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

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The approximate normality of the difference in network- aggregated pumpage D,, can be used with the mean and the standard deviation to make proba- bility statements about likely differences in total network pumpage obtained by TFM and PCC approach. Using a mean of —0.91 percent and a stan- dard deviation of 1.25 percent, for example, results in a conclusion that, for any given year, there is a 95- percent probability that the difference in aggre- gated pumpage between the TFM and PCC approach would be between about —3.41 and 1.59 percent for a network of 103 wells. To predict the difference in aggregated pumpage for a larger network, the distribution of total TFM pumpage (the values of Vi) will be assumed to be the same, the estimate of the mean remains the same ( -0.91 percent), but the standard deviation decreases in proportion to the square root of the ratio of numbers of wells. For n =1,000 wells, the 1.25 percent standard deviation for 103 wells decreases by a factor of f 103 resulting in an estimated standard deviation of TO _00 0.40 percent. Therefore, for a network of 1,000 wells, there is a 95- percent probability that the difference in aggregated pumpage between the TFM and the PCC approach for any given year would be between —1.71 and —0.11 percent. CONCLUSIONS This report compares two approaches for determining instantaneous ground -water discharge and pumpage. The data collected and analyzed as part of this study included (1) logarithmically trans- formed differences of well discharge computed from 747 paired discharge measurements made at 105 wells during 1997 and 1998; (2) power conversion coeffi- cients ( PCC's) derived for 104 wells during 1997 and 1998; (3) ranked, logarithmically transformed differences of pumpage computed from 553 paired pumpage comparisons made at 103 wells during 1998, and (4) State - approved PCC's that were made from 1994 -97. Given the data analysis presented in this report, the main conclusions are: 1. More than 80 percent of the differences in well discharge were less than 10 percent. The overall mean difference in well discharge for all sites was 0.0 percent, indicating no difference on average between TFM's and portable flow - meter instantaneous discharge measurements. For varying site characteristics, mean differences in well discharge range from a —4 percent to 4 percent. 2. Variations in PLC's measured during the 1998 irri- gation season indicated that 58 percent of the wells had less than 10- percent change, and 86 percent of the wells had less than 20- percent change. Systematic seasonal variations in PCC's generally were not evident for the measurements made during the 1998 irrigation season. 3. Ninety percent of the sites had at least one PCC measured during 1997 that was less than the range of PLC's measured in 1998, indicating the range in PLC's measured at majority of sites between 1997 and 1998 were similar. 4. About 48 percent of the State - approved PCC's made between 1994 through 1997 were within 10 percent of the 1998 site average PCC's and about 67 percent of the State - approved PCC measurements made between 1994 through 1997 were within 20 percent of the 1998 site average PCC's. 5. About 80 percent of the differences in pumpage between the TFM and PCC approaches were less than 10 percent. The overall mean difference in pumpage was 0.01 percent, indicating no signifi- cant difference on average between pumpage as measured by TFM's and pumpage as computed by the PCC approach. For varying site character- istics, mean differences in pumpage were gener- ally less than ±3 percent and, for most instances, the mean differences in pumpage were not signif- icantly different from zero at the 5- percent signif- icance level. 6. There are several potential sources of discrepancy between pumpage as measured by a TFM and pumpage as computed by the PCC approach. With data currently available, it is not possible to give reliable estimates of the magnitude of each of the potential sources of pumpage error. However, using available data, an estimate of errors caused by temporal variability of PCC's can be made. The year -to -year variance was about nine times the date - within -year variance, indicating that year -to -year variability of the PCC's may make a significant contribution to error in the PCC approach for estimating pumpage. This conclusion is based on an assumption that the State - approved PCC's from 1994 -97 are of the same quality as the 1998 PLC's. 38 Comparison of Two Approaches for Determining Ground -Water Discharge and Pumpage in the Lower Arkansas River Basin, Colorado, 1997 -98