Positive semi-definite variants of CBM4 and CBM05 chemistry schemes for atmospheric composition models

Abstract. Carbon bond chemistry models are widely used to describe tropospheric chemistry reactions in atmospheric chemistry transport models. The standard implementation of these carbon bond models includes a species for paraffin carbon bond which is positioned in chemistry reactions such that its concentration can be easily driven to negative unless additional mechanisms have been implemented around the scheme. Here we describe an alternative formulation which is positively semi-definite, while preserving the main structure of the carbon bond mechanism. We apply the formulation to CBM4 and CBM05 schemes. The new formulation substantially improves the numerical robustness of the schemes and relaxes the need for external mechanisms to enforce positive concentrations.