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## Governing Mass-Balance Relationship

The model accounts for various processes that affect the net methane (CH4) surface flux, including CH4 production, ebullition, aerenchyma transport, diffusion, and oxidation. This is captured in a transient reaction-diffusion equation:

(2.25.1) ∂(RC)/∂t = ∂FD/∂z + P(z,t) - E(z,t) - A(z,t) - O(z,t)

where R represents the partitioning of CH4 between aqueous and gaseous phases, and C is the CH4 or O2 concentration.

An analogous equation is solved for O2, but without production or ebullition terms, and with oxidation including demand from methanotrophs, heterotrophs, nitrifiers, and autotrophic root respiration.

The model represents both inundated and non-inundated fractions of each grid cell, solving the mass-balance equations four times per grid cell and time step. The water table interface is defined for non-inundated areas, and the inundated fraction is allowed to change, with CH4 conservation accounted for.

The key processes and governing equations are visually depicted in the schematic (Figure 2.25.1).