Disentangling Source and Sink Contributions to Atmospheric Methane Isotope Evolution: Insights from Two-Box Model Experiments

Understanding the drivers of atmospheric CH₄ variability requires separating emission changes from sink perturbations—a challenge that arises when either alter CH₄ concentrations. Stable isotopes (δ¹³C, δD) provide additional constraints because sources have distinct signatures, while sinks fractionate isotopes through kinetic isotope effects (KIEs). We use complementary two-box modelling approaches to quantify how isotopes respond when CH₄ observations alone cannot distinguish mechanisms.

Our forward model simulates the evolution of hemispheric CH₄, ¹³CH₄, and CH₃D, where emissions add mass with source-specific signatures (thermogenic, biogenic, and pyrogenic), chemical sinks (OH, stratosphere, and soil) remove mass and accordingly fractionate isotopes, and interhemispheric mixing transfers methane across hemispheres. During spin-up, baseline emissions balance removal, yielding steady-state atmospheric isotopic trajectories.

Following the equilibrium period in the spin-up, we enforce OH perturbation, where we impose emission compensation to hold CH₄ constant while varying OH trends (-1.0 to +1.0%/yr). Four compensation strategies, proportional (maintains baseline mix), microbial-dominated, fossil-dominated, and pyrogenic-dominated, produce different isotopic trajectories despite identical CH₄ evolution. For +1.0%/yr OH, Northern Hemisphere δ¹³C shifts range from -3.7‰ (microbial compensation, depleted sources balance enriched removal) to +3.3‰ (pyrogenic compensation, enriched sources overcompensate). Isotopic phase-space analysis reveals cumulative compensation masses of 1200-1900 Tg over 45 years, with δD providing orthogonal constraints (Δδ¹³C/ΔδD slopes distinguish microbial vs thermogenic sources). Forward simulations without compensation show transient isotope responses with ~8-year relaxation timescales, demonstrating that observed 2000-2006 methane stabilization (δ¹³C flattening at ~-47.3‰) requires near-cancellation of source and sink trends. Our dual-isotope framework demonstrates that atmospheric composition networks can attribute decadal CH₄ variability to specific emission sectors even when concentration trends vary, critical for verifying bottom-up inventories and climate-policy targets.