Downhole fractionation (DHF), a known phenomenon in static spot laser ablation, remains one of the most significant sources of uncertainty for laser-based geochronology. A given DHF pattern is unique to a set of conditions, including material, inter-element analyte pair, laser conditions, and spot volume/diameter. Current modelling methods (simple or complex linear models, spline-based modelling) for DHF do not readily lend themselves to uncertainty propagation, nor do they allow for quantitative inter-session comparison, let alone inter-laboratory or inter-material comparison.</p> <p>In this study, we investigate the application of orthogonal polynomial decomposition for quantitative modelling of LA-ICP-MS DHF patterns with application to an exemplar U–Pb dataset across a range of materials and analytical sessions. We outline the algorithm used to compute the models and provide a brief interpretation of the resulting data. We demonstrate that it is possible to quantitatively compare the DHF patterns of multiple materials across multiple sessions accurately, and use uniform manifold approximation and projection (UMAP) to help visualise this large dataset.</p> <p>We demonstrate that the algorithm presented advances our capability to accurately model LA-ICP-MS DHF and may enable reliable decoupling of the DHF correction for non-matrix matched materials, improved uncertainty propagation, and inter-laboratory comparison. The generalised nature of the algorithm means it is applicable not only to geochronology but also more broadly within the geosciences where predictable linear relationships exist.