The effects of the Penry Wellfield on well-water quality

Ohio Journal of Science, The, Dec, 2007 by Keith O. Mann

[Y.sub.[??]] = response

[[beta].sub.0] = Y intercept

incorporated two predictor variables (well depth and geography) with model parameters ([[beta].sub.1] and [[beta].sub.2]) and the error term ([[epsilon].sub.[??]],); and the second model

Y = [[beta].sub.0] [[beta].sub.1] (well depth) [[beta].sub.2](geography) [[beta].sub.3] [[epsilon].sub.[??]]

Equation 2

contained the interactingeffect, [[beta].sub.3] (well depth x geography), among the predictor variables.

The adjusted [R.sup.2] values of the multiple regression analyses for sampling round 1 data (Table 3) demonstrate that the data poorly fit the various regression models and that the majority of the regression models (nine of 14) explain less then 15% of the variation, with the best model responsible for only 27% of the measured variation. Such findings indicate that well depth and geography have insignificant controlling effects upon water chemistry within the study area. The results for the other sampling rounds (2, 3, and 4) of the Background Phase are very similar to, and in fact poorer than, the results for sampling round 1.

Pooling the data from the first four sampling rounds into a single Background-phase data set allowed the impact of time (sampling round), geography, and well depth to be tested over an extended period (July-December 2000). A similar statistical approach was used on these pooled-background data as was used for individual sampling rounds. Linear regression, including the variable time (sampling round), was applied to the data followed by several multiple-regression analyses using the following independent variables and groupings: geography and well depth; well depth and an interaction variable (geography x well depth); and finally geography, well depth, and time (sampling round). Table 3 shows the adjusted [R.sup.2] values for both linear and multiple regression models. These regression models perform no better than those models built solely on sampling round 1 data and in fact most of these models perform worse than those of sampling round 1. Note that the temporal variable accounts for less than 5% of the variation for six of the seven parameters measured and it explains only 19% of the variation for dissolved solids.

Pumping Phase

Only the results for the regression analyses of sampling-round 7 data (Table 4) are presented here, because it was the last sampling round of the Pumping Phase and so any effects caused by pumping would have a higher probability of being detected during this sampling round than sampling rounds 5 and 6, which, incidentally, had very similar results to those of sampling round 7. The same statistical approach used previously was also applied to sampling-round 7 data, with one important difference: instead of using the independent variable geography (west to east) a new independent variable, distance (measured radially outward from production well TW-5), was used. The statistical results for sampling round 7 are nearly equivalent to the regression results obtained from the Background-Phase data. The adjusted [R.sup.2] values of the linear-regression models do not exceed 0.25 (Table 4). Only alkalinity experiences a correlation greater than 0.20 and 11 of the remaining 13 adjusted Rivalues are less than 0.15. The multivariate-regression models perform similar to the previous sampling rounds with all adjusted [R.sup.2] values below 0.30. Taken as a whole, combining the data of sampling rounds 5-7 (Table 4) produces similar correlation patterns and the linear models function no better than the models based on sampling round 7 or the Background Phase, with only two of the water-quality parameters possessing adjusted [R.sup.2] values above 0.10, but below 0.21. Likewise, multivariate regression models of the pooled data (sampling rounds 5-7) behaved similarly to those performed solely on sampling round 7, with only five of 21 values rising above 0.20, yet below 0.31.