Remove a trend before kriging
Segment 7 of 18
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In the second segment you saw how to use the default parameters to map ozone concentration. However, this did not take into account the statistical properties of the sample data. For example, when exploring the data, it appeared that the data exhibited a trend. This can be incorporated into the interpolation process.
In the next six segments you will see how to improve the ozone prediction surface. You will again use the ordinary kriging interpolation method, but you will incorporate the trend in your model to create better predictions.
To do so, click the Geostatistical Analyst drop-down arrow and click Geostatistical Wizard. Click the Input data 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. By default, Ordinary Kriging and Prediction Map are selected.
From the exploration of your data in Exercise 2, you discovered a global trend. After refinement with the Trend Analysis tool, you determined that a second-order polynomial seemed reasonable and the trend was from the southeast to the northwest. This trend can be represented by a mathematical formula and removed from the data. Once the trend is removed, the statistical analysis will be performed on the residuals or the short-range variation component of the surface. The trend will automatically be added back before the final surface is created so that the predictions produce meaningful results. By removing the trend, the analysis that is to follow will not be influenced by the trend, and once it is added back, a more accurate surface will be produced.
On the Geostatistical Method Selection dialog box, click the Order of trend removal drop-down arrow and click Second.
A second-order polynomial will be fitted because a U-shaped curve was detected in the southwest–northeast direction on the Trend Analysis dialog box in Exercise 2.
By default, Geostatistical Analyst maps the global trend in the dataset. The surface indicates the most rapid change in the southwest-northeast direction and a more gradual change in the northwest-southeast direction (causing the ellipse shape).
Trends should only be removed if there is justification for doing so. The southwest-northeast trend in air quality can be attributed to an ozone buildup between the mountains and the coast. The elevation and prevailing wind direction are contributing factors to the relatively low values in the mountains and at the coast. The high concentration of humans also leads to high levels of pollution between the mountains and coast. The northwest-southeast trend varies much more slowly due to the higher populations around Los Angeles and extending to lesser numbers in San Francisco. Hence you can justifiably remove these trends.
Click Next on the Detrending dialog box.