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

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the

COLORADO DIVISION OF WATER RESOURCES and the

COLORADO WATER CONSERVATION BOARD

Scientific Investigations Report 2005–5063
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

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Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.
Contents iii

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Description of Study Area and Hydrologic Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Methods of Investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Methods of Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Dependent Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Explanatory Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Statistical Models for Discharge and Power Conversion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Statistical Models for Pumpage Differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Estimation of Year-to-Year Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Variability in Instantaneous Discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Variability of Power Consumption and Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Summary of Primary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Details of Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Variability in Ground-Water Pumpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Year-to-Year Variability of Pumpage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Fixed-Year Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Total Time Trend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Additional Explanatory Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Implications of Year-to-Year Variability for the PCC Approach to Pumpage Estimation . . . . . . . . . . . . . . . . . 34

Estimation of Total Network Pumpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Primary Results for Total Network Pumpage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Details of Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Selected References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Evaluation of Outliers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Estimates of Variance Components for Differences in Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figures

1. Map showing location of study area and irrigation wells used in the study during 

years (A) 1998, (B) 1999, (C) 2000, (D) 2001, and (E) 2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

2. Graph showing percent differences in static water level in relation to depth of well, 

1998–2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

3. Boxplots showing variations in pumping water levels for network wells by year, 1998–2002 . . . . . . . .9

4. Graphs showing (A) relation of diffQ to totalizing flowmeter instantaneous discharge, 

and (B) relation of diffP to totalizing flowmeter pumpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5. Boxplots showing diffQ (A) for the entire network, and (B) by portable flowmeter method, 

and (C) by year, 1998–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6. Graphs showing variations in diffQ (A) by year at network sites,and (B) by year with respect 

to pumping water levels, 1998–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

7. Histogram showing types of problems and failures for totalizing flowmeters, 1998–2002 . . . . . . . . . . 23

8. Boxplots showing variations in diffC and diffL (A) by various discharge distribution types, 

and (B) by year for each type of discharge distribution system, 1998–2002 . . . . . . . . . . . . . . . . . . . . . . . . 25

9. Histogram showing distribution of time-trend coefficients (slope) for diffC, 1998–2002. . . . . . . . . . . . . 27
iv 

10. Graphs showing relation between power conversion coefficients and pumping 

water levels for various discharge distribution systems, 1998–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

11–12. Boxplots showing:

11. Variability of diffP when power conversion coefficient measurements and 

power consumption were made in the same year (A) for the entire network, 

(B) by year, (C) by type of discharge distribution system, and (D) by portable 

flowmeter method, 1998–2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

12. Variability of diffP for the number of years lagged between when the power 

conversion coefficient measurement was made and when total power consumption

 was used to estimate pumpage, 1998–2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

13–14. Graphs showing:

13. Average year effects on diffP for the number of years lagged between when 

the power conversion coefficient measurement was made and when total 

power consumption was used to estimate pumpage, 1998–2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

14. Estimation of differences in total pumpage for varying number of wells . . . . . . . . . . . . . . . . . . . . . . . 38

Tables

1. Explanatory variables for statistical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2. Estimates of intercept and method fixed effects parameters for the diffQ model. . . . . . . . . . . . . . . . . . . . 20

3. Estimates of the mean and variance for random variables in the diffQ model of 

ground-water discharge differences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4. Estimates of the intercept and method and type fixed effects parameters in the diffC and 

diffL models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5. Estimates of mean and variance for random variables in the diffC and diffL models . . . . . . . . . . . . . . . . . 26

6. Estimates of parameters in the diffP model of differences in ground-water pumpage 

between the power conversion approach and totalizing flowmeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7. Estimates of the mean and variance for random variables in ground-water pumpage 

using the diffP model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

8. Estimates for year effect in the diffQ, diffC, and diffL models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

9. Estimates for year effect in the diffP models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Supplemental Information tables

10. Outlier data that were removed in models diffC and diffL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

11. Data used in the diffQ model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

12. Data used in the diffC model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

13. Data used in the diffL model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

14. Data used in the diffP model where PCC measurements and power consumption were

 made in the same year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

15. Data used in the diffP model where PCC measurements and pumpage estimates were 

made in different years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133
 v

Conversion Factors, Abbreviations, and Acronyms

The following terms, abbreviations, and acronyms are used in this report:

Colorado Division of Water Resources (CDWR)

Colorado Water Conservation Board (CWCB)

Interquartile range (IQR)

Power conversion coefficient (PCC)

Pumping water level (PWL) is the measurement of the depth to water in the well below the 

centerline of the discharge pipe, while the well is pumping, but after the water level had 

stabilized.

Southeastern Colorado Water Conservancy District (SECWCD)

Total dynamic head (TDH)

Totalizing flowmeter (TFM)

Ultrasonic thickness gage (UTG)

U.S. Geological Survey (USGS)

Method of portable flowmeter:

C (Collins flowmeter)

M (McCrometer flowmeter)

P (Polysonic flowmeter)

Make of inline totalizing flowmeter:

M (new McCrometer TFM)

 S (new Signet TFM)

 X (existing McCrometer TFM)

 B (existing Badger TFM)

Type of discharge distribution system:

L (low-pressure)

O (open)

S (sprinkler)

C (complex)

CH (complex high)

CL (complex low)

Multiply By To obtain

acre-foot (acre-ft) 1,233 cubic meter 

foot (ft) 0.3048 meter 

gallon per minute (gal/min) 0.06309 liter per second 

inch 2.54 centimeter 

kilowatthour (kWh) 3,600,000 joule 

kilowatthour per acre-foot 2,919 joule per cubic meter
vi 

Statistical models used for data analysis:

diffQ is log portable flowmeter discharge minus log totalizing flowmeter discharge

diffC is log PCC

diffL is log total power consumption for season minus log totalizing flowmeter pumpage for 

the same season

diffP is log total pumpage using PCC minus log total pumpage using totalizing flowmeter

Note: Log is the natural logarithm (base e).

Variables used in statistical models:

 is the intercept term

 is the effect (fixed) for the portable flowmeter method

 is the effect (fixed) for distribution system type

 is the effect (random) for site

 is the effect (random) for an instantaneous flow or PCC measurement year 

 is the effect (random) for a year within site

Z is the year effect (random) for a year in which total power consumption was 

used to estimate pumpage

 is the effect (random) for date

 is measurement time (in fractional years, t=0 for Jan. 1, 1998 and t=0.5 for 

June 30, 1998)

 is the time-trend coefficient (random)

 s is time when power consumption at the well was used to estimate pumpage (in years, s=

0 for 1998)

 is log of pumping water level at time of measurement (PWL)

 is average log PWL for a given site in a given year

 is average log PWL for a given site

 is the PWL trend coefficient

u is the diffP lag time, defined as a difference between (s – t)

 is the random error term

E is the expected value (mean)

Var is the variance.

(Note: the subscripts Q, C, and L associated with these variables in the text refer to the 

specific model—diffQ, diffC, or diffL.)

μ

α

γ

S

Y

(SY)

D

t

A

w

w

w

U

e
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 

Executive Summary

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 the CDWR and 

Colorado Water Conservation Board, to evaluate the variability 

in differences in pumpage between the two approaches, including the effects of time trends.

During the study period (1998–2002), hydrologic conditions varied substantially as streamflow in the Arkansas River 

ranged from 928,500 acre-feet in 1999 to 205,780 acre-feet in 

2002. Less streamflow decreased the amount of surface water 

diverted to agricultural lands; cumulative diversions in 2001 

and 2002 were substantially less than diversions in 1998, 1999, 

and 2000. In general, depth to ground water increased as annual 

surface-water diversions decreased, and the depth of pumping 

water levels measured in 2001 and 2002 increased relative to 

depths of pumping water levels measured in 1998, 1999, and 

2000. 

Historically, changes in ground-water levels for wells in 

the Arkansas River alluvial aquifer from 1965 to 2001 have 

tended to be gradual. The gradual and relatively small changes 

in ground-water levels occurred even during periods of large 

variations in magnitude and timing of streamflow. Significant 

operational changes, such as construction and operation of 

Pueblo Reservoir, implementation of the Winter Water Storage 

Program, the 1980 operating plan for John Martin Reservoir, 

and implementation of the ground-water measurement rules, 

historically have had relatively small effects on ground-water 

levels. From 1965 to 2001, the mean annual streamflow ranged 

from less than 362,000 acre-feet at Arkansas River at Avondale 

during the 1977 drought to greater than 1,000,000 acre-feet 

during 1983. These data indicate that static ground-water 

levels in the study area tend to exhibit small variations over 

multidecadal time scales with a high degree of temporal correlation, and trends that appear approximately linear over shorter 

periods of time, such as 5-year periods, are not uncommon in 

such slowly varying time series even under highly varying 

hydrologic conditions.

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. Specifically, for the purposes of this report, four 

dependent variables—diffP, diffC, diffL, and diffQ—were analyzed: diffP was defined as the natural log of total pumpage for 

a season using PCC minus the natural log of total pumpage for 

that season using TFM; diffC was defined as the natural log of 

the power conversion coefficient (PCC); diffL was defined as 

the natural log of total season power consumption minus the 

natural log TFM pumpage for the same season; and diffQ was 

defined as the natural log of portable flowmeter discharge 

minus the natural log of TFM discharge. Because of a property 

of logarithmic transforms, the variable diffP multiplied by 100 

can be interpreted as a percent difference between pumpage 

estimated for a given season by the PCC and TFM approaches, 

and diffQ multiplied by 100 is a percent difference between portable and TFM instantaneous discharge. The variables diffC and 

diffL measure the relation between flow volume and power consumption; the difference between diffC and diffL is one of time 

scale: diffC is obtained using instantaneous values of power 

consumption and flow, whereas diffL is obtained using seasonally integrated values of power consumption and flow. 

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. Most years showed a slight negative 

bias, indicating that pumpage computed with the PCC approach 

tended to be less than pumpage using TFMs when PCC measurements and power consumption for the same year were used. 

However, when diffP was computed using PCC measurements 

applied to the next year’s power consumption, the median diffP
2 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

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, +4.9 percent for a 3-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. The best statistical estimate of 

the mean of the time trend indicated that there was about a 

1.6-percent increase in diffP for each year increase in the lag 

time. For example, if a PCC measurement was made in one year 

and this PCC value was used to estimate pumpage two years 

after the PCC measurement was made, then diffP on the average 

would tend to be 3.2 percent more than if pumpage had been 

estimated in the same year the PCC measurement was made.

Because of the importance in quantifying the temporal 

variability, other independent analyses of year-to-year changes 

in the dependent variables were performed for the 5-year period 

of study. The analyses of diffC and diffL indicated that the relation between flow and power consumption was similar for short 

time scales (diffC) and yearly time scales (diffL). Generally a 

monotonically increasing trend with time occurred over the 

5-year period for both models, and the average increase per year 

was close to the mean slopes of 1.5 and 1.7 percent for diffC and 

diffL, respectively. Individual year effects obtained by analyzing diffP data were similar to those indicated by the diffC and 

diffL data. As with the other time-trend analyses, there was 

about a 1.6 percent per year increase in diffP per year of lag 

between the time the PCC measurement was made and the year 

pumpage was estimated. 

Additional analyses were performed in order to better 

understand the causes of the time trend. The time trend of 

1.6 percent per year in diffP was obtained using a statistical 

model that included a pumping water-level (PWL) term as one 

of the explanatory variables, thus statistically correcting for 

changing PWL. Because PWL also tended to increase with time 

over this period, an estimate of the overall trend with time 

(uncorrected for PWL changes) was made by fitting a model 

without a PWL term, yielding a trend of about 2.2 percent per 

lag year for diffP. A separate analysis also was done incorporating a surface-water diversion term in the statistical model; this 

analysis rendered the time-trend term insignificant. This result 

indicates that the time trend in the models serves 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 results from applying a PCC to estimate pumpage under 

hydrologic conditions different from those under which the 

PCC was measured. There is no evidence to conclude that the 

increasing time trend determined in the data for this 5-year 

period would hold in the future, and it is feasible that future 

periods could exhibit downward trends or nonmonotonic variability. 

Although detailed long-term analyses have not been 

performed for this report, historical static ground-water levels 

in the study area generally have exhibited small variations over 

multidecadal time scales with a high degree of temporal correlation, and monotonic trends that appear approximately linear 

over a 5-year period such as the one detected in this study are 

not uncommon in such slowly varying time series. 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. Periodic PCC data are 

needed to determine actual future changes that may occur in 

diffC. A subset of this network could be used to quantify future 

changes in diffP that may occur.

Statistical modeling was used to evaluate the effect of 

changes in pumping water level on diffC, diffL, and diffP.

Modeling of diffC indicated that PCCs tend to increase with 

pumping water level by about 1.3 percent per 10-percent 

increase in pumping water level, and dependence of diffL on 

pumping water level was similar to that for diffC. Likewise, 

modeling of diffP indicated that increasing the depth to water 

under which pumpage was estimated relative to the pumping 

water-level conditions under which the PCC was measured 

caused an increase in diffP, that is, an increase in pumpage estimated by the PCC approach relative to that measured by a TFM. 

Each 10-percent increase of pumping water level for the year in 

which pumpage was estimated relative to pumping water level 

when the PCC was measured caused a 1.0-percent increase in 

pumpage as estimated by the PCC approach. The average time 

trends and average pumping water level effects for the various 

statistical models are summarized in the table on page 3.

Under the ground-water pumpage measurement rules, 

CDWR allows the PCC approach to be used to estimate groundwater pumpage for complex sites provided PCCs are measured 

using the site’s lowest total dynamic head. An analysis was 

done to evaluate the discharge distribution-system type effects 

on diffP and to quantify the differences in pumpage at complex 

sites depending on whether PCC measurements were made 

under low total dynamic head (CL) or high total dynamic head 

(CH) conditions. The CL effect indicated that pumpage estimated by the PCC method was 6 to 7 percent greater than that 

measured by a TFM for complex sites using a low total dynamic 

head PCC. Conversely, the CH effect indicated that pumpage 

estimated by the PCC method was 6 to 7 percent less than that 

measured by a TFM for complex sites if the PCC was computed 

under high total dynamic head conditions. 

Comparisons also were made between total, or aggregated, 

pumpage for a network of wells as computed by the PCC 

approach and the TFM approach. Estimates of the mean and 

standard deviation of the difference in total network pumpage 

were determined using the two approaches as a function of 

number of sites in the network and of lag time between PCC 
Abstract 3

100 wells and a lag of 4 years between PCC measurement and 

pumpage estimation, the mean difference was 9.8 percent of 

total network pumpage and the standard deviation was 

2.3 percent of total network pumpage. Under the assumption of 

normality, 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 3-year lag would be between about 6.1 and 

8.8 percent greater than pumpage measured using a TFM; and 

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.

Discharge measured with a TFM was compared with discharge measured by portable flowmeter using the dependent 

variable diffQ. The overall mean of diffQ using all three portable flowmeter methods was –0.015, or about 1.5 percent less 

than TFM measurements. Three types of portable flowmeter 

were used: a pitot tube/manometer device (method C), an ultrasonic flowmeter (method P), and a propeller-type meter 

(method M). Statistical modeling of diffQ revealed that there 

were significant differences among portable flowmeter 

methods. Portable flowmeter method P tended to be about 

1.9 percent below average of all three methods, meaning that 

flowmeter method P tended to measure a smaller discharge than 

the TFM as compared to other portable sampling methods. 

Discharge measured using method C was about 1.7 percent 

above average as compared to other portable sampling methods, 

and method M was about average. The median diffQ value for 

methods C, M, and P was 0.5 percent, –0.6 percent, and –4 percent, respectively. Overall, portable flowmeter discharge measurements made with method C provided the smallest differences in diffQ. Portable flowmeter discharge measurements 

made with method P provided the largest differences in diffQ 

and indicated a fairly strong negative bias, or a tendency to 

underestimate discharge with respect to TFMs.

The variable diffQ indicated no observable persistent temporal trends when all sites were combined; however, individual 

sites often exhibited upward or downward temporal trends that 

were modeled with random time slopes. Pumping water level

accounted for only a negligible amount of the variance of diffQ, 

indicating that pumping water level had very little influence on 

differences in discharge. Overall, the quality of discharge measurements associated with TFMs did not degrade over time 

(1998–2002); however, problems did occur with some TFMs. 

CDWR staff documented 27 problems with TFMs during 

1998–2002. Equipment problems, including debris clogs and 

reasons unknown, occasionally resulted in loss of TFM data. 

Debris clogs in the meter components generally were observed 

early in the irrigation season during startup operations.

Abstract

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.

measurement and pumpage estimation. As an example, for 

[PWL, pumping water level; s, year when pumpage is estimated; [t], year when PCC is made;%, percent; log, natural logarithm; NA, not applicable; NS, mean 

is not significantly different from zero at the 5-percent significance level] 

Statistical model Average time 

trend effect Average PWL effect Remarks

diffP (where s not equal to [t], 

PWL is included in model)

1.6 % per lag year 1.0% per 10% PWL change Differences between log of PCC pumpage and 

log of TFM pumpage.

diffP (where PWL is excluded 

from model)

2.2% per lag year NA Overall time trend. Determined without PWL

in the model.

diffC (where PWL is included in 

model)

1.5% per year 1.3% per 10% PWL change Log of the power conversion coefficient 

(PCC). 

diffL (where PWL is included in 

model)

1.7% per year 0.92% per 10% PWL change Differences between log of seasonally 

integrated power consumption and log of 

TFM pumpage for the same season. 

diffQ (where PWL is included in 

model)

NS NS Differences between log of portable flowmeter 

discharge and log of TFM discharge. 
4 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

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.

Introduction

Ground-water pumpage is needed for many hydrologic 

and water-management studies. Two approaches used to estimate ground-water pumpage include (1) metered discharge, and 

(2) a power conversion coefficient (PCC) approach. The 

metered discharge approach uses a totalizing flowmeter (TFM) 

to directly measure instantaneous discharge and cumulates the 

volume of water pumped at a well. The PCC approach uses 

measurements of instantaneous well discharge and electrical 

power consumption at the well to compute the volume of water 

pumped. Electrical power consumption is related directly to the 

amount of pumped water, pump efficiency, pressure head, and 

the total lift of water. Total lift is the sum of static water level, 

drawdown, and discharge pressure head. 

In Colorado, ground water that is part of the stream-aquifer 

system is classified as tributary water. In general, streams in the 

Arkansas River Basin are in hydraulic connection with aquifers. 

Withdrawals of ground water are administered within the priority system by Colorado Division of Water Resources (CDWR) 

to minimize the effect of junior wells on senior surface-water 

rights. Substantial ground-water development in the lower 

Arkansas River Basin between Pueblo and the ColoradoKansas State line began in the 1950s (Major and others, 1970), 

and by 1980 more than 2,900 irrigation wells tapped the unconfined valley-fill aquifer of the Arkansas River. In 1995, the U.S. 

Supreme Court found that pumping wells in the Arkansas River 

Basin had affected the flow of usable water to the State line and 

required that out-of-priority depletions by pumping wells be 

replaced by augmentation plans.

Beginning in 1994, the CDWR adopted measurement rules 

and regulations (Office of the State Engineer, 1994 and 1996) 

that required well owners in the Arkansas River Basin in Colorado to report how much ground water was pumped monthly by 

each well that discharged greater than 50 gal/min. The rules 

allowed for two approaches to be used: (1) a well owner could 

install a TFM on the well; or (2) if the well was electric powered, have the well tested to determine a PCC that would relate 

the number of kilowatt hours used to pump an acre-ft of ground 

water. The rules specified that the TFM or PCC rating must be 

checked at least once every 4 years by a person approved by the 

State Engineer. Thus, 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. Additionally, the rules allowed the 

PCC approach to be used to estimate ground-water pumpage for 

complex sites provided PCCs were measured using the site’s 

lowest total dynamic head, which, theoretically, would result in 

an overestimate of actual ground-water pumpage. The use of 

PCCs to estimate ground-water pumpage from wells is most 
Introduction 5

accurate when the relation of well discharge to power demand 

remains stable. Over time, hydrologic and pump operating conditions may change, thus altering the relation between discharge 

and power demand. Depth to ground water may increase during 

a drought or after an extended period of pumping, or the pump 

efficiency may decrease as the irrigation system ages. These 

well operations can result in variations in the PCC over time and 

can result in errors when using the PCC approach to estimate 

ground-water pumpage. The effect of varying pumping lift and 

temporal variability of PCCs on the accuracy of ground-water 

pumpage is not well known. There also have been concerns 

about the long-term reliability of TFMs. Specifically, there 

have been concerns about the accuracy of the inline flowmeters 

as a result of excessive wear or malfunctions during operation. 

In 1999, the U.S. Geological Survey (USGS), in cooperation with the CDWR, completed a study that compared these 

two approaches for determining ground-water discharge and 

pumpage (Dash and others, 1999). Ground-water discharge is 

the instantaneous flow being discharged from the well in gallons per minute, and ground-water pumpage is the total volume 

of water pumped from the well in acre-feet. This study used data 

collected from 105 randomly selected irrigation wells completed in the alluvial aquifer of the Arkansas River Basin 

between Pueblo, Colorado, and the Colorado-Kansas State line 

(fig. 1). This study was based largely on 1 year of data. Analysis 

of 747 paired measurements indicated no mean difference in 

instantaneous discharge between portable flowmeters and 

TFMs. The mean difference in 553 paired ground-water pumpage estimates made in 1998 was 0.01 percent for the network of 

study wells. About 80 percent of the individual site differences 

in discharge and pumpage measurements were less than 

10 percent (Dash and others, 1999). 

Because the USGS study was based largely on data collected for about 1 year, robust evaluations of temporal variations in PCCs, long-term variations in TFMs, and temporal variations in differences between the two approaches for 

determining ground-water pumpage were not done. However, a 

limited analysis of available CDWR-approved PCC data collected over time indicated that the PCC may vary substantially 

between years and may contribute to errors when estimating 

pumpage for multiple years using a single previously measured 

PCC. Overall, data were insufficient to adequately address 

potential errors associated with the temporal variability in PCCs 

or the reliability of using PCCs over a 4-year period to determine ground-water pumpage. Various site characteristics, 

including method of discharge measurement, manufacture 

make of TFM, type of discharge distribution system, and 

changes in pumping water level were evaluated as sources of 

variation in ground-water pumpage. In 1999 the USGS, in 

cooperation with CDWR and Colorado Water Conservation 

Board (CWCB), began a second phase of the study to collect 

additional data and evaluate variations of differences in discharge and pumpage between PCCs and TFMs for multiple 

years, including an analysis of time trends and other sources of 

variation in pumpage estimates. 

Purpose and Scope 

This report evaluates variability in the differences between 

two approaches used to determine ground-water pumpage—

metered discharge using TFMs and electrical power consumption using PCCs. The report compares measured pumpage using 

TFMs to computed pumpage using PCCs by developing statistical models of relations between explanatory (independent) 

variables, such as site, time, and pumping water level and 

dependent variables that are based on discharge, PCC, and 

pumpage. Specifically, the report evaluates the following:

1. Variability of differences in instantaneous discharge 

between a TFM and portable flowmeters used with the 

PCC, including an evaluation of time trends and effects of 

changes in pumping water levels;

2. variability of PCCs, including an evaluation of time 

trends and effects of changes in pumping water levels;

3. variability of differences in ground-water pumpage 

estimated with the TFM and PCC approaches, including 

an evaluation of time trends and effects of changes in 

pumping water levels;

4. year-to-year variability of differences in ground-water 

pumpage estimated with the TFM and PCC approaches; 

and

5. aggregated differences in total pumpage estimated by the 

two approaches for a network of wells.

This report contains data collected by CDWR during 

1998–2002 from a network of wells that were originally identified as part of the phase I study (Dash and others, 1999). Reductions in the network occurred during 1998–2002; the number of 

wells and the number of site visits varied (figs. 1A–1E). In 1998, 

data collected from 81 of the wells were used for the second 

phase of the study. The number of wells measured in subsequent years varied as follows: 70 wells in 1999, 72 wells in 

2000, 61 wells in 2001, and 58 wells in 2002. The number of 

wells varied annually for a variety of reasons: (1) some well 

owners preferred to cease participation in the study and 

removed the TFM from their well after 1998; (2) because one of 

the primary purposes of the second phase of the study was to 

determine temporal variability in the differences in pumpage, 

sites were dropped from the well network if the discharge system was reconfigured or if the TFM was broken and not 

repaired; and (3) sites also were eliminated if the well was not 

pumped after 1998. 

Description of Study Area and Hydrologic Setting

The Arkansas River alluvial aquifer between Pueblo and 

the Colorado-Kansas State line consists of unconsolidated fine 

sand near the surface, grading to coarse sand and gravel at the 

base, with minor beds of confining clay. The alluvial aquifer is 

in hydraulic connection with the Arkansas River along the main 

stem and its major perennial tributaries. Ground-water recharge 
6 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

Study Area 

COLORADO

Denver

Pueblo

County

Crowley

Otero

County Bent

County

Prowers

La Junta Las Animas

Pueblo

EXPLANATION

Irrigation well

COLORADO

KANSAS

Lamar

John Martin

 Res.

ARKANSAS RIVER

Founta ni Cr

H u e rfano R

Apisha p a R

P u rga to i r e R

Two B u tte s Cr

County

County

 

Pueblo

County

Crowley

Otero

County Bent

County

Prowers

La Junta Las Animas

Pueblo

COLORADO

KANSAS

Lamar

John Martin

 Res.

ARKANSAS RIVER

Founta ni Cr

H u e rfano R

Apisha p a R

P u rga to i r e R

Two B u tte s Cr

County

County

A

B

Figure 1. Location of study area and irrigation wells used in the study during years (A) 1998, (B) 1999, (C) 2000, (D) 2001, and

(E) 2002.
Introduction 7

Pueblo

County

Crowley

Otero

County Bent

County

Prowers

La Junta Las Animas

Pueblo

COLORADO

KANSAS

Lamar

John Martin

 Res.

ARKANSAS RIVER

Founta ni Cr

H u e rfano R

Apisha p a R

P u rga to i r e R

Two B u tte s Cr

County

County

Pueblo

County

Crowley

Otero

County Bent

County

Prowers

La Junta Las Animas

Pueblo

COLORADO

KANSAS

Lamar

John Martin

 Res.
8 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

is mostly from leakage and percolation of water diverted from 

surface-water systems. Ground water moves toward and discharges to the principal streams. The principal use of water in 

the area is for crop irrigation. 

Between 1998 and 2002, streamflow in the Arkansas River 

varied substantially. Annual flows measured at Arkansas River 

near Avondale (USGS station 07109500) ranged from 928,500 

acre-ft in 1999 to 205,780 acre-ft in 2002. In 1999, the annual 

flow was 26 percent greater than the long-term annual average; 

in 2002, the annual flow was 70 percent less than the long-term 

annual average. Beginning in July 2000, streamflows were consistently less than the mean flow. Decreased streamflow 

affected the amount of surface-water diversions; cumulative 

diversions in 2001 and 2002 were about 35 percent and about 

70 percent less than diversions in 1998, 1999, and 2000. Significant correlations (p<0.05) were detected between surfacewater diversion volumes and pumping-water levels measured in 

wells completed on lands irrigated by surface-water diversions. 

More than two-thirds of the wells had correlation coefficients of 

0.7 or greater, indicating that 50 percent or more of the variations in pumping-water levels were associated with the amount 

of surface water diverted to nearby croplands. The variability in 

static-water levels measured during 1998–2002 in the network 

of study wells is shown in figure 2. Static-water levels are measurements of depth to ground water when the well is not pumping. These data were collected after the irrigation season in both 

years and show that depth to water in the majority of wells 

(72 percent) increased by more than 10 percent. In addition, 

static water levels measured in 44 of 62 wells as part of a cooperative program between the USGS and Southeastern Colorado 

Water Conservancy District (SECWCD) showed water-level 

declines during 1998–2002. Twenty-eight percent of the wells 

measured during 1998–2002 recorded the deepest depths to 

water for the period of record (generally before 1966). Prior to 

1998, more than 60 percent of these wells indicated little to no 

change as compared to measurements made between the mid1960s and the early 1970s. In addition, Steger (2002) indicated 

that changes in ground-water levels for 35 wells in the Arkansas 

River alluvial aquifer from 1965 to 2001 tended to be gradual. 

The gradual and relatively small changes in ground-water levels 

occurred even during periods of large variations in magnitude 

and timing of streamflow. Significant operational changes, such 

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

TOTAL DEPTH OF WELL, IN FEET

-20

-10

0

10

20

30

40

50

60

70

80

90

100

PERCENT DIFFERENCE IN STATIC WATER LEVEL, 1998-2002

Figure 2. Percent differences in static water level in relation to depth of well, 1998–2002.
Introduction 9

as construction and operation of Pueblo Reservoir, implementation of the Winter Water Storage Program, the 1980 operating 

plan for John Martin Reservoir, and implementation of the 

ground-water measurement rules (Office of the State Engineer, 

1994 and 1996), historically have had relatively small effects on 

ground-water levels. From 1965–2001, the mean annual 

streamflow ranged from less than 362,000 acre-ft at Arkansas 

River at Avondale during the 1977 drought to greater than 

1,000,000 acre-ft during 1983. These data indicate that static 

ground-water levels in the study area tend to exhibit small variations over multidecadal time scales with a high degree of temporal correlation, and trends that appear approximately linear 

over shorter periods of time, such as 5-year periods, are not 

uncommon in such slowly varying time series even under 

highly varying hydrologic conditions. Although water levels 

have tended to respond gradually to extreme hydrologic events 

(very wet and very dry years), water levels are influenced by 

streamflow and the amount of surface water that is available for 

irrigation. In drought years, water-level declines have occurred 

where surface-water availability was reduced for irrigation. 

Annual variations in pumping-water levels measured during 

1998–2002 are shown in figure 3. Pumping-water levels are 

measurements of depth to ground water when the well is pumping, and in this report, were measured as the distance, in feet, 

from the centerline of the discharge pipe to the depth to ground 

water. The pumping-water level (PWL) used in this report represents the depth to water in a pumping well after the water level 

had stabilized according to the ground-water measurement rules 

0

10

20

30

40

50

60

70

80

PUMPING WATER LEVEL, IN FEET BELOW CENTERLINE 

OF WELL DISCHARGE

1998 1999 2000 2001 2002

(Note: data values exceeding 80 feet are not shown; 6 in 1998, 4 in 1999 and 2000, 3 in 2001, and 2 in 2002)

(385) (182) (254) (202) (179)

EXPLANATION

Extreme outlier value

Outlier value

25th percentile

Median

75th percentile

Value less than or equal to 1.5 times the Interquartile range

Interquartile range

(385) Number of observations

Figure 3. Variations in pumping water levels for network wells by year, 1998–2002.
10 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

(Office of the State Engineer, 1994 and 1996). In general, 

depth-to-water levels in pumping wells measured in 2001 and 

2002 were greater than depth-to-water levels measured during 

1998–2000. 

Acknowledgments

This report is possible because of the continued data collection by CDWR—Division II personnel who measured and 

processed well measurements on an ongoing basis. The authors 

extend thanks to the many private landowners in the Arkansas 

River Valley who allowed their irrigation wells to be used in 

this study.

Methods of Investigation

In 1997, CDWR identified more than 1,300 large-capacity 

irrigation wells with electrical pumps in the study area (wells 

that discharge more than 50 gal/min) for which the PCC 

approach might be used to determine ground-water pumpage 

under the amended rules established by the Office of the State 

Engineer (1996). A computer program (Scott, 1990) was used 

to randomly select candidate wells for the TFM/PCC evaluation. Each candidate well was reviewed by CDWR and inventoried to determine its suitability for inclusion in the study. Ultimately, 106 wells were selected, and each well was assigned a 

site number from 1 to 106. Shortly after the 106-well network 

was selected, one well was eliminated from the network. Eleven 

wells had TFMs already installed; in all other wells, new TFMs 

were installed in a full-flowing section of water pipe on the discharge side of the pump where the measurement of discharge 

was made. Because one of the primary purposes of the second 

phase of the study was to determine temporal variability in the 

differences in pumpage, data from 81 of the wells measured in 

1998 were used for the second phase of the study. As stated previously, other reductions in the network occurred during the 

study period. Several different types or makes of TFMs were 

used during the study, including propeller flowmeters (make M, 

make X, make B) and a rotating-blade flowmeter (make S). 

Accuracy of different types of TFMs installed to manufacturer’s specifications generally is reported to be within 2 to 

3 percent when operated within the design range of discharge. 

Each well in the study network was classified by discharge 

distribution-system type characteristics. During the study, four 

major types were identified. The network included open-discharge (type O), low-pressure (type L), sprinkler (type S), and 

complex (type C) discharge distribution systems. For data-analysis purposes, site measurements made at type C wells were 

divided into two additional types to reflect total dynamic head 

(TDH) operating conditions; complex high (type CH) and complex low (type CL). The type of discharge distribution system 

being used at each well was verified onsite before making subsequent measurements.

During 1999–2002, data were collected in the same manner as the data collected during 1998 (Dash and others, 1999). 

During each site visit, instantaneous flow rate was determined 

by reading the odometer dial of the TFM and timing the index 

pointer for one complete revolution, then dividing the total volume by the elapsed time; the procedure was repeated nine more 

times, resulting in an average of the 10 values for the recorded 

instantaneous TFM discharge. The volume of water pumped 

between site visits was determined by recording the register 

dials of the TFM at the beginning of each visit. The total volume 

of water pumped at a study site was determined as the difference between TFM readings made at the beginning and the end 

of the selected monitoring period. Independent instantaneous 

discharges were measured concurrently by using at least one of 

three commercially available portable flowmeters: a pitot tube/

manometer device (method C), an ultrasonic flowmeter 

(method P), and a propeller-type meter (method M). More 

detailed information about each type of portable flowmeter 

used in the study is provided in Dash and others (1999). These 

portable flowmeters provided three different measurement 

techniques to determine the average velocity of water flowing 

through the discharge pipe. The average velocity, multiplied by 

the cross-sectional area of the discharge pipe, was used to compute the discharge in gallons per minute. Whenever possible, 

discharge measurements using all three types of portable flowmeters were made at each site. The collection of multiple discharge measurements allowed for verification and explanation 

of any unusual discharge data collected in the field. All discharge and power-demand measurements were collected in the 

same time interval after the pumping water level in the well had 

stabilized (Office of the State Engineer, 1996).

To compute well discharge for two of the three portable 

flowmeters (method M and method P), the inside pipe diameter 

was needed. Throughout the study, the wall thickness of discharge pipes was measured using an ultrasonic thickness gage 

(UTG). A coupling compound was applied to the section of discharge pipe to be measured; the UTG probe was placed on the 

pipe surface, and the wall thickness was determined. A test 

block was mounted to the UTG for field calibration and ensured 

correct operation of the instrument and probe. The outside circumference of the discharge pipe was determined using a thin, 

flexible metal tape.

Method M and method P portable flowmeters used in the 

study were tested annually at the Great Plains Meter, Inc., facility in Aurora, Neb. The results of the wet-flow calibration 

checks indicated the accuracies for the portable flowmeters and 

the performance expected of these meters under optimal conditions. The portable flowmeters used in the study were tested 

before the start of each irrigation season and again following the 

final 2002 irrigation season. The discharge measured by the 

method M portable flowmeter ranged from 98 to 102 percent of 

the known laboratory discharge. The rate of flow used during 

these tests ranged from about 100 gal/min for the 4-inch flowmeter to about 1,680 gal/min for the 10-inch flowmeter. The 

discharge measured by the method P portable flowmeter ranged 

from 97 to 116 percent of the known discharge for flows that 

ranged from 520 to about 810 gal/min. The test facility did not 

make any calibration adjustments to either the method M or the 
Introduction 11

method P portable flowmeters. The flows measured by portable 

flowmeters in this study generally were within the limits of reliability provided by the test facility.

During the 1998–2002 irrigation seasons, the number of 

PCC measurements made by CDWR personnel during a single 

site visit ranged from one to three, depending on the conditions 

and the number of different portable flowmeters that could be 

used at the site. The PCC is defined as the number of kilowatt 

hours required to pump 1 acre-ft of water, and combines a concurrent measurement of well discharge (in gallons per minute) 

with the power demand of the pump (in kilowatts). Electrical 

power meters contain a disk that revolves as electricity passes 

through the meter. During a field test, the meter disk was timed 

with a stopwatch for at least 10 complete disk revolutions to 

measure the rate per revolution. This timing measurement was 

repeated three times and used to determine the average rate of a 

disk revolution. 

Power demand, in kilowatts, was calculated from the equation:

power demand = (rate) × (3.6) × (Kh factor), (1)

where

rate is the average rate of disk revolution, in revolutions 

per second,

3.6 is the conversion factor (kilowatt seconds per 

watthour), and

Kh factor is the watthours per revolution (imprinted on 

the front of power meter).

