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.

[1]  L. Ahonen,et al.  Overview of measurements and current instrumentation for 1–10 nm aerosol particle number size distributions , 2020, Journal of Aerosol Science.

[2]  Jingkun Jiang,et al.  Theoretical and experimental analysis of the core sampling method: Reducing diffusional losses in aerosol sampling line , 2019, Aerosol Science and Technology.

[3]  Jingkun Jiang,et al.  Parameters governing the performance of electrical mobility spectrometers for measuring sub-3 nm particles , 2019, Journal of Aerosol Science.

[4]  T. Petäjä,et al.  Ion-induced sulfuric acid–ammonia nucleation drives particle formation in coastal Antarctica , 2018, Science Advances.

[5]  L. Ahonen,et al.  Data inversion methods to determine sub-3 nm aerosol size distributions using the particle size magnifier , 2018, Atmospheric Measurement Techniques.

[6]  T. Petäjä,et al.  The initial stages of multicomponent particle formation during the gas phase combustion synthesis of mixed SiO2/TiO2 , 2018 .

[7]  L. Ahonen,et al.  Data inversion methods to determine sub-3 nm aerosol size distributions using the particle size magnifier , 2018 .

[8]  Jingkun Jiang,et al.  Aerosol surface area concentration: a governing factor in new particle formation in Beijing , 2017 .

[9]  J. Kangasluoma,et al.  On the sources of uncertainty in the sub-3 nm particle concentration measurement , 2017 .

[10]  Mindong Chen,et al.  Laboratory observations of temperature and humidity dependencies of nucleation and growth rates of sub‐3 nm particles , 2017 .

[11]  L. Ahonen,et al.  Measurements of sub-3 nm particles using a particle size magnifier in different environments: from clean mountain top to polluted megacities , 2017 .

[12]  F. Carbone,et al.  Challenges of measuring nascent soot in flames as evidenced by high-resolution differential mobility analysis , 2016 .

[13]  G. Biskos,et al.  General Approach to the Evolution of Singlet Nanoparticles from a Rapidly Quenched Point Source , 2016 .

[14]  L. Ahonen,et al.  Operation of the Airmodus A11 nano Condensation Nucleus Counter at various inlet pressures, various operation temperatures and design of a new inlet system , 2015 .

[15]  T. Petäjä,et al.  Methods for determining particle size distribution and growth rates between 1 and 3 nm using the Particle Size Magnifier , 2014 .

[16]  J. Seinfeld,et al.  Molecular understanding of sulphuric acid–amine particle nucleation in the atmosphere , 2013, Nature.

[17]  A. Mirme,et al.  The mathematical principles and design of the NAIS – a spectrometer for the measurement of cluster ion and nanometer aerosol size distributions , 2011 .

[18]  T. Petäjä,et al.  Particle Size Magnifier for Nano-CN Detection , 2011 .

[19]  Peter H. McMurry,et al.  Electrical Mobility Spectrometer Using a Diethylene Glycol Condensation Particle Counter for Measurement of Aerosol Size Distributions Down to 1 nm , 2011 .

[20]  Peter H. McMurry,et al.  First Measurements of Neutral Atmospheric Cluster and 1–2 nm Particle Number Size Distributions During Nucleation Events , 2011 .

[21]  A. Arneth,et al.  EUCAARI ion spectrometer measurements at 12 European sites – analysis of new particle formation events , 2010 .

[22]  C. O'Dowd,et al.  Laboratory Verification of PH-CPC's Ability to Monitor Atmospheric Sub-3 nm Clusters , 2009 .

[23]  M. Stolzenburg,et al.  Equations Governing Single and Tandem DMA Configurations and a New Lognormal Approximation to the Transfer Function , 2008 .

[24]  J. Erman,et al.  QRP05-4: Internet Traffic Identification using Machine Learning , 2006, IEEE Globecom 2006.

[25]  Miikka Dal Maso,et al.  Formation and growth of fresh atmospheric aerosols: eight years of aerosol size distribution data from SMEAR II, Hyytiälä, Finland , 2005 .

[26]  Hanna Vehkamäki,et al.  Formation and growth rates of ultrafine atmospheric particles: a review of observations , 2004 .

[27]  P. Mcmurry,et al.  Modification of the TSI 3025 Condensation Particle Counter for Pulse Height Analysis , 1996 .

[28]  Douglas W. Cooper,et al.  Evaluation of aerosol deconvolution algorithms for determining submicron particle size distributions with diffusion battery and condensation nucleus counter , 1989 .

[29]  Nan M. Laird,et al.  Em algorithm reconstruction of particle size distributions from diffusion battery data , 1985 .

[30]  Donald E. Hagen,et al.  Linear inversion method to obtain aerosol size distributions from measurements with a differential mobility analyzer , 1983 .

[31]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .