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<p>A powerful methodology, based on the multivariate curve resolution alternating least squares (MCR-ALS) method with quadrilinearity constraints, is proposed to handle complex and incomplete four-way atmospheric data sets, providing concise results that are easy to interpret. Changes in air quality by nitrogen dioxide (NO<span class="inline-formula">₂</span>), ozone (O<span class="inline-formula">₃</span>), and particulate matter (PM<span class="inline-formula">₁₀</span>) in eight sampling stations located in the Barcelona metropolitan area and other parts of Catalonia during the COVID-19 lockdown period (2020) with respect to previous years (2018 and 2019), are investigated using such methodology. The MCR-ALS simultaneous analysis of the three contaminants among the eight stations and for the 3 years allows the evaluation of potential correlations among the pollutants, even when having missing data blocks. Correlated profiles are shown by NO<span class="inline-formula">₂</span> and PM<span class="inline-formula">₁₀</span> due to similar pollution sources (traffic and industry), evidencing a decrease in 2019 and 2020 due to traffic restriction policies and the COVID-19 lockdown period, especially noticeable in the most transited urban areas (i.e., Vall d'Hebron, Granollers and Gràcia). The O<span class="inline-formula">₃</span> evidences an opposed interannual trend, showing higher amounts in 2019 and 2020 with respect to 2018 due to the decreased titration effect, more significant in rural areas (Begur) and in the control site (Obserbatori Fabra).</p>