Wide-Positive Matrix Factorisation of particle number size distributions: A new approach accounting for cyclically changing source profiles

Particle number size distributions (PNSDs) in the atmosphere are a composite from various sources, and Positive Matrix Factorization (PMF) is commonly used to identify these sources by separating the data into multiple factors, each representing a source which is assumed to emit a constant PNSD over time. However, assuming a constant PNSD for each source overlooks the regular growth and shrinkage of atmospheric particles, which often follow diurnal cycles. 'Wide-PMF' restructures the data matrix to place each hourly observation side-by-side; each wide-PMF factor represents a diurnal cycle in the PNSD, capturing formation, emission, growth, shrinkage, and losses, unlike narrow-PMF which presents a time-invariant size distribution whose diurnal cycle has to be inferred from the G-matrix. Using data measured at an urban background site, Wide-PMF reveals diurnal trends in PNSD from each source, and is able to separate photochemical nucleation from traffic nucleation, which are typically inadequately resolved in narrow PMF.