Empiric equations of coagulation sink of fine nanoparticles on background aerosol optimized for boreal zone

Fundamental models of aerosol nanoparticle coagulation sink in the atmosphere are sophisticated and require detailed knowledge about the size distribution of background aerosol particles. Here, we present empiric equations which help to make quantitative relations graspable and support quick and rough estimation of the coagulation sink according to background aerosol particle concentration and vice versa when browsing limited data. Accuracy of an empiric equation is described by a deviation between the results obtained according to two methods: fundamental models and empiric equations. Optimizing empiric equations is discussed considering a set of aerosol size distributions measured at the SMEAR II station, Finland, during years 2008–2010. Fundamental models include the particle-particle coagulation model by Dahneke and the air ion attachment model by Hoppel and Frick. Small air ions are considered a special kind of nanoparticles. The background aerosol is characterized with a power-weighted integral concentration in a restricted range of particle diameters. The power exponent and borders of the diameter range are adjusted when optimizing the equation. Nanoparticles are represented with a power function of the diameter or with the electric mobility. Compromises between the simplicity of the equation and the accuracy of the approximation are considered and different versions of empiric equations are proposed.