| 19 Dec 2025
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 (Ni), geometric standard deviation (ðg), and geometric mean diameter (DÌ 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.
Competing interests: Fred J. Brechtel is CEO and owner of Brechtel Manufacturing Incorporated.
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The work is done and presented well. There are no major questions about the quality of the work. The main question this reviewer has is "why"? The manuscript is about fitting functions to a multimodal particle size distribution. This is basic data analysis and all major scientific software suites include this capability. An argument was made that the presented work simplifies the process so that the user does not have to learn how to find the peaks (which in itself could be problematic since now there's a black box doing the analysis). However, the code is written in R (using existing R packages for analysis - so again, where's the novelty?) which limits its usefulness to those using R (as opposed to e.g., Python or Matlab). As such, there is little scientific merit to be reviewed here. In conclusion, this manuscript does not offer anything novel to meet the standards of AMT and qualify as a full research paper. The manuscript could be re-submitted as a technical note or the focus could be shifted to analyzing the data from SPL using the R functions described.