The PCC, in kilowatthours per acre-foot, then is calculated 

from the equation:

PCC = (power demand) × (5,433)/(well discharge), (2)

where

 5,433 is the conversion factor (in gallon hours per 

acre-foot minutes), and

well discharge is the instantaneous ground-water 

discharge, in gallons per minute.

A new PCC rating was calculated at a well each time a 

measurement of instantaneous discharge and power demand 

was made. The PCCs were applied to the total annual power 

consumption recorded between the initial and final electric 

meter readings made by CDWR at the site during each irrigation 

season to estimate ground-water pumpage by year. Pumpage 

differences were computed by subtracting the pumpage associated with the PCC approach at each well from the total pumpage 

associated with the TFM for the same monitoring periods. 

In this report, the PCC analysis at complex discharge distribution system type differed from the weighted PCC analysis 

used at complex sites in the earlier USGS phase I study (Dash 

and others, 1999). In June 2000, the CDWR revised the policy 

for a complex system using the PCC method to accept the lowest operating PCC for calculating pumpage from the well 

(Office of the State Engineer, 2000). The lowest PCC occurs 

when a well is discharging under the condition of lowest total 

lift or total dynamic head (TDH) at the pump. Sites classified as 

complex wells by CDWR can vary the TDH at the pump outlet 

during a single irrigation season. This change in TDH may 

result from multiple wells that discharge into a common pipeline, a pipeline with multiple outlet locations, or wells where the 

method of water delivery varies between different types of distribution systems, such as open-discharge, low-pressure gated 

pipe, or sprinkler systems.

Quality-control procedures were similar to the phase I 

study (Dash and others, 1999). The field data collected and processed by CDWR were transmitted electronically and in paper 

files to the USGS for review and analysis. USGS personnel 

periodically visited TFM sites with CDWR personnel to 

observe onsite data collection and to ensure that techniques 

were consistent and correct. During each measurement, critical 

site information was verified and essential test information was 

recorded on CDWR field forms. The USGS reviewed tabulations for completeness and consistency with established collection procedures. About 10 percent of the electronic data was 

checked against copies of the original field forms, and all 

received data were scrutinized for anomalies. 

Raw data and data transformed to natural logarithms were 

reviewed using scatterplots, histograms, and boxplots to 

evaluate measurements, identify anomalous data, and obtain 

preliminary indications of appropriateness of the logarithmic 

transformation. Differences in discharge or pumpage were 

computed by subtracting the natural logarithm of well discharge 

or pumpage associated with the PCC approach from the natural 

logarithm of the well discharge or pumpage associated with the 

TFM. Henceforth, the term log will be used to refer to natural 

logarithm. Plots of the resulting differences for discharge are 

shown in figure 4A and for pumpage in figure 4B. These plots 

indicate there was a small proportion of differences in pumpage 

that tended to be outside the range of the majority of the data. 

Before data were discarded, anomalous data were reviewed by 

referencing written field documentation, or by doing additional 

statistical analysis, or both. Examination of residuals after 

statistical models were developed resulted in elimination of 

30 values or seven site-year combinations from the data set. A 

detailed discussion of outliers is provided in the “Supplemental 

Information” section at the back of this report.

Boxplots graphically show the variability among data 

sets, unusual values, and selected summary statistics. An 

example of a boxplot is shown below: 

 Outlier value (less than or equal to 3 and more than l.5 times 

 the IQR from the box)

Data value less than or equal to 1.5 times the IQR 

75th percentile 

Median

25th percentile 

o Extreme outlier value (more than 3 times the IQR from the box)

* 
12 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

0.1 1.0 10 100 1,000

TOTALIZING FLOWMETER PUMPAGE, IN ACRE-FEET

–1.5

–1.2

–0.9

–0.6

–0.3

0

0.3

0.6

0.9

1.2

1.5

diffP (LOG OF TOTAL PUMPAGE USING POWER 

CONVERSION COEFFICIENT MINUS LOG OF TOTAL 

PUMPAGE USING TOTALIZING FLOWMETER)

B

100

TOTALIZING FLOWMETER INSTANTANEOUS DISCHARGE, IN GALLONS PER MINUTE

–0.3

–0.2

–0.1

0

0.1

0.2

0.3

diffQ (LOG OF PORTABLE FLOWMETER DISCHARGE

MINUS LOG OF TOTALIZING FLOWMETER DISCHARGE)

50 500 1,000 5,000

A

Figure 4. (A) Relation of diffQ to totalizing flowmeter instantaneous discharge, and (B) relation of diffP to totalizing flowmeter pumpage.
Introduction 13

The horizontal line within the box represents the median 

value (50 percent of the data are greater than this value and 50 

percent of the data are less than this value). The lower horizontal line of the box is the 25th percentile or lower quartile (25 percent of the data are less than this value). The upper horizontal 

line of the box is the 75th percentile or upper quartile (75 percent of the data are less than this value). The interquartile range 

(IQR) contains the values between the 25th and 75th percentiles 

and is the difference between the 25th and 75th percentiles. The 

bottom of the vertical line on the boxplot is the smallest value 

within 1.5 times the IQR of the box. The top of the vertical line 

on the boxplot is the largest value within 1.5 times the IQR of 

the box. Outlier values are greater than 1.5 times the IQR from 

the box, and extreme outlier values are greater than 3 times the 

IQR from the box.

Methods of Statistical Analysis

Statistical models are used to examine the relation between 

certain dependent variables of interest and certain explanatory 

variables that are expected to be important in influencing the 

dependent variables. In applying these statistical models, 

assumptions usually are made, such as normality and constancy 

of variance of the modeled dependent variables for different 

values of the explanatory variables. Selecting the appropriate 

dependent variables for analysis was required to develop the 

statistical models, followed by defining the explanatory variables that were believed to be important in explaining the variability of the dependent variables. 

Dependent Variables

The four dependent variables selected for analysis in 

this report are diffQ, diffC, diffL, and diffP and are defined as 

follows:

diffC = log PCC

where

log is the natural logarithm (base e),

is portable flowmeter instantaneous discharge 

(gallons per minute),

Q is TFM instantaneous discharge (gallons per minute),

PCC is power conversion coefficient from equation 2 

(kilowatthours per acre-foot),

L is total power consumption for season (kilowatthours),

, which is total pumpage for season using PCC 

method (acre-feet),

P is total pumpage for season using TFM (acre-feet).

The variable diffC is therefore just the log of the PCC value 

as computed by equation 2. Also, diffP, the main variable of 

interest in this report, is the difference in log-transformed 

pumpage computed by the PCC and TFM approaches and is 

related to diffC and diffL by 

. (3)

The PCC is essentially a ratio between power consumption 

and pumpage over a very short period of time (instantaneous), 

so that diffC and diffL are seen to have similar definitions. The 

difference between diffC and diffL is one of time scale; diffC is 

obtained using essentially instantaneous values of power consumption and flow, whereas diffL is obtained using seasonally 

integrated values of power consumption and flow. The variable 

diffQ also compares two instantaneous flows, and diffP mixes 

time scales by using instantaneous PCC to estimate seasonal 

pumpage. Because of the similarity in definitions of diffC and 

diffL, these models provide additional information needed to 

evaluate the compensating effects that occur in their difference, 

diffP. 

Explanatory Variables

Explanatory variables were developed after selection of 

the dependent variables. The explanatory variables characterize 

conditions under which a measurement of a dependent variable 

was made. Incorporation of the explanatory variables in a statistical model for the dependent variable enables an assessment of 

the effect of this explanatory variable on the dependent variable. 

For example, one explanatory variable used in this report is the 

portable flowmeter measurement method. As discussed previously, three methods were used in this study and were identified 

as C, P, and M. When a method is used as an explanatory variable in the model for diffQ, for example, it can be determined if 

there is any significant difference in diffQ resulting from the use 

of different methods. In this report, a statistically significant 

finding, unless otherwise denoted, is significant at the 5-percent 

significance level (p<0.05). In addition, the explanatory variables in the statistical models are considered either quantitative 

or qualitative. Quantitative variables have a numerical value 

that specifies some quantity, whereas qualitative variables are 

used to define different categories. Pumping water-level 

measurement is an example of a quantitative variable, and the 

portable flowmeter measurement method is an example of a 

qualitative variable. The models used in this report have incorporated both types of variables. The statistical technique known 

diffQ Q logQ ~ = log −

diffL = log L − log P

diffP P log P ~ = log −

Q

~

PCC

L P = ~

diffP = diffL − diffC
14 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

as regression analysis typically uses quantitative explanatory 

variables, the technique known as analysis of variance uses 

qualitative explanatory variables, and the technique known as 

analysis of covariance combines both. Therefore, the statistical 

methodology used in this report may be referred to as analysis 

of covariance, although this terminology usually refers to statistical models that are not as complex as the ones used in this 

report. Analysis of covariance combines features of simple linear regression with analysis of variance. Analysis of covariance 

is used to assess the statistical significance of mean differences 

among variables and explains the amount of variation in the 

dependent variables diffQ, diffC, diffL, and diffP that is attributable to each of the explanatory variables.

The number of categories associated with a qualitative 

variable is referred to as the number of “levels” for that variable. 

For example, there are three levels for the portable flowmeter 

measurement method (C, P, and M), which is a qualitative variable. Qualitative variables in modeling may be classified further 

as having either fixed or random effects (Snedecor and 

Cochran, 1967). Fixed effects are regarded as fixed but 

unknown quantities to be estimated, but random effects are 

regarded as varying randomly (for example, from site to site), 

so that interest focuses on estimating properties (such as the 

variance) of the probability distribution of the effects. Both 

fixed and random effects are used in the models in this report. 

The various explanatory variables that are included in the statistical models, together with the symbols used, the type of variable, and the levels for the qualitative variables are listed in 

table 1.

A brief description of these explanatory variables and 

some remarks on their usage are given here:

1. Portable flowmeter measurement method (Method). This 

variable accounts for the tendency for measurements 

made with one method to differ from those made with 

another method. 

2. Type of discharge distribution system (Type). This 

variable accounts for the tendency for measurements 

made for one type of discharge system to be different 

from those made for another type.

3. Site (S). This variable accounts for the tendency for 

measurements at one site to differ systematically from 

measurements at other sites. For example, if 

measurements at a given site have a tendency to be larger 

than average, the site effect at this site will be positive, 

and including this qualitative variable enables the model 

to account for this.

4. Year (Y or Z). This variable accounts for the tendency of 

measurements made in one year to differ systematically 

from measurements made in another year. When 

modeling pumpage differences (diffP), it will be 

necessary to have two year-effect terms, one for the year 

in which the PCC measurement was made (this is yeareffect Y in table 1) and one for the year in which 

electrical power consumption was used to estimate 

pumpage (this is year-effect Z). 

5. Site/Year (SY). This is a site/year “interaction” term that 

accounts for site-specific year-to-year variation. That is, 

the site variable (S) represents an average effect at a 

given site for all years, and the year variable (Y or Z) 

represents an average effect for a given year at all sites; 

but this site/year term represents the tendency for 

measurements made for a given site/year combination to 

deviate from the site and year average effects.

6. Date (D). This variable accounts for the tendency of 

measurements made on a given date at a given site to 

differ systematically from measurements made on a 

different date at the same site.

7. Time (t or s). This variable enters the models as a linear 

trend term in time. It accounts for the tendency for 

measurements to change systematically over the period 

of record, increasing or decreasing linearly with time. 

The magnitude of the time trend is determined by a 

coefficient that is the slope of the line when the 

dependent variable is plotted in relation to time. This 

coefficient represents the rate of change of the dependent 

variable with respect to time. This coefficient will be 

made random in the models, meaning that the coefficient 

Table 1. Explanatory variables for statistical models.

[Log PWL, log of pumping water level; --, not applicable; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer 

flowmeter; L, low pressure; O, open; S, sprinkler; CH, complex high; CL, complex low]

Variable Symbol Type Levels

Method fixed qualitative C, P, M

Type fixed qualitative L, O, S, CH, CL

Site S random qualitative one for each site

Year Y or Z random qualitative one for each year

Site/Year SY random qualitative one for each site-year combination

Date D random qualitative one for each site-date combination

Time t or s quantitative --

Log PWL w quantitative --

α

γ
Introduction 15 8. may vary randomly from site to site. Also, when 

modeling diffP, it will be necessary to consider two 

times; one (t in table 1) for when the PCC measurement 

was made, and one (s in table 1) for the year electrical 

power consumption was used to estimate pumpage.

9. Pumping water level (PWL). This variable accounts for 

the tendency for measurements to change systematically 

with pumping water-level changes. In the statistical 

models, a logarithmic transformation was made on 

pumping water level; this variable is expressed in the 

models as a deviation from an average value. There is, as 

with the time explanatory variable, a coefficient 

associated with this term, which can vary randomly from 

site to site. 

Four of these explanatory variables (Year [Y], Site/Year 

[SY], Date [D], and Time [t or s]) were included to facilitate 

assessment of temporal variability. The time variable enables 

the models to evaluate tendencies to increase or decrease monotonically with time over the period of interest, and the date and 

year variables, including the Site/Year variable enable the models to estimate the tendency for measurements that are close 

together in time to be correlated. For example, measurements 

made on the same date may tend to be more similar than measurements on two different dates, so the date variable accounts 

for this. 

The statistical modeling thus is based on expressing the 

dependent variables in terms of the explanatory variables and an 

error term, which accounts for unexplained variability of the 

dependent variable. The magnitude of the variance of the error 

term relative to the total variability of the dependent variable 

provides an indication of how much of the variability in the 

dependent variable is accounted for by the explanatory variables. The statistical fitting procedure used to estimate 

unknown parameters (fixed effects and variances) in the models 

is restricted maximum likelihood estimation, using the software 

package SPLUS (Mathsoft, 1998).

Statistical Models for Discharge and Power Conversion 

Coefficients

The statistical models for discharge and power conversion 

coefficients are

(4)

(5)

(6)

where 

 is the intercept term,

 is the effect (fixed) for the portable flowmeter method 

(C, M, P),

 is the effect (fixed) for discharge distribution system 

type (L, O, S, CH, CL),

 is the effect (random) for site,

 is the effect (random) for an instantaneous flow or 

PCC measurement year, 

 is the effect (random) for a year within site,

Z is the year effect (random) for a year in which total 

power consumption was used to estimate pumpage, 

 is the effect (random) for date,

 is the time-trend coefficient (random),

 is measurement time (in fractional years, t=0 for 

January 1, 1998 and t=0.5 for June 30, 1998),

s is time when power consumption at the well was used to 

estimate pumpage (in years, s=0 for 1998),

 is the pumping water level coefficient,

 is log of pumping water level at time of measurement 

(PWL),

 is average log PWL for a given site,

 is average log PWL for a given site in a given year, 

and

 is the random error term.

 (Note: the subscripts Q, C, and L associated with these variables refer to the specific model – diffQ, diffC, or diffL.)

The fixed effect term, , models the differences in the 

dependent variables caused by differences in portable flowmeter method (three levels: C, M, and P) and the fixed effect 

term, , accounts for differences caused by discharge distribution system type (five levels: L, O, S, CH, and CL). All sites 

were classified as L, O, S, or complex. Measurements of diffC

at complex sites were assigned a CH or CL level depending on 

whether the PCC measurement was made at a high or low TDH. 

For the diffL model, a site-year was classified as CH or CL on 

the basis of whether the first PCC measurement for that siteyear was made under high or low TDH. Initially, a fixed effect 

term for TFM make was included in the diffQ, diffC, and diffL

models as in the Phase I study (Dash and others, 1999). SimiQ Q Q Q

Q Q Q Q Q

D A t U w w e

diffQ S Y SY

+ + + − +

= + + + +

( )

μ α ( )

C C C C

C C C C C C

D A t U w w e

diffC S Y SY

+ + + − +

= + + + + +

( )

μ α γ ( )

L L L

L L L L

A s U w w e

diffL S Z

+ + − +

= + + +

( )

μ γ

μ

α

γ

S

Y

(SY )

D

A

t

U

w

w

w

e

α

γ
16 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

larly, the fixed effect term for the distribution system type ( ) 

was included in the diffQ model. However, data analyses using 

these initial models indicated that TFM make was statistically 

insignificant for diffQ, diffC, and diffL models; the fixed effect 

term for the distribution system type ( ) was statistically insignificant for the diffQ model. Therefore, these variables were not 

included in the final models. 

The time-trend term, t, in the diffQ and diffC models was 

included to account for the observed tendency for diffQ and 

diffC to show a systematic linear trend with time. This trend 

changes from site to site, so the slope, or coefficient, of the 

time-trend line, variable A, is a random effect that varies randomly from site to site. As a result, the models for diffQ, diffC, 

and diffL are treated as random slope models. Similarly, 

because PWL varied during the course of the study, it was 

important to evaluate the tendency for diffQ and diffC to change 

systematically with PWL. The term involving log of PWL, w, 

accounts for this tendency. In the diffQ and diffC models, the 

trend effect of PWL is represented as a coefficient, , multiplied by , where w is the log of PWL and is the siteaverage log of PWL. Thus, by setting , or , 

diffQ and diffC can be evaluated for average PWL conditions. 

The coefficient U is random—varying randomly from site to 

site. 

A time-trend term exists in the diffL model, similar to the 

time-trend term in the diffQ and diffC models, but time in this 

model is denoted by the variable, s, which stands for year in 

which total power and pumpage were measured. The coefficient is allowed to vary randomly from site to site. Also, in 

the diffL model, the effect of PWL enters as a linear term in 

, where is average log PWL for a given site in a given 

year. Thus, there is only one diffL value per site per year, and 

similarly, there is one associated value per site per year. 

Therefore, the model was expressed in terms of the difference 

of from the overall site average . 

The random factor S in all three models (eqs. 4, 5, and 6) 

accounts for the site-to-site variation of the “intercept” of the 

linear models, and the random factors Y and Z account for yearto-year variation. The variable S measures the tendency for data 

at one site to differ systematically from data at another site, and 

Y and Z measure an analogous tendency for different years. The 

distinction between Y and Z is similar to that between t and s; Y

is the year effect corresponding to a portable flowmeter or PCC 

measurement, and Z is the year effect corresponding to a period 

in which total power consumption and annual pumpage were 

measured. For the diffQ and diffC models, while S represents 

site variation across all years, and Y represents yearly variation 

across all sites, the random factor (SY) is an interaction term 

representing site-specific year-to-year variation. Finally, there 

also was a tendency for diffQ and diffC data collected on one 

day to exhibit a difference from data collected on a different day 

at the same site in the same year; this tendency is measured by 

the date effect, D. 

The statistical assumptions made in the analyses are: All 

random variables are assumed to be normally distributed, and 

all except A and U have mean of zero. The explanatory site variables in the diffQ model that can vary randomly from site to site 

are denoted by . In the diffQ model, the is 

assumed to be independent and identically distributed (i.i.d.), 

the are i.i.d, the are i.i.d., the are i.i.d.; , , 

, and are further assumed to be independent of each 

other. Note that the three site variables making up may not 

be independent of each other. Analogous assumptions are made 

for the diffC and diffL models. 

The main purposes of the diffQ, diffC, and diffL statistical 

analyses were to obtain: (1) estimates of the fixed effects, and 

(2) estimates of the means and variances for the random effects 

that included time trends and trends in PWL.

Statistical Models for Pumpage Differences

The equation for diffP in equation 3 contains two different 

times: time t, when the portable flowmeter measurement was 

used to obtain a PCC, and time s, the year for which power consumption was used to estimate pumpage. Time t is incorporated 

in the equation for diffC, and time s is incorporated in the equation for diffL; therefore, diffP contains both s and t. 

Currently (2004), under the rules adopted and subsequently amended by CDWR for measurement of tributary 

ground-water diversions in the Arkansas River Basin, a PCC 

could be applied to the electrical power usage up to 4 years in 

the future to estimate ground-water pumpage (Office of State 

Engineer, 1994, 1996). One of the main purposes of this study 

was to evaluate the effect of this lag (the difference between s

and t) on differences in pumpage (diffP) between the PCC and 

TFM methods. Toward this purpose, a new variable, u, was 

defined as the difference between s and t, which represents the 

lag time; therefore, diffP will be expressed in terms of u rather 

than s and t. 

To obtain a statistical model for diffP, the variables in the 

diffC and diffL models were substituted in equation 3. In the 

combined model, there is an assumption of independence of the 

random effects. However, diffC and diffL each have year 

effects, Y and Z, that are unlikely to be independent of each 

other unless diffC and diffL are associated with different years. 

Thus, two different cases must be distinguished. For a PCC 

measurement made at a time t, a notation of will be used to 

represent the year in which the measurement was made, and s

represents the year in which the power consumption at the well 

was used and pumpage was estimated. The two different cases 

are therefore:

 case (i). (PCC measured and pumpage estimated 

in different years).

 case (ii). (PCC measured and pumpage estimated 

in the same year).

Considering case (i) first, substituting the models for diffL

(eq. 6) and diffC (eq. 5) into equation 3 and removing statistically insignificant terms as described later in this section yields

(7)

γ

γ

U

w − w w

w = w w − w = 0

AL

w − w w

w

w w

( , , ) Q Q AQ UQ V = S VQ

YQ Q (SY ) Qe VQ YQ

Q (SY ) Qe

VQ

[t]

s ≠ [t]

s = [t]

P P P P P P

P P P P P P

Z SZ D A u U w w e

diffP S Y SY

+ + + + − +

= + + + + + +

( ) ( )

μ α γ ( )
Introduction 17

where 

diffP model variables can be expressed by the differences 

in the diffL and diffC variables as follows:

 and

.

In this model, there are two terms for the year effect, 

(representing the year in which the PCC value was measured) 

and (representing the year in which power consumption was 

used to estimate pumpage). Note, because all of the random 

site-year effect in the diffP model for the year in which pumpage was estimated comes from the error term in the diffL model, 

. Also, two terms were omitted from this model 

because they were statistically insignificant. The first term 

omitted was ; presence of this term would mean that 

time trends in diffP are a function not only of the lag time u but 

also of the time t when the PCC measurement was made. The 

fact that this term proved very small in the data analyses reflects 

the fact that and are highly positively correlated. The 

second term omitted was , which was small 

because of the high positive correlation between and . 

The PWL dependence in the final diffP model (eq. 7) is only 

through , the difference between (average log PWL

for the site and year when power consumption was used to estimate pumpage) and w (the log PWL when the PCC was calculated). The difference can be interpreted as a “lag” in 

PWL conditions just as u represents a lag in time.

Next consider case (ii). The model for diffP may in this 

case be written as

(8)

where

and

.

In this case, the term is a year effect representing the combined effects of and ; and represents the combined effects of and . The time-trend term (t) is 

statistically insignificant and has been omitted.

There are two ways to obtain estimates for the parameters 

in the diffP model. One is to use the fitted models for diffC and 

diffL. The second is to use diffP data to fit the model for equation 7 where ( ) and for equation 8 where ( ) 

directly. That is, at each site, PCC values were obtained for a set 

of measurement times (t) and total electrical power consumption for a set of years (s). The diffP data were obtained by applying each PCC value to each total electrical power consumption 

value by using all possible combinations of t and s. When fitting 

the equation 7 model or the equation 8 model using diffP data, 

the assumption of independence of the errors must be met. 

This assumption is met for the diffP data with because 

the diffC errors, , are assumed to be independent and 

, indicating that the diffP errors, , also are independent. However, for the diffP data for which , the assumption of independence of the errors, , is violated if all possible 

combinations of PCC values and total power consumption are 

used. This assumption is violated because will be the same 

for all the diffP values for which the same PCC value is used. 

To overcome this problem, the diffP data set for was 

compiled by associating each PCC measurement at a site with 

only one total power consumption value in a randomly chosen 

year different from the year in which the PCC measurement was 

made.

In summary, three sets of estimation results will be shown 

for diffP. Comparing these three sets of results will provide a 

valuable crosscheck on consistency. The three sets of results 

are:

1. Results obtained using diffP data under case (i) ( ), 

fitting the model for equation 7. For these results each 

PCC measurement is associated with one total power consumption value in a randomly chosen year different from 

the year in which the PCC measurement was made.

2. Results obtained using diffP data under case (ii) ( ), 

fitting the model for equation 8.

μ P = μL − μC

αP = −α C

P L C γ = γ − γ

SP = SL − SC

YP = −YC

SY P SY C ( ) = −( )

ZP = ZL

P L (SZ) = e

DP = −DC

AP = AL

UP = UL

P C e = −e

YP

ZP

P L (SZ) = e

A A t L C ( − )

AL AC

(U U )(w w) L − C −

UC UL

w − w w

w − w

P P P P

P P P P P P

D A u U w w e

diffP S Y SY

+ + + − +

= + + + + ′ + ′

( )

μ α γ ( )

YP = ZL −YC ′

P L SY C (SY ′) = e − ( )

YP

′

ZL YC SY P ( ′)

L e SY C ( )

s ≠ [t] s = [t]

Pe

s = [t]

Ce

P C e = −e Pe

s ≠ [t]

Pe

Ce

s ≠ [t]

s ≠ [t]

s = [t]
18 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

3. Results obtained using the individually fitted diffC and 

diffL models.

The main purposes of the diffP statistical analysis was to 

obtain: (1) estimates of fixed effects, and (2) estimates of the 

means and variances for the random effects which included 

time trends and pumping water level (PWL) trends. 

Estimation of Year-to-Year Variability 

Estimation of year-to-year variability was one of the most 

important goals in this report because understanding this variability was crucial to determining whether PCCs obtained in 

one year could be accurately applied in other years. The two 

explanatory terms in the statistical models presented above that 

enable an assessment of this variability are the year (Y, Z, ) 

and time-trend (t, s, and u) terms. In the models described 

above, the year terms are random variables with a mean of zero 

indicating that all the systematic year-to-year variation is represented in the time-trend terms. However, the interpretation of 

the time-trend term is complicated by the fact that the models 

also include a PWL term, and PWL also may change systematically with time. Therefore, the effects of time trend and PWL 

must be considered together. 

If a power conversion coefficient estimated in 1 year was 

applied to estimate pumpage several years in the future, then a 

time trend would mean that conditions had changed between the 

time of PCC measurement and pumpage estimation (the difference in these times is the lag u in equations (7) and (8)) so that 

a bias may be introduced in estimating pumpage. This turns out 

to be a crucial issue for the data set analyzed in this report 

because hydrologic conditions did change systematically over 

the period of data collection, and this is reflected as significant 

time-trend terms in the statistical models.

If a time trend is present, some interpretation must be 

given to the meaning of this trend before any predictions of 

future trends (after the period of data collection in this report) 

can be made. It is important to recognize that there are reasons 

for any time trend and that detailed data on certain variables 

(such as climate, water availability, and ground-water conditions) might allow a definitive assessment of the reasons for the 

trend. Hence, the time-trend term in the statistical models 

should be regarded as a surrogate for these other variables, and 

if extensive data on these other variables were available and 

incorporated in the models, it probably would not be necessary 

to include the time-trend term. In the analyses done in this 

report, detailed data on PWL were available, and incorporation 

of this term in the statistical models accounted for some of the 

systematic change through time for this data set; and yet, the 

time-trend term in many of the analyses still appeared to be a 

significant predictor over and above PWL. In addition, some of 

the physical reasons underlying the variability in PWL and 

trends through time might be similar; thus, the PWL and timetrend terms, in part, may be reflecting some of the same causative factors. On the other hand, there may be factors resulting 

in a time trend that may be unrelated to variation in PWL. For 

example, variations in diffP that are associated with a progressive decline of TFM accuracy over a period of years due to clogging or wear and tear would be unrelated to variations in PWL. 

In summary, there is some uncertainty about the cause of time 

trends in the data analyzed in this report, and this uncertainty 

must be kept in mind when trying to extrapolate the results in 

this report to make future predictions.

The time-trend terms in the statistical models (eqs. 4–8) 

that are associated with the time variables (t, s, and u) were 

assumed to be linear. This implies that average changes from 

one year to the next are constant over a period of several years. 

This is a reasonable way to approximate, over short periods of 

time (several years), the gradual changes that have occurred in 

multidecadal static ground-water levels in the study area 

(Steger, 2002). However, changes through time may not be 

truly linear; thus, the assumption of linearity represents an 

approximation of the actual temporal changes over the 5-year 

study period. This oversimplifying assumption can be evaluated 

independently and in more detail by analyzing the year-effect 

variables (Y, Z, ) on the time trend. Recall variable Y represents the year the PCC was made, variable Z represents the year 

the power consumption was used to estimate pumpage, and 

variable represents the combined effects of ZL and YC. In the 

discussion so far, these variables have been made random with 

a mean of zero, so that data analysis provides an estimate of the 

variance of these terms. In order to use the year effects to extract 

more information about year-to-year variability, additional data 

analyses were performed in which Y, Z, and were fixed 

rather than random effects. This provides information about the 

mean value (and its standard error) for each year, whereas doing 

the analysis with Y, Z, and as random effects was based simply on an assumption that Y, Z, and for each year were random samples from a population with variances to be estimated. 

Both perspectives can be justified, and both sets of analyses 

provide useful information. When the year effects Y, Z, and 

are fixed effects, no linear time-trend term is included in the 

models, so that all year-to-year variability is associated with the 

Y, Z, and terms. Thus, a comparison of the mean time-slope 

estimates in the random-year effect model with the behavior of 

the year effect estimates in the fixed-year effect models provides valuable information on time trends.

Variability in Instantaneous Discharge 

As defined earlier, diffQ is a measure of the difference in 

instantaneous discharge measured between the portable flowmeters and the TFMs. DiffQ was computed by subtracting the 

log of the TFM discharge from the log of the portable flowmeter 

discharge. The difference in log of discharges allows diffQ to be 

interpreted as a relative or fractional difference for small differences. Therefore, diffQ multiplied by 100 may be interpreted as 

a percent difference. The number of values of diffQ used in the 

statistical modeling was 1,266. 

Y ′

Y ′

Y ′

Y ′

Y ′

Y ′

Y ′

Y ′
Variability in Instantaneous Discharge 19

Boxplots showing the differences in discharge data (diffQ) 

for the entire study network and for the three portable flowmeter 

methods are shown in figure 5. Almost 90 percent of the differences in paired discharge measurements for the entire network 

of wells were less than 10 percent, almost 70 percent of the differences were less than 5 percent, and the median difference 

was –0.5 percent (fig. 5A). The overall mean of the 1,266 diffQ

values was –0.0151. Results of fitting the statistical model in 

equation 4 are listed in tables 2 and 3. The estimated intercept 

of the statistical model for diffQ was –0.0193, with a standard 

error of 0.0050, indicating that, at time t=0 (the beginning of 

1998) and under average PWL conditions ( ), the 

average diffQ was about –1.93 percent. On average, the portable 

flowmeter discharge measurement was about 2 percent less 

than the TFM discharge (table 2).

The distribution of the differences varied with the selected 

portable flowmeter method. The median diffQ values and interquartile ranges for method C and M were smaller than for 

method P (fig. 5B), with the median diffQ value for methods C 

and M being 0.5 percent and – 0.6 percent, respectively. The 

median diffQ value for method P was –4 percent, a value 6 to 8 

times greater than for methods C and M. Additionally, the 

aggregated diffQ values computed using method C indicated no 

overall bias; whereas, the aggregated diffQ values computed 

using method M indicated a slight negative bias and the aggregated diffQ values computed using method P indicated a fairly 

strong negative bias (fig. 5B). A negative bias indicates that portable flowmeter method P tended to measure a smaller discharge than the TFM. The statistical model for diffQ indicated 

that the method effects accounted for about 7 percent of the total 

variance of diffQ. The estimated effect for method C relative to 

all three methods was about 1.7 percent; for method M, the estimated effect relative to all three methods was 0.2 percent; and 

for method P, the estimated effect relative to all three methods 

was about –1.9 percent (table 2). The positive sign on the effects 

for methods C and M indicated that these methods tended to 

have higher than average instantaneous discharge than was 

computed using data for all three methods; conversely, method 

P indicated a negative sign on the effects, indicating the method 

tended to have smaller discharge than the overall average. 

Figures 5C and 6 show the temporal variability in diffQ

during 1998–2002. The boxplots (fig. 5C) for diffQ show that 

portable flowmeter methods do not exhibit any observable persistent temporal trends. Figure 6 shows temporal variations in 

diffQ with respect to site (fig. 6A) and pumping water level 

(fig. 6B). Again, no persistent trends were observable. Estimates of the mean and variance of the random coefficients of 

the time-trend term and pumping water level term in the statistical model for diffQ are given in table 3. The time-trend term 

variable, , represents the rate of change (slope) of diffQ with 

respect to time t. The mean of for diffQ was estimated to be 

0.0009 with a standard error of 0.0018, indicating the mean was 

not significantly different from zero (table 3). The variance of 

 was estimated to be 0.0000313, giving a standard deviation 

(square root of the variance) of 0.0056. Thus, the time-trend 

coefficient may be considered a random variable with a mean 

slope of 0 percent per year and standard deviation of about 

0.56 percent per year. For a normal distribution, the probability 

of drawing a value within one standard deviation of the mean is 

about 68 percent and is about 95 percent within two standard 

deviations of the mean. Thus, if diffQ (which may be interpreted 

as a percent) is plotted against time t and the slope is measured 

for all the sites, about 68 percent of the sites would have a 

change in diffQ between –0.56 and +0.56 percent per year, and 

about 95 percent of the sites would have a change in diffQ

between –1.12 and +1.12 percent per year. If these estimates 

were extended, for example, to a 4-year period, about 

68 percent of sites would have a change in diffQ between 

–2.24 percent and +2.24 percent (2.24 = 4 × 0.56), and about 

95 percent of sites would have a change between –4.48 percent 

and +4.48 percent. 

The statistical model developed for diffQ indicated that 

site-to-site variability accounted for the largest amount (about 

46 percent) of the total variance of diffQ, and the time trend 

accounted for only about 6 percent of the total variance. Almost 

all of this time-trend variance resulted from site-to-site variability in the time slope, whereas the mean slope was near zero, 

indicating no tendency of diffQ from these sites to increase or 

decrease. The PWL term accounted for only a negligible 

amount of the variance of diffQ, indicating that changes in PWL 

had very little influence on differences in discharge. A detailed 

discussion of estimating the contributions of the different 

explanatory variables to the total variance (0.00323) for the 

diffQ model is provided in the “Supplemental Information” 

section in the back of the report.

Data analysis indicated that, overall, the quality of discharge measurements associated with TFMs did not degrade 

over time (during 1998–2002). However, problems did occur 

with some TFMs. During site visits, CDWR staff documented 

27 performance problems associated with TFMs (fig. 7). In 

addition, near the beginning of the 5-year study, there were 

three failures of make M meters soon after the meters were initially installed. Total mechanical failures and recurring electronic failures generally resulted in dropping the well from the 

study. Equipment problems, including debris clogs and reasons 

unknown, occasionally resulted in loss of TFM data. Debris 

clogs in the meter components generally were observed early in 

the irrigation season during startup operations. In these cases, 

simply loosening, adjusting, and retightening the saddle mounting often solved this minor problem. During the installation 

period (1997–98), make S was in the research stage of development and did not include integrally sealed electronics. This prototype meter incurred a high frequency of electronic failures 

onsite when the wiring connection failed, often by cutting or 

breaking. Intermittent hardware and wiring problems with the 

prototype make S TFM commonly led to electronic malfunctions at the remotely located liquid crystal display (LCD) unit 

that stored total cumulative pumpage. Data were unrecoverable 

w − w = 0

AQ

AQ

AQ
20 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

Table 2. Estimates of intercept and method fixed-effects parameters for the diffQ model.

[C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; S, mean is significantly 

different from zero at the 5-percent significance level; NS, mean is not significantly different from zero

at the 5-percent significance level; the parameter estimates can be expressed as a percent difference 

by multiplying the respective value by 100]

Parameter Estimate Standard 

error

Significance at the 

5-percent level

Intercept – 0.0193 0.0050 S

Method of portable flowmeter (fixed)

 C 0.0173 0.0013 S

 M 0.0019 0.0015 NS

 P –0.0192 0.0014 S

P is Polysonic

M is McCrometer

PORTABLE FLOWMETER

METHOD

EXPLANATION

(1266) Number of measurements

C is Collins

PORTABLE FLOWMETER METHOD

ENTIRE NETWORK

A

(1,266)

B

CMP

(570) (337) (359)

 0.3

0.2

 0.1

0

0.1

0.2

0.3

0.3

0.2

0.1

0

0.1

0.2

0.3

1998 1999 2000 2001 2002

YEAR

C

 0.3

 0.2

 0.1

0

0.1

0.2

0.3

(223)(136)

(142)

(78)(47)

(64)

(105)

(72)

(75)

(96)(48)

(52)

(68)

(34)

(26)

_

_

_ _

_

_

_

_

_

diffQ (LOG OF PORTABLE FLOWMETER DISCHARGE MINUS 

LOG OF TOTALIZING FLOWMETER DISCHARGE)

Extreme outlier value

Outlier value

75th percentile

Median

25th percentile

Value less than or equal to 1.5 times the IQR

IQR

Figure 5. Boxplots showing diffQ (A) for the entire network, (B) by portable flowmeter method, and (C) by year, 1998–2002.
Variability of Power Consumption and Flow 21

for these missing periods of TFM operation. Although the make 

S TFMs performed well during the initial year of the study 

(1998), a large percentage of these prototype meters failed over 

the course of the 5-year study. 

