Curve fitting algorithm for multimodal particle size distributions – a theoretical basis

Abstract. In this article, we detail an open-source curve fitting algorithm for multimodal particle size distributions (MPSDs) and evaluate it against a ten-year dataset of ambient particle size distribution (PSD) measurements collected at Storm Peak Laboratory, a remote mountainous research site. This algorithm is grounded in traditional aerosol statistics and assumes measured particle distributions are the sum of several lognormal PSDs. It is designed to be free of any predefined mode templates or mode number constraints. For a MPSD measurement, the total number concentration (N_i), geometric standard deviation (𝜎_g), and geometric mean diameter (D̅_pg ) of each mode is estimated using a Levenberg-Marquardt nonlinear least-squares algorithm. These fitted modes are then iteratively subtracted from the measured PSD until convergence and/or accuracy thresholds are met. Rigorous evaluation of ambient aerosol data reveals a tri-modal distribution is a poor assumption for Storm Peak Laboratory, particularly during new particle formation events. Four or more modes were necessary for 55.7% of data associated with new particle formation. Furthermore, the algorithm was used to characterize complex laboratory PSDs where size selected ammonium sulfate aerosol was coated in oxidized biogenic secondary organic matter. In summary, this algorithm provides an effective method to analyze PSD datasets for in situ laboratory and ambient measurements. To improve accessibility of this algorithm to the broader aerosol research community, we also include supplemental functions to format datasets from common mobility particle size spectrometers.