Fixed-Mode inverse-Gamma Fitting of Aerosol Particle Number Size Distributions

Quantitative analysis of aerosol particle number size distributions (PNSDs) measured with a Differential Mobility Particle Sizer (DMPS), commonly relies on modal representations to describe dominant particle populations and their evolution. While lognormal models are widely used, they may inadequately represent skewed or heavy-tailed size spectra frequently observed in atmospheric measurements. However, observational PNSD data often exhibit strong skewness, multimodality, and occasional abnormal spikes arising from instrumental noise or transient sampling artefacts, which complicate conventional fitting approaches.

We present a robust, automated fixed-mode fitting framework for aerosol multi-mode inverse-gamma (AeroMiG) distributions to measured PNSDs across large datasets. The method represents each PNSD as a superposition of inverse-gamma modes, with parameters estimated via a differential evolution technique based on global optimization methods. Model parameters, including shape, scale, and amplitude of each inverse-gamma mode, are estimated by minimizing a robust objective function that combines reconstruction error (mean squared error) and goodness-of-fit measures (R-square). To evaluate fit quality and ensure consistency across time-resolved data, standard statistical metrics such as MSE, Akaike and Bayesian information criteria, and coefficients of determination are computed for each fitted spectrum.

The framework is designed for high-throughput applications to large datasets and supports parallel processing, enabling efficient analysis of long-term aerosol observations. Application to atmospheric PNSD measurements demonstrates that fixed mixtures of inverse-gamma modes effectively capture asymmetric and heavy-tailed distribution features, providing a flexible alternative to conventional lognormal parameterizations. This approach facilitates consistent intercomparison of modal parameters across time and supports improved interpretation of aerosol processes and source contributions.