Uncovering temporal and spatial patterns in public transport demand: A functional data analysis of smart card transactions in Bogotá

Smart card data provides a rich, continuous record of public transport demand. However, most studies rely on disaggregate analyses over relatively short periods, typically treating the data as discrete observations modelled through multivariate statistical techniques, which limits their ability to capture collective and long-term dynamics. This paper develops a Functional Data Analysis (FDA) approach to examine station-level demand dynamics using multi-year smart card data from Bogotá’s bus rapid transit (BRT) system. We analyse smart card transaction records at the station level, at 15-minute intervals, for 138 stations between January 2018 and July 2025. To respect the assumptions of the methods, Functional Principal Component Analysis (FPCA) is applied separately to two time windows (January 2018–February 2020 and March 2020–July 2025) to exclude the influence of the pandemic. FPCA allows the data to be decomposed into a set of components, recognising the continuous nature of demand and facilitating the identification and interpretation of patterns. The results show that the first three components and their associated scores capture most of the variability in demand patterns, explaining over 99% of the variance observed in the data. Mapping the mean functions and component scores across stations highlights distinct spatial patterns, with peripheral stations exhibiting stronger morning peaks and central stations showing more balanced profiles. These findings demonstrate that FPCA provides a tractable and interpretable framework for uncovering the dominant temporal structures of station-level demand and informing service planning and network monitoring in large-scale public transport systems.