Author response to Referees

Determining the particle size distribution of atmospheric aerosol particles is an important component task to understand new particle formation and growth. This is particularly crucial at the sub-3 nm range because of the growth of 15 newly-formed nanoparticles. The challenge in recovering the size distribution is due its complexity and the fact that not many instruments currently measure at this size range. In this study, we used the particle size magnifier (PSM) to measure atmospheric aerosols. Each event day was classified into one of the three event types: new particle formation (NPF) event, non-event and haze event. We then compared four inversion methods (step-wise, kernel, Hagen and Alofs and expectationmaximization) to determine their feasibility to recover the particle size distribution. In addition, we proposed a method to pre20 treat measured data and introduced a simple test to estimate the efficacy of the inversion itself. Results showed that all four methods inverted NPF events well; but the step-wise and kernel methods fared poorly when inverting non-event and haze events. This was due to their algorithm, such that when encountering noisy data (e.g. air mass fluctuations or low sub-3 nm particle concentrations) and under the influence of larger particles, these methods overestimated the size distribution and reported artificial particles during inversion. Therefore, using a statistical hypothesis test to discard noisy scans prior to 25 inversion is an important first step to achieve a good size distribution. As a first step after inversion, it is ideal to compare the integrated concentration to the raw estimate (i.e., the concentration difference at the lowest supersaturation and the highest supersaturation) to ascertain whether the inversion itself is sound. Finally, based on the analysis of the inversion methods, we provide procedures and codes related to the PSM data inversion.