Examining covariation among multiple datasets

The Crosscovariance Cloud tool can be used to investigate cross-correlation between two datasets. Consider ozone (dataset 1) and NO₂ (dataset 2). Notice that the cross-correlation between NO₂ and ozone seems to be asymmetric. The red area shows that the highest correlation between both datasets occurs when taking NO₂ values that are shifted to the west of the ozone values. The Search Direction tool will help identify the reasons for this. When it is pointed toward the west, this is shown:

When it is pointed toward the east, this is shown:

It is clear that there are higher covariance values when the Search Direction tool is pointed toward the west. You can use the Crosscovariance Cloud and Histogram tools to examine which pairs contribute the highest cross-covariance values. If you use the Search Direction tool pointed in the west direction and brush some of the high cross-covariance points in the cloud, you can see that most of the corresponding data points are located in central California. You can also see that the NO₂ values are shifted to the west of the ozone values. The histograms show that the high covariance values occur because both NO₂ (blue bars in the NO₂ histogram) and ozone (orange bars in the ozone histogram) values for the selected points are above the mean NO₂ and ozone values, respectively. From this analysis, you have learned that much of the asymmetry in the cross-covariance is due to a shift occurring because high NO₂ values occur to the west of the high ozone values.

You could also obtain high cross-covariance values whenever the pairs selected from both datasets have values that are below their respective means. In fact, you would expect to see high cross-covariance values from pairs of locations that are both above and below their respective means, and these would occur in several regions within the study area. By exploring the data, you can identify that the cross-covariance in central California seems to be different from that in the rest of the state. Based on this information, you might decide that the results from Crosscovariance Cloud are due to a nonconstant mean in the data and try to remove trends from both NO₂ and ozone.