Functional Data Analysis of Particulate Matter (PM10) in Chungbuk, Korea: An Application of Penalized B-Spline Smoothing and Functional Inference

Functional data analysis (FDA) provides a framework for representing high-frequency or longitudinal observations as smooth functions, enabling principled dimension reduction and feature extraction. We develop a B-spline-based FDA approach with a total variation penalty to model daily PM10 trajectories, with smoothing parameters selected via AIC and BIC. Functional principal component analysis (FPCA) is applied to identify dominant temporal patterns, including overall levels, seasonal deviations, and episodic peaks, while preserving abrupt changes. This methodology allows for flexible and interpretable summaries of complex time series and comparisons across spatial or temporal domains. We apply this framework to 365-day PM10 curves from 28 monitoring stations in Chungcheongbuk-do, Korea, for 2022. The first four principal components capture over 80% of total variation, reflecting winter peaks, early spring fluctuations, and summer troughs. Urban–rural contrasts examined via functional two-sample t-tests and FPCA scores reveal minimal differences at the functional level. This study illustrates how FDA, combined with penalized B-splines, can concisely summarize complex temporal dynamics, quantify dominant patterns, and offer a flexible framework for analyzing environmental time series and other functional datasets. The approach provides a general strategy for understanding temporally structured processes in various scientific fields.