Statistical Analysis of the Impact of Ground Water Pumpage on Low-1 low Hydrology 319
either side of the mean should include 50% of the streamflows (Leopold, 1969). For the
period of record of the Yahara River 13 of 28 values, or 47%, lie in this range. Likewise,
82% of the data should fall within two probable deviations of the mean, which is approxi-
-l mately the case for the period 193 1-1959 (actual value 79%).
The frequency distribution of the data plot as a straight line on probability paper
indicating the data are approximately normally distributed. This has been done on
o Figures 6 and 7. A linear-probability curve was established by the mean streamflow
(plotted at 50% probability), the streamflow one probable deviation greater than the
mean (plotted at 75% probability) and the streamflow one probable deviation less than
the mean (plotted at 25% probability).
c FUTURE LOW-FLOW PROBABILITIES
o Larger diversions of sewage effluent from. the upper Yahara drainage basin will lower
S. the mean-annual discharge. This will not be a one-to-one relationship as growing pumping
cones in the future will induce additional ground water inflow to the basin. McLeod
(1975b) using a two-layer digital ground water model calculated the diversion ot water
S, t -from the drainage basin of the upper Yahara River due to ground water going to con-
,4 1 sumptive uses and sewage diversions. These computed values are reproduced in Table 1.
| TABLE 1. Source of Ground Water Diverted to Wells in Madison Area
Year From paper Yahara River Basin From Adjacent River Basins
1970 52 c.f.s. 5 C.f.s.
S"| .15 c.f.s.
_4 4 I o o 5 2 8 C:f.S f> "^ \
< 1980 67 c.f.s. 8 C.f.s.
0 x9
| 1990 81 c.f.s. 12 c.f.s.
S0 < .
As the water is diverted from the river, it represents a reduction in annual discharge.
o \ These diversions will reduce the annual flow by the specified amount. ,
\\-.If'one assumes that the April 1931 to March 1959 frequency distribution is represent.-
SIm tive, and that diversions do not change the slope of the line, then a family of trequencV ,:
ci \r -c es for varying rates of diversion can be established. This was done on Fi,,ues 6 and 7
by lowering the linear-frequency curve by an amount equal to varying rates ot divet:ion.
Lines for 56. 67 and 81 c.f.s. diversions are given. .
SBy combining each of the regression curves with the family of tequency curves, n
^ assessment of the probability of future low flows may be made for both a seven-day and a
sixty-day period.
S ercn-ID .- /.(t- I .. k.. .
A heavy dashed line is drawn on Figure 5 at 85 c.f.s. mean-annual flow, which is t -,h,
X-intercept of the seven-day low flow regression line.
______ ^ ,,.r,.,....____X-^^ ^&W^. ______ --