Variability of Power Consumption and Flow

The use of PCCs to estimate ground-water pumpage from 

wells is most accurate when the relation of well discharge to 

power consumption remains stable. Over time, hydrologic and 

pump operating conditions may change, thus altering the relation between discharge and power consumption. Depth to 

ground water may increase during a drought or after an 

extended period of pumping, or the pump efficiency may 

decrease as the irrigation system ages. These well operations 

can result in variations in the PCC over time and can result in 

errors when using the PCC approach to estimate ground-water 

pumpage.

A comparison of the 1998–2002 PCC values was made 

using two different statistical models: diffC and diffL. Recall 

that diffC was defined simply as the log of PCC. DiffL was 

defined as the log of total power consumption for the season 

minus the log of TFM pumpage for the same season. DiffP was 

defined as the log of total pumpage using the PCC minus the log 

of total pumpage using TFM. Mathematically, diffP is equal to 

diffL minus diffC.

The difference between diffC and diffL was one of time 

scale: diffC was obtained using instantaneous values of power 

consumption and flow, whereas diffL was obtained using seasonally integrated values of power consumption and flow. 

Because of the similarity in diffC and diffL, a comparison of 

their statistical behavior is important, particularly in evaluating 

variability in diffP. It is also important to understand the compensating effects that occur in the differences between diffC and 

diffL, which provides an understanding of the sources of variability in diffP. Therefore, the following section summarizes the 

primary results from the statistical models for diffC and diffL

followed by a subsequent section that provides a detailed discussion of the analysis of variance. Statistical modeling for 

diffC used 1,245 values, whereas the diffL analysis used 

336 measurements (one diffL value per site per year).

Summary of Primary Results

Estimates for the method fixed effects for diffC (table 4) 

were very close to those for the diffQ model (table 2), except 

with opposite sign (because log portable flowmeter discharge 

was subtracted from the log of power demand to compute log 

PCC). However, significant differences were detected among 

the types of discharge distribution systems (table 4). PCCs for 

type S (sprinkler) discharge distribution systems were higher 

than PCCs for the other types; and type L (low pressure) PCCs 

were the lowest (fig. 8). The estimates for type fixed effects in 

the diffL model for L, O, and S distribution systems also were 

similar to the corresponding effects for the diffC model (table 4, 

fig. 8). A comparison of the statistical results, however, indicated a discrepancy between the CH and CL effects for the diffC

and diffL models. These differences were not discernible in 

figure 8, probably as a result of the large site-to-site variability. 

The statistical models indicated the high and low TDH complex 

sites (CH and CL) had a fixed-effect difference of 0.149 using 

the diffC data but only 0.030 using the diffL data. The seasonal 

averaging of the values in diffL balanced the differences 

between high and low TDH in the complex system. 

The results of statistical analysis indicated that distribution 

system type and site variables accounted for 94.8 percent of the 

Table 3. Estimates of the mean and variance for random variables in the diffQ model of ground-water discharge 

differences. 

[PWL, pumping water level; --, not applicable]

Random variables Symbol Mean Standard error 

of the mean Variance

Percentage of total 

variance explained 

by each variable

Time-trend coefficient AQ 0.0009 0.0018 0.0000313 5.5

PWL trend coefficient UQ – 0.018 0.0170 0.00392 1.2

Site effect SQ0 -- 0.00147 45.5

Year effect YQ 0 -- 0.0000156 0.5

Site/year effect (SY)Q 0 -- 0.000251 7.7

Date effect DQ0 -- 0.000190 5.9

Random error term eQ 0 -- 0.000820 25.4
22 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

PUMPING WATER LEVEL, IN FEET BELOW CENTERLINE OF WELL DISCHARGE 

SITE

A

B

1998 1999 2000 2001 2002

1998 1999 2000 2001 2002

0.2

0.1

0

–0.1

–0.2

0

10

50

100

20010

50

100

20010

50

100

20010

50

100

20010

50

100

20

20 40 60 80 100 120

0.2

0.1

0

–0.1

–0.2

0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 120 0 20 40 60 80 100 12

Figure 6. Variations in diffQ (A) by year at network sites, and (B) by year with respect to pumping water levels, 1998–2002.
Variability of Power Consumption and Flow 23



.5-"%2/&02/",%-3

9%!2/&02/",%-

%XISTING
4OTALFAILURE 

-ANUFACTURE-AKE3
%LECTRONICFAILURE    -ANUFACTURE-AKE-
/THER   -ANUFACTURE-AKE-
$EBRISCLOG   -ANUFACTURE-AKE-
4OTALFAILURE 

    



 

 









 

























Figure 7. Types of problems and failures for totalizing flowmeters, 1998–2002.
24 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

total variance in diffC, and the model with all explanatory 

variables accounted for 99.5 percent of the variance. The distribution system type and site variables accounted for 97.8 percent 

of the total variance in diffL, and the model with all explanatory 

variables accounted for 99.4 percent of the variance. Variables 

other than type and site only had a small influence on diffC and 

diffL. However, as described in the following section “Details 

of Analysis,” the other variables were important because of 

their effect on diffP. 

Estimates of mean and variance for the random coefficients of the quantitative variables in the diffC and diffL models 

(table 5) differed from those in the diffQ model (table 3). In the 

diffC model, the estimate for the mean of the time-trend coefficient, , was 0.0149, which indicated a tendency of PCC values to increase by about 1.5 percent per year on the average. 

This indicates that the ratio of power consumption relative to 

amount of water pumped (as measured over a very short period 

of time) increased over the period of record; that is, depth to 

water increased and(or) pump efficiency decreased with time. 

About 90 percent of the sites showed a positive time-trend 

coefficient (fig. 9). 

The mean of the coefficient describing the change in 

diffC with respect to pumping water level was significantly positive (0.1310), indicating a tendency for PCCs to increase with 

PWL by about 1.3 percent for a 10-percent increase in PWL

(table 5). Generally this may be interpreted as indicating a 

decrease in pump efficiency with increasing PWL. Figure 10 

shows the overall relation between PCCs and pumping water 

levels (PWLs). Although there is a large amount of variance 

(scatter) in the relation, the PCC data indicated an overall tendency to increase as PWL increases. 

In the diffL model, the estimated mean of the time 

trend, , was 0.0166 (table 5), which indicated an upward 

trend with time equal to about 1.7 percent per year on average, 

similar to the time trend for diffC (table 5). The pumping water 

level (PWL) trend observed for diffL also was similar to that for 

diffC. The mean of the coefficient describing the change in 

diffL with respect to pumping water level was significantly positive (0.0919, table 5), again, indicating a tendency for diffL to 

increase with PWL— about 0.92 percent for a 10-percent 

increase in PWL. 

Details of Analysis

Results of the analysis of variance are listed in tables 4 and 

5 for diffC and for diffL and were analogous to the results for the 

instantaneous discharge data (diffQ) presented in tables 2 and 3. 

Differences in estimates of the mean differences listed in 

table 4 that are more than 2 standard errors from zero are indicated as being statistically significant. 

The total variance of diffC was 0.215, so the model 

accounted for about 100 × (0.215 – 0.00116)/0.215 = 99.5 percent of the total variance of diffC. The contribution of type was 

0.108, which represented about 100 × 0.108/0.215 = 50.2 percent of the total variance. PCCs for type S (sprinkler) discharge 

distribution systems tended to be much larger than those for 

other types, and type L (low) and O (open) tended to be smaller. 

These tendencies were quantified by the type fixed-effect estimates provided in table 4. There was significant variability in 

AC

UC

AL

UL

Table 4. Estimates of the intercept and method and type fixed effects parameters in the diffC and diffL models.

[C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; O, open; L, low-pressure; S, sprinkler; CH, complex high; CL, complex low; 

s, mean is significantly different from zero at the 5-percent significance level; ns, mean is not significantly different from zero at the 5-percent significance 

level; --, not applicable]

Parameter Estimate

(diffC)

Standard 

error

(diffC)

Significance at the 

5-percent level

(diffC)

Estimate

(diffL)

Standard 

error

(diffL)

Significance at the 

5-percent level 

(diffL)

Intercept 4.735 0.045 -- 4.727 0.047 --

Method of portable flowmeter (fixed)

 C –0.0171 0.0016 s -- -- --

 M – 0.0025 0.0018 ns -- -- --

 P 0.0196 0.0017 s -- -- --

Type of discharge distribution system (fixed)

 O –0.289 0.058 s –0.303 0.061 s

 L –0.425 0.091 s –0.417 0.094 s

 S 0.780 0.100 s 0.790 0.110 s

 CH 0.040 0.054 ns –0.020 0.057 ns

 CL – 0.109 0.054 s –0.050 0.057 ns
Variability of Power Consumption and Flow 25

L O S CH

DISCHARGE DISTRIBUTION TYPE

3.6

3.9

4.2

4.5

4.8

5.1

5.4

5.7

6.0

6.3

6.6

3.6

3.9

4.2

4.5

4.8

5.1

5.4

5.7

6.0

6.3

6.6

(Note: logarithms can be converted to original units by taking the anti-logarithm) 

CL

diffC

diffL

A

L distribution type

3.5

4.0

4.5

5.0

5.5

6.0

CH distribution type

3.5

4.0

4.5

5.0

5.5

6.0

YEAR

O distribution type

3.5

4.0

4.5

5.0

5.5

6.0

3.5

4.0

4.5

5.0

5.5

6.0

YEAR

S distribution type

3.5

4.0

4.5

5.0

5.5

6.0

YEAR

CL distribution type

B

3.5

4.0

4.5

5.0

5.5

6.0

3.5

4.0

4.5

5.0

5.5

6.0

(115, 39) (709, 175) (123, 33) (145, 33) (153, 39)

(41, 9) (22, 9) (26, 9) (11, 5) (15, 7)

(253)

(42)

(115)

(38)

(160)

(39)

(114)

(30)

(67)(26)

(47, 7) (17,7) (27, 7) (22, 7) (10, 5)

(71,12) (20,11) (18, 8) (22,10) (14, 9)

(82, 9) (15, 5) (16, 8) (26, 8) (14, 9) EXPLANATION

(115) Number of measurements

TYPE OF DISCHARGE 

DISTRIBUTION SYSTEM:

1998 1999 2000 2001 2002 1998 1999 2000 2001 2002

1998 1999 2000 2001 2002 1998 1999 2000 2001 2002

1998 1999 2000 2001 2002

diffL (LOG OF TOTAL SEASONAL POWER CONSUMPTION

MINUS LOG OF TOTALIZING FLOWMETER PUMPAGE) diffL (LOG OF TOTAL SEASONAL POWER CONSUMPTION

MINUS LOG OF TOTALIZING FLOWMETER PUMPAGE)

diffC (LOG OF POWER CONVERSION COEFFICIENT)

diffC (LOG OF POWER CONVERSION COEFFICIENT)

Extreme outlier value

Outlier value

75th percentile

Median

25th percentile

Value less than or equal to 

1.5 times the IQR

IQR

L is low pressure 

O is open

S is sprinkler 

CH is complex high

CL is complex low

Figure 8. Variations in diffC and diffL (A) by various discharge distribution types, and (B) by year for each type of discharge 

distribution system, 1998–2002.
26 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

PCCs among different types of distribution systems that made 

this variable an important explanatory variable for diffC. In 

addition, the site term accounted for about 100 × 0.103/0.215 =

47.9 percent of the total variance (again disregarding the correlation among the three random terms , , and ), indicating that there was a large degree of site-to-site variability of 

PCCs, over and above that which could be accounted for by different discharge distribution-system types. Therefore, the statistical analysis indicated the type fixed effect and the site random 

effect were the most important terms in the model and 

accounted for almost all of the total variance of the (log transformed) PCCs. To confirm this and to get a more precise estimate of their combined effect, a second statistical analysis was 

performed with only two terms in the model—type and site. 

This analysis provided an error variance (measuring unexplained variation) of 0.00557, indicating that these two terms 

accounted for 100 × (0.215 – 0.00557)/0.215 = 94.8 percent 

of the total variance in diffC. The contribution of method 

to the total variance of diffC was calculated to be 0.000235. A 

break down of the effects of the mean (E) and variance (V) of 

the time trend and PWL random coefficients was given by 

, , , . 

(The reader is referred to the section titled “Estimates of Variance Components for Differences in Discharge” in the “Supplemental Information” section in the back of the report for a discussion of how these terms were computed.) The variance terms 

(V) were much larger than the mean terms (E), and, although the 

contribution of the time-trend slope variance (measured by 

0.00208) was more important than the contribution from the 

PWL slope variance (measured by 0.00133), the two quantitative variables accounted for a relatively small percentage of the 

total variance of diffC. Although these quantitative explanatory 

variables (time and PWL) accounted for only a small percentage of the total variance of diffC, these variables had an important influence on pumpage differences (diffP equals diffL minus 

diffC) through their effects on diffC and diffL. Therefore, a 

detailed discussion of the effect of these variables on diffC follows. The mean of the random coefficients AC (time coefficient) 

and U C (PWL trend coefficient) were significantly different 

from zero (table 5). The estimated mean of AC was 0.0149, 

which indicated that PCCs for all sites taken as a whole tended 

to increase by about 1.5 percent a year. The estimated mean of 

UC was 0.1310, which indicated, for example, that a 

10-percent increase in PWL resulted in about a 1.3-percent 

(using 0.10 × 0.1310 = 0.0131) increase in PCCs. 

As stated earlier, statistical modeling for diffL used 336 

measurements (one diffL value per site per year) and integrated 

values of power consumption and flow. Though similarly 

defined, the diffL analysis was independent of the diffC analysis. The total variance of the diffL model was 0.220, indicating 

the model accounted for about 100 × (0.220 – 0.00139)/0.220 =

99.4 percent of the total variance of diffL. The contribution of 

type to the variance was 0.111, or about 100 × 0.111/0.220 =

50.5 percent. The importance of this explanatory variable can, 

once again, be discerned from figure 8 and quantified in the 

fixed-effect estimates in table 4. The site random-effect term 

accounted for about 100 × 0.113/0.220 = 51.4 percent of the 

total variance. Thus, as was the case for diffC, the type fixed

effect and the site random effect together accounted for almost 

all of the total variance (note, the total for these two terms was 

greater than 100 percent because of sampling errors in the estimates and because errors were introduced by not considering 

SC AC UC

Vt = 0.00208 Et = 0.000417 Vw = 0.00133 Ew = 0.000159

Table 5. Estimates of mean and variance for random variables in the diffC and diffL models. 

[PWL, pumping water level; --, not applicable]

Random variables Symbol Mean

(diffC)

Standard error 

(diffC)

Variance

(diffC) Symbol Mean(diffL)

Standard 

error 

(diffL)

Variance

(diffL)

Time-trend coefficient AC0.0149 0.0048 0.000375 AL0.0166 0.0053 0.000526

PWL trend coefficient UC 0.1310 0.0570 0.144 UL0.0919 0.0580 0.112

Site effect SC0 -- 0.103 SL0 -- 0.113

Year effect YC0 -- 0.000118 -- -- -- --

Site/year effect (SY)C0 -- 0.000770 -- -- -- --

Date effect DC0 -- 0.00182 -- -- -- --

Year pumpage is estimated 

effect -- -- -- -- ZL

0 -- 0 .000153

Error term eC0 -- 0.00116 eL0 -- 0.00139
Variability in Ground-Water Pumpage 27

the correlation among the three random terms , , and 

). Similar to the diffC analysis, a more precise estimate of 

the combined effect of these two terms on diffL was done using 

a second statistical analysis with only two terms in the model 

for diffL—type and site. The error variance for this model was 

0.00480, indicating that type and site accounted for 100 ×

(0.220 – 0.00480)/0.220 = 97.8 percent of the variance of diffL. 

A breakdown of the effects of the mean (E) and variance 

(V) of the time trend and PWL random coefficients in the diffL

model was given by , , 

, and . Similar to the diffC results, 

estimates of the time trend and pumping water level (PWL) 

trend accounted for a small percentage of the total variance of 

diffL. The estimated mean values of AL and UL (table 5) had 

magnitudes and standard errors comparable to those of the diffC

model. In several respects, the results for the diffC model and 

the diffL model were similar. Both models had a very high percentage (about 95 percent and 98 percent, respectively) of the 

total variance explained by two explanatory variables—type 

and site. 

Other explanatory variables that explained only between 2 

to 5 percent of the total variance in diffC and diffL were important in evaluating the differences in pumpage, diffP. This 

occurred because diffP was calculated as the difference between 

diffL and diffC. When diffC was subtracted from diffL, the type 

and site effects in the two models tended to cancel, so the 

importance of these two variables was greatly diminished in the 

diffP model. The other explanatory variables such as date, time, 

and PWL that were relatively unimportant in the diffC and diffL

models became important in the diffP model. This explains the 

importance of keeping these other explanatory variables in the 

diffC and diffL models. The physical interpretation of what is 

happening is that PCC measurements made at a given site 

tended to be greatly influenced by the particular conditions 

unique to that site (such as discharge distribution-system type). 

However, in order to estimate pumpage by the PCC approach, 

these PCC values were applied to total seasonal kilowatthour 

measurements that were influenced by the same particular site 

conditions as the PCCs. Thus, the effects of the particular site 

conditions were canceled in estimating total pumpage. This will 

be observed in the next section when type and site are relatively 

much less important explanatory variables for diffP. 

Variability in Ground-Water Pumpage 

Using data collected at network wells during 1998–2002, 

the magnitude of discrepancy between ground-water pumpage 

as measured by TFMs and pumpage as computed by the PCC 

approach was evaluated. Statistical modeling was used to analyze variability in differences in ground-water pumpage (diffP) 

and evaluate temporal trends and effects of changes in pumping 

water levels. 

As discussed in the “Statistical Models for Pumpage Differences” section, three estimation techniques were used to 

evaluate diffP. The results of the statistical modeling for diffP

are discussed according to whether model fitting was done with 

the diffP values themselves or whether results from the diffC

and diffL models were used, and whether s was equal to [t], 

where s stands for year in which pumpage was estimated, and 

[t] stands for year in which the PCC measurement was made. 

The three cases are listed again here for ease of reference:

1. Results obtained using diffP data under case (i) ( ), 

fitting equation 7. For these results each PCC measurement was associated with one total power consumption

SL AL

UL

Vt = 0.00280 Et = 0.00054

Vw = 0.00111 Ew = 0.00008

s ≠ [t]

–3.00

–2.25

–1.50

–0.75

0

0.75

1.50

2.25

3.00

3.75

4.50

5.25

6.00

6.75

TIME-TREND COEFFICIENT (SLOPE) FOR diffC, 

IN PERCENT PER YEAR

0

2

4

6

8

10

12

14

16

18

20

22

24

26

NUMBER OF MEASUREMENTS

0

0.1

0.2

0.3

PROPORTION OF MEASUREMENTS 

PER BAR

–3.25

Figure 9. Distribution of time-trend coefficients (slope) for diffC, 1998–2002.
28 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

value in a randomly chosen year different from the year in 

which the PCC measurement was made.

2. Results obtained using diffP data under case (ii) ( ), 

fitting equation 8.

3. Results obtained using the individually fitted diffC and 

diffL models (eqs. 5 and 6).

Figure 11 shows the distribution and variations in diffP for 

case (ii), when PCC measurements and power consumption for 

the same year were used to compute pumpage. The overall 

mean of the 1,245 diffP values was –1.8 percent. The median 

diffP, depending on the year, ranged from +0.1 to –2.9 percent; 

the median diffP for the entire network was –1.5 percent. About 

60 percent of all diffP values were between –6 and +6 percent, 

and about 80 percent of diffP values were between –10 and +10 

percent, regardless of the year. Most years showed a slight negative bias. A negative bias indicates that pumpage computed 

with the PCC approach tended to be smaller than pumpage 

using TFMs. Similar to diffQ, differences in pumpage that were 

computed using portable flowmeter method P showed an overall negative bias. There was no discernible bias in diffP when 

pumpage was computed using portable flowmeter method C. 

Final results for the intercept and fixed effects estimates 

are listed in table 6 and are analogous to the results for the differences in instantaneous discharge data (diffQ) presented in 

table 2. The method effects were similar using all three estimation techniques, and these values were similar for diffQ and 

diffC models. The discharge distribution system type effects for 

L, O, and S types were not significantly different from zero. 

Evidently the large L, O, and S type effects detected in the diffC

and diffL models tended to cancel when diffP was computed. 

For example, even though PCCs tended to be much larger for 

sprinkler (type S) distribution systems, the fact that these PCCs 

were applied to total electrical power-consumption values, 

which showed the same tendency in relation to total pumpage, 

made this type effect vanish. This was not the case for the CL 

and CH effects. The CL effect for the three estimation techniques ranged from 0.059 to 0.074, indicating that pumpage 

estimated by the PCC method was 6 to 7 percent greater than the 

pumpage measured by a TFM for complex sites using a low 

dynamic head PCC. The CH effect ranged from –0.060 to 

–0.066, indicating that pumpage estimated by the PCC method 

was 6 to 7 percent less than the pumpage measured by a TFM 

for complex sites for which the PCC was computed under high 

dynamic head conditions. 

The best estimates (those with the lowest standard errors) 

of the mean of the time trend, , were those using diffP data 

( ) or using the diffC and diffL data in table 7. These estimates (0.0158 and 0.0166, respectively) indicated that there 

was about a 1.6 or 1.7 percent increase in diffP for each year 

increase in the lag time u, and the standard errors of these numbers indicated a high degree of statistical significance. As an 

s = [t]

AP

s ≠ [t]

PUMPING WATER LEVEL, IN FEET BELOW CENTERLINE OF WELL DISCHARGE

POWER CONVERSION COEFFICIENT

Complex high discharge distribution type (CH )

0 40 80 120

Complex low discharge distribution type (CL)

0 40 80 120

50

120

190

260

330

400

50

120

190

260

330

400

50

70

90

110

130

150

Low pressure discharge

 distribution type (L)

POWER CONVERSION COEFFICIENT

0 10 20 30 40 0 20 40 60 80 100

40

70

100

130

160

190

220

250

Open discharge distribution type (O)

0 40 80 120

80

160

240

320

400

Sprinkler discharge distribution type (S)

PUMPING WATER LEVEL, IN FEET BELOW CENTERLINE OF WELL DISCHARGE

Figure 10. Relation between power conversion coefficients and pumping water levels for various discharge distribution systems, 

1998–2002.
Year-to-Year Variability of Pumpage 29

example of how these estimates are to be interpreted, if a PCC 

measurement was made in one year and this PCC value was 

used to estimate pumpage 2 years after the PCC measurement 

was made (that is, lag u=2 years), then diffP would on average 

tend to be about 3.2 percent more than if pumpage had been 

estimated in the same year the PCC measurement was made (lag 

u=0 years). The overall effect of the time trend and effects from 

the other variables on diffP are shown in figure 12. Recall that 

when lag year is zero, pumpage computed with the PCC 

approach tended to be smaller than pumpage using TFMs 

(figs. 11 and 12). Therefore, when diffP were 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 with 

respect to power consumption measurements, median diffPs

were +1.8 percent for a 2-year forward lag, +4.9 percent for a 

3-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. Figure 12 shows the distribution and 

variability in diffP when a PCC measurement made in one year 

was applied to total power consumption for another year (lag u

of –4 to +4 years). This figure shows a fairly linear change in 

the median diffP values for about years. However, there was 

no discernible change between the third and fourth year lags. 

Overall, these results indicate that there was a time trend present 

in these data. This trend has important implications for estimation of pumpage by the PCC approach. Therefore, additional 

analysis was done to independently evaluate the time trend and 

evaluate the effect of water availability on the time trend. This 

independent analysis is presented in the next section.

The estimated mean of pumping water level effects, , 

ranged from 0.0919 to 0.159, indicating that increasing the 

PWL conditions under which pumpage was measured relative 

to the PWL conditions under which the PCC was measured 

tended to cause an increase in diffP. The estimate of the mean 

of PWL, , with the smallest standard error in table 7 was 

0.0984; this value provided the best estimate of the magnitude 

of this effect. The standard error of the estimate 0.0984 was 

0.052; so at the 5-percent level, this term was not significantly 

different from zero. However, the estimate of the mean of 

PWL, , was significant at the 10-percent level. In addition, 

other estimates for PWL, , were of comparable magnitude, 

indicating that the effect was real. If the mean slope was 0.0984 

and if the pumping water level for the year in which pumpage 

was estimated was 10 percent higher than the pumping water 

level when the PCC measurement was made ( ), 

then on average, diffP would be 0.00984 (0.0984 × 0.10) higher 

than if pumpage had been estimated under the same pumping 

water level conditions as the PCC value. An increase in diffP of 

0.00984 translates into about a 1.0 percent increase in pumpage 

using the PCC approach relative to pumpage estimated using 

the TFM approach. 

The total variance of diffP ( ) was 0.0141, so the 

model accounted for about 100 × (0.0141 – 0.00107)/0.0141 =

92.4 percent of the total variance of diffP. The contribution of 

method to the variance was 0.000209, and the contribution of 

type to the variance was 0.00125. As previously stated, the 

method term was relatively unimportant, and the type term was 

much less important in explaining the variance of diffP than it 

was in explaining the variance of diffC and diffL. This is 

because diffP was calculated as the difference between diffL and 

diffC, so the type effect tended to cancel. This cancellation held 

for L, O, and S system types, but the difference between low 

total dynamic head and high total dynamic head PCC measurements in complex systems in fact was more evident in the diffP

data than it was in the diffC or diffL data. The net effect was that 

type did not explain a high percentage of variance as it did for 

diffC and diffL, but type still accounted for a substantial percentage (100 × 0.00125/0.0141 = 8.9 percent) of the total variance. 

The same cancellation was detected in the random site effect 

term; the estimated site variance for diffP was 0.00216, which 

was much smaller than the site variance for either diffC or diffL

and made the contribution of this variance to the total variance 

of diffP relatively smaller. A breakdown of the effects of the 

mean (E) and variance (V) of the time trend and PWL random 

coefficients in the diffP model was given by , 

, , and . The total 

contribution from the time trend was and the 

total contribution from PWL was , which 

indicates the numbers are of comparable magnitude. Based on 

these computations and the results in tables 6 and 7, the type 

fixed effect, the time-trend term, the PWL term, the site term S, 

the site/year terms (SY) and (SZ), and the date term D all had 

variance contributions in the range of 0.001 to 0.003 compared 

to the total variance of 0.0141. Therefore, no single explanatory 

variable stood out as being more important than the rest. However, combined, the explanatory variables accounted for 92.4 

percent of the total variance of diffP. This situation is in contrast 

to the diffC and diffL models, for which the two variables, type 

and site, dominated the other variables in explaining a large percentage of the total variance.

Year-to-Year Variability of Pumpage 

Year-to-year variability in conditions affecting the relation 

between ground-water pumpage and electrical power consumption can have a large influence on differences between pumpage 

determined by the PCC approach and pumpage determined by 

a TFM. Results discussed in the previous section indicated that 

there was a time trend in diffP that resulted in about a 1.6 to 1.7 

percent increase in diffP for each year increase in the lag time 

between PCC measurement and pumpage estimation. This section provides independent analyses of this finding. The independent analyses will involve (1) modeling year effects as fixed 

rather than random, (2) estimation of total time trends, and (3) 

modeling diffP with an additional explanatory variable reflecting water availability.

±3

UP

UP

UP

UP

w − w = 0.10

s ≠ [t]

Vu = 0.00215

Eu = 0.00119 Vw = 0.00309 Ew = 0.00024

Vu + Eu = 0.00334

Vw + Ew = 0.00333
30 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

1998 1999 2000 2001 2002

YEAR

-0.30

-0.24

-0.18

-0.12

-0.06

0.06

0.12

0.18

0.24

0.30

-0.30

-0.24

-0.18

-0.12

-0.06

0 0

0.06

0.12

0.18

0.24

0.30

ENTIRE NETWORK

A B

-0.30

-0.24

-0.18

-0.12

-0.06

0

0.06

0.12

0.18

0.24

0.30

CMP

PORTABLE FLOWMETER METHOD

L O S CH CL

TYPE OF DISCHARGE DISTRIBUTION SYSTEM

-0.30

-0.24

-0.18

-0.12

-0.06

0

0.06

0.12

0.18

0.24

0.30

C D

(1,236) (488) (187) (247) (194) (120)

(113) (709) (122) (145) (147) (558) (325) (353)

(1,236) Number of observations

(note: 9 values greater than 0.30 or less than -0.30 are not shown)

diffP (LOG OF TOTAL PUMPAGE USING POWER CONVERSION COEFFICIEN

T

MINUS LOG OF TOTAL PUMPAGE USING TOTALIZING FLOWMETER)

Extreme outlier value

Outlier value

75th percentile

Median

25th percentile

Value less than or equal to 1.5 times the IQR

IQR

EXPLANATION

TYPE OF DISCHARGE DISTRIBUTION SYSTEM

L is Low pressure

O is Open

S is Sprinkler

CH is Complex high

CL is Complex low

PORTABLE FLOWMETER METHOD

C is Collins

M is Mc Crometer

P is Polysonic

Figure 11. Variability of diffP when power conversion coefficient measurements and power consumption were made 

in the same year (A) for the entire network, (B) by year, (C) by type of discharge distribution system, and (D) by 

portable flowmeter method, 1998–2002.
Year-to-Year Variability of Pumpage 31

Fixed-Year Effects

Results in the previous sections were obtained under an 

assumption that year effects, Y and Z, were random and that systematic changes over the period of record were modeled by a 

linear trend in time. In this section, the year effects, Y and Z, 

were made to be fixed effects, and the assumption of a linear 

trend was eliminated, thus allowing a more detailed evaluation 

of year-to-year changes. 

Tables 8 and 9 provide estimates of the year effects when 

Y and Z are fixed effects. In the diffQ model, the only year effect 

that was significantly different from zero was 2001, and the 

magnitude of this effect was only 0.0085 (table 8). In the diffC

and diffL models (table 8), there were similarities in the year 

effects for the 5 years under consideration for the two models, 

indicating similarities in the relation between flow and seasonal 

power consumption for short time scales (diffC) and yearly time 

scales (diffL). The largest positive year effect was for 2002, 

which was about 4 percent for both diffC and diffL. The largest 

negative year effect was for 1999, which was about –3 percent 

for diffC and about –2 percent for diffL. Similarly, in 1998, there 

was a negative year effect of about –2 percent. The year effects 

for diffC and diffL for 1998, 1999, and 2002 were significant 

when compared with their associated standard errors. 

Generally, a monotonically increasing trend with time 

over the 5-year period existed for both models (although the 

1999 effect for diffC was somewhat less than the 1998 effect) 

and the average increase per year was close to the mean slopes 

of 1.5 percent (0.0149) and 1.7 percent (0.0166) given in 

table 5 for diffC and diffL, respectively. 

Estimates of (year effect for the year the PCC measurement was made) and (year effect for the year total power 

consumption was used to estimate pumpage) in the model for 

diffP data in table 9 were similar to each other in magnitude 

(with opposite sign), and the values obtained using diffP where 

 were similar to those obtained using the diffC and diffL

data. One interesting feature was that the effects were 

monotonically increasing from 1998 to 2002, whereas the 

effects exhibited an increase from 1998 to 1999 but then 

decreased monotonically from 1999 to 2002. The pattern for 

was the same as that for average PWLs, which is one indication 

that the factors causing temporal changes in may be related 

to factors causing temporal changes in PWLs.

Estimates of (the year effect for data where the PCC 

measurement and pumpage estimate were made in the same 

year) provided in table 9 tended to be near zero; the only statistically significant value was 0.0143 for 1999, obtained in the 

analysis of the diffP data with s=[t]. (Notice in table 9 that 

results of the analysis of diffP with could be used to 

obtain estimates of even though did not appear explicitly 

in the fitted model; the standard errors, however, were considerably larger than those obtained using the diffP data with 

s=[t]). In this situation, the year effects associated with PCC 

measurement and pumpage estimate tended to cancel each 

other.

YP

ZP

s ≠ [t]

ZP

YP

YP

YP

YP

′

s ≠ [t]

YP

′ YP′

Table 6. Estimates of parameters in the diffP model of differences in ground-water pumpage between the power conversion 

approach and totalizing flowmeters.

[C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; O, open; L, low pressure; S, sprinkler; CH, 

complex high; CL, complex low; s, year when pumpage is estimated (s=0 for 1998); [t], year when PCC measurement is made 

([t]=0 for 1998; --, not applicable]

 diffP data, diffP data, diffC, diffL data

Estimate Standard

error

Estimate Standard

error

Estimate Standard

error

Intercept –0.014 0.011 –0.006 0.010 –0.008 --

Method of portable flowmeter 

 C 0.0170 0.0015 0.0153 0.0017 0.0171 0.0016

 M 0.0023 0.0018 0.0040 0.0020 0.0025 0.0018

 P –0.0194 0.0017 –0.0192 0.0019 –0.0196 0.0017

Type of discharge distribution system

 L –0.010 0.017 –0.012 0.016 0.008 --

 O –0.012 0.010 –0.009 0.010 –0.014 --

 S 0.016 0.018 0.014 0.018 0.008 --

 CH –0.064 0.010 –0.066 0.010 –0.060 --

 CL 0.069 0.010 0.074 0.010 0.059 --

s = [t] s ≠ [t]
32 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

Table 7. Estimates of the mean and variance for random variables in ground-water pumpage using the diffP model.

[s, year when pumpage is estimated (s=0 for 1998); [t], year when PCC measurement is made ([t]=0 for 1998); Ap, time trend coefficient; Up, 

pumping water level coefficient; Sp, site effect; Yp, year effect for discharge or PCC measurement; (SY) p, site/year effect; Zp, year effect for a year 

total pumpage is estimated; (SZ) p, site/year effect for a year in which total pumpage is estimated; Y'

p, year effect when PCC measurement and 

pumpage estimate are made in same year; (SY') p, site/year effect when PCC measurement and pumpage estimate are made in same year; Dp, date 

effect; ep, random error term; -- not applicable]

 diffP data, diffP data, diffC, diffL data

Estimate Standard

error

Estimate Standard

error

Estimate Standard

error

Mean 

AP 0.001 0.057 0.0158 0.0037 0.0166 0.0053

UP 0.159 0.083 0.0984 0.052 0.0919 0.058

Variance 

AP 0.00315 -- 0.000448 -- 0.000526 --

UP 0.287 -- 0.126 -- 0.112 --

SP 0.00187 -- 0.00216 -- -- --

YP -- -- 0.000162 -- 0.000118 --

(SY)P -- -- 0.000781 -- 0.000770 --

ZP -- -- 0.0000358 -- 0.000153 --

(SZ)P -- -- 0.00222 -- 0.00139 --

Y'P 0.0000349 -- -- -- -- --

(SY')P 0.00136 -- -- -- -- --

DP 0.00160 -- 0.00159 -- 0.00182 --

eP 0.00115 -- 0.00107 -- 0.00116 --

s = [t] s ≠ [t]
Year-to-Year Variability of Pumpage 33

To obtain the net year effects when PCC measurement and 

pumpage estimate are made in different years, the appropriate 

values of (for the year in which the PCC measurement was 

made) and (for the year in which pumpage was estimated) 

in table 9 must be summed. This calculation was done for all 25 

possible combinations of pairs of years and plotted as a function 

of yearly lag in figure 13. The scatter plot has a strong 

linear pattern with a slope close to the 1.58 percent per year 

mean time-lag slope (AP) given for diffP in table 7. Thus, the 

fixed effects analysis reflects the same upward trend as the random effects analysis. The pattern in figure 13 and the connection between the random and fixed effects analyses may be 

summarized by the relation , where the carets over the year effects on the left side of the relation indicate 

estimates from the fixed effects analysis and u on the right side 

of the relation is time lag in years. 

