Statistics - Field Sampling: Principles and Practices in Environmental Analysis - page 163

FIGURE 6.5 Recurrent pattern of soil bulk densities due to wheeled traffic
across a field.
6.12.2. Variograms
A variogram is a graphical representation of the variation in a measurement over distance
and is a basic component of any kriging. Four different types of variograms plotted as
variance versus distance are used as models. * (See Figures 6.6-6.9.) Except for Figure
6.8 (the linear model that does not have a corresponding covariance function), each of
these can have a covariance function, and this can be plotted and also used in
calculations. In Figure 6.6 the variance is 0 at a distance of 0. It increases linearly in a
straight line to a value at which it becomes a flat line, a slope of 0. The y value where the
line has a slope of 0 is called the sill. The distance from the start, x= 0, y= 0, to where the
slope becomes 0 or where the y axis reaches its maximum value, is called the range. The
range is the maximum distance at which components are still correlated. The graph in
Figure 6.6 is called a linear model with a sill.
A second linear model (Figure 6.7) has the variance at some value above 0 at 0
distance. The variance increases linearly to some value at which
* Although the term modeling is applied to these graphs they are not the same as the modeling we
will discuss in Chapter 7.