Abstract This paper describes the application of a parameterisation procedure to reduce a comprehensive atmospheric chemical mechanism to a set of algebraic polynomials. This is achieved here by the numerical fitting of orthonormal polynomial functions to changes in species concentrations from one time point to the next, using the Gram–Schmidt orthonormalisation technique. Polynomials are then optimised by the use of Horner equations. Some reduction of the number of species to only those which influence the concentration of the important species has been carried out previously by the removal of fast time-scale species and stable products, without significant loss of accuracy. Consequently the repro-model is fitted to a subset of the original mechanism, with polynomials generated for each of the species in the lower dimensional subspace. This method has been successfully applied to diurnal tropospheric cycles and several results are shown here. Deviations between the repro-model results and those of the original mechanism are consistently less than 1% across the scenario for all key species, with the repro-model running up to 25 times faster than the numerical solution of the original scheme. The repro-modelling technique is thus highly suited to replacing the system of ordinary differential equations in the chemical sub-model of a dispersion code—significantly reducing the computational burden without loss of accuracy.