1. Declustering in the Spatial Interpolation of Air Quality Data Stefan R. Falke and Rudolf B. Husar

2. ABSTRACT Air quality monitoring stations are generally located in or near urban areas while station coverage in rural regions is sparse. Clusters of urban sites cause traditional inverse distance weighting interpolation of pollutant concentrations to be biased toward urban concentrations. A new spatial declustering method has been developed that incorporates distance and station density to alleviate much of this bias. Sites located within a cluster are assigned smaller radii of influence and are weighted less than remote sites whose areas of representativeness are large. The uncertainties in the estimates and interpolation performance are analyzed using the statistical method of cross validation. The newly developed spatial interpolation method has been tested in the mapping of tropospheric ozone concentration data.

3. Figure 1. Examples of clustered and declustered monitor configurations, a) three single, non-clustered stations, b) a cluster of four sites that gets 4 times the weight of each of the two single sites, c) a cluster of four sites that is declustered so that it receives the same weight as the two single sites.

4. Figure 2. Relative distance dependence when defining a cluster. Point A is in the middle of the group of stations and "views" each of the stations as single, independent sites. Point B is at a distance from the group of stations where it views them as a cluster.

5. Figure 3. Declustering weights for three spatial configurations. a) X j has a decluster weight near 1, or not part of a cluster. b) X j has a decluster weight of 1/4, or part of a cluster. c) X j has a decluster weight of 1/4.

6. Figure 4. Declustering weights example. Station X 1 is not part of a cluster and has a cluster weight of 1. Stations X 2 and X 3 are clustered and receive a cluster weight of about 0.5 each.

7. Figure 5. Estimate grids from 3 single, low value sites and a group of 10 co-located, high value sites. a) 1/r 2 interpolation causes the group of ten sites to "spread" over most of the grid. b) Incorporating declustered weights contains the influence of the cluster.

8. Figure 6. Estimated 90 th percentile daily maximum ozone concentrations for 1991-1995, a)Simple inverse distance weighted interpolation, b) Inverse distance weighted interpolation with declustering weighting.

9. Figure 7. Difference between simple inverse distance weighted interpolation and inverse distance weighted interpolation with declustering weighting. The declustering decreases concentrations in many rural areas surrounding urban centers.

10. Figure 8. Difference between cross validation errors for simple inverse distance and declustered inverse distance weighted interpolation schemes.

11. Figure 9. Example of a spatial configuration where the declustering scheme causes a cluster to carry more weight than a single site that is equal distant from the estimation point, i.