In earlier segments you saw how to use ordinary kriging to map ozone concentration in California using different parameters. In the decision-making process, care must be taken in using a map of predicted ozone for identifying unsafe areas because it is necessary to understand the uncertainty of the predictions. For example, suppose the critical threshold ozone value is 0.12 ppm for an eight-hour period and you want to determine if any locations exceed this value. To aid the decision-making process, you can use Geostatistical Analyst to map the probability that ozone values exceed the threshold.

While Geostatistical Analyst provides a number of methods that can perform this task, for this exercise you will use the indicator kriging technique. This technique does not require the dataset to conform to a particular distribution. The data values are transformed to a series of 0s and 1s according to whether the values of the data are below or above a threshold. If a threshold above 0.12 ppm is used, any value below this threshold will be assigned a value of 0, whereas the values above the threshold will be assigned a value of 1. Indicator kriging then uses a semivariogram model that is calculated from the transformed 0-1 dataset.

To do so, click the Geostatistical Analyst drop-down arrow and click Geostatistical Wizard. Click the Layer drop-down arrow and click ca_ozone_pts. Click the Attribute drop-down arrow and click the OZONE attribute. Click Kriging in the Methods list box. Click Next on the Choose Input Data and Method dialog box. Click Indicator Kriging; notice that Probability Map is selected. Set the Primary Threshold Value to 0.12. Click the Exceed button. Click Next on the Geostatistical Method Selection dialog box.

Click Next on the Additional Cutoffs Selection dialog box. Click Anisotropy to account for the directional nature of the data. Type "20000" for the lag size and "10" for the number of lags.

Click Next on the Semivariogram/Covariance Modeling dialog box. Click Next on the Searching Neighborhood dialog box.

The blue line represents the threshold value (0.12 ppm). Points to the left have an indicator-transform value of 0, whereas points to the right have an indicator-transform value of 1.

Click and scroll right until the Measured, Indicator, and Indicator Prediction columns are displayed. Click to select a row in the table with an indicator value of 0. The selected point will be shown in green on the scattergraph, to the left of the blue threshold line.

The Measured and Indicator columns display the actual and transformed values for each sample location. The indicator prediction values can be interpreted as the probability of exeeding the threshold. The indicator prediction values are calculated using the semivariogram modeled from the binary (0,1) data, created as indicator transformations of your original data. Cross-validation sequentially omits a point and calculates indicator prediction values for each.

For example, the highest measured value is 0.1736. If this location had not actually been measured, a prediction of about a 90 percent chance that it was above the threshold based on the indicator kriging model would have been made.

Click Finish on the Cross Validation dialog box. Click OK on the Output Layer Information dialog box.

The probability map will appear as the top layer in the ArcMap data view.

The map displays the indicator prediction values, interpreted as the probability that the threshold value of 0.12 ppm was exceeded on one or more days in the year 1996.

It is clear from the map that near Los Angeles, the probability that ozone concentrations exceed the threshold of 0.12 ppm is likely.

Drag the Indicator Kriging layer to reposition it between the ca_outline and Trend Removed layers.