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A new mathematical model describing air ion balance was developed and tested.It has improved approximations and includes dry deposition of ions onto the forest canopy.The model leads to an explicit algebraic solution of the balance equations.This allows simple calculation of both the ionization rate and the average chargeof aerosol particles from measurements of air ions and aerosol particles,with some parameters of the forest. Charged aerosol particles are distinguishedfrom cluster ions by their size, which exceeds 1.6 nm diameter. The relative uncertaintyof the ionization rate is about the same or less than the relative uncertaintiesof the measurements. The model was tested with specific air ion measurementscarried out simultaneously at two heights at the Hyytiälä forest station,Finland. Earlier studies have shown a difference in the predictions of theionization rate in the Hyytiälä forest when calculated in two different ways:based on the measurements of the environmental radioactivity and based onthe air ion and aerosol measurements. The new model explains the differenceas a consequence of neglecting dry deposition of ions in the earlier models.The ionization rate during the 16 h campaign was 5.6±0.8 cm−3 s−1at the height of 2 m and 3.9±0.2 cm−3 s−1 at the height of 14 m,between the tops of the trees. The difference points out the necessityto consider the height variation when the ionization rate is used as a parameterin studies of ion-induced nucleation. Additional results are some estimatesof the parameters of air ion balance. The recombination sink of cluster ionson the ions of opposite polarity made up 9–13%, the sink on aerosol particles65–69%, and the sink on forest canopy 18–26% of the total sinkof cluster ions. The average lifetime of cluster ions was about 130 sfor positive and about 110 s for negative ions. At the height of 2 m,about 70% of the space charge of air was carried by aerosol particles,and at the height of 14 m, about 84%

Factors of air ion balance in a coniferous forest according to measurements in Hyytiälä, Finland