Water-Quality Examples

ETL 1110-1-175

30 Jun 97

Table 5-2

Univariate Statistics for Gridded Kriging Estimates in Example Applications1

Minimum

Maximum

Mean

Median

Standard

Example

(Base

base

deviation

Skewness

Identifier

Transformation

units)

(base units)

(dimensionless)

Water level A

Drift

24.34

65.00

45.86

44.46

10.15

0.11

Water level B

Drift

24.59

65.00

45.84

44.45

10.14

0.11

Bedrock B

None

26.13

64.88

41.45

39.78

7.71

0.82

Bedrock C

None

26.72

64.39

41.50

39.69

7.63

0.82

Water

Natural log

2.92

7.07

5.17

5.03

0.72

-0.06

quality A

1

Base units for water level A and B and bedrock B and C is feet; base unit for water quality A is log concentration, concentration in

micrograms per liter.

deviations are shown in Figures 5-6a and 5-6b,

determined for a contaminant. The principal pur-

respectively, and the univariate kriging estimate

poses of the examples are to familiarize the reader

statistics are listed in Table 5-2 (bedrock B). The

with a kriging exercise using water-quality infor-

kriging results indicate channel-like features in the

mation and to illustrate indicator kriging. The

bedrock surface, as well as a prominent bedrock

examples also will familiarize the reader with data

high at the south border of the area; the results are

that are strongly anisotropic and need transforma-

a good representation of the results from other

tion. The data come from a water-table aquifer

more elaborate studies.

developed in alluvial sediments where the depth to

water was less than about 23 m. Several analytical

g. For an example of block kriging, an invest-

laboratories were involved in measuring the con-

igative goal of establishing block values of bedrock

centration of the contaminant in the water-quality

elevation for a finite-difference groundwater model

examples. Each of the analytical laboratories was

grid having about 120- by 120-m cells was

required to follow rather comprehensive guidelines

assumed. The same variogram and search criteria

that specified tests of instrument performance

were used to estimate block values for a 13-by-

before sample determinations were made, as well

13 grid with about 120- by 120-m spacing; a

as measurement of extraction efficiencies.

4-by-4 block was specified. Each kriging value

Because of these performance guidelines, the

shown in Figure 5-6c is interpreted as an estimate

opportunity for errors due to instrument error was

of the average value of bedrock elevation over the

considered to be either known or relatively low. In

about 120- by 120-m block. The standard devi-

addition to using performance guidelines, field

ation for the block estimates is less than the stan-

quality-assurance samples were also collected.

dard deviation for the point estimates (Table 5-2).

These samples can be used to evaluate other types

Gray-scale maps of the kriging estimates and the

of possible errors, such as cross-contamination

kriging standard deviations are shown in Fig-

and representativeness of the sample. Duplicate

ures 5-6c and 5-6d, and the univariate kriging

samples for the contaminant in the water-quality

estimate statistics are listed in Table 5-2

examples indicate as much as 15 percent varia-

(bedrock C).

bility in reported results. This variability is not

entirely unusual and is most likely related to the

integrity of the analytical method or the method in

5-4. Water-Quality Examples

which the sample media was aggregated during

sample collection.

a. The following examples are for water-

quality information consisting of concentrations

5-13