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

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flowmeter and TFM discharge measurements, and the date variance 6� is a measure of the deviation of TFM discharge from the average of the discharges for portable flowmeters at the same site on the same day. The error variance 62 is a measure of the internal consistency of discharge measurements by different portable flowmeters at the same site and same day. If the consistency of measurements among portable flowmeters at the same site on the same day indicates an accurate estimate of true discharge, the magnitudes of the variances 6S and 6C maybe interpreted as reflecting inaccuracy in the TFM discharge measure- ment value relative to the true value. The initial analysis of variance indicated a significant difference (at the 5- percent level) between all pairs of portable flowmeter methods, between makes M and S, and between types O and C. To assess appropriate pooling of the different makes, makes B and X were compared to make M and make S using an estimated difference divided by the standard error of the difference, revealing that the makes B and X data could be pooled with the make S data. This pooling resulted in two levels for the make factor: M and other (B, S, X). Similarly, it was determined that types L and S could be pooled with type C, resulting in two levels of type: O and other (C, L, S). The analysis was redone using the same mathematical model but with only two make levels, M and (B, S, X), and two type levels, O and (C, L, S). Diagnostic plots were examined following the analysis, including a plot of residuals versus fitted and normal quantile - quantile plots for the three random terms in the model. These plots indicated no serious violation of model assump- tions that would adversely affect final results. Final estimates of the means and the differences in means associated with the fixed effects are presented in tables 1 -3. [See Graybill (1976) for a discussion of important technical estimability issues associated with these estimates]. A standard error is given for each of the values in these tables, and values that are significantly different from zero (i.e., greater than 2 standard errors from zero) at the (approxi- mately) 5- percent level are noted. Final estimates of the grand mean (overall average difference of diffQ) and fixed effects are listed in table 1. The grand mean is 0.0000; the uncertainty in this number as measured by the standard error is 0.0045 or 0.45 percent. The mean difference for method C is about 1.1 percent, for method M is 0.0 percent, and for method P is about —1.1 percent. The positive sign on the mean for method C indicates that instantaneous discharge measured by portable flowmeters tends to be greater than instantaneous discharge measured by TFM's, and the opposite holds for method P. The mean differences for each method are very comparable to the differences measured during the quality - control checks done at the Great Plains Meter facility (see "Quality Control of Data" section). Table 1. Estimates of mean differences in instantaneous ground -water discharge between portable flowmeters and totalizing flowmeters for the grand mean and fixed effects of method, make, and type tNS, mean is not significantly different from zero at the 5- percent significance level; S, mean is significantly different from zero at the 5- percent significance level; the mean and the standard error can be expressed as a percent difference by multiplying the respective value by 1001 Mean differences Mean Standard error Significance at the 5- percent level Grand mean 0.0000 0.0045 NS Method of portable flowmeter (fixed) C .0109 .0047 S M .0000 .0048 NS P —.0108 .0047 S Make of totalizing flowmeter (fixed) M —.0152 .0047 S BSX .0152 .0075 S Type of discharge distribution system (fixed) O —.0130 .0054 S CLS .0131 .0067 NS COMPARISON OF INSTANTANEOUS GROUND -WATER DISCHARGE MEASUREMENTS 17