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The formation rates of 3 nm particles were estimated at SMEAR IV, Puijo\ud(Finland), where the continuous measurements extend only down to 7 nm in\uddiameter. We extrapolated the formation rates at 7 nm (J7) down to 3 nm (J3) based on an approximate solution to the aerosol general dynamic equation, assuming a constant condensational growth rate, a power-law size-dependent scavenging rate, and negligible self-coagulation rate for the nucleation mode particles. To evaluate our method, we first applied it to new particle formation (NPF) events in Hyytiälä (Finland), which extend down to 3 nm, and, therefore, J3 and J7 can be determined directly from the measured size distribution evolution. The Hyytiälä results show that the estimated daily mean J3 values slightly overestimate the observed mean J3, but a promising 91 % of the estimated J3 values are within a factor of 2 from the measured ones. However, when considering\uddetailed daily time evolution, the agreement is not as good due to\udfluctuations in data as well as uncertainties in estimated growth rates, which\udare required in order to calculate the time lag between formation of 3 and\ud7 nm particles. At Puijo, the mean J7 for clear NPF days during April 2007–December 2015 was 0.44 cm−3 s−1, while the extrapolated mean J3 was 0.61 cm−3 s−1

Estimation of atmospheric particle formation rates through an analytical formula: validation and application in Hyytiälä and Puijo, Finland