A scaling analysis of ozone photochemistry

Abstract. A scaling analysis has been used to capture the integrated behaviour of several photochemical mechanisms for a wide range of precursor concentrations and a variety of environmental conditions. The Buckingham Pi method of dimensional analysis was used to express the relevant variables in terms of dimensionless groups. These grouping show maximum ozone, initial NO_x and initial VOC concentrations are made non-dimensional by the average NO₂ photolysis rate (j_av) and the rate constant for the NO–O₃ titration reaction (k_NO); temperature by the NO–O₃ activation energy (E_NO) and Boltzmann constant (k) and total irradiation time by the cumulative j_avΔt photolysis rate. The analysis shows dimensionless maximum ozone concentration can be described by a product of powers of dimensionless initial NO_x concentration, dimensionless temperature, and a similarity curve directly dependent on the ratio of initial VOC to NO_x concentration and implicitly dependent on the cumulative NO₂ photolysis rate. When Weibull transformed, the similarity relationship shows a scaling break with dimensionless model output clustering onto two straight line segments, parameterized using four variables: two describing the slopes of the line segments and two giving the location of their intersection. A fifth parameter is used to normalize the model output. The scaling analysis, similarity curve and parameterization appear to be independent of the details of the chemical mechanism, hold for a variety of VOC species and mixtures and a wide range of temperatures and actinic fluxes.