Isotopic models of CH ₄ oxidation for lakes: theory

The ¹³C isotopic signature of dissolved methane (CH₄) is widely used to infer the extent of microbial oxidation in lakes, yet considerable inconsistency exists in how isotopic models are selected and interpreted. This paper develops a unified framework of isotopic models for CH₄ oxidation spanning seven distinct physical and experimental configurations, ranging from bottle incubations to diffusion-reaction models applicable to different lake strata. The assumption of complete and instantaneous mixing underlying conventional one-box models is rarely satisfied in stratified lake systems, where CH₄ originating from littoral sediments is transported horizontally by turbulent diffusion and progressively consumed by methanotrophs. Under these conditions, diffusion-reaction models better capture the resulting spatial gradients in both CH₄ concentration and δ¹³CH₄. The relationships between the extent of oxidation (fox) and δ¹³CH₄ differ between models. I further propose that the joint distribution of [CH₄] and δ¹³CH₄ samples across a lake, rather than individual isotopic values, provides a more informative basis for characterizing methanotrophic activity and estimating sedimentary CH₄ fluxes and oxidation rate constants. The framework presented here is intended to help researchers identify the isotopic model most appropriate to their experimental or field context and to avoid common misinterpretations of isotopic enrichment in lake CH₄.