SStatistical Analysis of the Impact of Ground Water Pumpage on Low-Flow Hydrology 317
S all of the variation, there is a probability that actual values of Q7 will not be the
calculated values. Confidence intervals can be established for the regression line for differ-
K ent probability levels (Draper and Smith. 1967, p. 17-24). The 95% confidence band for
the regression was determined and plotted on Figure 4. For this problem we are especially
interested in the X-intercept of the regression line. This is the value of the mean-annual
"0 flow where the value of the seven-day low flow is calculated as zero. The regression
equation yields a value of 85.4 cubic feet per second for the X-intercept. The 95%
Confidence band indicates the Q7 low-flow at a Q365 of 85.4 would fall in the range of 0
S to 18 c.f.s.
Sixty-Da)y Low Flows.
A similar regression analysis was made for the sixty-day low flow for the period April 1,
_0 0 1959. through March 31. 1974. The regression equation is:
>a 60 .583 Q365 37.9
< The regression line is given on Figure 5. The regression is also statistically significant at
sevean-ay low o ul bes e period. n
the 0.01 level with an F value of 24.4 The value of R2 was .65" so that the regression
Accounts for 65.2 of the variation in the data. This is greater than the value for the
CJter pumpag -tdesewager dischares o; l '
\ wseven-day low flow, as would be expected since the sixty-day period represents a greater
portion of the year than a seven-day period. The value of the X-intercept is 65.2 c.f.s. The
95m% confidence limit for c 7 is 0 to 26 c.f.s. at a value of 65.2 c.f.s. for Q 365
FREQUENCY OF MEAN ANNUAL FLOW
0 In determining the mean annual flow there are several time periods which could be
Y utilized. They include the entire period of record, 1931-1974, the post-diversion period,
S1959-1974, and the pre-diversion period. 1931-1959. Since the regression analysis was
,. =,made for the post-diversion period it might be desirable to determine the frequency for
th mean annual flow for the same period.
S However, it has been shown through the double-mass curve that the post-diversion
data of mean annual flow are biased since water was diverted from the basin. It would
z seem desirable to avoid these data. and only analyze the pre-diversion data. 1931-1959.
"Mean annual flows during this period were probably not significantly affected by ground
water pumpage and sewage discharges.
It should be noted that by using the data from 1959-1974 for the regression analysis
0 and 1931-1959 for the frequency analysis, the results may not be totally compatible since
different hydrologic periods are involved. However, the low flows in the pre-diversion
"period were a'fectcd by low- low augmentation with effluent, and the mean-annual flows
S in the post-diversion period were affected by eftlient diversions from the basin.
The frequency of the mean-annual discharge for the Yahara River for the period April
1, 1931, through March 31, 1q59, was determined. During this period median-anntial
S streamfiow was 143 c.f.s. and the mean-annual streamflow was 149.6 c.f.s. with a stan-
dard deviation of 40.69, and a probable deviation of 26.35. If there is a normal distribu-
tion of strcainflow. the median should qoual the mean and one probable deviation on