PROJ00326

• Contract/PO #: C153498
• Contractor Name: U. S. Geological Survey
• Water District: 0
• County: Boulder
• Bill Number: SB 87-15
• Loan Projects - Doc Type: Contract Documents

Table 1. Regression equations and statistics for grain.size and specific-retention characteristics

[SR, specific retention; DS()t 50th-percentile grain diameter, in millimeters; D90t 90th-percentile grain diameter, in millimeters; D70t
70th-percentile grain diameter, in millimeters; P.0625, percent finer than 0.0625 millimeter; P.l25, percent finer than 0.125 millimeter]

Regression equation Number of data Coefficient of Standard error of
points correlation estimate
SR = 0.0550 - 0.1335 log DSO 126 .0.80 0.045
SR = .1255 - .1096 log D.Jo 128 -.77 .048
SR = .0521 - .I 024 log O>7o-Dsol 126 -.75 .049
SR = .0694 + .0034 P.0625 128 .79 .045
SR = .0648 + .0019 P.I25 129 .80 .045

The coefficients of correlation (R) for the regres-
sion equations range in absolute value from 0.75 to
0.80 (table 1), and the standard error of estimate ranges
from 0.045 to 0.049 specific-retention units. The
residuals of all the regression equations are normally
distributed. The scatter plots, lines of regression,
and standard errors of estimate for each regression
are shown in figure 4. Sixty-eight percent of the
specific-retention estimates derived by using the
regression equation can be expected to be within plus
or minus one standard error of estimate of the labora-
tory specific-retention value. A mean specific retention
that is based on several samples generally will provide
a better estimate of the specific retention of a geologic
unit than will an individual sample.
Each of the five regression equations has an inde-
pendent variable that is a characteristic of the grain-size
distribution of a sample. The similar coefficients of
correlation and standard errors of estimate for the five
equations indicate that each equation should produce a
similar estimate of specific retention. The similarity of
the estimates was confirmed by examining numerous
specific-retention estimates from each equation.
Improved estimates of specific retention generally were
achieved by use of a predictive model that consists of
the mean of the five dependent variables because this
mean can be less affected by an error in any single inde-
pendent variable.
The predictive ability of the model based on the
mean of the five regression equations was further ana-
lyzed by comparison with specific-retention data avail-
able in a verification data set that was not used in
developing the regression equations. The verification
data were developed as a part of earlier studies of aqui-

fer characteristics in the Denver basin (McConaghy
and others, 1964; Robson, 1983) and consist of grain-
size analyses and specific-retention determinations for
37 samples. Mean specific-retention values for sam-
ples from the upper three aquifers in the Denver basin
are listed in table 2. The mean specific retention based
on laboratory analyses of core is similar to the mean
specific retention that is based on the model for the
regression data set and for the verification data set.

In both data sets, the model slightly underesti-
mated the specific retention for the Dawson and Denver
aquifers and slightly overestimated the specific reten-
tion for the Arapahoe aquifer, which may be due to
factors other than grain size (such as diagenesis) that
can affect specific retention and might be more signifi-
cant in the older, more deeply buried Arapahoe aquifer.
Whatever the cause, the differences in specific reten-
tion are not large enough to warrant development of
separate regression equations for each aquifer.

The model was used on another data set to test
whether or not the method could be used to estimate
specific yield for unconsolidated materials. A verifica-
tion data set that is based on grain-size analyses and
specific-retention determinations from 12 samples of
unconsolidated alluvium (Johnson, 1967, p. 40-42)
was compared to model specific-retention values. The
mean laboratory specific retention of 0.16 compared
favorably with the mean model specific retention of
0.18. Although the data are few, they indicate that the
model could provide a means of estimating specific
retention for unconsolidated materials as well as the
poorly to moderately well-consolidated materials used
in the development of the model.

6 Techniques for Estimating Specific Yield and Specific Retention from Greln-51ze Data and Geophysical Logs from
Clastic Bedrock Aquifers