Carbon isotope composition of ambient CO₂ and recycling: a matrix simulation model

The relationship between isotopic composition and concentration of ambient CO₂ in a canopy and its associated convective boundary layer was modeled. The model divides the canopy and convective boundary layer into several layers. Photosynthesis, respiration, and exchange between each layer can be simulated by matrix equations. This simulation can be used to calculate recycling; defined here as the amount of respired CO₂ re-fixed by photosynthesis relative to the total amount of respired CO₂. At steady state the matrix equations can be solved for the canopy and convective boundary layer CO₂ concentration and isotopic profile, which can be used to calculate a theoretical recycling index according to a previously developed equation. There is complete agreement between simulated and theoretical recycling indices for different exchange scenarios. Recycling indices from a simulation of gas exchange between a heterogeneous vegetation canopy and the troposphere also agreed with a more generalized form of the theoretical recycling equation developed here.