Total Time Trend

It was mentioned in the “Methods of Statistical Analysis” 

section that it was necessary to consider the PWL and timetrend terms jointly in the models. That is, there may be some 

interaction between these terms that may have a bearing on 

interpreting the analyses. The results presented so far indicate 

that diffC and diffL tended on the average to exhibit an increase 

ZP

s − [t]

YP ZP 0.0158u ˆ ˆ + ≈

-4 -3 -2 -1 0 1 2 3 4

NUMBER OF YEARS BETWEEN POWER CONVERSION COEFFICIENT MEASUREMENT

 AND TOTAL POWER CONSUMPTION USED TO ESTIMATE PUMPAGE

-0.30

-0.24

-0.18

-0.12

-0.06

0

0.06

0.12

0.18

0.24

0.30

(note: 34 values greater than 0.30 or less than —0.30 are not shown)

(39) (76) (142) (1,236) (217) (276) (231) (150) (114)

(39) Number of observations

diffP (LOG OF TOTAL PUMPAGE USING POWER CONVERSION 

COEFFICIENT MINUS LOG OF TOTAL PUMPAGE

 USING TOTALIZING FLOWMETER)

Extreme outlier value

Outlier value

75th percentile

Median

25th percentile

Value less than or equal to 1.5 times the IQR

IQR

EXPLANATION

Figure 12. Variability of diffP for the number of years lagged between when the power conversion coefficient measurement was 

made and when total power consumption was used to estimate pumpage, 1998–2002.
34 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

with both PWL and time. PWL tended on the average to 

increase with time; the increase of PWL over the period of 

record (1998 – 2002) was on the average 3.2 percent per year 

for all sites. Factors including availability of surface water for 

irrigation, regional ground-water conditions, and climate likely 

caused PWL to change over this 5-year period influencing the 

time trend in the models. In other words, the coefficients of the 

PWL term and time-trend term may be interrelated and may be, 

to some extent, reflecting the same underlying hydrologic conditions. On the other hand, it is possible that the time trend 

reflects additional factors that may be for the most part unrelated to PWL. For example, the time trend in diffL may be partly 

caused by a tendency for drift (associated with debris clogging) 

in the TFM at certain sites. Available data are insufficient to distinguish with certainty all the causative factors that might be 

affecting the observed time trend. Nevertheless, one useful 

analysis was to evaluate the time trend by fitting the models 

without the PWL term. This analysis provided an overall estimate of time trend without allowing any compensating adjustments for PWL. When this analysis was done using diffC data, 

the estimate of the mean value of the time coefficient was 

0.0214 (standard error 0.0055), indicating about a 2.1 percent 

per year increase in diffC as compared to the 1.5 percent per 

year increase in diffC when the PWL term was included in the 

model. This indicated that the presence of the PWL term 

accounted for some of the increase with time. Likewise, when 

this analysis was done for the diffP data ( ), the estimate 

of the mean of was 0.0217 (standard error 0.0041), indicating about a 2.2-percent increase per year, compared to 1.6 percent per year when PWL was included in the model. A fixedyear effects analysis similar to that discussed in the previous 

section produced the relation , which gives 

the approximate relation between fixed-year effects and trend in 

the random effects model when PWL was not included in the 

models. 

Additional Explanatory Variables

It was discussed previously that the time-trend term in 

the models may be a surrogate for other explanatory variables 

for which data may not be available. It is reasonable to assume 

that there are underlying factors that cause any trend in time, but 

it is usually not known exactly what these factors may be or 

what variables would provide the most explanatory power in a 

statistical model. In this section, some additional data were used 

to evaluate the effect of incorporating another explanatory variable on the time trend. For many of the site-year combinations, 

an associated volume of ditch diversions for surface-water irrigation was known. There was one value for each combination 

of pumping season and ditch, and there may be more than one 

site associated with each ditch. The statistical model for diffC

was fitted with this diversion (logarithmically transformed and 

corrected for the ditch average, exactly as the PWL was transformed and corrected in equation 5) as an additional explanatory variable. There were 1,081 diffC values for which data on 

the diversion variable were available. This analysis resulted in 

rendering the time-trend term insignificant and, thus, the timetrend term could be dropped from the model, leaving PWL and 

the diversion variable as the only quantitative explanatory variables. It is not known whether such a diversion variable is, in 

general, the best way to account for temporal variability of 

hydrologic conditions or whether other variables or combinations of variables would be more quantitative. This is left as a 

topic for further investigation. However, the fact that the timetrend term became insignificant in the presence of the diversion 

variable is additional evidence that the time trend in these data 

serves as a surrogate variable for other climate-related processes that caused the PWL changes through time. 

Implications of Year-to-Year Variability for the PCC 

Approach to Pumpage Estimation

Results of the statistical analyses presented in this report 

reflect the changing hydrologic conditions in the Arkansas 

River alluvial aquifer for the period from 1998 through 2002. 

AC

s ≠ [t]

AP

YP ZP 0.0217u ˆ ˆ + ≈

Table 8. Estimates for year effect in the diffQ, diffC, and diffL models.

Year

 diffQ diffC diffL

Estimate Standard 

error

Estimate Standard 

error

Estimate Standard 

error

 1998 –0.0020 0.0026 –0.0203 0.0058 –0.0234 0.0056

 1999 –0.0027 0.0033 –0.0308 0.0071 –0.0175 0.0063

 2000 –0.0057 0.0030 –0.0015 0.0065 –0.0094 0.0058

 2001 0.0085 0.0032 0.0111 0.0070 0.0064 0.0063

 2002 0.0018 0.0038 0.0416 0.0086 0.0438 0.0080
Year-to-Year Variability of Pumpage 35

Streamflows and surface-water diversions for irrigation varied 

substantially during the study period and substantially 

decreased in 2001 and 2002. PWLs generally showed an 

upward trend, indicating that depth to ground water tended to 

increase. Statistical modeling of diffC (the log of PCC) and diffL

showed similar upward trends with time and a positive dependence on PWL. The time trend for both variables was in the 

range of 1.5 to 1.7 percent per year for models including a PWL 

term, which statistically corrected for changes in PWL. However, given that PWLs also were increasing with time, the overall time trend of diffC and diffL, without correcting for PWL, 

was about 2.1 percent per year. The variables diffC and diffL

both measure the relation of electrical power consumption to 

pumpage (that is, pump efficiency), but diffC and diffL corresponded to different times—diffC reflects the conditions under 

which the PCC was obtained and diffL reflects the conditions 

under which seasonal pumpage was estimated. When these two 

sets of conditions are different, then bias will be introduced in 

using the PCC method to estimate pumpage. In the relation 

, the term corresponds to the year effect 

for the year in which the PCC was measured, and corresponds to the year effect for the year in which pumpage was 

estimated, and these added together produced an overall average bias of about 2.2 percent per year of lag between the PCC 

measurement year and pumpage estimation year. The implication of such a trend, for example, is that for a 2-year lag, pumpage estimated by the PCC approach would be about 4.4 percent 

higher relative to TFM-estimated pumpage than if the lag was 

zero years, and for a 4-year lag pumpage estimated by the PCC 

approach would be about 8.8 percent higher relative to TFMestimated pumpage. Again, recall that when lag is zero years, 

pumpage computed with the PCC approach tended to be smaller 

than pumpage using TFMs. Therefore, as shown in figure 12, 

the aggregate diffP for each forward-lag year was less than 

2.2 percent per year of lag. 

The model results with the surface-water diversion term 

indicates that much of the trend of 2.2 percent per lag year in 

diffP results from applying a PCC to estimate pumpage under 

hydrologic conditions different from those under which the 

PCC was measured. The analysis also indicates that the modeled time trend is a surrogate for changes in underlying hydrologic conditions. 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, and it is feasible that future periods 

could exhibit downward trends or nonmonotonic variability. 

Although detailed long-term analyses have not been performed 

YP ZP 0.0217u ˆ ˆ + ≈ YP

ˆ

ZP

ˆ

Table 9. Estimates for year effect in the diffP models.

[s, year when pumpage is estimated (s=0 for 1998); [t], year when PCC measurement is made ([t]=0 for 1998); Yp, year PCC measurement 

is made; Zp, year pumpage is estimated; Y’p, year effect when PCC measurement and pumpage estimate are made in the same year; 

-- not applicable]

diffP data, s = [t] diffP data, s = [t] diffC, diffL data

Estimate Standard 

Error Estimate Standard error

Estimate Standard 

error

Effect Yp

1998 -- -- 0.0191 0.0060 0.0203 0.0058

1999 -- -- 0.0318 0.0072 0.0308 0.0071

2000 -- -- -0.0003 0.0066 0.0015 0.0065

2001 -- -- –0.0061 0.0071 –0.0111 0.0070

2002 -- -- –0.0446 0.0085 –0.0416 0.0086

Effect Zp

1998 -- -- –0.0230 0.0074 –0.0234 0.0056

1999 -- -- –0.0206 0.0078 –0.0175 0.0063

2000 -- -- –0.0107 0.0072 –0.0094 0.0058

2001 -- -- 0.0158 0.0079 0.0064 0.0063

2002 -- -- 0.0386 0.0087 0.0438 0.0080

Effect Y′p

1998 0.0002 0.0051 –0.0039 0.0098 –0.0031 --

1999 0.0143 0.0061 0.0112 0.0103 0.0133 --

2000 –0.0095 0.0058 –0.0110 0.0098 –0.0079 --

2001 0.0003 0.0062 0.0097 0.0106 –0.0047 --

2002 –0.0053 0.0068 –0.0060 0.0111 0.0022 --
36 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

for this report, other studies have shown (Steger, 2002) that 

static ground-water levels in the study area have exhibited small 

variations over multidecadal time scales with a high degree of 

temporal correlation, and monotonic trends that appear approximately linear over a 5-year period such as the one detected in 

this study are not uncommon in such slowly varying time series. 

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. Periodic PCC data are 

needed to determine actual future changes that may occur in 

diffC. A subset of wells in the network described in this report 

could be used to quantify future changes in diffP that may occur.

Estimation of Total Network Pumpage

The analysis presented earlier in the report, in the “Variability in Ground-Water Pumpage” section, provided estimates 

of diffP, the mean or average differences between the logtransformed PCC estimated total pumpage and TFM-measured 

total pumpage 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 for Total Network Pumpage

Total network pumpage differences can be estimated by 

using techniques outlined in Dash and others (1999) and by 

following certain assumptions about average conditions and 

random sampling. The average pumpage per site per year for 

the network studied was 147 acre-ft, and the variance was 

28,600 acre-ft squared (giving a standard deviation of 

169 acre-ft). These values together with results from the analysis of the diffP data were used to estimate the mean and variance 

of differences between total network pumpage using the TFM 

method and the PCC method as a function of number of sites in 

the network and of lag between the time the PCC was measured 

and time total pumpage was estimated. 

For small year effects, the average difference in TFM and 

PCC network pumpage, as a fraction of total network pumpage, 

is slightly greater than average individual well year effects in 

diffP independent of the number of wells in the network. The 

standard deviation of this difference, again relative to total net-

–4 –3 –2 –1 0 1 2 3 4

–0.10

–0.05

0

0.05

0.10

NUMBER OF YEARS BETWEEN POWER CONVERSION COEFFICIENT MEASUREMENT

 AND TOTAL POWER CONSUMPTION USED TO ESTIMATE PUMPAGE

diffP (LOG OF TOTAL PUMPAGE USING POWER CONVERSION 

COEFFICIENT MINUS LOG OF TOTAL PUMPAGE USING 

TOTALIZING FLOWMETER)

Figure 13. Average year effects on diffP for the number of years lagged between when the power conversion coefficient measurement was made and when total power consumption was used to estimate pumpage, 1998–2002.
Estimation of Total Network Pumpage 37

work pumpage, also depends on individual well year effects and 

decreases as the number of wells in the network increases.

For 100 wells and a lag of 4 years between PCC measurement and pumpage estimation, the standard deviation is 2.3 percent of total network pumpage. Under assumptions of normality, there is a 95-percent probability that the total network 

pumpage for 100 wells estimated by the PCC approach would 

be between 5.2 and 14.4 percent greater than pumpage measured using a TFM. Figure 14 shows the estimated mean and 

expected range in differences in total pumpage for varying 

number of network wells and for varying lag years using the 

same assumptions as above. For 1,000 wells, the estimated difference in total network pumpage for a 4-year lag 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 3-year lag would be between about 6.1 and 8.8 

percent greater than pumpage measured using a TFM; and 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.

Details of Analysis and Results

The variable diffP is the difference between log annual 

pumpage using the PCC method and log annual pumpage using 

a TFM, for a single site. These results may be extended to estimate aggregated discrepancies between PCC pumpage and 

TFM pumpage for a number of sites by using the basic approach 

described in Dash and others (1999). Let stand for the difference in aggregated total pumpage for n wells for a single 

year, or

 (9)

where

 is pumpage calculated by PCC, and

 is total pumpage measured by a TFM.

An estimate of the mean and variance of this difference can 

be obtained by using results of the diffP data analyses. As discussed in Dash and others (1999), the fact that is a sum of 

independent (under current assumptions and others discussed 

below) random variables makes it reasonable to apply the central limit theory and conclude that is approximately normally distributed. This assumption can be used, together with 

estimates of the mean and variance of derived below, to 

make probability statements about the likely range of —the 

difference in aggregated total pumpage for n wells for a single 

year. 

The model for diffP ( ) in equation 7 is used for all 

wells, with the same assumptions on site-to-site independence 

and normality of random terms stated before. In addition, certain other assumptions make the analysis easier, but similar derivations could be done for more general conditions. None of the 

wells is complex, so that the type effect of (insignificant in 

table 6) may be ignored. The intercept term, (also insignificant in table 6), is ignored. Portable flowmeter methods (C, M, 

and P) are assumed to be assigned randomly to wells with relative frequency of the different methods such that there is no net 

bias due to method. 

It is assumed further that a PCC measurement is made for 

all n wells in the same year; the year effect ( ) is therefore the 

same for all n wells. Similarly, pumpage is estimated for the 

same year at all wells; the year effect for pumpage estimation 

( ) is therefore the same for all n wells. These year effects are 

assumed to be fixed effects, and it is assumed that PWL is not 

included in modeling diffP so that the sum of the year effects 

may be approximated:

(10)

The diffP are taken to be independent of and TFM 

pumpage ( ) for n wells are sampled independently from a 

population with mean and variance . Using the sample 

mean and variance for all available sites and years (except those 

for which diffL outliers were identified) estimates for these 

quantities are acre-ft and acre-ft squared. 

(Note: a caret is added over a parameter to denote sample estimate.)

Under these assumptions, normality of diffP may be used 

to show that the mean (that is, expectation E) of is

(11)

and the variance is

 (12)

These depend on the mean and variance of diffP, which are now 

obtained. Using equation 7 and the assumptions, the mean of 

diffP is

(13)

 

and the estimated mean of diffP is therefore 

 (14)

Dn

Vi

~

Vi

Dn

Dn

Dn

Dn

s ≠ [t]

P γ

μ P

YP

ZP

0.0217 . ˆ ˆ YP + ZP ≈ u

Vi

Vi

μV

2 σ V

μˆV = 147 ˆ 28600 2 σ V =

Dn

( 1) ]

[( ) ( 1)

[ ( 1)]

( ) [ ( 1)]

2 ( ) 2

1 ( ) 2

2 2 2 ( ) ( ) ( )

1

+ −

= + −

= −

= ∑ −

+

+

=

E diffP Var diffP

V

E diffP Var diffP Var diffP

V V

diffP

n

i

diffP

n i

e

n e e

nVar V e

Var D Var V e i

σ

μ σ

( ) , E diffP = YP + ZP

. ˆ ˆ ( ) ˆE diffP = YP + ZP

) ( 1) ~( ~

11 1 1

= ∑∑∑ ∑ − = − = − == = =

n

i

n

i

n

i

n

i

diffP

n i i i i i i D V V V V V e

( 1)

( 1) ( 1)

( ) 2

1 ( )

1

= −

= ∑ − = −

+

=

E diffP Var diffP

V

diffP

V

n

i

diffP

n i

n e

ED E V e n E e i

μ

μ
38 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

0

3

6

9

12

15

For a network of 100 wells

–4 –3 –2 –1 0 1 2 3 4

NUMBER OF YEARS BETWEEN POWER CONVERSION COEFFICIENT MEASUREMENT

AND TOTAL POWER CONSUMPTION USED TO ESTIMATE PUMPAGE

–15

–12

–9

–6

–3

–4 –3 –2 –1 0 1 2 3 4

–15

–12

–9

–6

–3

0

3

6

9

12

15

18

–4 –3 –2 –1 0 1 2 3 4

–12

–10

–8

–6

–4

–2

–4 –3 –2 –1

–12

–10

–8

–6

–4

–2

0

2

4

6

8

10

12

DIFFERENCES IN TOTAL PUMPAGE, IN PERCENT

For a network of 500 wells

01234

For a network of 1,000 wells

0

2

4

6

8

10

12

DIFFERENCES IN TOTAL PUMPAGE, IN PERCENT

For a network of 50 wells

NUMBER OF YEARS BETWEEN POWER CONVERSION COEFFICIENT MEASUREMENT

AND TOTAL POWER CONSUMPTION USED TO ESTIMATE PUMPAGE

Upper 95-percent prediction limit

Lower 95-percent prediction limit

Upper 95-percent prediction limit

Lower 95-percent prediction limit

Lower 95-percent prediction limit

Lower 95-percent prediction limit

Upper 95-percent prediction limit

Upper 95-percent prediction limit

Mean

Mean

Mean

Mean

Figure 14. Estimation of differences in total pumpage for varying number of wells.
Summary and Conclusions 39

Equation 7 may be used to obtain in terms of 

the variance components and then estimates of the variance 

components from the data analysis substituted to obtain an estimate of , but a more straightforward approach simply using the total variance of the diffP data given above is

.

Inserting these values into equations 10 and 11 yields final 

formulas for estimated mean and variance of :

 (15)

 (16)

Also, the standard deviation is the square root of the variance, or

 (17)

It is useful to look at these as a fraction of the mean network total TFM pumpage, or . 

 (18)

(19)

For small , . 

Therefore, the mean of , as a fraction of network total pumpage, is slightly greater than individual well year effects, independent of the number of wells in the network. Also, the 

presence of the term in the standard deviation indicates 

that the standard deviation decreases as the number of wells in 

the network increases. 

Figure 14 shows equations 18 and 19 in relation to lag u for 

several values of n, where equation 10 is used to evaluate the 

year effects. The mean exhibits a nearly linear dependence on 

lag year (u), but the standard deviation reflects little dependence 

on u. As an example of the calculation, letting u=4 lag years 

between PCC measurement and pumpage estimation gives 

 and the mean from equation 18 is

 (20)

and the standard deviation from equation (19) is

 (21)

For n=100 wells, standard deviation is equal to 0.0229, or 

the standard deviation is about 2.3 percent of the total network 

pumpage. This is comparable in size to the estimate given in 

Dash and others (1999). Under normality of , there is about a 

95-percent probability that the fractional difference between 

total network pumpage obtained by the PCC method and that 

obtained using a TFM will be between 0.0983 – 2(0.0229) =

0.0525, or 5.25 percent, and 0.0983+2(0.0229) =0.1441, or 

14.41 percent, for 100 wells with a lag of 4 years between time 

of PCC measurements and pumpage estimation year. The standard deviation is relatively small, and the major source of the 

difference is coming from the trend in the mean caused by the 

4-year lag. For 1,000 wells, the estimated difference in total network pumpage for a 4-year lag 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 3-year lag 

would be between about 6.1 and 8.8 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 

(fig. 14).

Summary and Conclusions

This report evaluates the variability in the differences 

between two approaches used to determine ground-water 

pumpage; the two approaches are power conversion coefficient 

(PCC) and totalizing flowmeter (TFM). The report compares 

measured pumpage using TFMs to computed pumpage using 

PCCs by developing statistical models of relations between 

explanatory variables, such as site, time, and pumping water 

level and the dependent variables based on discharge, PCC, and 

pumpage. 

During the study period, 1998–2002, hydrologic conditions varied substantially as streamflow in the Arkansas River 

ranged from 928,500 acre-ft in 1999 to 205,780 acre-ft in 2002. 

Less streamflow affected the amount of surface-water diversions; cumulative diversions in 2001 and 2002 were substantially less than diversions in 1998, 1999, and 2000. In general, 

depth to ground water increased as annual surface-water diversions decreased; depth to ground water measured in 2001 and 

2002 tended to be greater than during 1998–2000.

For the purposes of this report, four dependent variables—

diffQ, diffC, diffL, and diffP—were developed. Variable diffQ

was defined as the log portable flowmeter discharge minus the 

log TFM discharge; diffC was defined as the log of the power 

conversion coefficient (PCC); diffL was defined as the log of 

total seasonal power consumption minus log TFM pumpage for 

Var(diffP)

Var(diffP)

( ) 0.0141 ˆVar diffP =

Dn

E D e n YP Z P

n ( ) 147( 1) ˆ 0.0070 ˆ ˆ

= − + +

28,600( 1) ] .

( ) [713( ) ˆ

0.0070 2 ˆ ˆ

0.0070 2 ˆ ˆ

e n

Var D e

P P

P P

Y Z

Y Z

n

+ −

=

+ +

+ +

[713( ) 28,600( 1) ] .

( ) ˆ

0.0070 2 ˆ ˆ 0.0070 2 ˆ ˆ

e e n

Std D

YP Z P YP Z P

n

+ −

=

+ + + +

∑ = = n E i 1Vi nμV

n e e n

Std D YP Z P YP Z P

V

n 1 0.033( ) 1.32( 1) ˆ

( ) ˆ 0.0070 2 ˆ ˆ 0.0070 2 ˆ ˆ

= + − + + + +

μ

YP ZP ˆ ˆ + 0.0070 ˆ ˆ 1 0.0070 ˆ ˆ

− ≈ + + + +

P P

Y Z e Y Z P P

Dn

1/ n

0.0868 ˆ ˆ YP + ZP =

. 1 0.229 ˆ

( ) ˆ

n n

Std D

V

n = μ

Dn

1 ˆ

( ) ˆ 0.0070 ˆ ˆ

= − YP +ZP +

V

n e n

E D

μ

0.0983 ˆ

( ) ˆ =

V

n

n

E D

μ
40 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

the same season; and diffP was defined as the log of total pumpage using PCC minus log of total pumpage using TFM. All four 

of these dependent variables represented differences in two 

logarithmically transformed variables.

Discharge measured with a TFM was compared with discharge measured by portable flowmeter using the dependent 

variable diffQ. Three types of portable flowmeter were used: a 

pitot tube/manometer device (method C), an ultrasonic flow

meter (method P), and a propeller-type meter (method M). The 

overall mean of diffQ using all three portable flowmeter methods was –0.015, or about 1.5 percent less than TFM measurements, indicating that, on average, the portable flowmeter discharge measurement was about 2 percent less than the TFM 

discharge. However, the distribution of the differences varied 

with the selected portable flowmeter method. The median values and interquartile ranges for method C and M were smaller 

than for method P with the median diffQ value for methods C, 

M, and P being 0.5 percent, –0.6 percent, and –4 percent, 

respectively. Additionally, the aggregated diffQ values computed using method C indicated no overall bias; whereas, the 

aggregated diffQ values computed using method P indicated a 

fairly strong negative bias. A negative bias indicates that portable flowmeter method P tended to measure a smaller discharge 

than the TFM. 

Graphs of diffQ categorized by portable flowmeter method 

exhibited no observable persistent temporal trends. Estimates of 

the mean and variance of the coefficients of the time-trend term 

and pumping water level term in the statistical model for diffQ

indicated the time-trend coefficient had a mean slope of 0 percent per year and standard deviation of about 0.56 percent per 

year, indicating no tendency for diffQ at all sites taken together 

to increase or decrease. For a normal distribution, about 95 percent of the sites would have a change in diffQ between –1.12 

and +1.12 percent per year. Extending these estimates to a 4-

year period, about 95 percent of sites would have a change 

between –4.48 percent and +4.48 percent. The pumping water 

level (PWL) term accounted for only a negligible amount of the 

variance of diffQ, indicating that PWL had very little influence 

on differences in discharge. Overall, the quality of discharge 

measurements associated with TFMs did not degrade over time 

(1998–2002).

A comparison of the 1998–2002 PCC values was made 

using two different statistical models: diffC and diffL. The difference between diffC and diffL was one of time scale: diffC was 

obtained using instantaneous values of power consumption and 

flow, and diffL was obtained using seasonally integrated values 

of power consumption and flow. Significant differences were 

detected among the types of discharge distribution systems. 

PCCs for type S (sprinkler) discharge distribution systems 

tended to be larger than PCCs for the other types, and type L 

(low pressure) PCCs tended to be the smallest. The statistical 

models indicated that the difference between the high and low 

total dynamic head conditions for complex sites was substantially less using the diffL model (0.030) than the diffC model 

(0.149), indicating that the seasonal averaging of the values in 

diffL balanced out the differences between high and low total 

dynamic head in the complex system.

The statistical models for diffC and diffL indicated the discharge distribution system type and site variables accounted for 

94.8 percent and 97.8 percent, respectively, of the total variance; with all explanatory variables, the models accounted for 

more than 99 percent of the total variance. In the diffC model, 

the estimate for the mean of the time-trend coefficient indicated 

a tendency of PCC values to increase by about 1.5 percent per 

year on the average. The mean of the change in diffC with 

respect to pumping water level indicated a tendency for PCCs 

to increase with pumping water level by about 1.3 percent for a 

10-percent increase in pumping water level. In the diffL model, 

the estimated mean of the time trend indicated an increasing 

trend with time equal to about 1.7 percent per year on average, 

similar to the time trend for diffC. The rate of change of diffL

was 0.92 percent for a 10-percent increase in pumping water 

level, also similar to that for diffC. 

When differences in pumpage (diffP) were computed 

using PCC measurements and power consumption for the same 

year, the median diffP for the entire network was –1.5 percent; 

about 60 percent of all diffP values were between –6 and +6 percent, regardless of the year. Most years showed a slight negative 

bias, indicating that pumpage computed with the PCC approach 

tended to be smaller than pumpage using TFMs. Similar to 

diffQ, differences in pumpage that were computed using portable flowmeter method P showed an overall negative bias. There 

was no discernible bias in diffP when pumpage was computed 

using portable flowmeter method C. The discharge distribution 

system type effects for complex sites, CL and CH, indicated that 

(1) pumpage estimated by the PCC method was 6 to 7 percent 

greater than the pumpage measured by a TFM for complex sites 

using a low dynamic head PCC; and (2) pumpage estimated by 

the PCC method was 6 to 7 percent less than the pumpage measured by a TFM for complex sites for which the PCC was computed under high dynamic head conditions.

Statistical modeling was used to analyze variability in 

diffP that was associated with temporal trends and effects of 

changes in pumping water levels. The modeling was done first 

using diffP data for which PCC measurement and seasonal 

power consumption measurement were made during the same 

year (lag time 0) and then using diffP data for which these measurements were made in different years (lag time different from 

0). The best statistical estimates of the mean of the time trend 

indicated that there was about a 1.6-percent increase in diffP for 

each year increase in the lag time. For example, if a PCC measurement was made in 1 year and this PCC value was used to 

estimate pumpage 2 years after the PCC measurement was 

made, then diffP would on the average tend to be 3.2 percent 

more than if pumpage had been estimated in the same year the 

PCC measurement was made. However, because at lag time 0 

diffP indicated a negative bias, 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 with 

respect to power consumption measurements, median diffPs
Summary and Conclusions 41

were +1.8 percent for a 2-year forward lag, +4.9 percent for a 

3-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. The analysis indicated a fairly linear 

change in the median diffP values for about years. However, 

there was no discernible change between the third and fourth 

year lags. Overall, these results indicated that there was a time 

trend present in these data. This trend has important implications for estimation of pumpage by the PCC approach. Therefore, additional analysis was done to independently evaluate the 

time trend and evaluate the effect of water availability on the 

time trend. 

The estimated mean of pumping water level effects indicated that increasing the depth to water under which pumpage 

was measured using the TFM relative to the pumping water 

level conditions under which the PCC was measured tended to 

cause an increase in diffP. For example, if the PCC was measured for a given depth to ground-water level and then this PCC 

was used to estimate pumpage in a different year when depth to 

ground water was 10 percent greater, then, on the average, diffP

would be about 1.0 percent larger than if the depth to ground 

water had not changed. 

An independent analysis of year-to-year variability was 

done, eliminating the assumption of a linear trend. The models 

indicated that the relation between flow and seasonal power 

consumption were similar for short time scales (diffC) and 

yearly time scales (diffL). The largest positive year effect was 

for 2002, which was about 4 percent for both diffC and diffL. 

The largest negative year effect was for 1999, which was about 

–3 percent for diffC and about –2 percent for diffL. Generally, a 

monotonically increasing trend with time over the 5-year period 

existed for both models, and the average increase per year was 

close to the mean slopes of 1.5 percent and 1.7 percent for diffC

and diffL, respectively. The year effects obtained by analyzing 

the diffP data were similar to those indicated by the diffC and 

diffL data. Overall, there was about a 1.6 percent per year 

increase in diffP per year of lag between the time the PCC measurement was made and the year pumpage was estimated. 

The time trend of about 1.6 percent per year in diffP was 

obtained using a statistical model that included a PWL term as 

one of the explanatory variables. That is, the magnitude of the 

time trend was based on statistically correcting for changing 

PWL. Because PWL also tended to increase with time over this 

period, an estimate of the overall time trend (uncorrected for 

PWL changes) was made by fitting a model without a PWL 

term, yielding a trend of about 2.2 percent per lag year for diffP. 

The implication of such a trend, for example, is that for a 2-year 

lag, pumpage estimated by the PCC approach would be about 

4.4 percent higher relative to TFM-estimated pumpage than if 

the lag was zero years, and for a 4-year lag pumpage estimated 

by the PCC approach would be about 8.8 percent higher relative 

to TFM-estimated pumpage. However, when lag was zero 

years, pumpage computed with the PCC approach tended to be 

smaller than pumpage using TFMs. Therefore, the aggregate 

diffP for each forward-lag year was less than 2.2 percent per 

year of lag. 

An analysis also was done in which a surface-water diversion term was included in the model, and in this analysis, the 

time-trend term was rendered insignificant. This result indicated that the time-trend term 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 indicates that much of the trend of 2.2 percent per lag 

year in diffP results from applying a PCC to estimate pumpage 

under hydrologic conditions different from those under which 

the PCC was measured. 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, and it is feasible that future 

periods could exhibit downward trends or nonmonotonic variability. Although detailed long-term analyses have not been 

performed for this report, other studies have shown that static 

ground-water levels in the study area have exhibited small variations over multidecadal time scales with a high degree of temporal correlation, and monotonic trends that appear approximately linear over a 5-year period such as the one detected in 

this study are not uncommon in such slowly varying time series. 

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. Periodic PCC data are 

needed to determine actual future changes that may occur in 

diffC. A subset of this network could be used to quantify future 

changes in diffP that may occur.

The differences between the PCC approach and the TFM 

approach in the total or aggregated pumpage for a network of 

wells was analyzed using certain assumptions about average 

conditions and random sampling. The average pumpage per site 

per year for the network studied was 147 acre-ft, and the variance was 28,600 acre-ft squared. These values together with 

results from the analysis of the diffP data were used to estimate 

the mean and variance of the difference between total network 

pumpage using the TFM method and the PCC method as a function of number of sites in the network and of lag between time 

of PCC measurement and pumpage estimation. For small year 

effects, the average difference in TFM and PCC network pumpage, as a fraction of total network pumpage, is slightly greater 

than average individual well year effects in diffP independent of 

the number of wells in the network. The standard deviation of 

this difference, again relative to total network pumpage, also 

depends on individual well year effects and decreases as the 

number of wells in the network increases.

For 100 wells and a lag of 4 years between PCC measurement and pumpage estimation, the standard deviation is 2.3 percent of total network pumpage. Under assumptions of normality, there is a 95-percent probability that the total network 

pumpage for 100 wells estimated by the PCC approach would 

±3
42 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

be between 5.2 and 14.4 percent greater than pumpage measured using a TFM. For 1,000 wells, the estimated difference in 

total network pumpage for a 4-year lag 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 

3-year lag would be between about 6.1 and 8.8 percent greater 

than pumpage measured using a TFM; and 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.

Selected References 

Barnett, Vic, and Lewis, Toby, 1978, Outliers in statistical data: 

New York, John Wiley and Sons, 604 p.

Collins, C.A., 1987, Ground-water pumpage from the Columbia Plateau Regional Aquifer System, Oregon, 1984: U.S. 

Geological Survey Water-Resources Investigations Report 

86–4211, 21 p.

Dash, R.G., Troutman, B.M., and Edelmann, Patrick, 1999, 

Comparison of two approaches for determining groundwater discharge and pumpage in the lower Arkansas River 

Basin, Colorado, 1997–98: U.S. Geological Survey WaterResources Investigations Report 99–4221, 39 p.

Graybill, F.A., 1976, Theory and application of the linear 

model: Belmont, Calif., Wadsworth Publishing Co., 704 p.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, Elsevier, Studies in Environmental Science 49, 522 p.

Hurr, R.T., and Litke, D.W., 1989, Estimating pumping time 

and ground-water withdrawals using energy consumption 

data: U.S. Geological Survey Water-Resources Investigations Report 89–4107, 27 p.

Mathsoft, Inc., 1998, S-Plus 5 for Unix, Guide to Statistics, 

Data Analysis Products Division, MathSoft, Seattle.

Major, T.J., Hurr, R.T., and Moore, J.E., 1970, Hydrogeologic 

data for the lower Arkansas River Valley, Denver, Colorado: 

Denver, Colorado Water Conservation Board Basic Data 

Release 21, 125 p.

Office of the State Engineer, 1994, Rules governing the measurement of tributary ground water diversions located in the 

Arkansas River Basin: Denver, 4 p. (dated July 6, 1994) 

[available online at www.water.state.co.us/pub/rule_reg.asp]

Office of the State Engineer, 1996, Amendments to rules governing the measurement of tributary ground water diversions 

located in the Arkansas River Basin: Denver, 6 p. (dated February 28, 1996) [available online at www.water.state.co.us/

pub/rule_reg.asp]

Office of the State Engineer, 2000, Variance approval policy for 

complex wells using the PCC method: Pueblo, 3 p. (dated 

June 14, 2000) [Unpublished report available on file at the 

Office of the State Engineer, Division of Water Resources, 

Colorado Department of Natural Resources, 1313 Sherman 

Street, Denver, CO 80203]

Scott, J.C., 1990, Computerized stratified random site selection 

approaches for design of a ground-water quality sampling 

network: U.S. Geological Survey Water-Resources Investigations Report 90–4101, 109 p.

Snedecor, G.W., and Cochran, W.G., 1967, Statistical methods 

(6th ed.): Ames, Iowa State University Press, 593 p.

Steger, R.,D., 2002, Changes in ground-water levels in selected 

wells in the Arkansas River Alluvial aquifer downstream 

from Pueblo Reservoir, Southeastern Colorado, 1965–2001: 

U.S. Geological Survey Fact Sheet 023–02.

Tornqvist, Leo, Vartia, Pentti, and Vartia, Yrjo O., 1985, How 

should relative changes be measured?: American Statistician, 

v. 39, no. 1, p. 43–46.
Supplemental Information
44 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
SUPPLEMENTAL INFORMATION 45

Supplemental Information

The section includes an explanation of evaluation of outliers, estimates of variance components for diffQ, and tables of supporting data used in the report.

Evaluation of Outliers

For discharge and pumpage data, outlier analysis was an essential step in the interpretation process. Graphical and statistical

tools were used to characterize raw data and locate potential outliers. As a result, several of the data points were classified as outliers and were not used in the final fitting of the statistical models. These outliers may be considered as having been sampled from 

a different population that does not fit the same statistical models as the majority of the data and therefore need to be analyzed 

separately. Examination of these points was important in that outliers may reflect possible instrument malfunctions or errors in 

data collection, although typically it is not possible to pinpoint exactly why outliers are present or to predict beforehand when outliers might occur. It is expected that such outliers will inevitably be present in a certain small percentage of data collected in the 

past and in the future. It is important to factor the presence of such problems into any decision making based on the data.

The most straightforward way to quantify the presence of outliers is to assume that there are two populations – one associated 

with the majority of the data, and the other associated with the outliers. A small probability, say , is associated with the outliers, 

and the probability associated with the majority of the data are . In other words, the data come from a mixture of two distributions, with determining the relative frequency of the two distributions (Barnett and Lewis, 1978). 

The general procedure that was followed in evaluating outliers was first to identify individual data points as potential outliers 

based on known problems with the data collection, or based on examination of residuals after fitting the statistical models. Because 

outliers may have a large detrimental effect on parameter estimates (especially estimates of variances), the next step is to fit the 

models with the potential outliers excluded from the analysis, and then to examine the identified points with respect to the fitted 

model to evaluate if the identified outliers do indeed qualify as statistical outliers. Consider for example diffQ. Let stand for 

the difference between a value of diffQ that is suspected as an outlier and the predicted value based on the fitted model in equation 

4. Then , where is the estimate of the variance of obtained from the analysis, may be used to test the suspected 

outlier. This approach is described in more detail in Snedecor and Cochran (1967).

