performed by the interactive kriging software

described in Grundy and Miesch (1987).

((*h*) characterizes the spatial continuity of a

regional variable for pairs of locations as a func-

tion of distance or lag *h *between the locations.

This variogram is sometimes called the theoretical

variogram because it is assigned a continuous

functional form that expresses the spatial correla-

tion for any lag in the region of analysis. The

function is estimated by fitting one of the equations

given in section 2-3 to empirical or sample vario-

8

gram points ((*h*) using data whose locations con-

8

tribute only a finite number of lags. Although ((*h*)

characterizes the spatial correlation of the data, it

is computed from residuals of the data off the spa-

tial mean. Therefore, without prior knowledge of

nonstationarity in the underlying spatial process,

the first step in computing the sample variogram is

to identify existing nonstationarity indicated for the

spatial mean.

2

begins by computing squared differences Di, *j *from

the data values *z(x*i), z(x2), ...z(xn) collected at loca-

tions *x*1, x2, ... xn

2

(4-1)

2

If the spatial mean is stationary, then the squared

differences of the data are equivalent to the

stationary; if the mean changes with location, then

squared differences of the residuals, and sample

it is spatially nonstationary. Generally, if the data

variogram computations can be continued using

have a stationary spatial mean, the discussions in

the data themselves. If the spatial mean is strongly

sections 4-3 and 4-7, which address nonstation-

nonstationary, the plot of Equation 4-1 versus the

arity and additional trend considerations, can be

distance between associated points may indicate a

omitted. If the spatial mean is not stationary, as

trend or drift that would need to be removed before

for this example data set, then sections 4-3 and 4-7

further variogram computations could be made.

become important, and the sequence of stages for

Drift would have to be considered in HTRW

obtaining a variogram becomes an iterative pro-

studies, such as determining contaminant concen-

cedure. All variogram and kriging computations

trations areally dispersed from localized sources or

for the Saratoga groundwater levels example were

4-2