by Stefan R. Falke,stefan@mecf.wustl.edu and Rudolf B. Husar , rhusar@mecf.wustl.edu

Center for Air Pollution Impact and Trend Analysis (CAPITA)

May, 1996

Spatial interpolation is frequently applied in estimating air pollutant concentrations. A common interpolation technique is the inverse distance weighted interpolation (1/r^

- Introduction
- Methodology
- Location Setting Analysis
- Number of Sites Analysis
- Additional Sites Analysis
- Conclusions
- Appendix

Map of randomly removed (red squares) and remaining (yellow squares) station locations.

AIRS sites contain a Location Setting Code in the sites' location names. Three code types were used: (1) Urban and center city, (2) suburban and (3) rural. AIRS also contains some sites that were not classified. The locations of the classified sites for the 1993 episode are shown in Figure 2. The 1993 episode was defined by 102 urban, 259 suburban, 238 rural, and 13 nonclassified sites totalling 612 total sites. The 1988 episode had 73 urban, 218 suburban, 186 rural, and 13 nonclassified sites, 490 total.

Figure 2. Ozone monitoring sites in the eastern half of the AIRS network for July 1993.

Four interpolation runs were conducted for each data set (1988 and 1993). The first consisted of a random removal of 10% of the sites, independent of location setting. The other three runs consisted of an interpolation with the removal of only urban, only suburban, and only rural sites.

Figure 4. Correlation plots and statistics for random, suburban, urban, and rural sites on 7/7/88.

Figure 5. Correlation plots and statistics for random, suburban, urban, and rural sites on 7/23/93.

Figure 6. Correlation plots for randomly selected sites on July 23, 1993.

Correlation plots from 10% removed AIRS set 1.

Correlation plots from 10% removed AIRS set 2.

The low R2 values were caused by large ozone concentration variation over a small spatial scale. The main outlyer in Figure x has an observed O3 concentration of about 70ppb while the interpolated value is about 35ppb. The 70ppb site which was removed from the intital AIRS data set was in an area of high station density. The reamining sites (those used in the interpolation calculation) in the immediate area surround the 70ppb site had concentrations considerably lower than 70ppb and as a result the interpolated concentration at that location was about half of the observed concentration.

It would be beneficial to do further interpolation test runs to solidify the jsut described results. The next section contains additional interpolation runs using a combination AIRS/CASTNet data set and will be compared to the above results.

Ozone monitoring sites for AIRS (yellow boxes) and CASTNet (red boxes) network.

Correlation plots from 10% removed AIRS/CASTNET set.

Ozone concentrations at the removed AIRS locations from the two sets used in the previous number of station analysis were estimated using the AIRS/CASTNet data set. The resulting correlation plots are shown below.

Correlation plots from 10% removed AIRS set 1.

Correlation plots from 10% removed AIRS set 2.

The second removed AIRS set used with the AIRS/CASTNet data in Figure x also exhibits slight improvement over just the AIRS data, from R2=0.314 to R2=0.324. Again, using four sites increased the R2, to 0.335.

The above correlation plots along with those in the number of sites analysis indicate that using either three or four sites during interpolation produces the "best" ozone concentration estimates. Since there was very little overall difference between three or four sites, the following interpolation evaluation used only three sites.

One outstanding point in the above figures is the high R2 (0.7) produced in Figure x compared to the lower R2 values (~0.4) in figure x and x. The removed set in figure x contained eight CASTNet stations and 85 AIRS stations. The removed set in Figure x and x contained 85 AIRS stations. The removed AIRS/CASTNet set did not exhibit the effects of large ozone concentration variation over small spatial scales. The 85 AIRS sites in the AIRS/CASTNet removed station set were removed from both the initial AIRS ozone concentration data set and the initial AIRS/CASTNet data set and were estimated using the same interpolation mehtod as previously. The resulting scatterplots are shown in Figure xx).

Correlation plots from 10% removed AIRS/CASTNET location set. Interpolated with AIRS (a) and AIRS/CASTNet (b) data.

Correlation plots from 10% removed AIRS set 3. Interpolated with AIRS (a)and AIRS/CASTNet (b) data.

Correlation plots from 20% removed AIRS set. Interpolated with AIRS and AIRS/CASTNet data.

- The results from the location setting analysis indicate that the spatial interpolation procedure used performs adequately in estimating ozone concentrations in the eastern half of U.S. The regional ozone of 1988 was better estimated overall (R2 between 0.71 and 0.86) than the more textured pattern of 1993 (R2 between 0.60 and 0.83) where the interpolation underestimated the concentrations more often. It was difficult to determine whether the location setting of a site had any effect on reducing or increasing the uncertainty in the interpolation due to the limited number of test runs.
- The number of sites producing the "best" interpolation performance in estimating ozone conentrations occured when using three or four sites.
- The addition of the CASTNet ozone monitoring network to the AIRS network did not substantially improve the estimation of ozone concentrations. Depending on the interpooation run, it either slightly improved the R2, slightly lower it, or left it unchanged.

While this work provides a foundation for quantifying the uncertainty in distance weighted spatial interpolation of ozone concentrations, additional test runs (tens or hundreds of runs, rather than the 5-10 used in this work) are required to obtain solid statistical measures. The AIRS ozone monitoring network has high spatial station density in the eastern U.S. which hampered some of the interpolation testing. For instance, highly varying ozone concentrations in an urban area (a single site measuring a concentration of 70 ppb while other stations in its immediate area measured concentrations of approximately 20 ppb) biased the results. The spatially dense network also caused the addition of sites to have no distinguishable effect on the ozone interpolation performance.

Contour Functionality: transform data from table format into grid format Input: Table - a set of data points WeightFunc - distance weight function Radius - distance constraint MinPoints - minimum required number of data points within Radius MaxPoints - maximum number of data points used in calculation of a grid cell Output: Grid - uniformly distributed set of data points function Contour(out Grid, in Table, in WeightFunc, in Radius, in MinPoints, in MaxPoints) { for each Cell in Grid CalcCell } CalcCell Functionality: calculate value of a grid cell given a table of data points around it function CalcCell(in out Cell, in Table, in WeightFunc, in Radius, in MinPoints, in MaxPoints) { PointList = an empty list of table points for each point in Table that is not null if the distance between the point and the cell is less than Radius then add point to the PointList, sorted by distance Cell value = Interpolate PointList } Interpolate Functionality: interpolate over a sorted list of data points function Interpolate(in PointList, in WeightFunc, in MinPoints, in MaxPoints) { if number of points in PointList < MinPoints return null value TotalWeight = 0 Sum = 0 WeightExp = 0 if WeightFunc = 1 1 if WeightFunc = 1/r 2 if WeightFunc = 1/r2, etc for first MaxPoints in PointList Dist = point distance from cell Weight = 1 / (Dist^WeightExp) TotalWeight = TotalWeight + Weight Sum = Sum + Weight * point value if TotalWeight = 0 return null value Sum = Sum / TotalWeight return Sum }

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