It is also useful to make a distinction between two types of outliers in these data. The first type is referred to as a “seasonal 

outlier” and may occur when persistent problems exist, at a given site during a given year, that result in large errors in all (or much 

of) the data for that site during a specific year (for example a malfunctioning electrical meter). The second type is referred to as 

an “instantaneous outlier” and may occur under circumstances unique to particular instantaneous measurements that result in a 

large error. DiffL may be only the first type, and diffQ and diffC may potentially be both types; diffP outliers will necessarily be 

caused by either diffL or diffC outliers. 

There were no outliers in the diffQ data, and there were none in the diffP data other than those identified using diffL and diffC. 

For the diffL data set, seasonal outliers were identified for seven site/year combinations (table 10). There were documented 

electrical power meter problems with site 9 (1998), and residuals examination was used to identify the other seasonal outliers. It 

is suspected, but not certain, that there are electrical power meter problems for site 15 (2002), site 49 (2001), site 82 (2001), and 

δ

1 − δ

δ

Q d

Q Q Q z = d s 2

Qs Qe

Table 10. Outlier data that were removed in models 

diffC and diffL.

[zL, outlier test statistic for diffL data; zC, outlier 

test statistic for diffC data]

 Seasonal 

Site 9, 1998 –25.6 –16.2

Site 36, 2002 4.7 7.2

Site 15, 2002 –32.8 –1.2

Site 49, 2001 –31.0 –0.9

Site 82, 2001 –27.4 0.2

Site 100, 2000 –6.5 0.3

Site 22, 1998 13.8 –2.9

 Instantaneous

Site 64, April 17, 2001 17.3

L z Cz
46 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

site 100 (2000) and that there is a TFM problem for site 22 (1998). The extreme residuals associated with these points may easily 

be seen in plots obtained after fitting the model with all data included. Outliers also were identified by omitting data points one at 

a time, starting with the full set and refitting the model each time, with the point having the largest absolute residual being omitted 

at each step. In order to quantify the magnitude of the anomalous values, the diffL data were analyzed with these seven values 

omitted, and then statistics were computed, where is observed minus model-predicted diffL and 

(square root of the estimated variance of , 0.00139, in table 5). Values of zL are listed in table 10. There were 344 

diffL data points altogether, and it may be shown that there was only a 1-percent probability that any of the 344 values sampled 

independently from a standard normal distribution was greater in absolute value than 4.18, so this may be used as a critical value 

with which to compare the magnitude of the . The value 4.18 is a solution x of , where F is the cumulative 

distribution of the absolute value of a standard normal random variable, and is therefore the cumulative distribution of the 

maximum of 344 independent absolute normal random variables (see Snedecor and Cochran, 1967, section 6.13). Thus, it is indeed 

unlikely that these data points came from the same population as the majority of the data. Using seven outlying points from the 

total sample of 344 gives a probability associated with diffL seasonal outliers of 7/344=0.020, or 2.0 percent. This assumes that 

all site and year combinations are equally likely to be outlying data. One can see from these seven numbers that deviations of

individual data points from behavior shown by the majority of the data can be quite large.

The seven site/year combinations identified as diffL seasonal outliers were flagged as potential seasonal outliers for the diffC

data, corresponding to 29 diffC data points. It was reasoned that site/year problems in the diffL data might be expected to show up 

in diffC data. One additional instantaneous outlying point was identified by residuals examination of the diffC data for site 64, April 

17, 2001. The diffC data were analyzed with these 30 values omitted and the results were then used to examine the omitted data 

points. The residuals for the first seven site/year combinations have the site/year effect ( in equation 5), date effect ( in 

equation 5), and random error ( in equation 5). The magnitude of a site/year effect was approximated by computing the average 

of the residuals for all diffC measurements made during that site/year. Letting this average be , outlier test statistics 

 may be obtained where is the standard deviation associated with this average. Let be the number of diffC

residuals in this average for the given site/year and be the number of measurements on date i for the given site/year . 

Because each residual has the three random components, the standard deviation may be shown to be the square root of 

, where the three variance component estimates are from table 5. For the instantaneous outlying point, is the residual and is the square root of the error variance 0.00116 in table 5. The values of are 

listed in table 10. The critical value 4.18 may again be used for the seven seasonal outliers. The values for site 9 (1998) and site 

36 (2002) are definitely rejected as outliers. Both and have the same sign, so this is consistent with an electrical power 

meter problem affecting both diffL and diffC. An estimate for the seasonal outlier probability for diffC data is 2/344=0.006, or less 

than 1 percent. The 1-percent critical value for the single instantaneous outlier is 4.47 (based on 1,275 values), so this data point 

is definitely rejected as an outlier. An estimate for the instantaneous outlier probability for diffC data is 1/1275=0.0008, or less 

than 0.1 percent. 

Because some of the site/years identified as seasonal outliers using the diffL data turned out not to be outliers using the 

diffC data, one option would be to re-analyze the diffC data including these data values. This was done, with virtually no change 

in the diffC results shown in tables 4 and 5. However, the final analysis was done with data for the seven site/years in table 10 

excluded so the related variables diffL, diffC, and diffP are analyzed with exactly the same set of data. 

Estimates of Variance Components for Differences in Discharge

Estimates of the fixed effects for the diffQ model are given in table 2, and estimates of the mean and variance of the random 

terms (site, year, site/year interaction, date, and random error terms) for the diffQ model are listed in table 3. The relative importance of the different terms in the diffQ model can be obtained from the numbers in tables 2 and 3. The total variance of diffQ is 

0.00323, so the model accounted for about 100 × (0.00323 – 0.000820)/0.00323 = 74.6 percent of the total variance of diffQ. The 

contribution of method differences to the variance of diffQ was estimated by the sample variance of the estimated method effects 

in table 2 with weighting based on the sample size in each of the three levels (Graybill, 1976, chapter 13); this variance is 0.000232, 

which is about 100 × 0.000232/0.00323 = 7.2 percent of the total variance. The most important term in the model is the site term, 

S, which has a variance that is 100 × 0.00147/0.00323 = 45.5 percent of the total variance. The magnitude of the influence of the 

quantitative explanatory variables, both of which have random slopes with an estimated mean and variance given by the data analysis, on diffQ can be estimated as follows. Note first that the magnitude of the variances of and in table 3 cannot be 

compared directly to total variance of diffQ because enters the model only through the product and enters only 

through the product . The other variances in table 3 on the other hand can be compared directly to total variance of 

diffQ. A technique to decompose the contribution of to the variance of diffQ into two parts, to be called , which is due to 

the mean of , and , which is due to the variance of , is described below. A similar decomposition is performed for , 

and the two components are called and . Note that to give a precise estimate of the combined contribution of the three ranL L L z = d / s d L

s L = 0.037 L e

L z 0.01 1 ( ) 344 = − F x 344 F

δ

SY C ( ) DC

Ce

dC

C C C z = d / s Cs nC

ni nC = Σni

Cs

ni nC nC 0.000770 0.00182( / ) 0.00116 / 2 2 + Σ +

dC Cs Cz

L z Cz

δ

AQ UQ

A t Q AQ UQ

U (w w) Q − AQ Et

AQ Vt AQ UQ

Ew Vw
SUPPLEMENTAL INFORMATION 47

dom terms , , and to the total variance would require taking into consideration the correlation among them, and this is 

not done here; instead, only the individual influence of the terms is considered. 

First-order analysis of the product can be used to show that the variance associated with this product can be approximated by the sum where , , is the sample average of in the data set, is the sample 

variance of t in the data set, is the estimated variance of (0.0000313 in table 3), and is the estimated mean of 

 (0.0009 in table 3). The component is a measure of the effect of the variance of the random slope, and the component 

is a measure of the effect of the mean of the random slope. For this data set, and , giving and 

. The sum of the last two numbers can be compared to the total variance 0.00323, indicating that the time-trend 

term is accounting for only about 100x0.000178/0.00323= 5.5 percent of the total variance. The same technique is used to assess 

the influence of the PWL term. Using a subscript w rather than t for the PWL term, , , , 

and indicating that PWL variability has a minor influence on diffQ. 

The random error variance (0.000820 in table 3) 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 discharges measured using two different portable flowmeters. The estimated 

variance of the difference will be 2 × 0.000820 (or 0.0016) because the variance of the difference between two independent random 

variables is the sum of their variances. This translates into a standard deviation of about 0.0405, or 4.05 percent. 

Q S AQ UQ

A t Q

Vt + Et ( ) ˆ t t AQ V = a Var 2

) ˆ ( t t EAQ E = b at

2

t bt

( ) ˆ AQ Var AQ EAQ ˆ

AQ Vt Et

at = 5.61 bt = 1.90 Vt = 0.000176

Et = 0.000002

aw = 0.00914 bw = 0.00914 Vw = 0.000036

E w = 0 .000003
48 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

Table 11. Data used in the diffQ model. 

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - diffQ

1 1998 35950 C 0.42192 -0.02363 0.01934

1 1998 35950 P 0.42192 -0.02363 -0.02507

1 1998 35989 C 0.52877 -0.01599 0.03602

1 1998 35989 M 0.52877 -0.01599 -0.01116

1 1998 35989 P 0.52877 -0.01599 -0.02387

1 1998 36026 C 0.63014 -0.06564 0.00586

1 1998 36026 M 0.63014 -0.06564 -0.00210

1 1998 36026 P 0.63014 -0.06564 -0.03875

1 1999 36343 C 1.49863 -0.09143 0.05279

1 1999 36343 P 1.49863 -0.09143 0.02802

1 1999 36369 C 1.56986 -0.18524 0.04145

1 1999 36369 P 1.56986 -0.18524 0.02955

1 1999 36397 C 1.64658 -0.22624 0.04442

1 1999 36397 P 1.64658 -0.22624 0.03929

1 2000 36650 C 2.33973 0.01132 0.04530

1 2000 36650 P 2.33973 0.01132 0.01753

1 2000 36727 C 2.55068 -0.02992 0.05820

1 2000 36727 P 2.55068 -0.02992 0.01899

1 2000 36752 C 2.61918 -0.06564 0.05282

1 2000 36752 P 2.61918 -0.06564 0.02291

1 2001 36990 C 3.27123 0.18406 0.03231

1 2001 36990 P 3.27123 0.18406 0.02690

1 2001 37084 C 3.52877 0.01468 0.05893

1 2001 37084 P 3.52877 0.01468 0.03846

1 2001 37111 C 3.60274 0.05255 0.05265

1 2001 37111 P 3.60274 0.05255 0.03376

1 2002 37351 C 4.26027 0.20369 0.02965

1 2002 37351 P 4.26027 0.20369 0.00822

1 2002 37449 C 4.52877 0.14653 0.03604

1 2002 37449 P 4.52877 0.14653 0.00993

1 2002 37476 C 4.60274 0.13172 0.04271

1 2002 37476 P 4.60274 0.13172 0.00870

2 1998 35936 C 0.38356 0.01061 -0.00468

2 1998 35936 P 0.38356 0.01061 -0.00485

2 1998 36048 C 0.69041 0.04031 0.00797

2 1998 36048 P 0.69041 0.04031 -0.01776

2 1998 36052 C 0.70137 0.03215 -0.00357

2 1998 36052 P 0.70137 0.03215 -0.03099

2 1999 36342 C 1.49589 -0.10843 0.00138

2 1999 36342 P 1.49589 -0.10843 -0.00642

2 1999 36348 C 1.51233 -0.02694 0.00130

2 1999 36348 P 1.51233 -0.02694 -0.02727

2 2000 36692 C 2.45479 -0.03567 0.02138

2 2000 36692 P 2.45479 -0.03567 0.08564

2 2001 37062 C 3.46849 -0.07139 0.00666

2 2001 37062 P 3.46849 -0.07139 0.03338

2 2001 37082 C 3.52329 0.00725 0.01402

w w
SUPPLEMENTAL INFORMATION 49

2 2001 37082 P 3.52329 0.00725 0.01799

2 2001 37123 C 3.63562 0.05644 0.00562

2 2001 37123 P 3.63562 0.05644 0.02413

2 2002 37337 C 4.22192 0.09566 0.00714

2 2002 37337 P 4.22192 0.09566 -0.07583

3 1998 35975 C 0.49041 -0.02272 0.01036

3 1998 35975 P 0.49041 -0.02272 0.01550

3 1998 36000 C 0.55890 -0.02133 0.02743

3 1998 36000 P 0.55890 -0.02133 -0.06190

3 1998 36053 C 0.70411 -0.15208 0.02254

3 1998 36053 P 0.70411 -0.15208 -0.02506

3 1999 36348 C 1.51233 -0.06984 0.01097

3 1999 36348 P 1.51233 -0.06984 -0.11002

3 1999 36367 C 1.56438 -0.11776 0.01011

3 1999 36367 P 1.56438 -0.11776 0.04894

3 1999 36395 C 1.64110 -0.09952 0.01203

3 1999 36395 P 1.64110 -0.09952 -0.08985

3 2000 36699 C 2.47397 0.03552 0.02868

3 2000 36720 C 2.53151 0.04599 0.02449

3 2000 36720 P 2.53151 0.04599 -0.00084

3 2000 36739 C 2.58356 0.03552 0.02186

3 2000 36739 P 2.58356 0.03552 -0.19043

3 2001 36986 C 3.26027 0.12121 0.04552

3 2001 36986 P 3.26027 0.12121 0.07136

3 2001 37069 C 3.48767 0.03552 0.08820

3 2001 37069 P 3.48767 0.03552 -0.10389

3 2001 37104 C 3.58356 0.01424 0.02648

3 2001 37104 P 3.58356 0.01424 -0.09542

3 2002 37328 C 4.19726 0.08180 0.02323

3 2002 37448 C 4.52603 0.11150 -0.00101

3 2002 37448 P 4.52603 0.11150 -0.05358

3 2002 37449 C 4.52877 0.12121 0.01610

5 1998 35934 C 0.37808 0.09478 0.06468

5 1998 35934 P 0.37808 0.09478 -0.20988

5 1998 35975 C 0.49041 0.12019 -0.00082

5 1998 35975 P 0.49041 0.12019 -0.07302

5 1998 36061 C 0.72603 -0.25540 0.07309

5 1998 36061 P 0.72603 -0.25540 0.01361

5 1999 36333 C 1.47123 -0.05848 -0.04008

5 1999 36333 P 1.47123 -0.05848 -0.10694

5 2001 37057 C 3.45479 -0.26612 0.03848

5 2001 37057 P 3.45479 -0.26612 -0.06132

5 2002 37385 C 4.35342 0.16467 0.00186

5 2002 37424 C 4.46027 0.18936 -0.03032

5 2002 37461 C 4.56164 0.21346 0.00087

7 1998 35937 M 0.38630 0.04206 -0.09059

7 1998 35937 P 0.38630 0.04206 -0.07725

7 1998 35999 M 0.55616 0.03677 -0.07944

7 1998 35999 P 0.55616 0.03677 -0.11470

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
50 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

7 1998 36028 M 0.63562 -0.03954 -0.08709

7 1998 36028 P 0.63562 -0.03954 -0.07879

7 1999 36406 M 1.67123 -0.13419 -0.09071

7 1999 36406 P 1.67123 -0.13419 -0.10190

7 2000 36672 P 2.40000 -0.00066 -0.10101

7 2002 37573 M 4.86849 0.19045 -0.12928

8 1998 35905 P 0.29863 0.07138 0.00671

8 1998 35975 C 0.49041 -0.00070 0.00311

8 1998 35975 P 0.49041 -0.00070 -0.04310

8 1998 36031 C 0.64384 -0.08278 0.07070

8 1998 36031 P 0.64384 -0.08278 0.03285

8 1999 36299 C 1.37808 -0.05916 0.01080

8 1999 36299 P 1.37808 -0.05916 -0.05740

8 2000 36713 C 2.51233 -0.03969 -0.01823

8 2000 36713 P 2.51233 -0.03969 -0.08643

8 2002 37379 C 4.33699 0.14664 -0.00024

8 2002 37379 P 4.33699 0.14664 -0.12247

9 1998 35936 M 0.38356 0.01022 -0.05321

9 1998 35936 P 0.38356 0.01022 -0.05314

9 1998 35978 M 0.49863 0.00406 -0.05118

9 1998 35978 P 0.49863 0.00406 0.02191

9 1998 36027 M 0.63288 -0.05751 -0.06166

9 1998 36027 P 0.63288 -0.05751 -0.07166

9 1999 36340 M 1.49041 0.00612 -0.05117

9 1999 36340 P 1.49041 0.00612 -0.07660

9 1999 36370 M 1.57260 -0.00076 -0.04897

9 1999 36370 P 1.57260 -0.00076 -0.06578

9 2000 36630 M 2.28493 -0.10996 -0.04696

9 2000 36734 M 2.56986 -0.00421 -0.03486

9 2000 36790 M 2.72329 0.01972 -0.04127

9 2001 37063 M 3.47123 0.08510 -0.06398

9 2001 37063 P 3.47123 0.08510 -0.12974

11 1998 35947 M 0.41370 0.00193 -0.00101

11 1998 35947 P 0.41370 0.00193 0.00432

11 1998 35998 M 0.55342 0.05854 -0.00635

11 1998 35998 P 0.55342 0.05854 -0.01652

11 1998 36020 M 0.61370 -0.01905 -0.00946

11 1998 36020 P 0.61370 -0.01905 -0.04853

11 1999 36355 M 1.53151 -0.03748 -0.02636

11 2000 36698 M 2.47123 -0.07850 -0.14192

11 2000 36698 P 2.47123 -0.07850 -0.08579

11 2001 36993 M 3.27945 0.05581 -0.01380

11 2001 36993 P 3.27945 0.05581 -0.02475

12 1998 35935 M 0.38082 0.02188 0.02278

12 1998 35935 P 0.38082 0.02188 0.00170

12 1998 35982 M 0.50959 0.02847 0.02342

12 1998 35982 P 0.50959 0.02847 0.04949

12 1998 36014 M 0.59726 0.01809 0.01705

12 1998 36061 M 0.72603 -0.03952 -0.02740

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 51

12 1999 36362 M 1.55068 -0.05828 0.02120

12 1999 36362 P 1.55068 -0.05828 -0.01342

12 2000 36630 M 2.28493 -0.05982 0.02707

12 2000 36630 P 2.28493 -0.05982 -0.01414

12 2001 37025 M 3.36712 0.05167 -0.00941

12 2001 37082 M 3.52329 0.10526 -0.01083

14 1998 35944 C 0.40548 -0.02562 -0.01679

14 1998 35944 P 0.40548 -0.02562 -0.02571

14 1998 35975 C 0.49041 -0.01164 -0.03126

14 1998 35975 P 0.49041 -0.01164 -0.02614

14 1998 36055 C 0.70959 0.00387 -0.03381

14 1998 36055 P 0.70959 0.00387 -0.02916

14 1999 36348 C 1.51233 -0.05420 -0.03629

14 1999 36348 P 1.51233 -0.05420 -0.04256

14 1999 36406 C 1.67123 -0.03981 -0.03386

14 1999 36406 P 1.67123 -0.03981 -0.03902

14 1999 36447 C 1.78356 0.00215 -0.04080

14 1999 36447 P 1.78356 0.00215 -0.06135

14 2000 36648 C 2.33425 0.05029 -0.03414

14 2000 36648 P 2.33425 0.05029 -0.09193

14 2000 36733 C 2.56712 0.03583 -0.04242

14 2000 36733 P 2.56712 0.03583 -0.07787

14 2000 36768 C 2.66301 0.03913 -0.03164

14 2000 36768 P 2.66301 0.03913 -0.07458

15 1998 35948 M 0.41644 0.04543 0.07357

15 1998 35948 P 0.41644 0.04543 0.06806

15 1998 35968 C 0.47123 0.05384 0.06550

15 1998 35968 M 0.47123 0.05384 0.06146

15 1998 36006 C 0.57534 0.01803 0.05565

15 1998 36006 M 0.57534 0.01803 0.05250

15 1999 36335 C 1.47671 -0.09429 0.04673

15 1999 36335 M 1.47671 -0.09429 0.04558

15 1999 36335 P 1.47671 -0.09429 0.01732

15 1999 36384 C 1.61096 -0.00302 0.06769

15 1999 36384 M 1.61096 -0.00302 0.05827

15 1999 36432 C 1.74247 -0.10366 0.06928

15 1999 36432 M 1.74247 -0.10366 0.06446

15 1999 36432 P 1.74247 -0.10366 0.05580

15 2000 36636 C 2.30137 -0.02127 0.05612

15 2000 36636 M 2.30137 -0.02127 0.03784

15 2000 36636 P 2.30137 -0.02127 0.02731

15 2000 36706 C 2.49315 -0.06143 0.05683

15 2000 36706 M 2.49315 -0.06143 0.01907

15 2000 36749 C 2.61096 0.02495 0.04760

15 2000 36749 M 2.61096 0.02495 0.04361

15 2001 37007 C 3.31781 -0.02091 0.03560

15 2001 37007 M 3.31781 -0.02091 0.02126

15 2001 37069 C 3.48767 0.01803 0.06180

15 2001 37069 M 3.48767 0.01803 0.04119

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
52 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

15 2001 37118 C 3.62192 0.10128 0.05801

15 2001 37118 M 3.62192 0.10128 0.06214

15 2002 37375 C 4.32603 0.02495 0.09989

15 2002 37375 M 4.32603 0.02495 0.04088

15 2002 37420 C 4.44932 0.05886 0.13564

15 2002 37420 M 4.44932 0.05886 0.06414

15 2002 37503 C 4.67671 0.06881 0.10873

15 2002 37503 M 4.67671 0.06881 0.03707

16 1998 35936 C 0.38356 -0.02336 -0.06646

16 1998 35936 P 0.38356 -0.02336 -0.06412

16 1998 35942 C 0.40000 0.02879 -0.04770

16 1998 35942 P 0.40000 0.02879 -0.05972

16 1998 35982 C 0.50959 -0.10787 -0.01882

16 1998 35982 P 0.50959 -0.10787 -0.03097

16 1998 36017 C 0.60548 -0.06899 -0.02716

16 1998 36017 P 0.60548 -0.06899 -0.05688

16 1998 36056 C 0.71233 -0.03872 -0.02710

16 1998 36056 P 0.71233 -0.03872 -0.03136

16 1999 36321 C 1.43836 -0.02336 -0.06603

16 1999 36321 P 1.43836 -0.02336 -0.07536

16 1999 36357 C 1.53699 -0.12501 -0.02658

16 1999 36357 P 1.53699 -0.12501 -0.03803

16 2001 37097 C 3.56438 0.10878 -0.00300

16 2001 37097 P 3.56438 0.10878 -0.03428

16 2001 37158 C 3.73151 0.11850 -0.02897

16 2001 37158 P 3.73151 0.11850 -0.07444

16 2002 37390 C 4.36712 0.26246 -0.01683

18 1998 35947 P 0.41370 -0.06630 0.07161

18 1998 35986 C 0.52055 -0.06749 -0.00195

18 1998 35986 P 0.52055 -0.06749 -0.02040

18 1998 36020 C 0.61370 -0.11308 -0.01442

18 1998 36020 P 0.61370 -0.11308 -0.03467

18 1999 36314 C 1.41918 -0.08186 -0.03625

18 1999 36314 P 1.41918 -0.08186 -0.06793

18 2000 36665 C 2.38082 -0.02845 -0.03357

18 2000 36665 P 2.38082 -0.02845 -0.10261

18 2000 36713 C 2.51233 -0.02960 -0.03296

18 2000 36713 P 2.51233 -0.02960 -0.10371

18 2000 36791 C 2.72603 -0.02276 -0.03687

18 2000 36791 P 2.72603 -0.02276 -0.15524

18 2002 37375 C 4.32603 0.14909 0.09265

18 2002 37375 P 4.32603 0.14909 0.04772

18 2002 37522 C 4.72877 0.22729 0.00093

18 2002 37522 P 4.72877 0.22729 -0.02494

19 1998 35964 C 0.46027 -0.08529 0.00266

19 1998 35964 P 0.46027 -0.08529 -0.05366

19 1998 35999 C 0.55616 0.03457 0.00535

19 1998 36038 C 0.66301 -0.03516 -0.02069

19 1998 36038 P 0.66301 -0.03516 -0.09285

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 53

19 1999 36334 C 1.47397 -0.09232 -0.05101

19 1999 36334 P 1.47397 -0.09232 -0.05838

19 2000 36643 C 2.32055 0.07020 -0.03953

19 2000 36643 P 2.32055 0.07020 -0.09905

19 2000 36732 C 2.56438 0.07020 -0.07510

19 2000 36732 P 2.56438 0.07020 -0.14572

19 2001 36997 C 3.29041 0.05509 -0.05089

19 2001 36997 P 3.29041 0.05509 -0.09184

20 1998 35920 M 0.33973 -0.04169 -0.12228

20 1998 35920 P 0.33973 -0.04169 -0.10384

20 1998 36020 M 0.61370 -0.01976 -0.10014

20 1998 36053 M 0.70411 -0.04710 -0.12053

20 1998 36053 P 0.70411 -0.04710 -0.11368

20 1999 36426 M 1.72603 -0.10411 -0.07256

20 1999 36426 P 1.72603 -0.10411 -0.08408

20 2000 36756 M 2.63014 -0.00695 -0.07738

20 2000 36756 P 2.63014 -0.00695 -0.09279

20 2001 37027 M 3.37260 0.08794 -0.08959

20 2001 37027 P 3.37260 0.08794 -0.08317

20 2002 37511 M 4.69863 0.24359 -0.09342

22 1998 35998 C 0.55342 0.05886 0.04462

22 1998 35998 P 0.55342 0.05886 0.01311

22 1998 36018 C 0.60822 -0.00238 0.02450

22 1998 36018 P 0.60822 -0.00238 0.00936

22 1998 36041 C 0.67123 -0.03447 0.01637

22 1998 36041 P 0.67123 -0.03447 0.00219

22 1999 36361 C 1.54795 -0.03992 -0.02501

22 1999 36361 P 1.54795 -0.03992 -0.00935

22 1999 36406 C 1.67123 0.09770 0.01557

22 1999 36406 P 1.67123 0.09770 0.06448

22 2000 36664 P 2.37808 0.04891 0.04223

22 2000 36754 P 2.62466 0.10953 -0.09862

22 2001 37008 C 3.32055 -0.13141 0.02732

22 2001 37084 C 3.52877 -0.11951 -0.04304

22 2001 37159 C 3.73425 -0.11361 -0.01191

22 2002 37396 C 4.38356 0.04891 0.03078

22 2002 37524 C 4.73425 -0.00238 0.03414

23 1998 35941 C 0.39726 -0.05709 -0.14666

23 1998 35972 C 0.48219 0.07142 -0.13167

23 1998 36013 C 0.59452 0.07576 -0.13956

23 1998 36013 P 0.59452 0.07576 -0.22362

23 1998 36056 C 0.71233 -0.01053 -0.10980

23 1999 36426 C 1.72603 0.01907 -0.11742

23 1999 36426 P 1.72603 0.01907 -0.16364

23 1999 36447 C 1.78356 -0.00284 -0.11643

23 1999 36447 P 1.78356 -0.00284 -0.14737

23 2000 36651 C 2.34247 -0.02785 -0.07267

23 2000 36651 P 2.34247 -0.02785 -0.21993

23 2000 36713 C 2.51233 0.00649 -0.08123

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
54 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

23 2000 36746 C 2.60274 0.02032 -0.08961

23 2001 37008 C 3.32055 -0.06794 -0.01097

23 2002 37476 C 4.60274 -0.09093 -0.00068

24 1998 35913 C 0.32055 -0.02585 -0.13061

24 1998 35913 P 0.32055 -0.02585 -0.18387

24 1998 35991 C 0.53425 -0.02816 -0.14892

24 1998 35991 P 0.53425 -0.02816 -0.23153

24 1998 36040 C 0.66849 -0.07419 -0.12194

24 1998 36040 P 0.66849 -0.07419 -0.22058

24 1999 36369 C 1.56986 -0.03590 -0.11661

24 1999 36369 P 1.56986 -0.03590 -0.22949

24 2001 37082 C 3.52329 0.05327 -0.13584

24 2001 37082 P 3.52329 0.05327 -0.19656

24 2002 37449 C 4.52877 0.11082 -0.15058

24 2002 37449 P 4.52877 0.11082 -0.21985

25 1998 35927 C 0.35890 0.07035 -0.10018

25 1998 35978 C 0.49863 0.01317 -0.13193

25 1998 35978 M 0.49863 0.01317 -0.16817

25 1998 35978 P 0.49863 0.01317 -0.16398

25 1998 36017 C 0.60548 -0.06006 -0.13248

25 1998 36017 M 0.60548 -0.06006 -0.18928

25 1998 36017 P 0.60548 -0.06006 -0.16821

25 1999 36381 C 1.60274 -0.07009 -0.08733

25 1999 36381 P 1.60274 -0.07009 -0.15941

25 2000 36678 C 2.41644 0.04338 -0.02740

25 2000 36678 M 2.41644 0.04338 -0.22439

25 2000 36678 P 2.41644 0.04338 -0.12581

25 2000 36713 C 2.51233 0.02944 -0.00967

25 2000 36713 M 2.51233 0.02944 -0.28542

25 2000 36713 P 2.51233 0.02944 -0.14794

25 2000 36734 C 2.56986 -0.00265 -0.07796

25 2000 36734 M 2.56986 -0.00265 -0.16153

25 2000 36734 P 2.56986 -0.00265 -0.13875

27 1998 36055 P 0.70959 -0.15313 -0.03292

27 1999 36335 P 1.47671 -0.01271 -0.03045

27 2000 36650 P 2.33973 0.03482 -0.06278

27 2001 37005 P 3.31233 0.16053 -0.04069

27 2001 37104 P 3.58356 -0.02951 0.02565

28 1998 35963 C 0.45753 -0.06754 -0.03858

28 1998 35963 M 0.45753 -0.06754 -0.05562

28 1998 36003 C 0.56712 -0.05385 -0.03084

28 1998 36003 M 0.56712 -0.05385 -0.03398

28 1998 36038 C 0.66301 -0.04258 -0.04263

28 1998 36038 M 0.66301 -0.04258 -0.03314

28 2000 36658 C 2.36164 0.01913 -0.01633

28 2000 36658 M 2.36164 0.01913 0.00819

28 2000 36732 C 2.56438 0.00555 -0.01041

28 2000 36732 M 2.56438 0.00555 0.01782

28 2000 36763 C 2.64932 0.06162 -0.01872

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 55

28 2000 36763 M 2.64932 0.06162 0.02766

28 2001 37047 C 3.42740 -0.00475 -0.01682

28 2001 37047 M 3.42740 -0.00475 0.02812

28 2001 37089 C 3.54247 0.02375 -0.00708

28 2001 37089 M 3.54247 0.02375 0.00381

28 2001 37141 C 3.68493 0.02668 -0.05914

28 2002 37375 C 4.32603 0.04533 -0.03651

28 2002 37375 M 4.32603 0.04533 0.00187

29 1998 35912 M 0.31781 -0.16760 0.01659

29 1998 35912 P 0.31781 -0.16760 -0.00628

29 1998 35990 M 0.53151 -0.10960 0.00840

29 1998 35990 P 0.53151 -0.10960 -0.01645

29 1998 35990 P 0.53151 -0.10960 -0.01036

29 1998 36047 M 0.68767 0.14723 0.00185

29 1998 36047 P 0.68767 0.14723 -0.04117

29 1999 36356 M 1.53425 -0.01479 0.00830

29 1999 36356 P 1.53425 -0.01479 -0.02872

29 1999 36356 P 1.53425 0.00314 -0.02267

29 2000 36755 M 2.62740 0.01881 0.00204

29 2000 36755 P 2.62740 0.01881 -0.05648

29 2002 37326 M 4.19178 0.35833 -0.03470

30 1998 35913 C 0.32055 0.09673 0.10103

30 1998 35913 M 0.32055 0.09673 0.06720

30 1998 35971 C 0.47945 -0.09114 0.07128

30 1998 35971 M 0.47945 -0.09114 0.07045

30 1998 36041 C 0.67123 0.12030 0.09239

30 1998 36041 M 0.67123 0.12030 0.08484

30 1999 36425 C 1.72329 -0.13057 0.07907

30 1999 36425 M 1.72329 -0.13057 0.09113

30 2000 36699 C 2.47397 -0.15723 0.06510

30 2000 36699 M 2.47397 -0.15723 0.07562

30 2001 37112 C 3.60548 0.13200 0.14082

30 2001 37112 M 3.60548 0.13200 0.14407

30 2002 37379 C 4.33699 0.11322 0.12649

30 2002 37379 M 4.33699 0.11322 0.12782

30 2002 37531 M 4.75342 -0.16660 0.09322

32 1998 35893 M 0.26575 0.16886 -0.05367

32 1998 35893 P 0.26575 0.16886 -0.04475

32 1998 35977 M 0.49589 0.00925 -0.04714

32 1998 35977 P 0.49589 0.00925 -0.08463

32 1998 36026 M 0.63014 -0.02250 -0.03455

32 1998 36026 P 0.63014 -0.02250 -0.12493

32 1999 36333 M 1.47123 0.02283 -0.03556

32 1999 36333 P 1.47123 0.02283 -0.10332

32 1999 36370 M 1.57260 -0.10658 -0.03289

32 1999 36370 P 1.57260 -0.10658 -0.09684

32 1999 36399 M 1.65205 -0.11982 -0.01617

32 1999 36399 P 1.65205 -0.11982 -0.05229

32 2000 36690 M 2.44932 -0.01047 -0.04679

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
56 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

32 2000 36690 P 2.44932 -0.01047 -0.10115

32 2000 36720 M 2.53151 -0.11097 -0.02680

32 2000 36720 P 2.53151 -0.11097 -0.12346

32 2000 36747 M 2.60548 -0.06786 -0.02060

32 2000 36747 P 2.60548 -0.06786 -0.09282

32 2001 37064 M 3.47397 0.02090 -0.00032

32 2001 37064 P 3.47397 0.02090 -0.04175

32 2001 37111 M 3.60274 0.07355 -0.03344

32 2001 37111 P 3.60274 0.07355 -0.12214

32 2002 37455 M 4.54521 0.28564 -0.05116

34 1998 35902 M 0.29041 0.09768 -0.03627

34 1998 35902 P 0.29041 0.09768 -0.03167

34 1998 35989 C 0.52877 -0.02368 -0.04366

34 1998 35989 P 0.52877 -0.02368 -0.06741

34 1998 36026 C 0.63014 -0.06604 -0.00586

34 1998 36026 P 0.63014 -0.06604 -0.05310

34 1999 36368 C 1.56712 -0.14089 -0.01862

34 1999 36368 M 1.56712 -0.15130 -0.04650

34 1999 36368 P 1.56712 -0.14089 -0.06305

34 2000 36690 C 2.44932 -0.02368 -0.03718

34 2000 36690 M 2.44932 -0.02368 -0.01442

34 2000 36690 P 2.44932 -0.02368 -0.16606

34 2000 36752 C 2.61918 -0.08301 -0.05074

34 2000 36752 M 2.61918 -0.08301 -0.03879

34 2000 36752 P 2.61918 -0.08301 -0.12179

34 2001 36983 C 3.25205 0.10581 -0.04462

34 2001 36983 P 3.25205 0.10581 -0.03775

34 2001 37083 C 3.52603 0.00807 -0.04893

34 2001 37083 P 3.52603 0.00807 -0.06890

34 2001 37111 C 3.60274 0.04703 -0.04137

34 2002 37445 C 4.51781 0.23121 -0.02565

34 2002 37445 P 4.51781 0.23121 -0.14029

35 1998 35920 P 0.33973 0.04177 -0.04066

35 1998 35970 P 0.47671 0.00429 0.12374

35 1998 36048 P 0.69041 -0.03999 -0.01584

35 1999 36333 P 1.47123 0.00153 -0.00664

35 2000 36692 P 2.45479 -0.00759 0.07660

36 1998 35915 M 0.32603 -0.06501 -0.06567

36 1998 35915 P 0.32603 -0.06501 -0.11171

36 1998 35985 M 0.51781 -0.08436 -0.06679

36 1998 35985 P 0.51781 -0.08436 -0.03736

36 1998 36054 M 0.70685 0.06045 -0.07656

36 1999 36339 M 1.48767 -0.03890 -0.05403

36 1999 36339 P 1.48767 -0.03890 0.04197

36 2000 36733 M 2.56712 -0.02565 -0.07197

36 2000 36733 P 2.56712 -0.02565 -0.08066

36 2001 37110 M 3.60000 0.10568 -0.06878

36 2002 37410 M 4.42192 0.11182 -0.13844

36 2002 37410 P 4.42192 0.11182 -0.15518

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 57

36 2002 37455 M 4.54521 0.03806 -0.13344

37 1998 35915 M 0.32603 0.05905 0.02146

37 1998 35915 P 0.32603 0.05905 0.01650

37 1998 35977 C 0.49589 -0.01746 -0.04670

37 1998 35977 M 0.49589 -0.01746 -0.01843

37 1998 35977 P 0.49589 -0.01746 -0.04098

37 1998 36035 C 0.65479 -0.06359 -0.04567

37 1998 36035 M 0.65479 -0.06359 0.01238

37 1998 36035 P 0.65479 -0.06359 -0.02343

37 1999 36395 C 1.64110 -0.08090 -0.03507

37 1999 36395 M 1.64110 -0.08090 0.01872

37 1999 36395 P 1.64110 -0.08090 -0.03411

37 2001 37134 C 3.66575 0.04220 -0.00419

37 2001 37134 M 3.66575 0.04220 -0.02221

37 2001 37134 P 3.66575 0.04220 -0.04250

37 2002 37483 C 4.62192 0.24112 -0.00020

38 1998 35892 M 0.26301 -0.09670 -0.03394

38 1998 35892 P 0.26301 -0.09670 0.00941

38 1998 35977 M 0.49589 -0.00884 -0.02747

38 1998 35977 P 0.49589 -0.00884 0.01436

38 1998 36021 M 0.61644 0.01168 -0.05118

38 1998 36021 P 0.61644 0.01168 -0.00275

38 1999 36341 M 1.49315 -0.04791 -0.01415

38 1999 36341 P 1.49315 -0.04791 0.00296

38 1999 36370 M 1.57260 -0.03126 -0.03468

38 1999 36370 P 1.57260 -0.03126 0.00460

38 1999 36395 M 1.64110 -0.05294 -0.01775

38 1999 36395 P 1.64110 -0.05294 0.02156

38 2000 36641 M 2.31507 0.00338 -0.02929

38 2000 36641 P 2.31507 0.00338 -0.02152

38 2000 36719 M 2.52877 0.03155 -0.04983

38 2000 36719 P 2.52877 0.02737 -0.00964

38 2000 36742 M 2.59178 0.02225 -0.02782

38 2000 36742 P 2.59178 0.02225 -0.01475

38 2001 37012 M 3.33151 0.05827 -0.05383

38 2001 37012 P 3.33151 0.05827 -0.02697

38 2001 37104 M 3.58356 0.00100 -0.04523

38 2001 37104 P 3.58356 0.00100 -0.01048

38 2002 37350 M 4.25753 0.06120 -0.00446

38 2002 37350 P 4.25753 0.06120 0.03303

38 2002 37483 P 4.62192 0.10085 -0.04015

39 1998 36021 C 0.61644 -0.03945 0.01685

39 1998 36021 P 0.61644 -0.03945 -0.03986

39 1998 36028 C 0.63562 -0.04032 0.01679

39 1998 36028 P 0.63562 -0.04032 -0.01038

39 1999 36341 C 1.49315 -0.07095 0.00015

39 1999 36341 P 1.49315 -0.07095 -0.02487

39 1999 36367 C 1.56438 -0.03602 -0.00359

39 1999 36367 P 1.56438 -0.03602 -0.05482

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
58 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

