A new balance formula to estimate new particle formation rate: reevaluating the effect of coagulation scavenging

A new balance formula to estimate new particle formation rate is proposed. It is derived from the aerosol general dynamic equation in the discrete form and then converted into an approximately continuous form for analyzing data from new particle formation (NPF) field campaigns. The new formula corrects the underestimation of the coagulation scavenging effect that occurred in the previously used formulae. It also clarifies the criteria for determining the upper size bound in measured aerosol size distributions for estimating new particle formation rate. An NPF field campaign was carried out from 7 March to 7 April 2016 in urban Beijing, and a diethylene glycol scanning mobility particle spectrometer equipped with a miniature cylindrical differential mobility analyzer was used to measure aerosol size distributions down to similar to 1 nm. Eleven typical NPF events were observed during this period. Measured aerosol size distributions from 1 nm to 10 mu m were used to test the new formula and the formulae widely used in the literature. The previously used formulae that perform well in a relatively clean atmosphere in which nucleation intensity is not strong were found to underestimate the comparatively high new particle formation rate in urban Beijing because of their underestimation or neglect of the coagulation scavenging effect. The coagulation sink term is the governing component of the estimated formation rate in the observed NPF events in Beijing, and coagulation among newly formed particles contributes a large fraction to the coagulation sink term. Previously reported formation rates in Beijing and in other locations with intense NPF events might be underestimated because the coagulation scavenging effect was not fully considered; e.g., estimated formation rates of 1.5 nm particles in this campaign using the new formula are 1.3-4.3 times those estimated using the formula neglecting coagulation among particles in the nucleation mode.