Spatiotemporal Interpolation Methods for the Application of Estimating Population Exposure to Fine Particulate Matter in the Contiguous U.S. and a Real-Time Web Application
Abstract
:1. Introduction
2. Methods
2.1. Shape Function-Based Spatiotemporal Interpolation Using the Extension Approach
2.1.1. General Formula of the SF-Based 3D Spatial Interpolation Method
2.1.2. Extension Approach of the SF-Based Spatiotemporal Interpolation Method
2.2. IDW-Based Spatiotemporal Interpolation Using the Extension Approach
2.2.1. General Formula of the IDW-Based Spatial Interpolation Method
2.2.2. Extension Approach of the IDW-Based Spatiotemporal Interpolation Method
2.3. Cross Validation
2.3.1. K-Fold Cross Validation
- The points in one fold (test data) of the PM2.5 data set are interpolated using the remaining nine folds (training data). Therefore, each point in the test data will have both the original PM2.5 concentration measurement and an interpolated PM2.5 concentration value.
- Error statistics are calculated to compare the original and interpolated PM2.5 values in the test data.
2.3.2. Error Statistics
2.4. Linking PM2.5 to Census Population
3. Experimental Data
3.1. PM2.5 Data Set with Measurements
3.2. Census Block Group Data Set to Interpolate
4. Results
4.1. Cross Validation Results of the SF-Based Method
4.1.1. Choice of Time Scale
4.1.2. Cross Validation and Error Statistics
4.2. Cross Validation Results of the IDW-Based Method
4.2.1. Choice of Time Scale, Number of Neighbors, and Exponents
4.2.2. Cross Validation and Error Statistics
4.3. Comparison of SF-Based and IDW-Based Extension Methods
4.4. Population Exposure Analysis
- 35 micrograms per cubic meter () for 24 h:We identify block groups that have PM2.5 values greater than for at least one day.
- 15 micrograms per cubic meter () for the annual mean:We identify block groups that have annual PM2.5 values greater than .
- there is a population of (27.8 million) residing in census block groups in the contiguous United States with an annual PM2.5 exceeding the national standard of ;
- more than one-third of the U.S. population () residing in census block groups where PM2.5 exceeded for at least one day in 2009.
4.5. Web Application
5. Discussion
- This study is limited to investigating only four choices for time scales, five choices for the number of nearest neighbors, and nine choices for the exponents. In future work, we plan to apply machine learning methods to efficiently learn the best possible configurations in the model, using a lightning-fast cluster computing framework Apache Spark [61].
- The SF-based and IDW-based methods are deterministic methods. In this paper, we did not compare our methods with geostatistical interpolation methods such as Kriging, neural networks, and land use regression. In future work, we plan to develop multidimensional and stochastic spatiotemporal interpolation methods suitable for ambient air pollution data (NO2, O3, PM2.5, and PM10) by incorporating factors associated with the environmental exposure of interest, and then make comparisons with other commonly-applied geostatistical interpolation methods.
- Finally, there is a limitation in the currently implemented SF-based algorithm with respect to missing data close to some boundaries of the contiguous United States. For example, along the west coast in Oregon and Washington, there are monitoring stations relatively far away from the coastal border. Because of missing data, an unrealistic stripe next to the coast is visible in our map presentations of the interpolated results. In order to avoid this type of problem, we will need additional measurements along the coast, or use meshless interpolation methods such as IDW with a limited number of neighboring measurements in future work.
