A new balance formula to estimate new particle formation rate : 1 reevaluating the effect of coagulation scavenging

A new balance formula to estimate new particle formation rate is proposed. It was derived from aerosol general 7 dynamic equation in the discrete form and then converted into an approximately continuous form for analysing data from new 8 particle formation (NPF) field campaigns. The new formula corrects the underestimation of the coagulation scavenging effect 9 occurred in previously used formulae. It also clarifies the criterions in determining upper size bound in measured aerosol size 10 distributions for estimating new particle formation rate. A NPF field campaign was carried out from March 7 to Apr. 7, 11 2016, in urban Beijing, and a diethylene glycol scanning mobility particle spectrometer equipped with a miniature cylindrical 12 differential mobility analyser was used to measure aerosol size distributions down to ~1 nm. 11 typical NPF events were 13 observed during this period. Measured aerosol size distributions from 1 nm to 10 μm was used to test the new formula and 14 those widely used ones. Previously used formulae that perform well in relatively clean atmosphere where nucleation intensity 15 is not strong were found to underestimate the comparatively high new particle formation rate in urban Beijing because of their 16 underestimation or neglect of the coagulation scavenging effect. Coagulation sink term is the governing component of the 17 estimated formation rate in the observed NPF events in Beijing, and coagulation among newly formed particles contributes a 18 large fraction to the coagulation sink term. Previously reported formation rates in Beijing and in other locations with intense 19 NPF events might be underestimated because the coagulation scavenging effect was not fully considered, e.g., formation rates 20 of 1.5 nm particles in Beijing are underestimated by 58.9% on average if neglecting coagulation among particles in nucleation 21 mode. 22