39 1999 36433 C 1.74521 -0.04118 0.01253

39 1999 36433 P 1.74521 -0.04118 -0.03119

39 2001 37104 C 3.58356 0.08890 0.03412

39 2001 37153 C 3.71781 0.07363 0.01068

39 2002 37326 C 4.19178 0.10020 0.01772

40 1998 35919 M 0.33699 0.00004 0.02046

40 1998 35919 P 0.33699 0.00004 0.05083

40 1998 35944 M 0.40548 -0.04793 -0.00204

40 1998 35944 P 0.40548 -0.04793 0.00435

40 1998 36010 M 0.58630 0.00559 -0.10680

40 1998 36010 P 0.58630 0.00559 -0.09430

40 1999 36341 M 1.49315 -0.02753 -0.01413

40 1999 36341 P 1.49315 -0.02753 -0.09326

40 2000 36649 M 2.33699 -0.01083 -0.02945

40 2000 36719 M 2.52877 0.03132 -0.02798

40 2000 36719 P 2.52877 0.03132 -0.02430

40 2000 36740 M 2.58630 0.04393 -0.12357

40 2000 36740 P 2.58630 0.04393 -0.08944

41 1998 35915 M 0.32603 0.03835 -0.02046

41 1998 35915 P 0.32603 0.03835 -0.04518

41 1998 36011 C 0.58904 0.06942 0.06671

41 1998 36011 C 0.58904 0.06942 0.06433

41 1998 36011 M 0.58904 0.06942 -0.01316

41 1998 36011 P 0.58904 0.06942 -0.04022

41 1999 36336 C 1.47945 -0.32145 0.14067

41 1999 36336 C 1.47945 -0.32145 0.13537

41 1999 36336 M 1.47945 -0.32145 0.08540

41 2000 36656 C 2.35616 0.06055 0.01674

41 2000 36656 C 2.35616 0.06055 -0.00021

41 2000 36656 M 2.35616 0.06055 -0.03866

41 2000 36656 P 2.35616 0.06055 -0.11290

41 2000 36740 C 2.58630 0.09267 -0.00306

41 2000 36740 M 2.58630 0.09267 -0.05335

41 2000 36763 C 2.64932 0.04259 0.02597

41 2000 36763 M 2.64932 0.04259 -0.01946

43 1998 35958 C 0.44384 -0.02180 0.00432

43 1998 35958 M 0.44384 -0.02180 0.01941

43 1998 35958 P 0.44384 -0.02180 0.00485

43 1998 36003 C 0.56712 -0.03317 -0.01169

43 1998 36003 M 0.56712 -0.03317 0.01214

43 1998 36003 P 0.56712 -0.03317 -0.04257

43 1998 36053 C 0.70411 -0.08242 -0.01942

43 1998 36053 M 0.70411 -0.08242 0.01434

43 1999 36336 C 1.47945 0.02462 0.01461

43 1999 36336 P 1.47945 0.02462 -0.02328

43 1999 36399 C 1.65205 -0.02861 -0.00398

43 1999 36399 M 1.65205 -0.02861 0.00446

43 1999 36399 P 1.65205 -0.02861 -0.01614

43 2000 36657 C 2.35890 0.04175 0.00116

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 59

43 2000 36657 M 2.35890 0.04175 -0.02268

43 2000 36657 P 2.35890 0.04175 -0.00893

43 2000 36720 C 2.53151 0.00938 0.00534

43 2000 36720 M 2.53151 0.00938 -0.00955

43 2000 36720 P 2.53151 0.00938 -0.06288

43 2000 36747 C 2.60548 -0.09208 0.00575

43 2000 36747 M 2.60548 -0.09208 -0.01143

43 2000 36747 P 2.60548 -0.09208 -0.08034

43 2001 36984 C 3.25479 -0.09695 0.00040

43 2001 36984 M 3.25479 -0.09695 -0.03465

43 2001 36984 P 3.25479 -0.09695 -0.17494

43 2001 37103 C 3.58082 0.04387 0.00608

43 2001 37103 M 3.58082 0.04387 -0.02714

43 2001 37103 P 3.58082 0.04387 -0.03573

43 2002 37419 C 4.44658 0.11343 0.01829

43 2002 37419 M 4.44658 0.11343 -0.03915

43 2002 37419 P 4.44658 0.11343 -0.09401

43 2002 37526 C 4.73973 0.15409 -0.00080

43 2002 37526 M 4.73973 0.15409 -0.02675

44 1998 35906 C 0.30137 -0.01602 -0.00326

44 1998 35906 P 0.30137 -0.01602 -0.06558

44 1998 35957 C 0.44110 -0.00808 0.03414

44 1998 35957 P 0.44110 -0.00808 -0.00625

44 1998 36047 C 0.68767 -0.05253 -0.00578

44 1998 36047 P 0.68767 -0.05253 0.00119

44 1999 36389 C 1.62466 -0.07764 -0.02105

44 1999 36389 P 1.62466 -0.07764 -0.04380

44 2000 36691 C 2.45205 -0.05584 -0.00160

44 2000 36691 P 2.45205 -0.05584 -0.01399

44 2000 36719 C 2.52877 0.07530 0.00657

44 2000 36719 P 2.52877 0.07530 -0.05990

44 2000 36740 C 2.58630 0.04203 0.02218

44 2000 36740 P 2.58630 0.04203 -0.07663

44 2001 37012 C 3.33151 0.05695 0.26982

44 2001 37012 P 3.33151 0.05695 0.17096

44 2001 37110 P 3.60000 0.07166 0.01504

45 1998 35899 C 0.28219 -0.02076 0.03483

45 1998 35899 P 0.28219 -0.02076 -0.00107

45 1998 35942 C 0.40000 0.03578 0.05288

45 1998 35942 P 0.40000 0.03578 0.01015

45 1998 36054 P 0.70685 0.05475 0.01398

45 1999 36370 P 1.57260 -0.04056 -0.00992

45 2000 36692 P 2.45479 -0.02011 0.00222

45 2000 36720 P 2.53151 0.02397 -0.01293

45 2000 36755 P 2.62740 0.01076 -0.00688

45 2001 37012 P 3.33151 0.00505 0.00913

45 2001 37063 P 3.47123 -0.04056 0.02840

45 2001 37153 P 3.71781 -0.00777 0.00272

45 2002 37418 P 4.44384 -0.00777 0.02683

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
60 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

45 2002 37418 P 4.44384 -0.00777 0.02683

46 1998 35915 C 0.32603 0.07498 -0.08912

46 1998 35915 M 0.32603 0.07498 -0.08059

46 1998 36000 C 0.55890 -0.01209 -0.08410

46 1998 36000 M 0.55890 -0.01209 -0.07807

46 1998 36038 C 0.66301 -0.02902 -0.08574

46 1998 36038 M 0.66301 -0.02902 -0.07522

46 1999 36241 C 1.21918 0.06353 -0.06815

46 1999 36241 M 1.21918 0.06353 -0.07604

46 2000 36683 C 2.43014 -0.33775 -0.07138

46 2000 36683 M 2.43014 -0.33775 -0.10481

46 2000 36683 P 2.43014 -0.33775 -0.15444

46 2000 36734 C 2.56986 0.01245 -0.02493

46 2000 36734 M 2.56986 0.01245 -0.07245

46 2000 36734 P 2.56986 0.01245 -0.11145

46 2000 36777 C 2.68767 0.00851 -0.08623

46 2000 36777 M 2.68767 0.00851 -0.09815

46 2001 36991 C 3.27397 0.12771 -0.07862

46 2001 36991 M 3.27397 0.12771 -0.09796

46 2001 36991 P 3.27397 0.12771 -0.10768

46 2001 37048 C 3.43014 0.01376 -0.04654

46 2001 37048 M 3.43014 0.01376 -0.04619

46 2001 37048 P 3.43014 0.01376 -0.04874

46 2002 37335 C 4.21644 0.07035 -0.05393

46 2002 37335 M 4.21644 0.07035 -0.05434

47 1998 35951 M 0.42466 0.00930 -0.03063

47 1998 35951 P 0.42466 0.00930 -0.08235

47 1998 36000 M 0.55890 -0.01705 -0.04120

47 1998 36000 P 0.55890 -0.01705 -0.05070

47 1998 36031 M 0.64384 0.00021 0.01330

47 1998 36031 P 0.64384 0.00021 -0.00512

47 1999 36241 M 1.21918 0.06213 -0.04107

47 2000 36683 M 2.43014 -0.38623 -0.02361

47 2000 36683 P 2.43014 -0.38623 -0.04304

47 2000 36734 M 2.56986 0.01568 0.00796

47 2000 36734 P 2.56986 0.01568 -0.05416

47 2000 36777 M 2.68767 0.00439 -0.04894

47 2001 36991 M 3.27397 0.08195 0.02310

47 2001 36991 P 3.27397 0.08195 0.02561

47 2001 37057 M 3.45479 0.01456 0.04459

47 2001 37152 M 3.71507 0.01155 0.00839

47 2001 37152 P 3.71507 0.01155 -0.00233

47 2002 37335 M 4.21644 0.06926 -0.00377

47 2002 37477 M 4.60548 0.20942 0.00602

47 2002 37477 P 4.60548 0.20942 0.03939

48 1998 35928 M 0.36164 -0.01175 -0.06261

48 1998 35928 P 0.36164 -0.01175 -0.07114

48 1998 35965 M 0.46301 -0.03255 -0.05036

48 1998 35965 P 0.46301 -0.03255 -0.04928

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 61

48 1998 36054 M 0.70685 0.02858 -0.06864

48 1998 36054 P 0.70685 0.02858 -0.09780

48 1999 36383 M 1.60822 -0.02312 -0.04009

48 1999 36383 P 1.60822 -0.02312 -0.05179

48 2000 36663 M 2.37534 0.03631 -0.09621

48 2000 36663 P 2.37534 0.03631 -0.06265

48 2000 36741 M 2.58904 0.00505 -0.04404

49 1998 35912 P 0.31781 0.08436 -0.00274

49 1998 35975 C 0.49041 -0.03170 0.03773

49 1998 35975 P 0.49041 -0.03170 -0.06614

49 1998 36035 C 0.65479 -0.15398 0.01846

49 1998 36035 P 0.65479 -0.15398 0.02294

49 2000 36763 C 2.64932 0.03386 0.01970

49 2001 37152 C 3.71507 0.10021 0.02328

49 2002 37446 C 4.52055 0.15294 0.02165

50 1998 35899 C 0.28219 -0.14739 0.06539

50 1998 35899 M 0.28219 -0.14739 0.04361

50 1998 35961 C 0.45205 -0.05340 0.07697

50 1998 35961 M 0.45205 -0.05340 0.04822

50 1998 36012 C 0.59178 0.10548 0.08703

50 1998 36012 M 0.59178 0.10548 0.06125

50 1998 36059 C 0.72055 0.13760 0.04371

50 1998 36059 M 0.72055 0.13760 0.01505

50 1999 36357 C 1.53699 -0.11431 0.04603

50 1999 36357 M 1.53699 -0.11431 0.01578

50 2000 36662 C 2.37260 -0.09818 0.03877

50 2000 36662 M 2.37260 -0.09818 0.01693

50 2001 37023 C 3.36164 0.15949 0.13890

50 2001 37118 C 3.62192 0.18091 0.13540

51 1998 35906 M 0.30137 -0.03036 0.05245

51 1998 35906 P 0.30137 -0.03036 0.00094

51 1998 35972 M 0.48219 0.02994 0.00499

51 1998 35972 P 0.48219 0.02994 0.01259

51 1998 36020 M 0.61370 -0.07828 0.01316

51 1998 36020 P 0.61370 -0.07828 0.03242

51 1999 36241 M 1.21918 0.04632 0.11703

51 1999 36241 P 1.21918 0.04632 0.09336

51 2000 36678 M 2.41644 0.02002 0.05444

51 2000 36678 P 2.41644 0.02002 0.02657

51 2001 36991 M 3.27397 0.03703 0.02027

51 2001 36991 P 3.27397 0.03703 -0.01106

51 2001 37048 M 3.43014 0.05105 0.00272

51 2001 37048 P 3.43014 0.05105 -0.01329

51 2002 37421 M 4.45205 -0.07573 -0.05591

51 2002 37421 P 4.45205 -0.07573 -0.07671

52 1998 35965 C 0.46301 -0.03601 -0.07317

52 1998 35965 M 0.46301 -0.03601 -0.02072

52 1998 35965 P 0.46301 -0.03601 -0.11713

52 1998 35992 C 0.53699 0.05810 -0.06194

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
62 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

52 1998 35992 M 0.53699 0.05810 -0.02104

52 1998 36034 M 0.65205 0.00299 -0.00487

52 1998 36034 P 0.65205 0.00299 -0.03540

52 1999 36349 C 1.51507 -0.01993 -0.03939

52 1999 36349 M 1.51507 -0.01993 -0.01095

52 1999 36405 C 1.66849 0.01285 -0.06251

52 1999 36405 M 1.66849 0.01285 -0.01050

53 1998 35949 M 0.41918 0.08052 -0.01158

53 1998 35949 P 0.41918 0.08052 -0.06151

53 1998 35991 C 0.53425 0.10402 -0.02339

53 1998 35991 M 0.53425 0.10402 -0.04521

53 1998 35991 P 0.53425 0.10402 -0.07028

53 1998 36035 C 0.65479 0.07631 -0.04935

53 1998 36035 M 0.65479 0.07631 0.00407

53 1999 36319 C 1.43288 -0.16383 0.01136

53 1999 36319 M 1.43288 -0.16383 0.03628

53 2000 36649 C 2.33699 0.13097 0.01811

53 2000 36649 M 2.33699 0.13097 -0.01707

53 2000 36649 P 2.33699 0.13097 -0.07578

53 2000 36712 C 2.50959 -0.08654 0.00327

53 2000 36712 M 2.50959 -0.08654 -0.02363

53 2000 36733 C 2.56712 -0.17822 0.00599

53 2000 36733 M 2.56712 -0.17822 -0.00026

53 2000 36733 P 2.56712 -0.17822 -0.04587

53 2001 36982 C 3.24932 -0.23794 -0.01725

53 2001 36982 M 3.24932 -0.23794 -0.03848

53 2001 36982 P 3.24932 -0.23794 -0.11558

53 2001 37070 C 3.49041 -0.09484 0.00135

53 2001 37070 M 3.49041 -0.09484 -0.00127

53 2001 37070 P 3.49041 -0.09484 -0.05321

53 2001 37110 C 3.60000 0.18280 -0.00221

53 2001 37110 M 3.60000 0.18280 -0.00961

53 2001 37110 P 3.60000 0.18280 -0.06411

53 2002 37347 C 4.24932 0.19908 0.00739

53 2002 37347 M 4.24932 0.19908 -0.02525

53 2002 37445 C 4.51781 0.23447 0.03088

53 2002 37445 M 4.51781 0.23447 -0.02200

53 2002 37504 C 4.67945 -0.20020 0.02420

53 2002 37504 M 4.67945 -0.20020 -0.02114

54 1998 35963 C 0.45753 0.00088 -0.10034

54 1998 35963 M 0.45753 0.00088 -0.01317

54 1998 36053 C 0.70411 0.00381 -0.03356

54 1998 36056 C 0.71233 0.01173 -0.03116

54 1999 36362 C 1.55068 -0.01116 0.01897

54 1999 36362 M 1.55068 -0.01116 -0.07421

54 2000 36656 C 2.35616 0.00540 0.01798

54 2002 37349 C 4.25479 -0.00418 0.02242

55 1998 35956 C 0.43836 -0.01350 0.00054

55 1998 35956 M 0.43836 -0.01350 0.00639

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 63

55 1998 35998 C 0.55342 -0.02394 -0.00302

55 1998 35998 M 0.55342 -0.02394 0.00275

55 1998 36035 C 0.65479 -0.09230 0.00383

55 1998 36035 M 0.65479 -0.09230 0.00317

55 2000 36769 C 2.66575 -0.01625 -0.01933

55 2000 36769 M 2.66575 -0.01625 -0.02802

55 2000 36769 P 2.66575 -0.01625 -0.08576

55 2002 37371 C 4.31507 0.05069 -0.02874

55 2002 37371 M 4.31507 0.05069 -0.03320

55 2002 37469 C 4.58356 0.10343 0.00495

55 2002 37469 M 4.58356 0.10343 -0.01281

56 1998 35901 C 0.28767 -0.06984 0.12087

56 1998 35901 M 0.28767 -0.06984 0.11673

56 1998 35956 C 0.43836 -0.05610 -0.15010

56 1998 35956 M 0.43836 -0.05610 -0.03395

56 1998 35956 P 0.43836 -0.05610 -0.11193

56 1998 36046 C 0.68493 -0.12113 -0.00284

56 1998 36046 P 0.68493 -0.12113 -0.02347

56 2000 36762 C 2.64658 -0.08287 -0.04716

56 2000 36762 M 2.64658 -0.08287 -0.02730

56 2001 37036 C 3.39726 -0.12821 0.07869

56 2001 37036 M 3.39726 -0.12821 0.06537

56 2001 37071 C 3.49315 0.14469 0.09653

56 2001 37071 M 3.49315 0.14469 0.09086

56 2001 37124 C 3.63836 0.12321 -0.09654

56 2001 37124 M 3.63836 0.12321 -0.09411

56 2002 37343 C 4.23836 0.21829 -0.03432

56 2002 37343 M 4.23836 0.21829 -0.02392

58 1998 35954 C 0.43288 -0.05753 -0.01343

58 1998 35990 C 0.53151 -0.12302 -0.00066

58 1998 36020 C 0.61370 -0.17546 -0.00406

58 1999 36378 C 1.59452 -0.15002 -0.00013

58 1999 36378 M 1.59452 -0.17731 -0.00506

58 2000 36748 C 2.60822 -0.11216 0.00242

58 2001 36999 C 3.29589 0.15335 -0.01726

58 2001 37056 C 3.45205 0.06293 0.02612

58 2001 37103 C 3.58082 0.02072 0.03134

58 2002 37335 C 4.21644 0.16945 0.02658

58 2002 37414 C 4.43288 0.15765 0.02064

58 2002 37515 C 4.70959 0.23138 0.01091

59 1998 35964 M 0.46027 -0.08554 -0.03136

59 1998 35964 P 0.46027 -0.08554 -0.03826

59 1999 36390 M 1.62740 0.24237 -0.05802

59 1999 36390 P 1.62740 0.24237 -0.04414

59 2000 36650 P 2.33973 -0.31367 -0.05252

60 1998 35901 C 0.28767 0.01419 -0.05251

60 1998 35901 M 0.28767 0.01419 -0.03092

60 1998 35901 P 0.28767 0.01419 -0.06851

60 1998 35978 C 0.49863 0.02147 -0.05745

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
64 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

60 1998 35978 M 0.49863 0.02147 -0.02944

60 1998 35978 P 0.49863 0.02147 -0.04777

60 1998 36046 C 0.68493 -0.14613 -0.06123

60 1998 36046 M 0.68493 -0.14613 -0.03237

60 1998 36046 P 0.68493 -0.14613 -0.05983

60 1999 36362 C 1.55068 -0.03549 -0.08646

60 1999 36362 C 1.55068 -0.02815 -0.06970

60 1999 36362 M 1.55068 -0.03549 -0.08191

60 1999 36362 P 1.55068 -0.03549 -0.09072

60 2000 36691 C 2.45205 -0.05228 -0.05144

60 2000 36691 M 2.45205 -0.05228 -0.05661

60 2000 36691 P 2.45205 -0.05228 -0.06382

60 2000 36721 C 2.53425 -0.03645 -0.05263

60 2000 36721 M 2.53425 -0.03645 -0.05926

60 2000 36721 P 2.53425 -0.03645 -0.07942

60 2000 36761 C 2.64384 -0.03293 -0.08319

60 2000 36761 M 2.64384 -0.03293 -0.06030

60 2000 36761 P 2.64384 -0.03293 -0.11042

60 2001 37015 C 3.33973 0.09748 -0.04210

60 2001 37015 M 3.33973 0.09748 -0.06882

60 2001 37077 C 3.50959 0.05655 -0.07170

60 2001 37077 M 3.50959 0.05655 -0.10221

60 2001 37077 P 3.50959 0.05655 -0.12413

60 2001 37111 C 3.60274 0.06615 -0.06368

60 2001 37111 M 3.60274 0.06615 -0.07597

60 2001 37111 P 3.60274 0.06615 -0.14827

60 2002 37337 C 4.22192 0.08932 -0.05954

60 2002 37337 M 4.22192 0.08932 -0.06920

60 2002 37337 P 4.22192 0.08932 -0.08332

61 1998 35957 C 0.44110 -0.05184 0.00966

61 1998 35957 M 0.44110 -0.05184 -0.01729

61 1998 36004 C 0.56986 0.03154 -0.03413

61 1998 36004 M 0.56986 0.03154 -0.00760

61 1998 36042 C 0.67397 0.06352 0.00988

61 1998 36042 M 0.67397 0.06352 -0.04266

61 1999 36383 C 1.60822 -0.04642 0.04436

61 1999 36383 M 1.60822 -0.04642 -0.01810

61 2000 36691 C 2.45205 -0.16083 0.02901

61 2000 36691 M 2.45205 -0.16083 -0.14937

61 2001 37134 C 3.66575 0.06110 0.03198

61 2001 37134 M 3.66575 0.06110 -0.09020

61 2002 37349 C 4.25479 0.10293 0.17407

61 2002 37349 M 4.25479 0.10293 0.00417

62 1998 35928 P 0.36164 -0.32894 -0.03479

62 1998 35965 C 0.46301 -0.04666 -0.07988

62 1998 35965 P 0.46301 -0.03548 -0.02847

62 1998 36034 C 0.65205 -0.02606 -0.10807

62 1998 36034 P 0.65205 -0.02729 -0.05414

62 1999 36433 C 1.74521 0.08093 -0.11970

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 65

62 1999 36433 P 1.74521 0.08093 -0.04404

62 2000 36663 C 2.37534 0.03214 -0.10862

62 2000 36663 P 2.37534 0.03214 -0.07583

62 2000 36741 C 2.58904 -0.01512 -0.16174

62 2000 36741 P 2.58904 -0.01512 -0.08082

62 2001 37096 C 3.56164 0.17524 -0.08737

62 2002 37505 C 4.68219 0.04665 -0.12914

62 2002 37505 P 4.68219 0.04665 -0.10006

63 1998 35902 C 0.29041 -0.38021 0.00558

63 1998 35949 C 0.41918 -0.37651 0.01087

63 1998 36047 C 0.68767 -0.39181 0.00822

63 1999 36357 C 1.53699 -0.35660 -0.00509

63 2000 36684 C 2.43288 0.26052 -0.03174

63 2000 36728 C 2.55342 0.26830 -0.00312

63 2000 36761 C 2.64384 0.16040 0.01874

63 2001 36998 C 3.29315 0.29863 0.01997

63 2001 37034 C 3.39178 0.29591 0.00672

63 2001 37069 C 3.48767 0.28177 0.00779

63 2002 37356 C 4.27397 -0.06041 -0.02088

64 1998 35921 C 0.34247 -0.04651 0.00554

64 1998 35949 C 0.41918 -0.03789 0.01118

64 1998 36047 C 0.68767 -0.04026 0.01422

64 1998 36054 C 0.70685 -0.03080 0.00500

64 1999 36313 C 1.41644 -0.04056 -0.00402

64 1999 36369 C 1.56986 -0.04085 0.00065

64 2000 36684 C 2.43288 0.18998 0.10154

64 2000 36726 C 2.54795 0.20357 0.09498

64 2000 36781 C 2.69863 -0.06217 0.09307

64 2001 36998 C 3.29315 -0.04502 -0.06288

64 2001 37035 C 3.39452 0.00274 0.04174

64 2001 37069 C 3.48767 -0.02904 0.06276

64 2002 37355 C 4.27123 -0.02319 -0.03716

65 1998 35900 C 0.28493 -0.04504 0.01377

65 1998 35900 M 0.28493 -0.04504 0.01918

65 1998 35949 C 0.41918 0.25873 0.01797

65 1998 35949 M 0.41918 0.25873 0.01822

65 1998 36032 C 0.64658 -0.09808 0.00769

65 1998 36032 M 0.64658 -0.09808 0.01814

65 1998 36053 C 0.70411 -0.04152 0.00579

65 1998 36053 M 0.70411 -0.04152 0.01695

65 1999 36313 C 1.41644 -0.04108 -0.04875

65 1999 36313 M 1.41644 -0.04108 -0.04845

65 1999 36364 C 1.55616 0.00700 -0.05431

65 1999 36364 M 1.55616 0.00700 -0.05644

65 2000 36685 C 2.43562 -0.02797 0.09861

65 2000 36685 M 2.43562 -0.02797 0.08494

65 2000 36728 C 2.55342 -0.01204 0.04906

65 2000 36728 M 2.55342 -0.01204 0.05772

66 1998 35958 C 0.44384 -0.10064 -0.00321

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
66 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

66 1998 35958 M 0.44384 -0.10064 -0.08667

66 1998 36005 C 0.57260 -0.12413 -0.00266

66 1998 36005 M 0.57260 -0.12413 -0.04489

66 1998 36017 C 0.60548 -0.17524 -0.00506

66 1998 36017 M 0.60548 -0.17524 -0.02309

66 1999 36294 C 1.36438 -0.11383 0.00166

66 1999 36294 M 1.36438 -0.11383 -0.01111

66 1999 36362 C 1.55068 -0.05134 0.01162

66 1999 36362 M 1.55068 -0.05134 0.00320

66 2000 36665 C 2.38082 -0.03123 -0.00725

66 2000 36665 M 2.38082 -0.03123 -0.00479

66 2000 36718 C 2.52603 -0.01873 -0.00975

66 2000 36718 M 2.52603 -0.01873 0.00219

66 2000 36754 C 2.62466 0.02514 0.01019

66 2000 36754 M 2.62466 0.02514 0.02107

66 2001 37047 C 3.42740 -0.00435 0.01421

66 2001 37047 M 3.42740 -0.00435 0.00835

66 2001 37091 C 3.54795 0.03728 -0.00111

66 2001 37091 M 3.54795 0.03728 0.00219

66 2001 37141 C 3.68493 0.05634 -0.00969

66 2001 37141 M 3.68493 0.05634 -0.09522

66 2002 37455 C 4.54521 0.23679 0.00297

66 2002 37455 M 4.54521 0.23679 0.00708

66 2002 37488 C 4.63562 0.26394 0.01656

66 2002 37488 M 4.63562 0.26394 0.00279

68 1998 35949 C 0.41918 -0.00010 0.00937

68 1998 35991 C 0.53425 -0.02429 0.01136

68 1998 36019 C 0.61096 -0.07676 0.00850

68 1998 36061 C 0.72603 -0.05664 0.01110

68 1999 36327 C 1.45479 -0.00369 0.01269

68 2000 36700 C 2.47671 -0.03785 0.01328

68 2001 37026 C 3.36986 -0.00219 -0.00053

68 2001 37140 C 3.68219 -0.02276 0.00887

68 2001 37162 C 3.74247 -0.01880 -0.00414

68 2002 37370 C 4.31233 0.06971 -0.02372

68 2002 37491 C 4.64384 0.17337 -0.00874

69 1998 35942 C 0.40000 -0.06328 0.02751

69 1998 35942 P 0.40000 -0.06328 0.01798

69 1998 36026 C 0.63014 0.02129 0.02145

69 1998 36026 P 0.63014 0.02129 0.01866

69 1998 36040 C 0.66849 0.00795 0.01489

69 2000 36747 C 2.60548 -0.01108 -0.00474

69 2001 37083 C 3.52603 0.00151 0.00276

69 2002 37419 C 4.44658 0.04281 0.01322

69 2002 37419 P 4.44658 0.04281 -0.01143

70 1998 35930 C 0.36712 0.01237 -0.02876

70 1998 35983 C 0.51233 0.04637 -0.02799

70 1998 36033 C 0.64932 0.00592 -0.02728

70 1999 36320 C 1.43562 0.05971 -0.02491

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 67

70 2000 36634 C 2.29589 0.00216 -0.03257

70 2000 36705 C 2.49041 0.05294 -0.02224

70 2000 36755 C 2.62740 0.00346 0.00630

70 2001 37008 C 3.32055 -0.07758 0.05184

70 2001 37105 C 3.58630 -0.10280 -0.00061

70 2002 37449 C 4.52877 -0.00253 0.02732

72 1998 35948 C 0.41644 -0.11268 0.00325

72 1998 35948 M 0.41644 -0.11268 -0.01188

72 1998 35992 C 0.53699 0.00737 0.00175

72 1998 35992 M 0.53699 0.00737 -0.00584

72 1998 36041 C 0.67123 -0.07947 0.00894

72 1998 36041 M 0.67123 -0.07947 -0.00338

72 1999 36355 C 1.53151 -0.00170 0.01046

72 1999 36355 M 1.53151 -0.00170 0.00655

72 2000 36719 C 2.52877 -0.00218 0.02014

72 2000 36719 M 2.52877 -0.00218 0.00311

72 2001 37070 C 3.49041 0.03317 0.03397

72 2001 37070 M 3.49041 0.03317 0.02370

72 2001 37140 C 3.68219 0.06911 0.00780

72 2001 37140 M 3.68219 0.06911 0.01962

72 2001 37161 C 3.73973 0.08639 0.01567

72 2001 37161 M 3.73973 0.08639 0.01619

74 1998 35935 C 0.38082 -0.07054 0.02185

74 1998 35935 M 0.38082 -0.07054 -0.01883

74 1998 36004 C 0.56986 -0.04915 0.03385

74 1998 36004 M 0.56986 -0.04915 0.00176

74 1998 36048 C 0.69041 -0.08808 0.02588

74 1998 36048 M 0.69041 -0.08808 0.00226

74 2000 36686 C 2.43836 0.03801 0.03739

74 2000 36686 M 2.43836 0.03801 0.02044

74 2001 37007 C 3.31781 0.18793 0.05089

74 2001 37007 M 3.31781 0.18793 0.03238

74 2002 37454 C 4.54247 -0.01816 -0.00831

74 2002 37454 M 4.54247 -0.01816 -0.01517

75 1998 35914 C 0.32329 0.05430 0.09522

75 1998 35914 M 0.32329 0.05430 0.08332

75 1998 36004 C 0.56986 -0.02450 0.07215

75 1998 36004 M 0.56986 -0.02450 0.06303

75 1998 36041 C 0.67123 -0.03010 0.04982

75 1998 36041 M 0.67123 -0.03010 0.04753

75 2000 36720 C 2.53151 0.00031 0.09582

75 2000 36720 M 2.53151 0.00031 0.07894

77 1998 35997 C 0.55068 -0.06278 0.02071

77 1998 35997 M 0.55068 -0.06278 -0.00445

77 1998 36005 C 0.57260 -0.03646 0.02129

77 1998 36005 M 0.57260 -0.03646 0.00376

77 1998 36040 C 0.66849 0.06506 0.02446

77 1998 36040 M 0.66849 0.06506 0.00870

77 1999 36363 C 1.55342 0.03418 0.03438

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
68 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

