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

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terms in equation 5. Site -to -site variability accounts for about 53 percent (100 x 0.001399/ 0.002639) of the sum of the variance components, the date within site variability accounts for about 27 percent of the sum of the variance components, and the random error terms accounts for the remaining 20 percent. Table 4. Estimates of the variances of the site, date, and error random terms in discharge measurements Random terms Variance Site 0.001399 Date .000701 Error .000539 Sum 0.002639 The total variance of diffQ around the overall mean (that is, the variance of diffQ without a model) is 0.003037, which indicates that the fixed effects account for about 13 percent [equals 100 x (0.003037 — 0.002639) / 0.003037] of the vari- ance of diffQ. This is a relatively small part of the total variability, but the data set is large enough to result in the statistically significant differences listed in tables 1 through 3. Similarly, the site, date, and error variance components expressed as a percent of the total vari- ance are 46 percent, 23 percent, and 18 percent, respectively. Overall, the largest portion of the variance of diffQ is accounted for by site -to -site variability. The random error variance (0.000539 in table 4) measures the amount of variability among different portable flowmeter measurements applied on the same day at the same site. The error variance can be used to determine the range in expected differences between (logarithmically transformed) instantaneous discharge measured using two different portable flow - meters. The estimated variance of the difference will be 2 x 0.000539 because the variance of the difference between two independent random variables is the sum of their variances. This translates into a standard devi- ation of about 3.28 percent. When this measure of the random component of the difference is considered in conjunction with the systematic differences in table 2 for different portable flowmeter methods, an estimate of the total error can be determined. For example, if measurements are made using P and M portable flowmeters, the systematic bias (M —P) is 1.08 percent with a standard deviation of 3.28 percent. If normality is assumed, about 95 percent of the differences between the measurements taken with the two portable flowmeters will be between —5.48 percent and 7.64 percent. The small size of the random error variance component is indicated by the precision with which differences among portable flowmeters can be esti- mated in table 2. The standard errors for portable flow - meter differences range from 0.25 to 0.27 percent, which is considerably smaller than standard errors for make differences (0.88 percent) or type differences (0.82 percent). A strength of the design for this data collection was the application of multiple portable flowmeter methods at the same well on the same date during a short period of time. TEMPORAL VARIATIONS IN POWER CONVERSION COEFFICIENTS The use of PCC's to estimate ground -water pumpage from wells is most accurate when the rela- tion of well discharge to power consumption remains stable. However, over time, hydrologic and pump operating conditions may change, thus altering the PCC relation to well discharge and power consump- tion. As examples, depth to ground water may increase after an extended period of pumping or pump effi- ciency may decrease as the irrigation pump ages. Any well operation that results in significant variations in the PCC over time can result in errors when using the PCC approach to estimate ground -water pumpage. Short -Term Variations in Power Conversion Coefficients Multiple PCC measurements repeated at the well sites during 1997 and 1998 are used to indicate the temporal variability in PCC's during one and two irrigation seasons. The range in PCC's at 104 sites during 1998 is shown in figure 5A. The PCC's for most sites (86 percent) did not fluctuate more than 20 percent throughout the 1998 irrigation season; however, for unknown reasons, a wide range in PCC's occurred at about 14 percent of the network sites. At some wells, a lower than expected PCC measurement (site 5) or several lower than expected PCC measure- ments (site 27) resulted in the wide range in PCC's that were measured. The percent difference for the TEMPORAL VARIATIONS IN POWER CONVERSION COEFFICIENTS 19