and snow cover insulation . The latter is especially important because changes to the snow cover affect soil thermodynamics, which, in turn, affects soil biogeochemistry and permafrost dynamics . The impact of improving the representation of snow processes in models for further reducing uncertainty in projecting Arctic methane emissions, has been shown by , who implemented a multi-layer snow-scheme into the LPJ-GUESS dynamic vegetation model and found a significant improvement to the simulated permafrost extent. Further model refinement of these processes is, consequently, needed to reduce this uncertainty in the Arctic methane budget .

Finally, the uncertainty of wetland extent and distribution as well as their poor representation in models remain some of the most important sources of uncertainty concerning the Arctic methane budget, as recently shown again by in their machine-learning-based upscaling study. Here in this paper, we present a framework for a more process-based portrayal of methanogenesis in LSMs and review which processes and factors need to be considered for capturing the dynamics of the CO2:CH4 production ratio. This development becomes a necessity if research questions such as the prediction of pan-Arctic greenhouse gas fluxes under a changing future hydrology want to be answered with a higher degree of confidence. However, the many other discussed processes that make up the total methane budget have high degrees of uncertainty as well and estimating their respective importance and quantifying their uncertainties will be crucial going forward. In the end, a more process-based methanogenesis approach in models could contribute to more reliable estimates of the carbon-climate feedback, for which the relative roles of carbon dioxide and methane emissions represent an important factor .