Geometric Identification and Consistent Estimation of Source Apportionment with Application to Greenland Summit Aerosols

Abstract

Over the last four decades, the Arctic has warmed nearly four times faster than the rest of the planet, with anthropogenic aerosols among the major forcings. Greenland Summit Station has collected size-resolved particulate matter year-round since 2003, yet these records remain underutilized. Attributing multipollutant measurements to their sources (source apportionment) can be cast as a non-negative matrix factorization (NMF) problem. Because NMF is non-unique, source apportionment imposes often unverifiable constraints such as structural sparsity or rotations tuned using prior scientific knowledge, which is scarce for remote regions like the Arctic. Geometric NMF approaches offer a more data-driven route to identification, but many suffer from scaling ambiguity, assume exact separability, and lack a statistical framework for consistent estimation. We address these limitations by formally establishing statistical identifiability of the source attribution matrix under a stochastic framework that replaces hard separability with soft probabilistic relaxations. We then present a scalable geometric algorithm to estimate this matrix and prove its consistency, to our knowledge the first such result requiring no exact sparsity, no parametric distributional assumptions, and accommodating spatio-temporal dependence. Analyzing the 2003--2016 Summit record with our framework and HYSPLIT trajectories, we characterize long-range transport of anthropogenic and natural species into the Arctic.