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

Abstract. The formation rates of 3 nm particles were estimated at SMEAR IV, Puijo (Finland), where the continuous measurements extend only down to 7 nm in diameter. 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 detailed daily time evolution, the agreement is not as good due to fluctuations in data as well as uncertainties in estimated growth rates, which are required in order to calculate the time lag between formation of 3 and 7 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.