Performance of four-parameter analytical models of atmospheric aerosol particle size distribution

•We compared the models on the basis of a large dataset of measurements.•Correlation of parameters reduces information transfer efficiency.•We recommend the two-power law for fitting the measurements.•Parameters of two-power law include explicit indicator of new particle formation.

We compared the ability of five analytical models to approximate size distributions of particles on the basis of a large three-year dataset of ground level measurements of atmospheric aerosols in Hyytiälä, Finland. The collection of models includes: modified gamma distribution; inverse modified gamma distribution; regularized power law; two-power law (called the KL-distribution in previous publications); and the two-power-square law, which is introduced in this study. Comprehensibility, approximation accuracy, and information transfer efficiency are considered to be the main attributes of a model. A model is comprehensible if its parameters have meaningful interpretation. Accuracy is measured by the divergence between the measured distribution and its closest approximation. Information transfer efficiency is characterized by the loss of measurement information at interpretation of model parameters when the part of information contained in the correlations between the parameters is abolished. The analysis allows us to recommend the two-power law to fit the distributions of atmospheric aerosol particles measured in Northern Europe and regions with a similar climate.