Abstract. The growth rate of atmospheric new particles is a key
parameter that determines their survival probability of becoming cloud
condensation nuclei and hence their impact on the climate. There have been
several methods to estimate the new particle growth rate. However, due to
the impact of coagulation and measurement uncertainties, it is still
challenging to estimate the initial growth rate of new particles, especially
in polluted environments with high background aerosol concentrations. In
this study, we explore the influences of coagulation on the appearance time
method to estimate the growth rate of sub-3 nm particles. The principle of
the appearance time method and the impacts of coagulation on the retrieved
growth rate are clarified via derivations. New formulae in both discrete and
continuous spaces are proposed to correct for the impacts of coagulation.
Aerosol dynamic models are used to test the new formulae. New particle
formation in urban Beijing is used to illustrate the importance of considering
the impacts of coagulation on the sub-3 nm particle growth rate and its
calculation. We show that the conventional appearance time method needs to
be corrected when the impacts of coagulation sink, coagulation source, and
particle coagulation growth are non-negligible compared to the condensation
growth. Under the simulation conditions with a constant concentration of
non-volatile vapors, the corrected growth rate agrees with the theoretical
growth rates. However, the uncorrected parameters, e.g., vapor evaporation
and the variation in vapor concentration, may impact the growth rate
obtained with the appearance time method. Under the simulation conditions
with 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 the
size-dependent growth rate is 150 %. During the test new particle
formation event in urban Beijing, the corrected condensation growth rate of
sub-3 nm particles was in accordance with the growth rate contributed by
sulfuric acid condensation, whereas the conventional appearance time method
overestimated the condensation growth rate of 1.5 nm particles by 80 %.