Estimating data

ERDC TN-DOER-C15

July 2000

indicator map would likely be most useful for visualizing material in a CDF falling within a

certain specification. However, a three-dimensional representation of the material in a CDF

is needed. Different elevations within the CDF could be mapped separately, and vertical

sections mapped in the same manner as the areal sections.

Another useful grouping tool is moving window statistics (Isaaks and Srivastava 1989). A

uniform grid of data points is divided into subareas, and the mean and standard deviation of

the parameters within each subarea are calculated and remapped at the center of the subarea.

This results in a location map in which the parameter value trends and variability are easily

seen. Overlapping the subareas can address the need for a sufficient number of data points

within each subarea to provide reliable statistics (mean and standard deviation) while keeping

areas small enough to capture local detail. Overlapping is particularly useful for small or

irregular data sets (Isaaks and Srivastava 1989). Contour maps may also provide a useful

visual description of material distribution, although their quantitative value may be limited

where extensive interpolation is required. Plots of standard deviation versus sample means,

h-scatter plots, correlation functions, covariance functions, and variograms are other available

interpretive tools (Isaaks and Srivastava 1989) that might be considered if the basic summary

statistics do not reveal a meaningful trend.

Estimating data. Estimating parameters for unsampled locations based on a limited data set is

central to environmental characterization problems. A number of methods have been developed

under the umbrella of geostatistics that have potential application. All are subject to the same

inaccuracies as a result of site variability. Local estimates based on data that are highly variable are

not likely to be very accurate, and should be interpreted in light of the confidence associated with

the data set and the degree of spatial continuity evidenced by the data set.

The first step in estimating is to define the problem. The following three features of estimating a

problem are adapted from Isaaks and Srivastava (1989):

Is a global or local estimate desired?

Is an estimate of the mean or the complete distribution of data values desired?

Are point estimates or block values desired?

To characterize the deposits within a CDF, some point estimates will most likely be needed to

identify extreme values (particularly with respect to contaminant levels), mean block values for

particle size, and some estimate of the variability of the data to estimate recoverable volumes of

material.

All of the methods discussed in Isaaks and Srivastava (1989) involve weighted linear combinations

of the known data points:

estimate = v = ∑ wi vi

(2)

i =1