Application of Proper Orthogonal Decomposition to Elucidate Spatial and Temporal Correlations in Air Pollution Across the City of Liverpool, UK
Abstract
:1. Introduction
2. Methods
2.1. Study Area and Descriptive Analysis
2.2. Proper Orthogonal Decomposition
3. Results and Discussion
3.1. Data Analysis—Descriptive Statistics
3.2. Data Analysis—Spatial Interpolation
3.3. Proper Orthogonal Decomposition
- The dominant shows correlated increases in the whole of the study area. PM2.5 pollution changes more in the south of the LCR, while PM10 increases both in the southern and northern regions, albeit to a lesser extent. The dominant periodicity of is daily, suggesting cyclic components such as TEM and RH linked to the pollution level changes in . However, considering that the spatial correlation between the meteorology variables and pollution levels in Figure 4 is not clear-cut, anthropogenic factors could also be driving PM changes. This is supported by the daily patterns of the time coefficients, in which the positive contributions of the PM mode are observed in the morning and evening. Overall, the increases in pollution levels can be linked to both temperature and changes in traffic, potentially due to transport from residential areas to workplaces.
- shows positive correlations with simultaneous reductions in PM. The patterns of PM2.5 and PM10 changes in share similarities between both pollutants suggesting a common source driving their changes. Areas with higher TEM positive changes experience more significant negative changes in PM magnitudes, supporting the inverse relationship observed in Figure 3. The most dominant frequencies showed weekly to 1-month periodicity, corresponding to shifts in activities on a weekly and fortnightly basis.
- PM2.5 decreases at varying rates across the LCR in , with higher reductions in the north compared to the south. PM10 tends to increase significantly from the center to the southern regions, with lower increases observed in the northeast. These simultaneous variations could reflect the movement of pollution throughout the LCR. dominant frequency is 57 days, and it may be associated with seasonal short-term changes (top 10 dominant frequencies ~1 month), as well as cyclic components such as temperature, considering its daily pattern.
- In , PM2.5 increases across the study area with higher increases in the changes across residential and urban areas transitioning into commercial/industrial features. In contrast, PM10 magnitudes decrease in the south of the LCR. While the contribution is limited, this mode may indicate isolated events or temporal changes resulting in correlated pollutant changes in specific regions. Temporal coefficients () vary significantly throughout 2023, with a dominant frequency of 21 days. Its daily pattern is similar to and , suggesting that these modes might share common sources or behavior.
3.4. Implications for Urban Air Pollution Management
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. POD Pseudocode
Algorithm A1: Proper orthogonal decomposition (POD) |
Algorithm A2: Function: mean_along_time |
Algorithm A3: Function: reshape_data |
Algorithm A4: Function: svd |
Algorithm A5: Function: create_diagonal_matrix |
Appendix B. Modes Details
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Acosta Ramírez, C.; Higham, J.E. Application of Proper Orthogonal Decomposition to Elucidate Spatial and Temporal Correlations in Air Pollution Across the City of Liverpool, UK. Urban Sci. 2025, 9, 166. https://doi.org/10.3390/urbansci9050166
Acosta Ramírez C, Higham JE. Application of Proper Orthogonal Decomposition to Elucidate Spatial and Temporal Correlations in Air Pollution Across the City of Liverpool, UK. Urban Science. 2025; 9(5):166. https://doi.org/10.3390/urbansci9050166
Chicago/Turabian StyleAcosta Ramírez, Cammy, and Jonathan E. Higham. 2025. "Application of Proper Orthogonal Decomposition to Elucidate Spatial and Temporal Correlations in Air Pollution Across the City of Liverpool, UK" Urban Science 9, no. 5: 166. https://doi.org/10.3390/urbansci9050166
APA StyleAcosta Ramírez, C., & Higham, J. E. (2025). Application of Proper Orthogonal Decomposition to Elucidate Spatial and Temporal Correlations in Air Pollution Across the City of Liverpool, UK. Urban Science, 9(5), 166. https://doi.org/10.3390/urbansci9050166