77 1999 36363 M 1.55342 0.03418 0.01017

80 1998 35907 C 0.30411 -0.05807 -0.00006

80 1998 35907 M 0.30411 -0.05807 0.01171

80 1998 35907 P 0.30411 -0.05807 -0.02650

80 1998 35997 C 0.55068 -0.03700 0.00132

80 1998 35997 M 0.55068 -0.03700 0.00772

80 1998 36027 C 0.63288 -0.02817 0.00218

80 1998 36027 M 0.63288 -0.02817 0.01258

80 1999 36356 C 1.53425 -0.06901 -0.00854

80 1999 36356 M 1.53425 -0.06901 0.01432

80 2000 36636 C 2.30137 0.00173 0.03127

80 2000 36636 M 2.30137 0.00173 0.01887

80 2000 36705 C 2.49041 -0.02247 0.03196

80 2000 36705 M 2.49041 -0.02247 0.01079

80 2000 36749 C 2.61096 0.02117 0.05926

80 2000 36749 M 2.61096 0.02117 0.05770

80 2002 37489 C 4.63836 0.22085 -0.03680

80 2002 37489 M 4.63836 0.22085 -0.00340

82 1998 35969 C 0.47397 -0.16112 0.00142

82 1998 35993 C 0.53973 -0.14613 0.00225

82 1998 36055 C 0.70959 -0.08830 0.00180

82 2001 37145 C 3.69589 0.00218 -0.00279

82 2002 37419 C 4.44658 0.18374 -0.04076

82 2002 37504 C 4.67945 0.20964 -0.04591

85 1998 35928 C 0.36164 -0.03246 0.00165

85 1998 35928 P 0.36164 -0.03246 -0.02512

85 1998 35970 C 0.47671 -0.28981 0.00232

85 1998 35970 P 0.47671 -0.28981 -0.02990

85 1998 36024 C 0.62466 0.01009 0.00206

85 1998 36024 P 0.62466 0.01009 -0.02761

85 1999 36356 C 1.53425 -0.00230 0.00856

85 1999 36356 P 1.53425 -0.00230 -0.03075

85 2000 36685 C 2.43562 0.00720 0.00907

85 2000 36685 P 2.43562 0.00720 -0.02830

85 2001 37055 C 3.44932 0.30729 -0.02090

85 2001 37055 P 3.44932 0.30729 -0.08249

86 1998 35920 C 0.33973 -0.10908 0.00933

86 1998 35920 P 0.33973 -0.10908 -0.04529

86 1998 35976 C 0.49315 0.02433 0.00771

86 1998 35976 P 0.49315 0.02433 -0.02389

86 1998 36021 C 0.61644 0.05794 0.00322

86 1998 36021 P 0.61644 0.05794 -0.02264

86 1998 36062 C 0.72877 0.05794 -0.00098

86 1998 36062 P 0.72877 0.05794 -0.02675

86 1999 36333 C 1.47123 0.00315 -0.01015

86 1999 36333 P 1.47123 0.00315 -0.02750

86 1999 36370 C 1.57260 0.05744 -0.02931

86 1999 36370 P 1.57260 0.05744 -0.06798

86 2000 36686 C 2.43836 0.11225 -0.01886

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 69

86 2000 36686 P 2.43836 0.11225 -0.07148

86 2001 37055 C 3.44932 0.03645 -0.00316

86 2001 37055 P 3.44932 0.03645 -0.04997

86 2002 37378 C 4.33425 -0.24043 -0.00052

86 2002 37378 P 4.33425 -0.24043 -0.00357

87 1998 35920 C 0.33973 -0.07827 -0.01632

87 1998 35920 P 0.33973 -0.07827 -0.07645

87 1998 35964 C 0.46027 -0.09757 -0.01475

87 1998 35964 P 0.46027 -0.09757 -0.05567

87 1998 36026 C 0.63014 -0.05233 -0.01203

87 1998 36026 P 0.63014 -0.05233 -0.04351

87 1998 36062 C 0.72877 -0.01113 0.00947

87 1998 36062 P 0.72877 -0.01113 -0.05248

87 1999 36370 C 1.57260 -0.01065 0.00514

87 1999 36370 P 1.57260 -0.01065 -0.05255

87 2000 36657 C 2.35890 0.00266 0.00637

87 2000 36657 P 2.35890 0.00266 -0.04752

87 2000 36735 C 2.57260 0.02369 0.01864

87 2000 36735 P 2.57260 0.02369 -0.03339

87 2000 36782 C 2.70137 0.03090 0.01652

87 2000 36782 P 2.70137 0.03090 -0.04108

87 2001 37070 C 3.49041 0.04140 0.01734

87 2001 37070 P 3.49041 0.04140 -0.04858

87 2001 37113 C 3.60822 0.04563 0.02268

87 2001 37113 P 3.60822 0.04563 0.00643

87 2001 37140 C 3.68219 0.05911 -0.00367

87 2001 37140 P 3.68219 0.05911 -0.04621

87 2002 37379 C 4.33699 0.04654 0.01513

87 2002 37379 P 4.33699 0.04654 0.00751

89 1998 35920 C 0.33973 -0.00449 -0.04186

89 1998 35920 M 0.33973 -0.00449 0.00495

89 1998 35950 C 0.42192 0.05452 -0.04254

89 1998 35950 M 0.42192 0.05452 0.00226

89 1998 36048 C 0.69041 0.09166 -0.02069

89 1998 36048 M 0.69041 0.09166 0.00179

89 1999 36322 C 1.44110 0.03597 -0.03007

89 1999 36322 M 1.44110 0.03597 0.00896

89 1999 36370 C 1.57260 -0.09735 -0.00647

89 1999 36370 M 1.57260 -0.09735 0.00790

89 2000 36720 C 2.53151 -0.08030 0.01064

89 2000 36720 M 2.53151 -0.08030 0.01392

90 1998 35922 C 0.34521 -0.03911 0.00861

90 1998 35922 P 0.34521 -0.03911 -0.00362

90 1998 35977 C 0.49589 -0.03659 0.00395

90 1998 35977 P 0.49589 -0.03659 -0.00094

90 1998 36021 C 0.61644 -0.01203 0.01290

90 1998 36021 P 0.61644 -0.01203 0.01987

90 1999 36356 C 1.53425 -0.04012 0.01275

90 1999 36356 P 1.53425 -0.04012 0.00396

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
70 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

90 2000 36686 C 2.43836 0.04072 0.00612

90 2000 36686 P 2.43836 0.04072 -0.01640

90 2001 37055 C 3.44932 0.06098 0.02206

90 2002 37379 C 4.33699 0.05664 0.00228

90 2002 37379 P 4.33699 0.05664 -0.01384

92 1998 35920 C 0.33973 -0.02916 -0.02267

92 1998 35920 P 0.33973 -0.02916 -0.04851

92 1998 35964 C 0.46027 -0.00023 -0.00314

92 1998 35964 P 0.46027 -0.00023 -0.01585

92 1998 36053 C 0.70411 -0.00319 -0.01559

92 1998 36053 P 0.70411 -0.00319 -0.04435

92 1998 36060 C 0.72329 -0.00274 -0.02209

92 1998 36060 P 0.72329 -0.00274 -0.03410

92 1999 36333 C 1.47123 -0.00148 -0.01477

92 1999 36333 P 1.47123 -0.00148 -0.05497

92 1999 36370 C 1.57260 0.01658 -0.01259

92 1999 36370 P 1.57260 0.01658 -0.05641

92 2000 36643 C 2.32055 -0.02134 -0.03869

92 2000 36643 P 2.32055 -0.02134 -0.09599

92 2000 36719 C 2.52877 0.00121 -0.02957

92 2000 36719 P 2.52877 0.00121 -0.09522

92 2000 36782 C 2.70137 -0.00148 -0.07115

92 2000 36782 P 2.70137 -0.00148 -0.13090

92 2001 37012 C 3.33151 -0.00391 -0.02141

92 2001 37012 P 3.33151 -0.00391 -0.09966

92 2001 37126 C 3.64384 0.01869 -0.02143

92 2001 37126 P 3.64384 0.01869 -0.06103

92 2001 37168 C 3.75890 0.02063 0.00638

92 2002 37386 C 4.35616 0.01676 0.01124

92 2002 37386 P 4.35616 0.01676 0.01273

95 1998 35921 C 0.34247 0.03804 0.04850

95 1998 35990 C 0.53151 -0.15220 0.05882

95 1998 35992 C 0.53699 0.11713 0.07598

95 1998 35992 P 0.53699 0.11713 0.01771

95 1998 36035 C 0.65479 0.01869 0.06526

95 1998 36035 P 0.65479 0.01869 -0.07972

95 1998 36047 C 0.68767 0.03012 0.04220

95 1999 36319 C 1.43288 -0.19872 0.04765

95 2000 36635 C 2.29863 0.02633 0.04481

95 2000 36649 C 2.33699 0.05259 0.05294

95 2000 36719 C 2.52877 0.08896 0.05197

95 2001 36991 C 3.27397 -0.00457 0.06076

95 2001 37064 C 3.47397 -0.15220 0.05652

97 1998 35929 C 0.36438 0.01355 -0.01323

97 1998 35929 C 0.36438 0.04902 -0.02228

97 1998 35984 C 0.51507 -0.03129 -0.00751

97 1998 35984 C 0.51507 0.00462 -0.00358

97 1998 36029 C 0.63836 -0.05281 -0.01231

97 1998 36029 C 0.63836 -0.02711 -0.01093

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 71

97 1999 36369 C 1.56986 -0.05680 0.00230

97 1999 36369 C 1.56986 -0.03972 -0.00392

97 2000 36692 C 2.45479 0.01355 -0.02606

97 2001 37119 C 3.62466 0.01498 0.04387

97 2002 37448 C 4.52603 0.11201 0.03211

98 1998 35927 C 0.35890 -0.01967 -0.03232

98 1998 35927 C 0.35890 0.01866 -0.02813

98 1998 35984 C 0.51507 -0.04150 -0.01317

98 1998 36047 C 0.68767 -0.06597 -0.01816

98 1998 36047 C 0.68767 -0.03027 -0.01829

98 1998 36056 C 0.71233 -0.02251 -0.02242

98 1999 36320 C 1.43562 -0.01711 -0.00062

98 2000 36651 C 2.34247 -0.00538 0.01255

98 2001 37011 C 3.32877 0.03947 0.01511

98 2001 37083 C 3.52603 0.01320 0.00044

98 2002 37356 C 4.27397 0.13109 -0.01023

99 1998 35928 C 0.36164 -0.15822 0.00553

99 1998 35928 C 0.36164 -0.04642 0.00319

99 1998 35976 C 0.49315 -0.14916 0.00150

99 1998 35976 M 0.49315 -0.14916 0.00129

99 1998 35976 C 0.49315 -0.03581 0.00243

99 1998 35976 M 0.49315 -0.03581 0.00249

99 1998 36061 C 0.72603 -0.09323 0.00820

99 1998 36061 M 0.72603 -0.09323 0.00362

99 1998 36061 C 0.72603 -0.00223 0.00524

99 1998 36061 M 0.72603 -0.00223 0.00110

99 2000 36735 C 2.57260 0.00871 0.02780

99 2000 36735 M 2.57260 0.00871 0.01022

99 2001 37007 C 3.31781 0.21179 0.02194

99 2001 37007 M 3.31781 0.21179 0.00872

99 2002 37385 C 4.35342 0.16226 0.02045

99 2002 37385 M 4.35342 0.16226 0.02548

100 1998 35942 C 0.40000 -0.14704 0.00833

100 1998 35942 C 0.40000 -0.10075 0.00595

100 1998 35942 M 0.40000 -0.14704 0.00128

100 1998 35942 M 0.40000 -0.10075 -0.00037

100 1998 35970 C 0.47671 -0.10249 0.00307

100 1998 35970 M 0.47671 -0.10249 0.00011

100 1998 36033 C 0.64932 -0.01095 0.00939

100 1998 36033 C 0.64932 0.02957 0.01166

100 1998 36033 M 0.64932 -0.01095 0.00238

100 1998 36033 M 0.64932 0.02957 0.00253

100 2000 36643 C 2.32055 -0.07923 0.00323

100 2000 36643 M 2.32055 -0.07923 -0.00429

100 2000 36749 C 2.61096 -0.07329 0.00580

100 2000 36749 M 2.61096 -0.07329 -0.00629

100 2000 36782 C 2.70137 0.09532 0.02316

100 2000 36782 M 2.70137 0.09532 0.00601

100 2001 36998 C 3.29315 0.05817 0.01953

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
72 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

100 2001 36998 M 3.29315 0.05817 -0.00606

100 2001 37091 C 3.54795 0.10245 0.02010

100 2001 37091 M 3.54795 0.10245 0.01714

100 2001 37160 C 3.73699 0.13149 0.01499

100 2001 37160 M 3.73699 0.13149 0.02417

100 2002 37349 C 4.25479 0.09675 0.01870

100 2002 37349 M 4.25479 0.09675 0.01584

101 1998 35935 C 0.38082 0.02515 0.02832

101 1998 35935 M 0.38082 0.02515 0.01670

101 1998 35935 C 0.38082 0.02433 0.02355

101 1998 35935 M 0.38082 0.02433 0.00691

101 1998 35991 C 0.53425 0.03250 0.05229

101 1998 35991 M 0.53425 0.03250 0.04194

101 1998 35991 C 0.53425 0.03087 0.03691

101 1998 35991 M 0.53425 0.03087 0.02777

101 1998 36025 C 0.62740 0.09551 0.02848

101 1998 36025 M 0.62740 0.09551 0.01331

101 1998 36025 C 0.62740 0.09322 0.02434

101 1998 36025 M 0.62740 0.09322 0.00857

101 1999 36364 C 1.55616 -0.10686 0.01280

101 1999 36364 M 1.55616 -0.10686 0.01389

101 2000 36672 C 2.40000 -0.19472 0.04057

101 2000 36672 M 2.40000 -0.19472 0.02921

102 1998 35934 C 0.37808 -0.14907 0.00596

102 1998 35934 M 0.37808 -0.14907 -0.00742

102 1998 35934 C 0.37808 -0.07080 0.01115

102 1998 35934 M 0.37808 -0.07080 -0.00252

102 1998 35985 C 0.51781 0.03800 0.00311

102 1998 35985 C 0.51781 0.08683 0.00341

102 1998 36067 C 0.74247 0.03378 0.00196

102 1998 36067 C 0.74247 0.08107 0.00485

102 1999 36335 C 1.47671 -0.00448 0.00434

102 2000 36747 C 2.60548 0.06673 0.02597

102 2001 37105 C 3.58630 -0.09530 0.08997

102 2002 37420 C 4.44932 0.23311 0.03028

103 1998 35913 C 0.32055 0.01604 0.00541

103 1998 35913 P 0.32055 0.01604 -0.00950

103 1998 35913 C 0.32055 0.04786 0.00962

103 1998 35913 P 0.32055 0.04786 -0.00334

103 1998 35963 C 0.45753 -0.03188 0.00749

103 1998 35963 P 0.45753 -0.03188 0.01420

103 1998 35963 C 0.45753 0.02837 0.00555

103 1998 35963 P 0.45753 0.02837 0.01105

103 1998 36039 C 0.66575 -0.13043 0.00494

103 1998 36039 P 0.66575 -0.13043 0.00851

103 1998 36039 C 0.66575 -0.05099 0.00778

103 1998 36039 P 0.66575 -0.05099 0.00912

103 1999 36329 C 1.46027 -0.05825 0.04292

103 1999 36329 P 1.46027 -0.05825 0.01099

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
SUPPLEMENTAL INFORMATION 73

103 2000 36693 C 2.45753 -0.03801 0.01779

103 2000 36693 P 2.45753 -0.03801 0.00269

103 2001 37062 C 3.46849 0.04804 -0.01949

103 2001 37062 P 3.46849 0.04804 -0.00194

103 2002 37413 C 4.43014 0.16925 -0.02553

103 2002 37413 P 4.43014 0.16925 -0.01449

104 1998 35922 C 0.34521 0.01289 0.03700

104 1998 35922 C 0.34521 0.02153 0.03401

104 1998 35922 M 0.34521 0.01289 -0.00576

104 1998 35922 M 0.34521 0.02153 -0.00615

104 1998 35964 C 0.46027 0.02306 0.02520

104 1998 35964 C 0.46027 0.02554 0.03187

104 1998 35964 M 0.46027 0.02306 0.00208

104 1998 35964 M 0.46027 0.02554 0.00122

104 1998 36021 C 0.61644 -0.02184 0.02159

104 1998 36021 C 0.61644 0.00222 0.02585

104 1998 36021 M 0.61644 -0.02184 0.00393

104 1998 36021 M 0.61644 0.00222 0.00669

104 1999 36334 C 1.47397 0.00883 0.04670

104 1999 36334 M 1.47397 0.00883 0.03870

104 2000 36649 C 2.33699 0.02478 0.11542

104 2000 36649 M 2.33699 0.02478 0.08602

104 2001 37013 C 3.33425 0.04478 0.09670

104 2001 37013 M 3.33425 0.04478 0.08976

104 2002 37379 C 4.33699 -0.14178 0.08415

104 2002 37379 M 4.33699 -0.14178 0.03749

105 1998 35927 C 0.35890 -0.08941 0.00760

105 1998 35927 C 0.35890 0.02271 0.00733

105 1998 35992 C 0.53699 -0.02501 0.00229

105 1998 35992 C 0.53699 0.04987 0.00827

105 1998 35992 C 0.53699 0.05310 0.01079

105 1998 36042 C 0.67397 -0.02709 0.00121

105 1998 36042 C 0.67397 0.05109 0.01464

105 1999 36335 C 1.47671 -0.08399 0.01023

105 2000 36649 C 2.33699 -0.07304 0.00588

105 2001 37064 C 3.47397 -0.01758 0.02653

105 2002 37492 C 4.64658 0.13933 -0.02307

106 1998 35955 C 0.43562 0.02125 0.04323

106 1998 36011 C 0.58904 0.00820 0.01157

106 1998 36055 C 0.70959 -0.03644 0.09346

106 1998 36055 C 0.70959 -0.02360 0.11021

106 2001 37162 C 3.74247 -0.14023 0.08767

106 2002 37372 C 4.31781 0.17082 -0.03938

Table 11. Data used in the diffQ model.—Continued

[Date, number of days from January 1, 1900; C, Collins flowmeter; M, McCrometer flowmeter; P, Polysonic flowmeter; 

t, measurement time in fractional years (t=0 for Jan. 1, 1998); w, log of pumping water level at time of measurement; 

w,

= average log PWL for a given site; diffQ, log portable flowmeter discharge minus log totalizing flowmeter discharge]

Site Year Date Method t - w diffQ

w
74 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

Table 12. Data used in the diffC model. 

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

1 1998 35950 C O 0.42192 -0.02363 4.29552

1 1998 35950 P O 0.42192 -0.02363 4.34003

1 1998 35989 C O 0.52877 -0.01599 4.33690

1 1998 35989 M O 0.52877 -0.01599 4.38402

1 1998 35989 P O 0.52877 -0.01599 4.39679

1 1998 36026 C O 0.63014 -0.06564 4.36080

1 1998 36026 M O 0.63014 -0.06564 4.36881

1 1998 36026 P O 0.63014 -0.06564 4.40550

1 1999 36343 C O 1.49863 -0.09143 4.30325

1 1999 36343 P O 1.49863 -0.09143 4.33060

1 1999 36369 C O 1.56986 -0.18524 4.27486

1 1999 36369 P O 1.56986 -0.18524 4.28675

1 1999 36397 C O 1.64658 -0.22624 4.37990

1 1999 36397 P O 1.64658 -0.22624 4.38502

1 2000 36650 C O 2.33973 0.01132 4.34847

1 2000 36650 P O 2.33973 0.01132 4.37626

1 2000 36727 C O 2.55068 -0.02992 4.29292

1 2000 36727 P O 2.55068 -0.02992 4.33218

1 2000 36752 C O 2.61918 -0.06564 4.29388

1 2000 36752 P O 2.61918 -0.06564 4.32387

1 2001 36990 C O 3.27123 0.18406 4.44817

1 2001 36990 P O 3.27123 0.18406 4.45353

1 2001 37084 C O 3.52877 0.01468 4.29620

1 2001 37084 P O 3.52877 0.01468 4.31669

1 2001 37111 C O 3.60274 0.05255 4.35234

1 2001 37111 P O 3.60274 0.05255 4.37122

1 2002 37351 C O 4.26027 0.20369 4.41316

1 2002 37351 P O 4.26027 0.20369 4.43450

1 2002 37449 C O 4.52877 0.14653 4.41546

1 2002 37449 P O 4.52877 0.14653 4.44159

1 2002 37476 C O 4.60274 0.13172 4.35221

1 2002 37476 P O 4.60274 0.13172 4.38627

2 1998 35936 C CL 0.38356 0.01061 4.34316

2 1998 35936 P CL 0.38356 0.01061 4.34329

2 1998 36048 C CL 0.69041 0.04031 4.37185

2 1998 36048 P CL 0.69041 0.04031 4.39753

2 1998 36052 C CL 0.70137 0.03215 4.38015

2 1998 36052 P CL 0.70137 0.03215 4.40757

2 1999 36342 C CH 1.49589 -0.10843 4.42041

2 1999 36342 P CH 1.49589 -0.10843 4.42819

2 1999 36348 C CL 1.51233 -0.02694 4.35799

2 1999 36348 P CL 1.51233 -0.02694 4.38652

2 2000 36692 C CL 2.45479 -0.03567 4.38875

2 2000 36692 P CL 2.45479 -0.03567 4.32440

2 2001 37062 C CH 3.46849 -0.07139 4.57523

2 2001 37062 P CH 3.46849 -0.07139 4.54849

2 2001 37082 C CL 3.52329 0.00725 4.49881

w

w

w w
SUPPLEMENTAL INFORMATION 75

2 2001 37082 P CL 3.52329 0.00725 4.49491

2 2001 37123 C CL 3.63562 0.05644 4.40550

2 2001 37123 P CL 3.63562 0.05644 4.38701

2 2002 37337 C CH 4.22192 0.09566 4.35581

2 2002 37337 P CH 4.22192 0.09566 4.43876

3 1998 35975 C O 0.49041 -0.02272 4.28428

3 1998 35975 P O 0.49041 -0.02272 4.27889

3 1998 36000 C O 0.55890 -0.02133 4.27986

3 1998 36000 P O 0.55890 -0.02133 4.36919

3 1998 36053 C O 0.70411 -0.15208 4.38078

3 1998 36053 P O 0.70411 -0.15208 4.42831

3 1999 36348 C O 1.51233 -0.06984 4.23873

3 1999 36348 P O 1.51233 -0.06984 4.35978

3 1999 36367 C O 1.56438 -0.11776 4.20185

3 1999 36367 P O 1.56438 -0.11776 4.16309

3 1999 36395 C O 1.64110 -0.09952 4.23584

3 1999 36395 P O 1.64110 -0.09952 4.33768

3 2000 36699 C O 2.47397 0.03552 4.24835

3 2000 36720 C O 2.53151 0.04599 4.21257

3 2000 36720 P O 2.53151 0.04599 4.23772

3 2000 36739 C O 2.58356 0.03552 4.21464

3 2000 36739 P O 2.58356 0.03552 4.42700

3 2001 36986 C O 3.26027 0.12121 4.28331

3 2001 36986 P O 3.26027 0.12121 4.25745

3 2001 37069 C O 3.48767 0.03552 4.17285

3 2001 37069 P O 3.48767 0.03552 4.36501

3 2001 37104 C O 3.58356 0.01424 4.26718

3 2001 37104 P O 3.58356 0.01424 4.38913

3 2002 37328 C O 4.19726 0.08180 4.29238

3 2002 37448 C O 4.52603 0.11150 4.38652

3 2002 37448 P O 4.52603 0.11150 4.45493

3 2002 37449 C O 4.52877 0.12121 4.35914

5 1998 35934 C CH 0.37808 0.09478 5.29235

5 1998 35934 P CH 0.37808 0.09478 5.56693

5 1998 35975 C CH 0.49041 0.12019 5.43228

5 1998 35975 P CH 0.49041 0.12019 5.50448

5 1998 36038 C CH 0.66301 0.08128 5.54181

5 1998 36038 P CH 0.66301 0.08128 5.58109

5 1998 36061 C CH 0.72603 -0.25540 5.53521

5 1998 36061 P CH 0.72603 -0.25540 5.59467

5 1999 36333 C CH 1.47123 -0.05848 5.55721

5 1999 36333 P CH 1.47123 -0.05848 5.62402

5 2001 37057 C CL 3.45479 -0.26612 5.33590

5 2001 37057 P CL 3.45479 -0.26612 5.43569

5 2002 37385 C CH 4.35342 0.16467 5.45091

5 2002 37424 C CL 4.46027 0.18936 5.44246

5 2002 37461 C CL 4.56164 0.21346 5.45993

7 1998 35937 M CL 0.38630 0.04206 5.09068

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
76 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

7 1998 35937 P CL 0.38630 0.04206 5.07730

7 1998 35999 M CL 0.55616 0.03677 4.89185

7 1998 35999 P CL 0.55616 0.03677 4.92711

7 1998 36028 M CL 0.63562 -0.03954 4.89672

7 1998 36028 P CL 0.63562 -0.03954 4.88839

7 1999 36406 M CL 1.67123 -0.13419 4.99002

7 1999 36406 P CL 1.67123 -0.13419 5.00126

7 2000 36672 P CH 2.40000 -0.00066 5.07060

7 2002 37573 M CL 4.86849 0.19045 5.16901

8 1998 35905 P L 0.29863 0.07138 4.32823

8 1998 35975 C L 0.49041 -0.00070 4.24935

8 1998 35975 P L 0.49041 -0.00070 4.29552

8 1998 36031 C L 0.64384 -0.08278 4.24219

8 1998 36031 P L 0.64384 -0.08278 4.27999

8 1999 36299 C L 1.37808 -0.05916 4.23498

8 1999 36299 P L 1.37808 -0.05916 4.30312

8 2000 36713 C L 2.51233 -0.03969 4.31227

8 2000 36713 P L 2.51233 -0.03969 4.38040

8 2002 37379 C L 4.33699 0.14664 4.31602

8 2002 37379 P L 4.33699 0.14664 4.43817

9 1999 36340 M O 1.49041 0.00612 4.18449

9 1999 36340 P O 1.49041 0.00612 4.20990

9 1999 36370 M O 1.57260 -0.00076 4.19253

9 1999 36370 P O 1.57260 -0.00076 4.20931

9 2000 36630 M O 2.28493 -0.10996 4.18205

9 2000 36734 M O 2.56986 -0.00421 4.18159

9 2000 36790 M O 2.72329 0.01972 4.19855

9 2001 37063 M O 3.47123 0.08510 4.27486

9 2001 37063 P O 3.47123 0.08510 4.34055

11 1998 35947 M O 0.41370 0.00193 4.44230

11 1998 35947 P O 0.41370 0.00193 4.43699

11 1998 35998 M O 0.55342 0.05854 4.46866

11 1998 35998 P O 0.55342 0.05854 4.47881

11 1998 36020 M O 0.61370 -0.01905 4.40988

11 1998 36020 P O 0.61370 -0.01905 4.44898

11 1999 36355 M O 1.53151 -0.03748 4.37977

11 2000 36698 M O 2.47123 -0.07850 4.51086

11 2000 36698 P O 2.47123 -0.07850 4.45481

11 2001 36993 M O 3.27945 0.05581 4.44746

11 2001 36993 P O 3.27945 0.05581 4.45841

12 1998 35935 M O 0.38082 0.02188 4.21715

12 1998 35935 P O 0.38082 0.02188 4.23816

12 1998 35982 M O 0.50959 0.02847 4.22946

12 1998 35982 P O 0.50959 0.02847 4.20335

12 1998 36014 M O 0.59726 0.01809 4.19855

12 1998 36061 M O 0.72603 -0.03952 4.26000

12 1999 36362 M O 1.55068 -0.05828 4.19540

12 1999 36362 P O 1.55068 -0.05828 4.23004

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 77

12 2000 36630 M O 2.28493 -0.05982 4.23859

12 2000 36630 P O 2.28493 -0.05982 4.27986

12 2001 37025 M O 3.36712 0.05167 4.23004

12 2001 37082 M O 3.52329 0.10526 4.27875

14 1998 35944 C L 0.40548 -0.02562 4.13308

14 1998 35944 P L 0.40548 -0.02562 4.13724

14 1998 35975 C L 0.49041 -0.01164 4.14313

14 1998 35975 P L 0.49041 -0.01164 4.13804

14 1998 36055 C L 0.70959 0.00387 4.17331

14 1998 36055 P L 0.70959 0.00387 4.16868

14 1999 36348 C L 1.51233 -0.05420 4.14504

14 1999 36348 P L 1.51233 -0.05420 4.15135

14 1999 36406 C L 1.67123 -0.03981 4.17022

14 1999 36406 P L 1.67123 -0.03981 4.17531

14 1999 36447 C L 1.78356 0.00215 4.21079

14 1999 36447 P L 1.78356 0.00215 4.23135

14 2000 36648 C L 2.33425 0.05029 4.28138

14 2000 36648 P L 2.33425 0.05029 4.33912

14 2000 36733 C L 2.56712 0.03583 4.28110

14 2000 36733 P L 2.56712 0.03583 4.31655

14 2000 36768 C L 2.66301 0.03913 4.27096

14 2000 36768 P L 2.66301 0.03913 4.31388

15 1998 35948 M O 0.41644 0.04543 4.55682

15 1998 35948 P O 0.41644 0.04543 4.56226

15 1998 35968 C O 0.47123 0.05384 4.52092

15 1998 35968 M O 0.47123 0.05384 4.52504

15 1998 36006 C O 0.57534 0.01803 4.52797

15 1998 36006 M O 0.57534 0.01803 4.53120

15 1999 36335 C O 1.47671 -0.09429 4.51009

15 1999 36335 M O 1.47671 -0.09429 4.51119

15 1999 36335 P O 1.47671 -0.09429 4.53946

15 1999 36384 C O 1.61096 -0.00302 4.49312

15 1999 36384 M O 1.61096 -0.00302 4.50247

15 1999 36432 C O 1.74247 -0.10366 4.46338

15 1999 36432 M O 1.74247 -0.10366 4.46820

15 1999 36432 P O 1.74247 -0.10366 4.47688

15 2000 36636 C O 2.30137 -0.02127 4.52027

15 2000 36636 M O 2.30137 -0.02127 4.53860

15 2000 36636 P O 2.30137 -0.02127 4.54913

15 2000 36706 C O 2.49315 -0.06143 4.48323

15 2000 36706 M O 2.49315 -0.06143 4.52103

15 2000 36749 C O 2.61096 0.02495 4.57574

15 2000 36749 M O 2.61096 0.02495 4.57975

15 2001 37007 C O 3.31781 -0.02091 4.58016

15 2001 37007 M O 3.31781 -0.02091 4.59451

15 2001 37069 C O 3.48767 0.01803 4.61175

15 2001 37069 M O 3.48767 0.01803 4.63240

15 2001 37118 C O 3.62192 0.10128 4.62536

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
78 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

15 2001 37118 M O 3.62192 0.10128 4.62124

16 1998 35936 C CH 0.38356 -0.02336 4.27792

16 1998 35936 P CH 0.38356 -0.02336 4.27555

16 1998 35942 C CL 0.40000 0.02879 4.30596

16 1998 35942 P CL 0.40000 0.02879 4.31789

16 1998 35982 C CL 0.50959 -0.10787 4.21316

16 1998 35982 P CL 0.50959 -0.10787 4.22523

16 1998 36017 C CL 0.60548 -0.06899 4.23454

16 1998 36017 P CL 0.60548 -0.06899 4.26437

16 1998 36056 C CH 0.71233 -0.03872 4.25972

16 1998 36056 P CH 0.71233 -0.03872 4.26395

16 1999 36321 C CL 1.43836 -0.02336 4.27764

16 1999 36321 P CL 1.43836 -0.02336 4.28703

16 1999 36357 C CH 1.53699 -0.12501 4.22654

16 1999 36357 P CH 1.53699 -0.12501 4.23801

16 2001 37097 C CL 3.56438 0.10878 4.33402

16 2001 37097 P CL 3.56438 0.10878 4.36526

16 2001 37158 C CL 3.73151 0.11850 4.35837

16 2001 37158 P CL 3.73151 0.11850 4.40379

16 2002 37390 C CL 4.36712 0.26246 4.53131

18 1998 35947 P L 0.41370 -0.06630 4.07550

18 1998 35986 C L 0.52055 -0.06749 4.13884

18 1998 35986 P L 0.52055 -0.06749 4.15732

18 1998 36020 C L 0.61370 -0.11308 4.13035

18 1998 36020 P L 0.61370 -0.11308 4.15072

18 1999 36314 C L 1.41918 -0.08186 4.16604

18 1999 36314 P L 1.41918 -0.08186 4.19765

18 2000 36665 C L 2.38082 -0.02845 4.17884

18 2000 36665 P L 2.38082 -0.02845 4.24792

18 2000 36713 C L 2.51233 -0.02960 4.16589

18 2000 36713 P L 2.51233 -0.02960 4.23671

18 2000 36791 C L 2.72603 -0.02276 4.21464

18 2000 36791 P L 2.72603 -0.02276 4.33310

18 2002 37375 C L 4.32603 0.14909 4.24061

18 2002 37375 P L 4.32603 0.14909 4.28552

18 2002 37522 C L 4.72877 0.22729 4.30474

18 2002 37522 P L 4.72877 0.22729 4.33060

19 1998 35964 C CH 0.46027 -0.08529 4.28041

19 1998 35964 P CH 0.46027 -0.08529 4.33677

19 1998 35999 C CH 0.55616 0.03457 4.34329

19 1998 36038 C CH 0.66301 -0.03516 4.32347

19 1998 36038 P CH 0.66301 -0.03516 4.39568

19 1999 36334 C CH 1.47397 -0.09232 4.30528

19 1999 36334 P CH 1.47397 -0.09232 4.31268

19 2000 36643 C CH 2.32055 0.07020 4.38751

19 2000 36643 P CH 2.32055 0.07020 4.44699

19 2000 36732 C CL 2.56438 0.07020 4.32810

19 2000 36732 P CL 2.56438 0.07020 4.39876

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 79

19 2001 36997 C CH 3.29041 0.05509 4.42209

19 2001 36997 P CH 3.29041 0.05509 4.46303

20 1998 35920 M O 0.33973 -0.04169 4.27221

20 1998 35920 P O 0.33973 -0.04169 4.25377

20 1998 36020 M O 0.61370 -0.01976 4.12600

20 1998 36053 M O 0.70411 -0.04710 4.18753

20 1998 36053 P O 0.70411 -0.04710 4.18068

20 1999 36426 M O 1.72603 -0.10411 4.04970

20 1999 36426 P O 1.72603 -0.10411 4.06130

20 2000 36756 M O 2.63014 -0.00695 4.08480

20 2000 36756 P O 2.63014 -0.00695 4.10016

20 2001 37027 M O 3.37260 0.08794 4.09551

20 2001 37027 P O 3.37260 0.08794 4.08900

20 2002 37511 M O 4.69863 0.24359 4.26732

22 1999 36361 C L 1.54795 -0.03992 4.70664

22 1999 36361 P L 1.54795 -0.03992 4.69098

22 1999 36406 C L 1.67123 0.09770 4.51612

22 1999 36406 P L 1.67123 0.09770 4.46717

22 2000 36664 P L 2.37808 0.04891 4.63754

22 2000 36754 P L 2.62466 0.10953 4.56205

22 2001 37008 C L 3.32055 -0.13141 4.74710

22 2001 37084 C L 3.52877 -0.11951 4.68822

22 2001 37159 C L 3.73425 -0.11361 4.68721

22 2002 37396 C L 4.38356 0.04891 4.47152

22 2002 37524 C L 4.73425 -0.00238 4.52418

23 1998 35941 C O 0.39726 -0.05709 4.48515

23 1998 35972 C O 0.48219 0.07142 4.51064

23 1998 36013 C O 0.59452 0.07576 4.47881

23 1998 36013 P O 0.59452 0.07576 4.55230

23 1998 36056 C O 0.71233 -0.01053 4.47927

23 1999 36426 C O 1.72603 0.01907 4.49669

23 1999 36426 P O 1.72603 0.01907 4.54361

23 1999 36447 C O 1.78356 -0.00284 4.49312

23 1999 36447 P O 1.78356 -0.00284 4.52407

23 2000 36651 C O 2.34247 -0.02785 4.48119

23 2000 36651 P O 2.34247 -0.02785 4.62850

23 2000 36713 C O 2.51233 0.00649 4.51896

23 2000 36746 C O 2.60274 0.02032 4.50014

23 2001 37008 C O 3.32055 -0.06794 4.67330

23 2002 37476 C O 4.60274 -0.09093 4.60247

24 1998 35913 C O 0.32055 -0.02585 4.95997

24 1998 35913 P O 0.32055 -0.02585 5.01330

24 1998 35991 C O 0.53425 -0.02816 4.95484

24 1998 35991 P O 0.53425 -0.02816 5.03747

24 1998 36040 C O 0.66849 -0.07419 4.87252

24 1998 36040 P O 0.66849 -0.07419 4.97120

24 1999 36369 C O 1.56986 -0.03590 4.96284

24 1999 36369 P O 1.56986 -0.03590 5.07517

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
80 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

