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Page Title: Estimating data (cont.)
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ERDC TN-DOER-C15
July 2000
where
$
v = the data point being estimated
wi = a weighting factor
vi = a data value
In estimating, adjustments are made to the sample weighting factor for distance from the point being
estimated and clustering of data points. Samples closest to the data point being estimated will be
given more weight than those at a greater distance. Data points that are clustered close together
rather than uniformly distributed over an area will be given less weight because they are not
representative of the larger area and may unduly influence the value of estimated global parameters.
Isaaks and Srivastava (1989) describe a number of two- and three-dimensional declustering
approaches. Additionally, closely spaced samples having similar values contain redundant infor-
mation, and sample weights should be adjusted for this factor as well.
An important point to note is that distributions estimated from data points are volume dependent
(Isaaks and Srivastava 1989); that is, if a homogenized 0.3-m (1-ft) section of core constitutes a
single data point, the distribution estimated with this and like data points constitutes the distribution
of parameter values for homogenized 0.3-m (1-ft) core sections. For this application, however,
parameter values are desired for larger volumes of a scale that can be practically and economically
excavated. Estimates of recoverable materials based on core analysis may not reflect the averaging
that occurs when the material is excavated in larger volumes. Correcting for the error introduced
by extrapolating small volume estimates to large volumes is a difficult problem, but some effort
should be made to evaluate the potential effect of this factor. One approach might be to examine
the standard deviation of the means of individual core sites.
Geostatistical estimating methods require identification of a model upon which the estimates are
based (Isaaks and Srivastava 1989). A deterministic model can be used if enough is known about
the process effects being measured to quantify them. For example, Stokes' law might be used to
model the expected distribution of grain sizes across a portion of a CDF based on settling velocities,
and extrapolate between data points to estimate the location of transitions across a certain grain size
threshold. (Note that Stokes' law applies only to discrete settling of individual, nonflocculating
particles. Discrete settling of fines does not normally occur in a CDF; thus the model would be
applicable only to the coarse material in the CDF.) However, it is unlikely that most CDFs have
been operated in a manner consistent enough to use this approach. Probabilistic models are used
when no suitable deterministic model is available; in this approach the sample data are viewed as
the result of some random process (Isaaks and Srivastava 1989). The most common parameters
used in probabilistic approaches are the mean, or expected value, and the variance.
Global estimation is the determination of mean parameter values for large areas. Point estimation
is the estimation of parameter values for small areas, or specific locations (Isaaks and Srivastava
1989). Declustering methods are used in both global and point estimation when samples are
clustered rather than distributed over the entire area of interest. Point estimation methods also
require weighting of sample values to reflect the relative distance from the point or area being
estimated. Two point estimation methods, polygons and the local sample mean method, are
10

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