Variability of Differences between Two Approaches for Determining GroundWater Discharge and Pumpage, Including Effects of Time Trends, Lower Arkansas River Basin, Southeastern Colorado, 1998–2002By Brent M. Troutman, Patrick Edelmann, and Russell G. DashUSGS Scientific Investigations Report 20055063, 47 p., 14 figs.ONLINE ONLY This document is available in pdf format: The citation for this report, in USGS format, is as follows:
AbstractIn the mid1990s, the Colorado Division of Water Resources (CDWR) adopted rules governing measurement of tributary groundwater pumpage for the Arkansas River Basin. The rules allowed groundwater pumpage to be determined using one of two approaches—power conversion coefficient (PCC) or totalizing flowmeters (TFM). In addition, the rules allowed a PCC to be applied to the electrical power usage up to 4 years in the future to estimate groundwater pumpage. As a result of concerns about potential errors in applying the PCC approach forward in time, a study was done by the U.S. Geological Survey, in cooperation with CDWR and Colorado Water Conservation Board, to evaluate the variability in differences in pumpage between the two approaches, including the effects of time trends. This report compared measured groundwater pumpage using TFMs to computed groundwater pumpage using PCCs by developing statistical models of relations between explanatory variables, such as site, time, and pumping water level, and dependent variables, which are based on discharge, PCC, and pumpage. When differences in pumpage (diffP) were computed using PCC measurements and power consumption for the same year (19982002), the median diffP, depending on the year, ranged from +0.1 to 2.9 percent; the median diffP for the entire period was 1.5 percent. However, when diffP was computed using PCC measurements applied to the next year's power consumption, the median diffP was 0.3 percent; and when PCC measurements were applied 2, 3, or 4 years into the future, median diffPs were +1.8 percent for a 2year forward lag and +5.3 percent for a 4year forward lag, indicating that pumpage computed with the PCC approach, as generally applied under the groundwater pumpage measurement rules by CDWR, tended to overestimate pumpage as compared to pumpage using TFMs when PCC measurement was applied to future years of measured power consumption. Analyses were done to better understand the causes of the time trend; an estimate of the overall trend with time (uncorrected for pumping waterlevel changes) yielded a trend of about 2.2 percent per lag year for diffP. A separate analysis that incorporated a surfacewater diversion term in the statistical model rendered the timetrend term insignificant, indicating that the time trend in the models served as a surrogate for other variables, some of which reflect underlying hydrologic conditions. A more precise explanation of the potential causes of the time trend was not obtained with the available data. However, the model results with the surfacewater diversion term indicate that much of the trend of 2.2 percent per lag year in diffP resulted from applying a PCC to estimate pumpage under hydrologic conditions different from those under which the PCC was measured. Although there is no evidence to conclude that the upward time trend determined in the data for this 5year period would hold in the future, historical static groundwater levels in the study area generally have exhibited small variations over multidecadal time scales. Therefore, the approximately 2 percent per lag year trend determined in these data is expected to be a reasonable guideline for estimating potential errors in the PCC approach resulting from temporally varying hydrologic conditions between time of PCC measurement and pumpage estimation. Comparisons also were made between total, or aggregated, pumpage for a network of wells as computed by the PCC approach and the TFM approach. For 100 wells and a lag of 4 years between PCC measurement and pumpage estimation, there was a 95percent probability that the difference between total network pumpage measured by the PCC approach and that measured using a TFM would be between 5.2 and 14.4 percent. These estimates were based on a bias of 2.2 percent per lag year estimated for the period 19982002 during which hydrologic conditions were known to have changed. Using the same assumptions, the estimated difference in total network pumpage for a 4year lag for 1,000 wells would be between about 8.4 and 11.3 percent greater than pumpage measured using a TFM; the estimated difference in total network pumpage for a 2year lag would be between about 3.9 and 6.4 percent greater than pumpage measured using a TFM. ContentsExecutive Summary Abstract Introduction Purpose and Scope Description of Study Area and Hydrologic Setting Acknowledgments Methods of Investigation Methods of Statistical Analysis Dependent Variables Explanatory Variables Statistical Models for Discharge and Power Conversion Coefficients Statistical Models for Pumpage Differences Estimation of YeartoYear Variability Variability in Instantaneous Discharge Variability of Power Consumption and Flow Summary of Primary Results Details of Analysis Variability in GroundWater Pumpage YeartoYear Variability of Pumpage FixedYear Effects Total Time Trend Additional Explanatory Variables Implications of YeartoYear Variability for the PCC Approach to Pumpage Estimation Estimation of Total Network Pumpage Primary Results for Total Network Pumpage Details of Analysis and Results Summary and Conclusions Selected References Supplemental Information Evaluation of Outliers Estimates of Variance Components for Differences in Discharge 
