[Paper Review] Dynamic Principal Component Analysis: Identifying the Relationship between Multiple Air Pollutants

О. В. Мельников, Loren Hopkins+1 more|arXiv (Cornell University)|Aug 10, 2016

Water Quality Monitoring and Analysis9 references3 citations

TL;DR

This study introduces dynamic principal component analysis (DPCA) to model time-varying correlations among five air pollutants (O3, CO, NO2, SO2, PM2.5) in Houston from 2009–2011, using hourly, day-of-year resolved data. DPCA captures diurnal and seasonal dynamics, revealing that two components explain up to 90% of variability in winter mornings (PC1: CO/NO2; PC2: SO2), with PC1 and PC2 together explaining up to 65% in afternoons, outperforming static PCA in capturing non-stationary pollutant relationships.

ABSTRACT

The dynamic nature of air quality chemistry and transport makes it difficult to identify the mixture of air pollutants for a region. In this study of air quality in the Houston metropolitan area we apply dynamic principal component analysis (DPCA) to a normalized multivariate time series of daily concentration measurements of five pollutants (O3, CO, NO2, SO2, PM2.5) from January 1, 2009 through December 31, 2011 for each of the 24 hours in a day. The resulting dynamic components are examined by hour across days for the 3 year period. Diurnal and seasonal patterns are revealed underlining times when DPCA performs best and two principal components (PCs) explain most variability in the multivariate series. DPCA is shown to be superior to static principal component analysis (PCA) in discovery of linear relations among transformed pollutant measurements. DPCA captures the time-dependent correlation structure of the underlying pollutants recorded at up to 34 monitoring sites in the region. In winter mornings the first principal component (PC1) (mainly CO and NO2) explains up to 70% of variability. Augmenting with the second principal component (PC2) (mainly driven by SO2) the explained variability rises to 90%. In the afternoon, O3 gains prominence in the second principal component. The seasonal profile of PCs' contribution to variance loses its distinction in the afternoon, yet cumulatively PC1 and PC2 still explain up to 65% of variability in ambient air data. DPCA provides a strategy for identifying the changing air quality profile for the region studied.

Motivation & Objective

• To address the limitations of static PCA in analyzing non-stationary, cyclostationary air quality data with time-varying correlations.
• To demonstrate a proper application of PCA to cyclostationary time-series by using a moving window approach (DPCA) across hours and days.
• To assess the relative performance of DPCA versus static PCA in capturing linear dependencies among air pollutants across diurnal and seasonal cycles.
• To interpret dynamic principal component loadings in terms of real-world air quality indicators (e.g., CO, NO2, SO2, O3).
• To reveal patterns of strong and weak linear dependence among pollutants at different times of day and seasons.

Proposed method

• DPCA is implemented as a moving window static PCA across a two-dimensional time domain: hours of the day × days of the year.
• Data are pre-processed using log differencing to normalize spatially-averaged observations (SAO), transforming them into NSAO (percent change in concentrations) to approximate multivariate normality.
• Dynamic components are computed independently for each hour, enabling analysis of time-varying principal component loadings and explained variance.
• The method evaluates explained variance (EV) and component loadings at key times (e.g., 7am and 2am) to identify diurnal patterns.
• Results are compared to static PCA applied to aggregated data (e.g., day/night, summer/winter) to assess performance differences.
• The approach avoids spatial modeling but uses spatially-averaged data to enhance robustness and reduce noise.

Experimental results

Research questions

• RQ1 How do the correlations among multiple air pollutants change across different hours of the day and seasons?
• RQ2 Can dynamic PCA better capture the time-varying structure of air pollution data than static PCA?
• RQ3 What proportion of total variability in the multivariate pollutant series is explained by the first two dynamic principal components at different times of day and year?
• RQ4 How do the loadings of dynamic principal components reflect real pollutant sources or chemical processes at specific times?
• RQ5 In which time periods (e.g., morning, afternoon, winter, summer) is the linear structure among pollutants most stable and informative?

Key findings

• In winter mornings, the first principal component (PC1), primarily driven by CO and NO2, explains up to 70% of the total variability in the multivariate air pollutant series.
• When augmented with the second principal component (PC2), mainly influenced by SO2, the cumulative explained variance rises to 90% in winter mornings.
• In the afternoon, O3 becomes prominent in the second principal component, reflecting photochemical activity.
• The seasonal profile of principal component contributions loses distinctiveness in the afternoon, yet PC1 and PC2 still explain up to 65% of the total variability.
• DPCA reveals that diurnal dynamics are most informative in the morning, where loading coefficients show consistent, non-local linear structures across seasons.
• Compared to static PCA, DPCA provides significantly higher explained variance—up to 75% for the first component in winter nights—demonstrating superior performance in capturing time-dependent correlations.