USGS Colorado Water Science Center

Variability of Differences between Two Approaches for Determining Ground-Water Discharge and Pumpage, Including Effects of Time Trends, Lower Arkansas River Basin, Southeastern Colorado, 1998–2002

By Brent M. Troutman, Patrick Edelmann, and Russell G. Dash

USGS Scientific Investigations Report 2005-5063, 47 p., 14 figs.--ONLINE ONLY

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The citation for this report, in USGS format, is as follows:
Troutman, B.M., Edelmann, Patrick, and Dash, R.G., 2005, Variability of differences between two approaches for determining ground-water discharge and pumpage, including effects of time trends, lower Arkansas River Basin, Southeastern Colorado, 1998–2002: U.S. Geological Survey Scientific Investigations Report 2005-5063, 47 p.


In the mid-1990s, the Colorado Division of Water Resources (CDWR) adopted rules governing measurement of tributary ground-water pumpage for the Arkansas River Basin. The rules allowed ground-water 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 ground-water 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 ground-water pumpage using TFMs to computed ground-water 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 (1998-2002), 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 2-year forward lag and +5.3 percent for a 4-year forward lag, indicating that pumpage computed with the PCC approach, as generally applied under the ground-water 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 water-level changes) yielded a trend of about 2.2 percent per lag year for diffP. A separate analysis that incorporated a surface-water diversion term in the statistical model rendered the time-trend 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 surface-water 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 5-year period would hold in the future, historical static ground-water 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 95-percent 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 1998-2002 during which hydrologic conditions were known to have changed. Using the same assumptions, the estimated difference in total network pumpage for a 4-year 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 2-year lag would be between about 3.9 and 6.4 percent greater than pumpage measured using a TFM.


Executive Summary



Purpose and Scope

Description of Study Area and Hydrologic Setting


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 Year-to-Year Variability

Variability in Instantaneous Discharge

Variability of Power Consumption and Flow

Summary of Primary Results

Details of Analysis

Variability in Ground-Water Pumpage

Year-to-Year Variability of Pumpage

Fixed-Year Effects

Total Time Trend

Additional Explanatory Variables

Implications of Year-to-Year 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

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