Mathematical models of methane consumption by soils: A review

This review explores mathematical models that assess methane (CH₄) uptake in aerated soils within terrestrial ecosystems. Methane, a potent greenhouse gas, is produced under anaerobic conditions. While substantial research has been dedicated to methane emissions from water-saturated soils over the past four decades, the absorption of CH₄ by non-saturated soils, despite their expansive coverage, has received less focus. In tropical and subtropical soils, methane consumption constitutes less than 5% of the global uptake. However, there's limited data concerning methane consumption in temperate non-saturated soils, which are prevalent in forests, grasslands, steppes, and croplands. This data scarcity has resulted in estimate uncertainty: methane consumption ranges between 1% to 15% of the global methane sink attributed to photochemical degradation.

The mechanism of methane uptake by soils primarily stems from the dominance of methanotrophy over methanogenesis. In aerated soils, methane production by methanogens is absent (or minimal), with the primary source being the atmosphere. Methanotrophs, active in the upper soil layer, uptake this atmospheric methane. This absorption rate is influenced by both microbial oxidation and the diffusion of methane into the soil. The diffusion rate is notably determined by the atmospheric concentration of CH₄ and the porosity of the soil's aeration – the fewer the pores filled with water, the more rapid the diffusion. The rate of oxidation, on the other hand, is influenced by the soil's temperature and moisture levels. Just as neither extremely dry soil (where microbial activity is limited due to water scarcity) nor overly wet soil (where microorganisms are deprived of oxygen) offer optimal conditions; temperature extremes – whether too cold or too hot – can also negatively impact the methane oxidation process.

Nowadays, direct measurements of both methane consumption and emission processes are routinely conducted using high-precision field gas analyzers. However, while CH₄ emissions have garnered significant attention, data collection on methane consumption is still limited, particularly in remote locations. When in situ data are limited, mathematical models offer a reliable approach for extrapolating site-specific data to regional or global scales, enhancing our understanding of soil methane oxidation processes and how they respond to climatic shifts. In this study, we critically evaluates various mathematical models related to the topic, examining their strengths, limitations, and suitability for estimating large-scale methane consumption in aerated soils.

The field of CH₄ cycle modeling currently employed a diverse range of mathematical models. These can be broadly classified into two main categories: (1) empirical models, and (2) physics-based models. The choice between these models often depends on the research objectives. On the other hand, models of regional ecology can be grouped into interpolation-extrapolation, analytical, and numerical categories. The interpolation-extrapolation models relate specific ecosystem properties (e.g. emissions) with their spatial or temporal coordinates. Analytical models capture the underlying physics, though achieving analytical solutions often requires simplifications to address the complexity of the equations. In contrast, numerical models are intricate and rely on numerical methods for their solutions.

The "simple inventory" is interpolation-extrapolation method that estimates methane uptake from soil-atmosphere interactions using basic formulations. Originally based on biome types, the accuracy of this method is relatively low but has been used in several global and regional methane studies. Recent approaches further classify soils into structural classes, linking methane absorption rates to these classifications. Dutaur and Verchot (2007) aimed to refine this method, investigating correlations with latitude, temperature, and precipitation. Their use of discrete categorization variables, like climate zones and ecosystem types, improved predictive accuracy of the model. However, extrapolating localized measurements to broader scales remains a challenge due to the limited data and ecosystem heterogeneity.

Analytical models leverage an understanding of the underlying physical processes to create equation-based representations. Early research indicated that the rate of soil methane absorption from the atmosphere was predominantly constrained by atmospheric diffusion (e.g. [Born et al., 1990; Potter et al., 1996]).  This is because the ability of methanotrophs to consume methane often surpasses the diffusion transport mechanism's capacity. As a result, the peak rate of soil methane absorption from the atmosphere is capped by diffusion.

As research deepened into the factors affecting CH₄ absorption in non-saturated soils, models grew in complexity. It became evident that microbial oxidation, alongside methane diffusion, played a pivotal role in determining methane consumption rates. For optimal methane oxidation, conditions must be warm and the soil should be neither too dry nor too wet. The relationship between nitrogen and methane absorption remains a topic of debate. Nitrogen fertilizers suppress methane oxidation, but these fertilizers also promote plant growth, affecting soil moisture and potentially influencing methane dynamics.

The MeMo model [Murguia-Flores et al., 2018] stands out as one of the most comprehensive adaptation, building upon the models of Ridgwell et al. [1999] (“R99”) and Curry [2007] (“C07”). The MeMo model incorporates factors, such as biome type, atmospheric methane concentration, soil temperature, nitrogen input, soil density, clay content, and soil moisture. Crucial enhancements were made to the original designs: a holistic analytical solution in a porous medium, refined nitrogen inhibition of methanotrophy, biome-specific influences on methane oxidation rate, and consideration of indigenous soil CH₄ sources on methane uptake from the atmosphere. These modifications have notably improved the model's alignment with observational data.

Regarding numerical models, few are specifically designed for assessing methane consumption, with more models being general ones that describe the methane dynamics in soil (incorporating oxidation, methane production, and transport). Intricate numerical models potentially offer more versatility than empirical or semi-empirical analytical ones: e.g. some analytical models often inherently assuming swamp methane oxidation as zero, not reflecting reality. However, numerical models usually require numerous site-specific parameters, such as soil usage, root zone depth, or even particular metabolic data. Because they're so tailored to specific sites, their use on a larger scale can be limited. Thus, using these models for regional methane uptake estimations doesn't guarantee high-quality results today.

A recent trend in modeling natural processes focus on the ensemble approach. This strategy involves averaging results from multiple independent models focused on a shared metric. Comparative analysis shows that the highest quality is usually demonstrated by the "ensemble average" model. This is due to the fact that systematic errors of different models do not depend on each other and can be mutually compensated when averaging over the ensemble. The success of this approach has been confirmed in regularly published IPCC reports. The use of ensembles of models is also used in the study of methane fluxes from soil, both in solving direct and inverse problems [Glagolev et al., 2014; Poulter et al., 2017; Bergamaschi et al., 2018], but this approach has apparently not yet been used directly to estimate methane uptake by soils.

Mathematical models don't always align with experimental data for specific research sites, as noted by authors such as Ridgwell et al. [1999] and Murguia-Flores et al. [2018]. These models can sometimes overestimate or underestimate certain metrics. This inconsistency is further evident when different researchers identify similar parameters in their models but, based on various datasets, arrive at different values. For instance, while R99 utilized a value based on 13 measurements from diverse locations, С07's value was derived from a five-year observation in Colorado. Meanwhile, the MeMo model introduced values for four distinct biome types. Nevertheless, when these models are applied on a global scale, they provide reasonably accurate estimates of the planet's total methane uptake by soils. These estimates are in line with both basic inventories, like those from [Born et al., 1990], and more advanced methods, such as the inverse modeling by Hein et al. [1997]. This suggests that for larger regions, the models can still yield sensible CH₄ absorption assessments, with overestimations in certain geographical areas being balanced out by underestimations in others.