Comparison of Two Approaces for Determining Ground-Water Discharge and Pumpage in the Lower Arkansas River Basin Colorado 1997-98

• Description: Comparison of Two Approaces for Determining Ground-Water Discharge and Pumpage in the Lower Arkansas River Basin Colorado 1997-98
• State: CO
• Basin: Arkansas
• Author: Dash, Russell; Troutman, Brent; Edelmann, Patrick
• Title: Comparison of Two Approaces for Determining Ground-Water Discharge and Pumpage in the Lower Arkansas River Basin Colorado 1997-98
• Water Supply Pro - Doc Type: Report/Study

and whether the overall mean difference is signifi-
cantly different from zero; (3) an estimate of the mean
differences for each combination of portable flow
meter, make of TFM, and discharge distribution type,
and whether these mean differences are significantly
different from zero; and (4) how much of the variation
in the differences is attributable to the site -to -site, date,
and random error components. The comparison of
ground -water discharge measurements was based on
747 paired measurements taken at 105 wells during a
2 -year period.
Primary Results
Analysis of variance was used to evaluate loga-
rithmically transformed differences between instanta-
neous discharge measured with portable flowmeters
and instantaneous discharge measured with a TFM.
The analysis was applied to 747 paired discharge
measurements made at 105 wells during the 2 -year
period. More than 80 percent of the differences were
less than 10 percent. The overall mean difference was
0.0 percent, indicating no difference on average
between portable flowmeter and TFM discharge
measurements. For varying site characteristics (the
method of portable flowmeter, the make of TFM,
and type of discharge distribution system), mean
differences range from —4 percent to 4 percent.
Details of Analysis and Results
For each paired discharge measurement, the
difference in well discharge (diffQ) was computed as
diffQ = log (Q)— log (Q), (3)
where Q denotes an instantaneous discharge measure-
ment made using a portable flowmeter at a particular
site on a particular date, and Q denotes a corre-
sponding (paired) instantaneous discharge measure-
ment made using a TFM at the same site on the same
day. (All logarithms in this report are base e.)
The relation between diffQ and Q is shown in
figure 2A, and the relation between differences in the
untransformed discharge, Q — Q , and Q is shown in
figure 2B. There is a marked tendency in figure 2B for
variability in differences to increase as Q increases.
That is, although untransformed differences generally
tend to be centered around an average value of zero,
the variance of untransformed differences tends to
increase with the magnitude of the discharge. In
contrast, the differences in log - transformed discharges
have variance that is much more nearly constant
for the entire range of well discharge values
(fig. 2A).
As mentioned earlier in the report, the natural
logarithmic transformation of the discharges allows
diffQ to be interpreted as a relative or fractional differ-
ence between discharges, and for small differences
between Q and Q,
diffQ — Q_QYQ —Q • (4)
Q Q
Thus, diffQ multiplied by 100 may be interpreted as a
percent difference.
Each measurement of Q and Q is made under
certain conditions; changes in these conditions may
cause the distribution (that is the mean and variance)
of diffQ to change in a systematic way. Each discharge
measurement Q is made with a particular type of
flowmeter. There are three portable flowmeters used,
resulting in three "levels" associated with this factor.
Likewise, the TFM's made by different manufacturers
may affect the distribution of diffQ. Finally, each pair
of measurements is made on a particular type of
discharge distribution system, so any systematic effect
of this factor also may be important. Therefore, the
effects associated with these three factors: portable
flowmeter method, make of the TFM, and type of
discharge distribution system were included in the
analysis of variance. (These three factors will herein-
after be referred to as simply method, make, and type.)
In addition to method, make, and type, there are
two other conditions that can affect diffQ; these are
site and date. For example, it is important to know
whether diffQ at a certain site tends to be consistently
larger or smaller than values at other sites. Similarly,
there may a tendency for diffQ to be larger or smaller
on certain dates at a given site. In analysis of variance,
effects may be treated as either random or fixed. The
site and date effects are treated as random, whereas the
method, make, and type effects are treated as fixed,
12 Comparison of Two Approaches for Determining Ground -Water Discharge and Pumpage in the
Lower Arkansas River Basin, Colorado, 1997 -98