Air Quality Index levels in the areas between monitors are estimated using a method called spatial interpolation. The interpolation technique used to generate the AirNow maps is called the inverse-distance weighted (IDW) method. The IDW method assumes that sites that are close to one another are more alike than sites that are farther apart. AQI values in areas without monitors are calculated using a weighted average of the values available at surrounding sites.
For those looking for more technical details, here is more information on the IDW method used to make AirNow maps:
Power (a measure of how heavily weighted the nearest sites’ values are): 5
Neighbors (the number of surrounding sites used to estimate a value in a location without a measurement): 10
The maps are interpolated to a resolution of 0.045 decimal degrees (roughly 5 km for most of the continental United States). The uncertainty of the interpolated AQI is also measured; areas with high uncertainty (due to sparse observations) are masked to prevent them from being shown on the AirNow maps.
Shepard, Donald (1968). A two-dimensional interpolation function for irregularly-spaced data. Proceedings of the 1968 ACM National Conference, pp. 517-524.
Frank, Richard & Nielson, Greg (1980). Smooth interpolation of large sets of scattered data. International Journal for Numerical Methods in Engineering, Volume 15, pp. 1691-1704.