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. The growth rate of atmospheric new particles is a keyparameter that determines their survival probability of becoming cloudcondensation nuclei and hence their impact on the climate. There have beenseveral methods to estimate the new particle growth rate. However, due tothe impact of coagulation and measurement uncertainties, it is stillchallenging to estimate the initial growth rate of new particles, especiallyin polluted environments with high background aerosol concentrations. Inthis study, we explore the influences of coagulation on the appearance timemethod to estimate the growth rate of sub-3 nm particles. The principle ofthe appearance time method and the impacts of coagulation on the retrievedgrowth rate are clarified via derivations. New formulae in both discrete andcontinuous spaces are proposed to correct for the impacts of coagulation.Aerosol dynamic models are used to test the new formulae. New particleformation in urban Beijing is used to illustrate the importance of consideringthe impacts of coagulation on the sub-3 nm particle growth rate and itscalculation. We show that the conventional appearance time method needs tobe corrected when the impacts of coagulation sink, coagulation source, andparticle coagulation growth are non-negligible compared to the condensationgrowth. Under the simulation conditions with a constant concentration ofnon-volatile vapors, the corrected growth rate agrees with the theoreticalgrowth rates. However, the uncorrected parameters, e.g., vapor evaporationand the variation in vapor concentration, may impact the growth rateobtained with the appearance time method. Under the simulation conditionswith a varying vapor concentration, the average bias in the corrected 1.5–3 nm particle growth rate ranges from 6 %–44 %, and the maximum bias in thesize-dependent growth rate is 150 %. During the test new particleformation event in urban Beijing, the corrected condensation growth rate ofsub-3 nm particles was in accordance with the growth rate contributed bysulfuric acid condensation, whereas the conventional appearance time methodoverestimated the condensation growth rate of 1.5 nm particles by 80 %.

Impacts of coagulation on the appearance time method for new particle growth rate evaluation and their corrections