Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UF00052643/00001
## Material Information- Title:
- Statistical Analysis of the Impact of Ground Water Pumpage on Law-Flow Hydrology
- Alternate Title:
- Fetter, C. W. Jr. "Statistical Analysis of the Impact of Ground Water Pumpage on Law-Flow Hydrology. 13 Water Resources Bulletin, American Water Resources Association
- Creator:
- Fetter, C. W. Jr. (
*Author*) - Publication Date:
- April 1977
- Language:
- English
- Physical Description:
- 3p.
## Subjects- Subjects / Keywords:
- Groundwater ( jstor )
Rivers ( jstor ) Stream flow ( jstor ) - Spatial Coverage:
- North America -- United States of America -- Florida
## Notes- General Note:
- Box 5, Folder 11 ( SF MEAN ANNUAL FLOOD ), Item 7
- Funding:
- Digitized by the Legal Technology Institute in the Levin College of Law at the University of Florida.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- Levin College of Law, University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
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WATER RESOURCES BULLETIN VOL. 13. NO. 2 AMERICAN WATIR RLSOURCLS ASSOCIATION APRIL 1977 STATISTICAL ANALYSIS OF THE IMPACT OF "GROUND WATER PUMIPAGE ON LOW-FLOW HYDROLOGY' SC. '. Fetter, Jr. ABSTRACT Ground-water pumpage withdrew 57 cubic feet per second from aquifers beneath Sthe Vahara River Basin in 1970. Forty-si\ cubic feet per second were exported by the diversion of treated wastewater from the drainage basin. I he lo\ -flow hydrology of the upper Yahara River has been impacted by this diversion. . Prior to 1959, the \wastewater was discharged into the ri\er, au.menting the baseflow during losw-flow periods. As much as 85" of streamflow was due to eftfhent discharge. In 1959 the wastewater wa-, transferred from the river basin. Tlie result was a dec rease of about one-third in mean annuiil streanfltow. and a decrease of more than 50 in the 70 and 70,10. Repression anal\ sis show cd tlhe annual 7-day low-flow and 60-day h m-tlow have a statistically significant correlation with mean annual flow. Using predictions of future mean annual discharge of the . rixer with increasin.L interbasin transfers, it is shown that by 1 91 i there is a significant proba- bility that in some \ cars the (O6-day low-flow in the river \\ ill be /ero. .- ,.-. (KIV'Y T1 R1S: low-flow hydrology: repression analysis: low-tow predict ions.) INTRODUCTION The cil\ of Madison. Wisconsin. is situated on a series of lakes which are part of the S Yahara River system. Tlie streams, lakes and ground water form interdependent parts of a S regional hydiologic system, and changes induced in one part of the system may affect other system parameters. . Ground water is pumped from a number of deep wells in the drainage basin. In 1970 ; an average of 57 cutbic feet per second was withdrawn from the deep aquifers. Of this amountt. 11 cubic feet per second was used consumptively or seeped back into the ground. lea ing -4o cubic feet per second of pumped ground water passing to the waste- water tIeattument plant. As a part of a water-quality improvement program for the lower Mladison lakes, an effluentt-divecsio. scheme was impletnmented in D)ecember, 1958. Wastewater which had been discharged into tlhe uttpper Yahara Riser via Lake Waubesa was diverted to Badfish Creek. a tributary of the lower Yahara River. It is the purpose of this paper to evaluate 1Paper \o. o, i, h :-C'tr sor'\( r''.s H /kt'tui. Discussions are open until lDecemnber 1. 1t77. "- \-,osi;ate P'ros:,,, i' < ,;l.,-\ t:isersit \\ iscottsin .Ost kosti. O S(.kosh. \\'isconsin 54901.1 30{ 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 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^. ______ -- |