Testing of "Cluster" Contourer

Introduction

Once the secotrs were defined, any data within each sector was averaged. These averaged sectors then formed a radial grid with single values at each node. These values were then applied to distance wieghted interpolation to derive the estimated value. Thus instead of a cluster of sites being counted individually in the interpolation only their average was.

A additional parameter in the interpolation algoritm was the number of sectors to be used in the interpolation. For instance, if only one sector was specified, then the nearest sector in each direction with data was used. This ensured that data from as many radial directions as possible were incorporated.

Point Contouring vs. Cluster Contouring

Figure 1 displays the contoured maps using the original contouring scheme, the cluster scheme, and the difference between the two. The setting for the orginal run were a weighting of 1/r2, a radius of influence of 0.055 radians (~300km), minimum number of sites of 1, and maximum of 3. In previous analysis these settings resulted in the "best" Contourer performance. The setting for the Cluster Contourer were a weighting of 1/r2, a radius of influence of 0.055 radians, a theta of 10 degrees, and internal radius of 0.0002 radians (~1.25 km), a internal radius function of 2^n*r, and a maximum number of sectors of 1. The determination of these settings is explained in the subsequent sections.

Figure 1. Point Contouring vs. Cluster Contouring
	Point Contour	Cluster Contour	Difference
Eastern U.S.
Western U.S.

Figure 1 shows that the the two contouring methods do not vary substantially in the Eastern U.S. Except for two areas in Nebraska and Tenessee, the difference in PM10 concentration is within 5 ug/m3 of one another. This is due to the high spatial density over much of the eastern U.S. which prevents urban clusters from having their PM10 concentrations spread out of a large domain. The western U.S. shows substantial differences between the two interpolation methods. Smearing is seen with the original Contourer from sites in California into Nevada where there are few stations. The Salt Lake City area and the Rocky Mountains in Colorado and Wyoming also show large reductions in PM10 concentrations. The Cluster contouring method restricted the influence of the clusters in those region by averaging them and by incorporating other surround station concentrations. The resulting maps from the cluster method looked simliar in pattern to previously derived concentration maps using the point contouring scheme without a maximum number of sites. Figure 2 contains the contoured maps of the point contourer with the settingw: weight=1/r2, radius of influence=0.55 radians, min number of sites=1, maximum number of sites=2000. These settings forced the Contourer to use all available stations within the radius of influence.

Figure 2. Point Contouring with no maximum number of site restriction
	Point Contour	Difference
Eastern U.S.
Western U.S.

Figure 2 also shows the difference maps between the point contouring maps using all stations and those produced from the clustering method. The differences are less than in Figure 1 but the western U.S. still shows large decreases in PM10 concentration in the Utah area but not so much in other areas of the west. Previous analysis indicated that using more than 3 or 4 sites in the contouring process decreased its accuracy in estimating concentrations. The interpolation methods were tested using the random removal testing methodlogy. Three seperate random sets were removed from both the western and eastern U.S. data sets and the remaining data was used to estimate the removed stations. Figure 3 shows the results. The scatter plots in Figure 3 contain the data from all three test runs.

Figure 3. Random removal interpolation tests.
	Point Contour with max sites=3	Cluster Contour	Point Contour with no max sites
Eastern U.S.
Western U.S.

The scatter plots indicate that the cluster contourer performs less adequately than the point contourer using three sites (PC3) but better than the point contourer using all sites (PCX). This is more evident in the east. The cluster contourer produced an overal R2 of 0.08 while the PC3 had an R2 of 0.16. The PCX gave a negative R2. In the west, the cluster contourer produced an R2 = 0.27 while PC3 had R2=0.29 and PCX had R2=0.21. All three test runs in the east had the highest R2 from PC3 while in the west one of the cluster contour runs had the highest R2. The reason that the east produced much lower results is due to the high station density. In the east, the nearest three sites were usually very close to the location to be estimated and therefore gave an acuurate estimate. The cluster contourer used data from all radial directions out to about 300 km distance from the estimated location. This diluted the estimate and reduced the accuracy of the estimate. In the west, the cluster contourer performed better in comparison to the point contourer because of the large gaps in station coverage. Fortunately, the cluster contourer performed better than the point contourer with all sites. Adding the wind should make the cluster contourer more accurate. Possibly a different internal radius funciton could produce better results. Other random sets might also be used to produce higher R2 values.