Interpolation of fine particulate matter across the U.S.

Fine particulate matter (PM2.5) refers to fine particulate matter with a diameter of 2.5 micrometers or smaller. These particles are small enough to be inhaled deeply into the lungs and can pose serious health risks.

This project applied spatial interpolation methods to estimate PM2.5 concentrations at unsampled locations using publicly available EPA AirNow data in order to determine which method — Inverse Distance Weighted (IDW), Spline, or Kriging — most accurately predicted PM2.5 concentrations across the contiguous U.S.

Study area

The study area for this analysis was the contiguous United States, which includes the 48 adjoining U.S. states and excludes Alaska, Hawaii, and U.S. territories. This region spans a wide range of geographic and climatic conditions, from coastal zones to mountain ranges and major urban centers.

The extent was defined by a generalized U.S. state boundaries dataset used to mask and constrain interpolated output surfaces.

Data

The PM2.5 data used in this project came from the EPA’s AirNow Air Quality Monitoring Site Data (Current) feature service, which provides near-real-time air quality observations from EPA-affiliated ground-based monitoring stations. The dataset included point features with pollutant readings, including raw concentration values for fine particulate matter (PM2.5).

The PM2.5 values in this dataset represent hourly concentrations of fine particulate matter measured in micrograms per cubic meter (µg/m³). For more information about PM2.5 and its health impacts, see the U.S. Environmental Protection Agency’s PM basics page.

All layers were projected to NAD 1983 Contiguous USA Albers (EPSG:5070), an equal-area projection optimized for U.S.-scale spatial analysis. This projection preserves area and supports accurate interpolation by ensuring consistent distance and spatial relationships between points.

The AirNow dataset included readings from monitoring stations located in multiple countries, including some outside the United States.

Dataset	AirNow Air Quality Monitoring Site Data (Current)
Year of publication	Updated continuously (accessed June 11, 2025)
Owner	US EPA, Office of Air and Radiation, Office of Air Quality Planning and Standards (OAQPS)
URL	AirNow feature service
Description	Provides current air quality values and AQI scores for pollutants measured at EPA monitoring sites, including PM2.5, PM10, and ozone.
Coordinate system	NAD 1983 Contiguous USA Albers (EPSG: 5070); Geodetic Datum: North American Datum 1983 (NAD83)
Geometry Type	Point (vector)

Data filtering

To focus the analysis on the contiguous U.S., I created a filtered layer based on the StateName field that includes only stations within the lower 48 states and Washington, D.C. The following SQL expression was used to select those records:

StateName IN (
  'AL', 'AZ', 'AR', 'CA', 'CO', 'CT', 'DE', 'FL', 'GA',
  'ID', 'IL', 'IN', 'IA', 'KS', 'KY', 'LA', 'ME', 'MD',
  'MA', 'MI', 'MN', 'MS', 'MO', 'MT', 'NE', 'NV', 'NH',
  'NJ', 'NM', 'NY', 'NC', 'ND', 'OH', 'OK', 'OR', 'PA',
  'RI', 'SC', 'SD', 'TN', 'TX', 'UT', 'VT', 'VA', 'WA',
  'WV', 'WI', 'WY', 'DC'
)

The original dataset contained 4,392 records representing air quality monitoring stations. To focus the analysis on relevant and reliable observations, the following station filtering rules were applied:

• Stations located within the lower 48 states and Washington, D.C. (based on the StateName field).
• Status = “Active”
• PM2.5 IS NOT NULL
• PM25 >= 0

After these steps, the final dataset used for interpolation included 746 monitoring sites, each representing a unique location with valid PM2.5 data.

Training and test sets

To evaluate the performance of the IDW, Spline, and Kriging interpolation methods, the dataset was split into training and test subsets:

• The training set (90%), consisting of 671 points, was used to generate the interpolation surfaces.
• The test set (10%), consisting of 75 points, was held out to assess the accuracy of each method.

Interpolation methods

Three spatial interpolation methods were used to estimate PM2.5 concentrations from the training data: IDW, Spline, and Kriging.

All three interpolation outputs were then symbolized following the EPA’s published PM2.5 breakpoints for Air Quality Index (AQI) categories (pages 8–9):

AQI Category	PM2.5 Range (µg/m³)
Good	0.0 – 12.0
Moderate	12.1 – 35.4
Unhealthy for Sensitive Groups	35.5 – 55.4
Unhealthy	55.5 – 150.4
Very Unhealthy	150.5 – 250.4
Hazardous	250.5+

Results

Since the maximum value in the dataset was 131 µg/m³, only the first four categories (Good through Unhealthy) were utilized in the classified rasters.

The table below compares summary statistics from each interpolation surface to the original observed PM2.5 values to assess how well the methods represent the overall data distribution.

Method	Minimum	Maximum	Mean	Standard Deviation
Observed points	0.30	131	14.21	13.37
IDW	0.31	131	14.52	15.54
Spline	-1,027.58	271	11.38	46.11
Kriging	0.35	131	13.76	15.09

In order to evaluate the interpolation performance compared to the observed points, I computed the following four accuracy metrics from the 75 test points:

• Mean Absolute Error (MAE)
• Mean Squared Error (MSE)
• Root Mean Squared Error (RMSE)
• R²

Interpolation method	Mean Absolute Error (MAE)	Mean Squared Error (MSE)	Root Mean Square Error (RMSE)	R²
Inverse Distance Weighted (IDW)	3.74	56.28	7.50	0.78
Spline	14.01	2198.53	46.89	-7.63
Kriging	3.50	38.39	6.20	0.85

Conclusion

Kriging produced the best overall results, with the lowest RMSE (6.20 µg/m³) and the highest R² (0.85), indicating strong predictive accuracy and spatial coherence. This is clearly the method that would best predict missing values for this dataset.

IDW performed slightly worse, with an RMSE of 7.50 and R² of 0.78.

Spline performed poorly, with a much higher RMSE (46.89) and a strongly negative R² (–7.63), suggesting that, for this data, the method performed worse than simply using the mean.

A key limitation of this analysis is the uneven spatial distribution of the monitoring stations across the U.S. Coverage appears to be densest in urban and highly populated areas, while large regions are sparsely monitored or entirely unrepresented.

In this dataset, there were no active stations in the following states:

• Arkansas
• Georgia
• Massachusetts
• Utah
• Virginia
• Washington
• Wyoming

This spatial imbalance may introduce interpolation bias, particularly in rural or data-scarce areas, where estimates rely on distant training points and may therefore be less reliable.