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

Home Browse Search

need detailed data on { PT(t) } , which are not available for any of the sites. Therefore, a simpler approach was used to obtain an idea of the short- and long -term vari- abilities in PCC. This approach uses the State - approved PCC's made from 1994 -97 together with the PCC's made in 1998 as part of this study. One poten- tial fallacy in this approach is the implicit assumption that the quality of the State - approved PCC's made from 1994 -97 is the same as the quality of the PCC's made during this study. If this assumption is accepted, then the temporal variability in PCC can be evaluated. If the PCC data are not of the same quality, then errors not associated with temporal variability could be attributed to the errors in temporal variability in the following analyses, resulting in an inflated estimate of the year -to -year variability. A nested variance- components analysis using random terms for site, year within site, and date within year and site, was performed using all the log - transformed PCC values, including the 1998 values and 106 State - approved PCC's from 1994-97. Once again, fixed effects (method, make, and type) were not included in the analysis. Such a nested model that has terms representing variability at different time scales is one way of modeling temporal correlation. The esti- mate of the variance for the year component was 0.02297, for the date - within -year component was 0.00254, and for the residual variance was 0.00077. The year component represents about a 15- percent standard deviation (obtained by taking the square root of the variance and multiplying by 100). This indicates that the year -to -year variability could be a major component of variability for this PCC data set; the year variance component is about nine times the vari- ance of date - within -year component. The PCC values used in this analysis contained uncertainty due to errors in instantaneous discharge as measured by the portable flowmeter as well as errors in instantaneous power meter reading (see eq. 14). This means that an estimate of the variance of U7 (error in instantaneous PCC) using this analysis is inflated somewhat. Based on the estimates given in the preceding paragraph, however, errors in discharge as measured by a portable flowmeter would not account for much of the year -to- year variability in the PCC (fig. 8B). To accurately quantify the temporal variability in the PCC, long- term time series PCC data are needed. Errors U, (TFM pumpage error) and U2 (electrical power meter error) represent errors in the long -term integrated values of discharge and power consumption, respectively. The first error (Ul) would result from a TFM that is malfunctioning and providing consistently biased readings, and the second error (U2) would result from a malfunctioning elec- trical meter. Although no data are available for evalu- ating the magnitude of these errors, one or both may be at least partly responsible for the extreme differ- ences in pumpage (diffP) seen in figure 9A. Compo- nent Ul (TFM pumpage error) would not be present when comparing PCC- estimated pumpage to true pumpage (eq. 15). Finally, errors U2 and U6 Jute- grated and instantaneous power meter error, may somewhat compensate for each other if the errors result from a malfunctioning power meter. ESTIMATION OF TOTAL NETWORK PUMPAGE The analysis presented earlier in the report, in the "Comparison of Ground -Water Pumpage Estimates" section, provided estimates of the mean or average differences between the log- transformed PCC- estimated total pumpage and TFM- measured total pumpage, diffP, at a well. However, it also is important to quantify the differences in the total or aggregated pumpage for a network of wells. Primary Results An analysis of the pumpage data was done to determine differences in the total or aggregated pumpage between the TFM and PCC approach for a network of wells. The difference in pumpage between the TFM and PCC approach varied with the volume of water pumped during the 1998 monitoring period. Some wells that recorded small pumpage exhibited larger percent differences than wells with larger pumpage. Because of these unequal differences with respect to total pumpage, it was necessary to group or stratify the data based on the magnitude of total pumpage for the 1998 monitoring period. Because the correct number of groupings, or strata, is not known with the information available, the mean and standard deviation of differences in the total pumpage was determined conditionally for several numbers of strata. For a network of 103 wells and a number of strata greater than 10, the resulting mean and standard devia- tion leads to a conclusion that, for any given year, ESTIMATION OF TOTAL NETWORK PUMPAGE 33