Eigenvectors corresponding to the second moment matrix for the different depths and different seasons for Soil temperature at Cub hill is shown in the figure above. The corresponding energies are Shown in the figure below:

We begin by looking at one month in the summer at depth 1. The figure below shows the raw time signals for July 1, 2009 to July 31, 2009. Out of 50 locations, around 4 loations have a lot of missing values and were removed from this analysis. The raw time signals for 5 representative signals are shown in the figure below. A number of signals are noisy and have a lot of gaps.

After removing the daily ramp signal, the signals look as follows:

The first 2 principal components are removed. The residual for the representative signals look like the figure shown below.

The median value of the variogram at a given distance is shown in the figure below. The figure also shows the number of samples using which the median was calculated.