needed from a kriging perspective because the cor-

relation matrix used to obtain the kriging weights

is constructed from the variogram values. Even

more directly, the variogram affects the computa-

tion of the kriging variance (Equations 2-36 and

2-47) through the product of the kriging weights

and variogram values. An accurate variogram also

has utility outside the strict context of kriging. For

foundation for geostatistics and the kriging tech-

example, in augmenting a spatial network with new

nique. One theme that pervades the technique is

data collection sites, the range parameter of the

the importance of the theoretical variogram. The

variogram could be used as the minimum distance

theoretical variogram, or what we will often refer

of separation between the new sites and between

to simply as the variogram, is a mathematical

new and existing sites to maximize overall

function or model which is fitted to sample-

additional regional information. In another non-

variogram points obtained from data. Permissible

kriging-specific application, the variogram is used

models, which include those given in Chapter 2,

in dispersion variance computations in which the

belong to a family of smooth curves having par-

variance of areal or block values is estimated from

ticular mathematical properties and are each speci-

the variance of point-data values (e.g., Isaaks and

fied by a set of parameters. Chapter 4 will

Srivastava (1989), p. 480).

describe a sequence of stages for estimating and

investigating sample variogram points and a cali-

bration procedure for specifying the parameters of

described using an example data set of ground-

the variogram model eventually fitted to the sample

water elevations measured near Saratoga, WY

points. Although the calibration procedure is

(Lenfest 1986), that are summarized in Table 4-1

largely an objective means for evaluating theoreti-

and whose relative locations are shown in

cal variograms, the process of obtaining sample

Figure 4-1.

variogram points and finalizing a theoretical vari-

ogram remains an art as much as a science. An

understanding of the material presented in Chap-

variogram points depends on the stationarity prop-

ter 2 as well as professional judgment achieved

erties of the regional variable represented by the

through experience in geostatistical studies is

data. If the mean of the regional variable is the

important in effectively using the guidelines pre-

same for all locations, then it is said to be spatially

sented in this section.

Standard

Example

Number of

Minimum

Maximum

Mean

Median

Deviation Skewness

Identifier

Measurements Transformation (Base units) (Base units) (Base units) (Base units) (Base units) (Dimensionless)

Saratoga

Drift

2,016.6

2,254.3

2,119.25

2,104.35

56.79

0.45

W ater level A

83

Drift

25.6

65.68

42.30

38.54

10.13

1.03

W ater level B

74

Drift

25.6

65.68

42.85

38.71

10.59

0.87

Bedrock A

108

None

22.64

80.48

44.42

42.82

10.76

0.89

Bedrock B

89

None

24.53

69.22

43.67

43.17

8.58

0.26

W ater quality A

66

Natural log

2.08

8.01

5.19

5.59

1.75

-0.42

1

Base unit for Saratoga, water levels, A and B, and Bedrock A and B is feet; base unit for water quality A is log concentration,

concentration in micrograms per liter.

4-1

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