Using the power law size distribution to extrapolate and compare microplastic number and mass concentrations in environmental media

<title>Abstract</title> Microplastic (MP) number concentrations in the environment increase exponentially with decreasing particle size. Studies reporting environmental MP concentrations typically do so for variable MP size ranges, depending on sampling, processing and analytical detection methods. This leads to difficulties in intercomparison and extrapolation of studies, which is critical for data reviews, plastic dispersion modeling, and environmental and human health risk assessment. In this study, we summarize the current understanding of the MP particle size distribution (PSD), based on the power law model. We highlight how standard linear regression of the power law slope is strongly biased by data binning, and show that fitting a cumulative PSD (C-PSD) removes the binning bias. The existing MP size-alignment framework is extended to C-PSDs to extrapolate observed MP number and mass concentrations to the full MP size range (1 to 5000 µm, noted MP _{1 − 5000µm} ), or any other sub-size range. We confront the C-PSD power law model with 62 published ocean and atmosphere PSDs from the literature, compiled in the MPsizeBase open access database. Fitted power law slopes for fragments (-2.76 ± 0.62) are steeper than for fibers (-1.84 ± 0.38), reflecting fragmentation dimensionality. Among MP fragments, PSD slopes do not vary significantly between the atmosphere, surface and subsurface ocean. We further demonstrate that the large discrepancy between surface ocean MP concentrations measured by net tows and discrete, pumped samples arise primarily from their different minimum detectable sizes. After aligning datasets to a common size range, fragment concentrations converge to within a factor of 10. In contrast, fiber concentrations from net tows remain lower than those from pumped samples, consistent with sampling losses and detection limitations for elongated particles. Across all 62 MP PSD datasets analysed, size-aligned \(\:{MP}_{1-5000\mu\:m}^{}\)number and mass concentrations are respectively 600x and 3x higher than reported concentrations, reflecting the high abundance of small particles predicted by the power law PSD. Together, these findings highlight that size extrapolation to a common range is essential to intercompare datasets and to distinguish environmental patterns from methodological artifacts.