The Multivariate Variogram Cloud Link

The second plot shows the multivariate variogram cloud view of precipitation for the third and fourth quarters of 1990. Essentially this plot is the variogram cloud plot split into two, one half of the points are plotted to the left and the other half to the right based on whether the distance is (to the left) or (to the right). For variogram clouds, the plot will be symmetric around the zero axis because the variable plotted to the right is the same as that plotted to the left. If there is asymmetry, it occurs in the cross-variogram cloud plots and suggests a shifted lag relationship between the two variables.

A shifted lag relationship would be one where the highest correlation between two variables is at different locations. A physical process that might conform to a shifted lag model would be a situation where there are two substances (say, phosphate and notrogen) deposited in the same area and one substance leaches into the ground water at a higher rate than the other. See Majure and Cressie (1996) for more details.

The third plot shows the smooth option used in XGobi to smooth the points in the different color groups. (The smooth option was added to XGobi for precisely this use.) In the smoothed plot it is easier to see the overall trends. The smoothing is done using a simple running mean smoother.

In the smoothed multivariate variogram cloud it can be seen that the low point for the northeast angle class (red) has a dip at a value to the left of zero. This suggests an asymmetric spatial relationship for points in this angle class, that is, there is a shifted lag relationship between points in the third quarter and those in the fourth quarter. Thus, this exploratory spatial data analysis, from the lagged scatterplot views, suggests that a wet third quarter tends to be followed by a dry fourth quarter (and vice-versa). And, curiously, a location with a wet (dry) third quarter tends to be displaced by approximately 5-8 km from a location with a wet (dry) fourth quarter.