Environmental Engineering Reference
In-Depth Information
two components. Another way of thinking about this is that one component is correlated
to the value of another component. A further assumption is that the changes occurring in
the environment occur in a regular, describable fashion over definable distances. The
distances used can vary, depending on the component and the needs of the analysis.
Technically distances can be anywhere between the atomic and the km scale. The
distance over which this influence is active can be estimated and used in calculating the
value of the missing data.
For field sampling these assumptions are put into mathematical form so that
estimations can be made at unsampled locations. Note that geostatistics is closely related
to modeling, which will be discussed in detail in Chapter 7. Indeed, geostatistical
methodology and calculations are essential in many environmental models.
Determining the distance over which measured values are interdependent is essential if
these calculations are to be useful. Some reported values of the range of interdependence
for pH measurements in two locations are given in Table 6.8. As can be seen from these
data, interdependence can sometimes range for large distances [10-12]. Interdependence
can also be scale-dependent in that it can be different, depending on the overall area of
interest.
Kriging could be used to estimate the missing values in A2 and A6 in Figure 6.1. In
this case the four nearest values could be used in the calculation; that is, for the missing
value X in A2 the value could be estimated using 190, 210, 510, and 321, and the missing
value Y in A6 could be estimated using 164, 94, 106, and 500. For this calculation the
distance between all points must also be known.
6.12.1. Correlograms
The first step is to think about how environmental measurements might change over a
distance. If there is a point source of contamination, we might expect that the level will
be high at the source and decrease with distance from the source. In Figure 6.1 the point
of contamination would appear to be area B3. A graph of the averages for each of the
areas from B1 to B6 is shown in Figure 6.4. The TPH values are seen to decrease with
distances from the source. This is true no matter which direction is taken away from area
B3. A regular decrease in the component over distance is thus one possible change.
TABLE 6.8 Ranges of pH Interdependence Reported for Two Locations
Location
Soil
Range (m)
Conditions
Source
Arizona Pima clay
loam
1.5
Four 20-meter transects, 20-cm spaces, 50-cm
depth
Gajem [10]
Pima clay
loam
21
Four 20-meter transects, 2-meter spacing, 50-
cm depth
Gajem [10]
Pima clay
loam
260
One transect, 20-meter spacing, 100 points,
50-cm depth
Gajem [10]
 
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