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Time | Scale A | Scale B | Scale C | Scale D |
---|---|---|---|---|
(c = 1) | (c = 1/10) | (c = 1/5) | (c = 1/15) | |
01/01/2009 | 1 | 0.1 | 0.2 | 0.067 |
01/02/2009 | 2 | 0.2 | 0.4 | 0.133 |
01/03/2009 | 3 | 0.3 | 0.6 | 0.2 |
01/04/2009 | 4 | 0.4 | 0.8 | 0.267 |
… | … | … | … | … |
12/31/2009 | 365 | 36.5 | 73 | 24.333 |
Error | Scale A | Scale B | Scale C | Scale D |
---|---|---|---|---|
Statistics | () | () | () | () |
3.1512 | 3.5576 | 3.2463 | 3.7307 | |
85.8621 | 78.5322 | 78.4890 | 77.1072 | |
8.8832 | 8.6045 | 8.6067 | 8.5023 | |
3.2162 | 0.4158 | 0.3745 | 0.4365 | |
0.3079 | 0.3226 | 0.3138 | 0.3382 |
Error | Scale A | Scale B | Scale C | Scale D |
---|---|---|---|---|
Statistics | () | () | () | () |
3.0941 | 3.4976 | 3.1812 | 3.6751 | |
42.2910 | 37.7745 | 35.6601 | 39.2077 | |
6.5032 | 6.1461 | 5.9716 | 6.2616 | |
3.2135 | 0.4128 | 0.3708 | 0.4349 | |
0.4817 | 0.5371 | 0.5630 | 0.5195 |
Error | Scale A | Scale B | Scale C | Scale D |
---|---|---|---|---|
Statistics | () | () | () | () |
3.1586 | 3.2856 | 3.1070 | 3.4207 | |
(N = 4, p = 1.0) | (N = 3, p = 2.0) | (N = 3, p = 2.0) | (N = 5, p = 2.5) | |
75.3792 | 67.8379 | 68.0293 | 68.2309 | |
(N = 7, p = 1) | (N = 7, p = 1.5) | (N = 6, p = 1.0) | (N = 7, p = 1.5) | |
8.3258 | 7.8888 | 7.8967 | 7.9143 | |
(N = 7, p = 1.0) | (N = 7, p = 1.5) | (N = 7, p = 1.0) | (N = 7, p = 1.5) | |
2.7005 | 0.3803 | 0.9717 | 0.3963 | |
(N = 7, p = 1.0) | (N = 3, p = 5.0) | (N = 3, p = 5.0) | (N = 3, p = 2.5) | |
0.3789 | 0.4413 | 0.4416 | 0.4374 | |
(N = 7, p = 1.0) | (N = 4, p = 1.0) | (N = 7, p = 1.0) | (N = 7, p = 1.0) |
Error Statistics | |||
---|---|---|---|
Scale B () | Scale B () | Scale B () | |
before Removing Outliers | before Removing Outliers | after Removing Outliers | |
3.4519 | 3.3378 | 3.2765 | |
68.0348 | 79.5497 | 37.5608 | |
7.8909 | 8.6320 | 6.1287 | |
1.2594 | 0.3803 | 0.3773 | |
0.4413 | 0.3359 | 0.5399 |
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Li, L.; Zhou, X.; Kalo, M.; Piltner, R. Spatiotemporal Interpolation Methods for the Application of Estimating Population Exposure to Fine Particulate Matter in the Contiguous U.S. and a Real-Time Web Application. Int. J. Environ. Res. Public Health 2016, 13, 749. https://doi.org/10.3390/ijerph13080749
Li L, Zhou X, Kalo M, Piltner R. Spatiotemporal Interpolation Methods for the Application of Estimating Population Exposure to Fine Particulate Matter in the Contiguous U.S. and a Real-Time Web Application. International Journal of Environmental Research and Public Health. 2016; 13(8):749. https://doi.org/10.3390/ijerph13080749
Chicago/Turabian StyleLi, Lixin, Xiaolu Zhou, Marc Kalo, and Reinhard Piltner. 2016. "Spatiotemporal Interpolation Methods for the Application of Estimating Population Exposure to Fine Particulate Matter in the Contiguous U.S. and a Real-Time Web Application" International Journal of Environmental Research and Public Health 13, no. 8: 749. https://doi.org/10.3390/ijerph13080749