24 2001 37082 C O 3.52329 0.05327 5.05625

24 2001 37082 P O 3.52329 0.05327 5.11704

24 2002 37449 C O 4.52877 0.11082 5.17083

24 2002 37449 P O 4.52877 0.11082 5.24005

25 1998 35927 C O 0.35890 0.07035 4.47666

25 1998 35978 C O 0.49863 0.01317 4.47938

25 1998 35978 M O 0.49863 0.01317 4.51568

25 1998 35978 P O 0.49863 0.01317 4.51152

25 1998 36017 C O 0.60548 -0.06006 4.44077

25 1998 36017 M O 0.60548 -0.06006 4.49758

25 1998 36017 P O 0.60548 -0.06006 4.47643

25 1999 36381 C O 1.60274 -0.07009 4.41824

25 1999 36381 P O 1.60274 -0.07009 4.49032

25 2000 36678 C O 2.41644 0.04338 4.35183

25 2000 36678 M O 2.41644 0.04338 4.54881

25 2000 36678 P O 2.41644 0.04338 4.45027

25 2000 36713 C O 2.51233 0.02944 4.42700

25 2000 36713 M O 2.51233 0.02944 4.70275

25 2000 36713 P O 2.51233 0.02944 4.56529

25 2000 36734 C O 2.56986 -0.00265 4.51360

25 2000 36734 M O 2.56986 -0.00265 4.59714

25 2000 36734 P O 2.56986 -0.00265 4.57440

27 1998 36055 P L 0.70959 -0.15313 4.19449

27 1999 36335 P L 1.47671 -0.01271 4.26788

27 2000 36650 P L 2.33973 0.03482 4.35786

27 2001 37005 P L 3.31233 0.16053 4.45411

27 2001 37104 P L 3.58356 -0.02951 4.26591

28 1998 35963 C CH 0.45753 -0.06754 4.76814

28 1998 35963 M CH 0.45753 -0.06754 4.78516

28 1998 36003 C CH 0.56712 -0.05385 4.73708

28 1998 36003 M CH 0.56712 -0.05385 4.74023

28 1998 36038 C CH 0.66301 -0.04258 4.74528

28 1998 36038 M CH 0.66301 -0.04258 4.73576

28 2000 36658 C CL 2.36164 0.01913 4.75083

28 2000 36658 M CL 2.36164 0.01913 4.72633

28 2000 36732 C CH 2.56438 0.00555 4.73602

28 2000 36732 M CH 2.56438 0.00555 4.70782

28 2000 36763 C CH 2.64932 0.06162 4.76192

28 2000 36763 M CH 2.64932 0.06162 4.71555

28 2001 37047 C CH 3.42740 -0.00475 4.73778

28 2001 37047 M CH 3.42740 -0.00475 4.69281

28 2001 37089 C CH 3.54247 0.02375 4.73171

28 2001 37089 M CH 3.54247 0.02375 4.72082

28 2001 37141 C CH 3.68493 0.02668 4.78156

28 2002 37375 C CH 4.32603 0.04533 4.77221

28 2002 37375 M CH 4.32603 0.04533 4.73383

29 1998 35912 M O 0.31781 -0.16760 4.18525

29 1998 35912 P O 0.31781 -0.16760 4.20812

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 81

29 1998 35990 M O 0.53151 -0.10960 4.12520

29 1998 35990 P O 0.53151 -0.10960 4.15009

29 1998 35990 P O 0.53151 -0.10960 4.13308

29 1998 36047 M O 0.68767 0.14723 4.29292

29 1998 36047 P O 0.68767 0.14723 4.33598

29 1999 36356 M O 1.53425 -0.01479 4.30082

29 1999 36356 P O 1.53425 -0.01479 4.33781

29 1999 36356 P O 1.53425 0.00314 4.29932

29 2000 36755 M O 2.62740 0.01881 4.30312

29 2000 36755 P O 2.62740 0.01881 4.36157

29 2002 37326 M O 4.19178 0.35833 4.48345

30 1998 35913 C O 0.32055 0.09673 4.48807

30 1998 35913 M O 0.32055 0.09673 4.52179

30 1998 35971 C O 0.47945 -0.09114 4.53120

30 1998 35971 M O 0.47945 -0.09114 4.53206

30 1998 36041 C O 0.67123 0.12030 4.50147

30 1998 36041 M O 0.67123 0.12030 4.50899

30 1999 36425 C O 1.72329 -0.13057 4.50976

30 1999 36425 M O 1.72329 -0.13057 4.49770

30 2000 36699 C O 2.47397 -0.15723 4.53131

30 2000 36699 M O 2.47397 -0.15723 4.52081

30 2001 37112 C O 3.60548 0.13200 4.51295

30 2001 37112 M O 3.60548 0.13200 4.50965

30 2002 37379 C O 4.33699 0.11322 4.53625

30 2002 37379 M O 4.33699 0.11322 4.53496

30 2002 37531 M O 4.75342 -0.16660 4.59219

32 1998 35893 M O 0.26575 0.16886 4.71716

32 1998 35893 P O 0.26575 0.16886 4.70818

32 1998 35977 M O 0.49589 0.00925 4.65110

32 1998 35977 P O 0.49589 0.00925 4.68859

32 1998 36026 M O 0.63014 -0.02250 4.68684

32 1998 36026 P O 0.63014 -0.02250 4.77719

32 1999 36333 M O 1.47123 0.02283 4.65710

32 1999 36333 P O 1.47123 0.02283 4.72482

32 1999 36370 M O 1.57260 -0.10658 4.61779

32 1999 36370 P O 1.57260 -0.10658 4.68176

32 1999 36399 M O 1.65205 -0.11982 4.62104

32 1999 36399 P O 1.65205 -0.11982 4.65719

32 2000 36690 M O 2.44932 -0.01047 4.66674

32 2000 36690 P O 2.44932 -0.01047 4.72108

32 2000 36720 M O 2.53151 -0.11097 4.62566

32 2000 36720 P O 2.53151 -0.11097 4.72233

32 2000 36747 M O 2.60548 -0.06786 4.63259

32 2000 36747 P O 2.60548 -0.06786 4.70483

32 2001 37064 M O 3.47397 0.02090 4.64526

32 2001 37064 P O 3.47397 0.02090 4.68675

32 2001 37111 M O 3.60274 0.07355 4.66400

32 2001 37111 P O 3.60274 0.07355 4.75273

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
82 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

32 2002 37455 M O 4.54521 0.28564 4.71805

34 1998 35902 M O 0.29041 0.09768 4.14298

34 1998 35902 P O 0.29041 0.09768 4.13852

34 1998 35989 C O 0.52877 -0.02368 4.05508

34 1998 35989 P O 0.52877 -0.02368 4.07889

34 1998 36026 C O 0.63014 -0.06604 4.02642

34 1998 36026 P O 0.63014 -0.06604 4.07363

34 1999 36368 C O 1.56712 -0.14089 3.98453

34 1999 36368 M O 1.56712 -0.15130 4.02482

34 1999 36368 P O 1.56712 -0.14089 4.02909

34 2000 36690 C O 2.44932 -0.02368 4.10890

34 2000 36690 M O 2.44932 -0.02368 4.08614

34 2000 36690 P O 2.44932 -0.02368 4.23772

34 2000 36752 C O 2.61918 -0.08301 4.08312

34 2000 36752 M O 2.61918 -0.08301 4.07108

34 2000 36752 P O 2.61918 -0.08301 4.15418

34 2001 36983 C O 3.25205 0.10581 4.16620

34 2001 36983 P O 3.25205 0.10581 4.15935

34 2001 37083 C O 3.52603 0.00807 4.09867

34 2001 37083 P O 3.52603 0.00807 4.11855

34 2001 37111 C O 3.60274 0.04703 4.11071

34 2002 37445 C O 4.51781 0.23121 4.28207

34 2002 37445 P O 4.51781 0.23121 4.39679

35 1998 35920 P O 0.33973 0.04177 5.45797

35 1998 35970 P O 0.47671 0.00429 5.28877

35 1998 36048 P O 0.69041 -0.03999 5.44294

35 1999 36333 P O 1.47123 0.00153 5.46802

35 2000 36692 P O 2.45479 -0.00759 5.37268

36 1998 35915 M O 0.32603 -0.06501 4.62094

36 1998 35915 P O 0.32603 -0.06501 4.66692

36 1998 35985 M O 0.51781 -0.08436 4.62918

36 1998 35985 P O 0.51781 -0.08436 4.59976

36 1998 36054 M O 0.70685 0.06045 4.66542

36 1999 36339 M O 1.48767 -0.03890 4.62134

36 1999 36339 P O 1.48767 -0.03890 4.52537

36 2000 36733 M O 2.56712 -0.02565 4.65224

36 2000 36733 P O 2.56712 -0.02565 4.66098

36 2001 37110 M O 3.60000 0.10568 4.64813

37 1998 35915 M O 0.32603 0.05905 4.18556

37 1998 35915 P O 0.32603 0.05905 4.19056

37 1998 35977 C O 0.49589 -0.01746 4.17669

37 1998 35977 M O 0.49589 -0.01746 4.14836

37 1998 35977 P O 0.49589 -0.01746 4.17084

37 1998 36035 C O 0.65479 -0.06359 4.26409

37 1998 36035 M O 0.65479 -0.06359 4.20604

37 1998 36035 P O 0.65479 -0.06359 4.24176

37 1999 36395 C O 1.64110 -0.08090 4.11660

37 1999 36395 M O 1.64110 -0.08090 4.06285

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 83

37 1999 36395 P O 1.64110 -0.08090 4.11562

37 2001 37134 C O 3.66575 0.04220 4.13068

37 2001 37134 M O 3.66575 0.04220 4.14867

37 2001 37134 P O 3.66575 0.04220 4.16899

37 2002 37483 C O 4.62192 0.24112 4.24792

38 1998 35892 M O 0.26301 -0.09670 4.89133

38 1998 35892 P O 0.26301 -0.09670 4.84796

38 1998 35977 M O 0.49589 -0.00884 4.57430

38 1998 35977 P O 0.49589 -0.00884 4.53249

38 1998 36021 M O 0.61644 0.01168 4.54404

38 1998 36021 P O 0.61644 0.01168 4.49558

38 1999 36341 M O 1.49315 -0.04791 4.52233

38 1999 36341 P O 1.49315 -0.04791 4.50524

38 1999 36370 M O 1.57260 -0.03126 4.57492

38 1999 36370 P O 1.57260 -0.03126 4.53539

38 1999 36395 M O 1.64110 -0.05294 4.71295

38 1999 36395 P O 1.64110 -0.05294 4.67367

38 2000 36641 M O 2.31507 0.00338 4.77845

38 2000 36641 P O 2.31507 0.00338 4.77068

38 2000 36719 M O 2.52877 0.03155 4.70121

38 2000 36719 P O 2.52877 0.02737 4.66108

38 2000 36742 M O 2.59178 0.02225 4.71680

38 2000 36742 P O 2.59178 0.02225 4.70375

38 2001 37012 M O 3.33151 0.05827 4.83953

38 2001 37012 P O 3.33151 0.05827 4.81267

38 2001 37104 M O 3.58356 0.00100 4.73646

38 2001 37104 P O 3.58356 0.00100 4.70175

38 2002 37350 M O 4.25753 0.06120 4.87893

38 2002 37350 P O 4.25753 0.06120 4.84143

38 2002 37483 P O 4.62192 0.10085 5.03533

39 1998 36021 C CH 0.61644 -0.03945 4.63279

39 1998 36021 P CH 0.61644 -0.03945 4.68951

39 1998 36028 C CH 0.63562 -0.04032 4.65615

39 1998 36028 P CH 0.63562 -0.04032 4.68333

39 1999 36341 C CL 1.49315 -0.07095 4.66843

39 1999 36341 P CL 1.49315 -0.07095 4.69346

39 1999 36367 C CL 1.56438 -0.03602 4.65947

39 1999 36367 P CL 1.56438 -0.03602 4.71070

39 1999 36433 C CL 1.74521 -0.04118 4.63084

39 1999 36433 P CL 1.74521 -0.04118 4.67460

39 2001 37104 C CL 3.58356 0.08890 4.70366

39 2001 37153 C CL 3.71781 0.07363 4.69602

39 2002 37326 C CL 4.19178 0.10020 4.61453

39 2002 37526 C CL 4.73973 0.19312 4.74988

40 1998 35919 M O 0.33699 0.00004 4.58129

40 1998 35919 P O 0.33699 0.00004 4.55093

40 1998 35944 M O 0.40548 -0.04793 4.52537

40 1998 35944 P O 0.40548 -0.04793 4.51896

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
84 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

40 1998 36010 M O 0.58630 0.00559 4.79876

40 1998 36010 P O 0.58630 0.00559 4.78632

40 1999 36341 M O 1.49315 -0.02753 4.49111

40 1999 36341 P O 1.49315 -0.02753 4.57027

40 2000 36649 M O 2.33699 -0.01083 4.66174

40 2000 36719 M O 2.52877 0.03132 4.53935

40 2000 36719 P O 2.52877 0.03132 4.53571

40 2000 36740 M O 2.58630 0.04393 4.72446

40 2000 36740 P O 2.58630 0.04393 4.69034

41 1998 35915 M O 0.32603 0.03835 4.33336

41 1998 35915 P O 0.32603 0.03835 4.35812

41 1998 36011 C O 0.58904 0.06942 4.28634

41 1998 36011 C O 0.58904 0.06942 4.26872

41 1998 36011 M O 0.58904 0.06942 4.36628

41 1998 36011 P O 0.58904 0.06942 4.39334

41 1999 36336 C O 1.47945 -0.32145 4.29633

41 1999 36336 C O 1.47945 -0.32145 4.28524

41 1999 36336 M O 1.47945 -0.32145 4.35170

41 2000 36656 C O 2.35616 0.06055 4.31589

41 2000 36656 C O 2.35616 0.06055 4.30474

41 2000 36656 M O 2.35616 0.06055 4.37134

41 2000 36656 P O 2.35616 0.06055 4.44559

41 2000 36740 C O 2.58630 0.09267 4.34653

41 2000 36740 M O 2.58630 0.09267 4.39679

41 2000 36763 C O 2.64932 0.04259 4.31655

41 2000 36763 M O 2.64932 0.04259 4.36195

41 2001 37070 C O 3.49041 0.04861 4.31842

41 2001 37070 M O 3.49041 0.04861 4.37563

43 1998 35958 C O 0.44384 -0.02180 4.98839

43 1998 35958 M O 0.44384 -0.02180 4.97328

43 1998 35958 P O 0.44384 -0.02180 4.98784

43 1998 36003 C O 0.56712 -0.03317 5.00005

43 1998 36003 M O 0.56712 -0.03317 4.97625

43 1998 36003 P O 0.56712 -0.03317 5.03096

43 1998 36053 C O 0.70411 -0.08242 5.00990

43 1998 36053 M O 0.70411 -0.08242 4.97611

43 1999 36336 C O 1.47945 0.02462 4.97508

43 1999 36336 P O 1.47945 0.02462 5.01297

43 1999 36399 C O 1.65205 -0.02861 4.98463

43 1999 36399 M O 1.65205 -0.02861 4.97618

43 1999 36399 P O 1.65205 -0.02861 4.99681

43 2000 36657 C O 2.35890 0.04175 5.00133

43 2000 36657 M O 2.35890 0.04175 5.02513

43 2000 36657 P O 2.35890 0.04175 5.01144

43 2000 36720 C O 2.53151 0.00938 4.99566

43 2000 36720 M O 2.53151 0.00938 5.01057

43 2000 36720 P O 2.53151 0.00938 5.06386

43 2000 36747 C O 2.60548 -0.09208 4.98189

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 85

43 2000 36747 M O 2.60548 -0.09208 4.99910

43 2000 36747 P O 2.60548 -0.09208 5.06796

43 2001 36984 C O 3.25479 -0.09695 5.02474

43 2001 36984 M O 3.25479 -0.09695 5.05981

43 2001 36984 P O 3.25479 -0.09695 5.20010

43 2001 37103 C O 3.58082 0.04387 5.00173

43 2001 37103 M O 3.58082 0.04387 5.03494

43 2001 37103 P O 3.58082 0.04387 5.04355

43 2002 37419 C O 4.44658 0.11343 5.00267

43 2002 37419 M O 4.44658 0.11343 5.06006

43 2002 37419 P O 4.44658 0.11343 5.11494

43 2002 37526 C O 4.73973 0.15409 4.96766

43 2002 37526 M O 4.73973 0.15409 4.99362

44 1998 35906 C S 0.30137 -0.01602 5.73773

44 1998 35906 P S 0.30137 -0.01602 5.80006

44 1998 35957 C S 0.44110 -0.00808 5.81006

44 1998 35957 P S 0.44110 -0.00808 5.85045

44 1998 36047 C S 0.68767 -0.05253 5.77007

44 1998 36047 P S 0.68767 -0.05253 5.76309

44 1999 36389 C S 1.62466 -0.07764 5.77641

44 1999 36389 P S 1.62466 -0.07764 5.79915

44 2000 36691 C S 2.45205 -0.05584 5.78000

44 2000 36691 P S 2.45205 -0.05584 5.79240

44 2000 36719 C S 2.52877 0.07530 5.75397

44 2000 36719 P S 2.52877 0.07530 5.82044

44 2000 36740 C S 2.58630 0.04203 5.72896

44 2000 36740 P S 2.58630 0.04203 5.82777

44 2001 37012 C S 3.33151 0.05695 5.46018

44 2001 37012 P S 3.33151 0.05695 5.55906

44 2001 37110 P S 3.60000 0.07166 5.78383

45 1998 35899 C S 0.28219 -0.02076 5.29907

45 1998 35899 P S 0.28219 -0.02076 5.33499

45 1998 35942 C S 0.40000 0.03578 5.25301

45 1998 35942 P S 0.40000 0.03578 5.29576

45 1998 36054 P S 0.70685 0.05475 5.30121

45 1999 36370 P S 1.57260 -0.04056 5.33836

45 2000 36692 P S 2.45479 -0.02011 5.35034

45 2000 36720 P S 2.53151 0.02397 5.30529

45 2000 36755 P S 2.62740 0.01076 5.26502

45 2001 37012 P S 3.33151 0.00505 5.30465

45 2001 37063 P S 3.47123 -0.04056 5.31281

45 2001 37153 P S 3.71781 -0.00777 5.31197

45 2002 37418 P S 4.44384 -0.00777 5.26093

45 2002 37418 P S 4.44384 -0.00777 5.26093

46 1998 35892 C O 0.26301 0.06632 4.32863

46 1998 35892 M O 0.26301 0.06632 4.31442

46 1998 35892 P O 0.26301 0.06632 4.37311

46 1998 35915 C O 0.32603 0.07498 4.31402

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
86 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

46 1998 35915 M O 0.32603 0.07498 4.30555

46 1998 36000 C O 0.55890 -0.01209 4.24406

46 1998 36000 M O 0.55890 -0.01209 4.23801

46 1998 36038 C O 0.66301 -0.02902 4.27569

46 1998 36038 M O 0.66301 -0.02902 4.26521

46 1999 36241 C O 1.21918 0.06353 4.32267

46 1999 36241 M O 1.21918 0.06353 4.33047

46 2000 36683 C O 2.43014 -0.33775 4.26956

46 2000 36683 M O 2.43014 -0.33775 4.30298

46 2000 36683 P O 2.43014 -0.33775 4.35260

46 2000 36734 C O 2.56986 0.01245 4.21346

46 2000 36734 M O 2.56986 0.01245 4.26099

46 2000 36734 P O 2.56986 0.01245 4.30000

46 2000 36777 C O 2.68767 0.00851 4.25689

46 2000 36777 M O 2.68767 0.00851 4.26872

46 2001 36991 C O 3.27397 0.12771 4.25320

46 2001 36991 M O 3.27397 0.12771 4.27249

46 2001 36991 P O 3.27397 0.12771 4.28221

46 2001 37048 C O 3.43014 0.01376 4.27151

46 2001 37048 M O 3.43014 0.01376 4.27123

46 2001 37048 P O 3.43014 0.01376 4.27375

46 2002 37335 C O 4.21644 0.07035 4.29060

46 2002 37335 M O 4.21644 0.07035 4.29101

47 1998 35951 M O 0.42466 0.00930 4.55860

47 1998 35951 P O 0.42466 0.00930 4.61026

47 1998 36000 M O 0.55890 -0.01705 4.53528

47 1998 36000 P O 0.55890 -0.01705 4.54478

47 1998 36031 M O 0.64384 0.00021 4.49914

47 1998 36031 P O 0.64384 0.00021 4.51754

47 1999 36241 M O 1.21918 0.06213 4.36386

47 2000 36683 M O 2.43014 -0.38623 4.32453

47 2000 36683 P O 2.43014 -0.38623 4.34407

47 2000 36734 M O 2.56986 0.01568 4.27165

47 2000 36734 P O 2.56986 0.01568 4.33376

47 2000 36777 M O 2.68767 0.00439 4.26014

47 2001 36991 M O 3.27397 0.08195 4.22567

47 2001 36991 P O 3.27397 0.08195 4.22318

47 2001 37057 M O 3.45479 0.01456 4.28372

47 2001 37152 M O 3.71507 0.01155 4.31375

47 2001 37152 P O 3.71507 0.01155 4.32440

47 2002 37335 M O 4.21644 0.06926 4.24692

47 2002 37477 M O 4.60548 0.20942 4.34238

47 2002 37477 P O 4.60548 0.20942 4.37223

48 1998 35928 M O 0.36164 -0.01175 4.34536

48 1998 35928 P O 0.36164 -0.01175 4.35388

48 1998 35965 M O 0.46301 -0.03255 4.35914

48 1998 35965 P O 0.46301 -0.03255 4.35812

48 1998 36054 M O 0.70685 0.02858 4.37437

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 87

48 1998 36054 P O 0.70685 0.02858 4.40354

48 1999 36383 M O 1.60822 -0.02312 4.29701

48 1999 36383 P O 1.60822 -0.02312 4.30878

48 2000 36663 M O 2.37534 0.03631 4.40477

48 2000 36663 P O 2.37534 0.03631 4.37122

48 2000 36741 M O 2.58904 0.00505 4.36932

49 1998 35912 P CL 0.31781 0.08436 4.31268

49 1998 35975 C CH 0.49041 -0.03170 4.26577

49 1998 35975 P CH 0.49041 -0.03170 4.36957

49 1998 36035 C CH 0.65479 -0.15398 4.23106

49 1998 36035 P CH 0.65479 -0.15398 4.22654

49 2000 36763 C CH 2.64932 0.03386 4.28785

49 2002 37446 C CH 4.52055 0.15294 4.36068

50 1998 35899 C L 0.28219 -0.14739 4.29497

50 1998 35899 M L 0.28219 -0.14739 4.31682

50 1998 35961 C L 0.45205 -0.05340 4.27875

50 1998 35961 M L 0.45205 -0.05340 4.30744

50 1998 36012 C L 0.59178 0.10548 4.29251

50 1998 36012 M L 0.59178 0.10548 4.31829

50 1998 36059 C L 0.72055 0.13760 4.25277

50 1998 36059 M L 0.72055 0.13760 4.28138

50 1999 36357 C L 1.53699 -0.11431 4.25362

50 1999 36357 M L 1.53699 -0.11431 4.28386

50 2000 36662 C L 2.37260 -0.09818 4.25774

50 2000 36662 M L 2.37260 -0.09818 4.27958

50 2001 37023 C L 3.36164 0.15949 4.32744

50 2001 37118 C L 3.62192 0.18091 4.33086

51 1998 35906 M CL 0.30137 -0.03036 4.73532

51 1998 35906 P CL 0.30137 -0.03036 4.78682

51 1998 35972 M CH 0.48219 0.02994 4.83007

51 1998 35972 P CH 0.48219 0.02994 4.82246

51 1998 36020 M CH 0.61370 -0.07828 4.69181

51 1998 36020 P CH 0.61370 -0.07828 4.67255

51 1999 36241 M CH 1.21918 0.04632 4.77567

51 1999 36241 P CH 1.21918 0.04632 4.79934

51 2000 36678 M CL 2.41644 0.02002 4.77567

51 2000 36678 P CL 2.41644 0.02002 4.80353

51 2001 36991 M CH 3.27397 0.03703 4.79049

51 2001 36991 P CH 3.27397 0.03703 4.82181

51 2001 37048 M CH 3.43014 0.05105 4.80000

51 2001 37048 P CH 3.43014 0.05105 4.81600

51 2002 37421 M CH 4.45205 -0.07573 4.80164

51 2002 37421 P CH 4.45205 -0.07573 4.82246

52 1998 35965 C O 0.46301 -0.03601 4.54860

52 1998 35965 M O 0.46301 -0.03601 4.49614

52 1998 35965 P O 0.46301 -0.03601 4.59249

52 1998 35992 C O 0.53699 0.05810 4.55303

52 1998 35992 M O 0.53699 0.05810 4.51207

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
88 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

52 1998 36034 M O 0.65205 0.00299 4.49714

52 1998 36034 P O 0.65205 0.00299 4.52775

52 1999 36349 C O 1.51507 -0.01993 4.49245

52 1999 36349 M O 1.51507 -0.01993 4.49077

52 1999 36405 C O 1.66849 0.01285 4.53978

52 1999 36405 M O 1.66849 0.01285 4.48774

53 1998 35949 M O 0.41918 0.08052 4.53828

53 1998 35949 P O 0.41918 0.08052 4.58823

53 1998 35991 C O 0.53425 0.10402 4.56299

53 1998 35991 M O 0.53425 0.10402 4.58476

53 1998 35991 P O 0.53425 0.10402 4.60986

53 1998 36035 C O 0.65479 0.07631 4.56830

53 1998 36035 M O 0.65479 0.07631 4.51492

53 1999 36319 C O 1.43288 -0.16383 4.53828

53 1999 36319 M O 1.43288 -0.16383 4.51338

53 2000 36649 C O 2.33699 0.13097 4.60217

53 2000 36649 M O 2.33699 0.13097 4.63735

53 2000 36649 P O 2.33699 0.13097 4.69611

53 2000 36712 C O 2.50959 -0.08654 4.64804

53 2000 36712 M O 2.50959 -0.08654 4.67498

53 2000 36733 C O 2.56712 -0.17822 4.63938

53 2000 36733 M O 2.56712 -0.17822 4.64564

53 2000 36733 P O 2.56712 -0.17822 4.69107

53 2001 36982 C O 3.24932 -0.23794 4.72064

53 2001 36982 M O 3.24932 -0.23794 4.74188

53 2001 36982 P O 3.24932 -0.23794 4.81899

53 2001 37070 C O 3.49041 -0.09484 4.68684

53 2001 37070 M O 3.49041 -0.09484 4.68951

53 2001 37070 P O 3.49041 -0.09484 4.74136

53 2001 37110 C O 3.60000 0.18280 4.70529

53 2001 37110 M O 3.60000 0.18280 4.71268

53 2001 37110 P O 3.60000 0.18280 4.76720

53 2002 37347 C O 4.24932 0.19908 4.65215

53 2002 37347 M O 4.24932 0.19908 4.68481

53 2002 37445 C O 4.51781 0.23447 4.68647

53 2002 37445 M O 4.51781 0.23447 4.73935

53 2002 37504 C O 4.67945 -0.20020 4.68868

53 2002 37504 M O 4.67945 -0.20020 4.73409

54 1998 35963 C L 0.45753 0.00088 4.55787

54 1998 35963 M L 0.45753 0.00088 4.47072

54 1998 36053 C L 0.70411 0.00381 4.50502

54 1998 36056 C L 0.71233 0.01173 4.51251

54 1999 36362 C L 1.55068 -0.01116 4.43580

54 1999 36362 M L 1.55068 -0.01116 4.52904

54 2000 36656 C L 2.35616 0.00540 4.47927

54 2000 36718 C L 2.52603 0.00381 4.52407

54 2002 37349 C L 4.25479 -0.00418 4.47027

55 1998 35956 C O 0.43836 -0.01350 4.39679

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 89

55 1998 35956 M O 0.43836 -0.01350 4.39099

55 1998 35998 C O 0.55342 -0.02394 4.36729

55 1998 35998 M O 0.55342 -0.02394 4.36144

55 1998 36035 C O 0.65479 -0.09230 4.32002

55 1998 36035 M O 0.65479 -0.09230 4.32068

55 2000 36769 C O 2.66575 -0.01625 4.42137

55 2000 36769 M O 2.66575 -0.01625 4.43010

55 2000 36769 P O 2.66575 -0.01625 4.48785

55 2002 37371 C O 4.31507 0.05069 4.44206

55 2002 37371 M O 4.31507 0.05069 4.44653

55 2002 37469 C O 4.58356 0.10343 4.78382

55 2002 37469 M O 4.58356 0.10343 4.80156

56 1998 35901 C O 0.28767 -0.06984 4.01332

56 1998 35901 M O 0.28767 -0.06984 4.01746

56 1998 35956 C O 0.43836 -0.05610 4.09418

56 1998 35956 M O 0.43836 -0.05610 3.97800

56 1998 35956 P O 0.43836 -0.05610 4.05595

56 1998 36046 C O 0.68493 -0.12113 3.93359

56 1998 36046 P O 0.68493 -0.12113 3.95412

56 2000 36762 C O 2.64658 -0.08287 3.93574

56 2000 36762 M O 2.64658 -0.08287 3.91582

56 2001 37036 C O 3.39726 -0.12821 4.03601

56 2001 37036 M O 3.39726 -0.12821 4.04935

56 2001 37071 C O 3.49315 0.14469 4.09966

56 2001 37071 M O 3.49315 0.14469 4.10528

56 2001 37124 C O 3.63836 0.12321 4.08816

56 2001 37124 M O 3.63836 0.12321 4.08581

56 2002 37343 C O 4.23836 0.21829 4.11464

56 2002 37343 M O 4.23836 0.21829 4.10413

58 1998 35954 C O 0.43288 -0.05753 4.14409

58 1998 35990 C O 0.53151 -0.12302 4.14456

58 1998 36020 C O 0.61370 -0.17546 4.10099

58 1999 36378 C O 1.59452 -0.15002 4.20110

58 1999 36378 M O 1.59452 -0.17731 4.22464

58 2000 36748 C O 2.60822 -0.11216 4.15466

58 2001 36999 C O 3.29589 0.15335 4.37727

58 2001 37056 C O 3.45205 0.06293 4.26816

58 2001 37103 C O 3.58082 0.02072 4.20155

58 2002 37335 C O 4.21644 0.16945 4.35466

58 2002 37414 C O 4.43288 0.15765 4.30744

58 2002 37515 C O 4.70959 0.23138 4.36042

59 1998 35964 M O 0.46027 -0.08554 4.48582

59 1998 35964 P O 0.46027 -0.08554 4.47050

59 1999 36390 M O 1.62740 0.24237 4.41207

59 1999 36390 P O 1.62740 0.24237 4.39827

59 2000 36650 P O 2.33973 -0.31367 4.31522

60 1998 35901 C O 0.28767 0.01419 4.45004

60 1998 35901 M O 0.28767 0.01419 4.42843

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
90 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

60 1998 35901 P O 0.28767 0.01419 4.46602

60 1998 35978 C O 0.49863 0.02147 4.45876

60 1998 35978 M O 0.49863 0.02147 4.43070

60 1998 35978 P O 0.49863 0.02147 4.44910

60 1998 36046 C O 0.68493 -0.14613 4.37827

60 1998 36046 M O 0.68493 -0.14613 4.34937

60 1998 36046 P O 0.68493 -0.14613 4.37689

60 1999 36362 C O 1.55068 -0.03549 4.43521

60 1999 36362 C O 1.55068 -0.02815 4.37563

60 1999 36362 M O 1.55068 -0.03549 4.43070

60 1999 36362 P O 1.55068 -0.03549 4.43947

60 2000 36691 C O 2.45205 -0.05228 4.40843

60 2000 36691 M O 2.45205 -0.05228 4.41365

60 2000 36691 P O 2.45205 -0.05228 4.42089

60 2000 36721 C O 2.53425 -0.03645 4.40036

60 2000 36721 M O 2.53425 -0.03645 4.40696

60 2000 36721 P O 2.53425 -0.03645 4.42712

60 2000 36761 C O 2.64384 -0.03293 4.44053

60 2000 36761 M O 2.64384 -0.03293 4.41763

60 2000 36761 P O 2.64384 -0.03293 4.46775

60 2001 37015 C O 3.33973 0.09748 4.39642

60 2001 37015 M O 3.33973 0.09748 4.42317

60 2001 37077 C O 3.50959 0.05655 4.44112

60 2001 37077 M O 3.50959 0.05655 4.47164

60 2001 37077 P O 3.50959 0.05655 4.49357

60 2001 37111 C O 3.60274 0.06615 4.43959

60 2001 37111 M O 3.60274 0.06615 4.45190

60 2001 37111 P O 3.60274 0.06615 4.52418

60 2002 37337 C O 4.22192 0.08932 4.48051

60 2002 37337 M O 4.22192 0.08932 4.49010

60 2002 37337 P O 4.22192 0.08932 4.50424

61 1998 35957 C O 0.44110 -0.05184 4.65928

61 1998 35957 M O 0.44110 -0.05184 4.68620

61 1998 36004 C O 0.56986 0.03154 4.68610

61 1998 36004 M O 0.56986 0.03154 4.65956

61 1998 36042 C O 0.67397 0.06352 4.64343

61 1998 36042 M O 0.67397 0.06352 4.69602

61 1999 36383 C O 1.60822 -0.04642 4.58149

61 1999 36383 M O 1.60822 -0.04642 4.64391

61 2000 36691 C O 2.45205 -0.16083 4.70221

61 2000 36691 M O 2.45205 -0.16083 4.88060

61 2001 37134 C O 3.66575 0.06110 4.76729

61 2001 37134 M O 3.66575 0.06110 4.88945

61 2002 37349 C O 4.25479 0.10293 4.70998

61 2002 37349 M O 4.25479 0.10293 4.87984

62 1998 35928 P L 0.36164 -0.32894 4.04445

62 1998 35965 C L 0.46301 -0.04666 4.19389

62 1998 35965 P L 0.46301 -0.03548 4.14250

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 91

62 1998 36034 C L 0.65205 -0.02606 4.22039

62 1998 36034 P L 0.65205 -0.02729 4.16651

62 1999 36433 C L 1.74521 0.08093 4.54116

62 1999 36433 P L 1.74521 0.08093 4.46545

62 2000 36663 C L 2.37534 0.03214 4.56299

62 2000 36663 P L 2.37534 0.03214 4.53023

62 2000 36741 C L 2.58904 -0.01512 4.61789

62 2000 36741 P L 2.58904 -0.01512 4.53700

62 2001 37096 C L 3.56164 0.17524 4.53625

62 2002 37505 C L 4.68219 0.04665 4.55745

62 2002 37505 P L 4.68219 0.04665 4.52840

63 1998 35902 C CL 0.29041 -0.38021 4.22523

63 1998 35949 C CL 0.41918 -0.37651 4.24176

63 1998 36047 C CH 0.68767 -0.39181 4.20170

63 1999 36357 C CH 1.53699 -0.35660 4.24907

63 2000 36684 C CL 2.43288 0.26052 4.25220

63 2000 36728 C CL 2.55342 0.26830 4.25106

63 2000 36761 C CH 2.64384 0.16040 4.23743

63 2001 36998 C CH 3.29315 0.29863 4.30757

63 2001 37034 C CH 3.39178 0.29591 4.31642

63 2001 37069 C CH 3.48767 0.28177 4.28041

63 2002 37356 C CH 4.27397 -0.06041 4.43876

64 1998 35921 C O 0.34247 -0.04651 4.35812

64 1998 35949 C O 0.41918 -0.03789 4.41920

64 1998 36047 C O 0.68767 -0.04026 4.39148

64 1998 36054 C O 0.70685 -0.03080 4.40305

64 1999 36313 C O 1.41644 -0.04056 4.42497

64 1999 36369 C O 1.56986 -0.04085 4.43592

64 2000 36684 C O 2.43288 0.18998 4.37739

64 2000 36726 C O 2.54795 0.20357 4.37450

64 2000 36781 C O 2.69863 -0.06217 4.43308

64 2001 37035 C O 3.39452 0.00274 4.41340

64 2001 37069 C O 3.48767 -0.02904 4.40672

64 2002 37355 C O 4.27123 -0.02319 4.66155

65 1998 35900 C O 0.28493 -0.04504 4.49714

65 1998 35900 M O 0.28493 -0.04504 4.49167

65 1998 35949 C O 0.41918 0.25873 4.51820

65 1998 35949 M O 0.41918 0.25873 4.51798

65 1998 36032 C O 0.64658 -0.09808 4.49032

65 1998 36032 M O 0.64658 -0.09808 4.47995

65 1998 36053 C O 0.70411 -0.04152 4.47141

65 1998 36053 M O 0.70411 -0.04152 4.46014

65 1999 36313 C O 1.41644 -0.04108 4.43153

65 1999 36313 M O 1.41644 -0.04108 4.43129

65 1999 36364 C O 1.55616 0.00700 4.47790

65 1999 36364 M O 1.55616 0.00700 4.48006

65 2000 36685 C O 2.43562 -0.02797 4.49256

65 2000 36685 M O 2.43562 -0.02797 4.50623

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
92 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

65 2000 36728 C O 2.55342 -0.01204 4.47438

65 2000 36728 M O 2.55342 -0.01204 4.46568

66 1998 35958 C O 0.44384 -0.10064 4.16806

66 1998 35958 M O 0.44384 -0.10064 4.25149

66 1998 36005 C O 0.57260 -0.12413 4.16418

66 1998 36005 M O 0.57260 -0.12413 4.20633

66 1998 36017 C O 0.60548 -0.17524 4.08648

66 1998 36017 M O 0.60548 -0.17524 4.10446

66 1999 36294 C O 1.36438 -0.11383 4.12180

66 1999 36294 M O 1.36438 -0.11383 4.13453

66 1999 36362 C O 1.55068 -0.05134 4.12050

66 1999 36362 M O 1.55068 -0.05134 4.12891

66 2000 36665 C O 2.38082 -0.03123 4.15151

66 2000 36665 M O 2.38082 -0.03123 4.14899

66 2000 36718 C O 2.52603 -0.01873 4.14520

66 2000 36718 M O 2.52603 -0.01873 4.13324

66 2000 36754 C O 2.62466 0.02514 4.16868

66 2000 36754 M O 2.62466 0.02514 4.15779

66 2001 37047 C O 3.42740 -0.00435 4.15638

66 2001 37047 M O 3.42740 -0.00435 4.16216

66 2001 37091 C O 3.54795 0.03728 4.14361

66 2001 37091 M O 3.54795 0.03728 4.14027

66 2001 37141 C O 3.68493 0.05634 4.18753

66 2001 37141 M O 3.68493 0.05634 4.27305

66 2002 37455 C O 4.54521 0.23679 4.25035

66 2002 37455 M O 4.54521 0.23679 4.24621

66 2002 37488 C O 4.63562 0.26394 4.27082

66 2002 37488 M O 4.63562 0.26394 4.28455

68 1998 35949 C L 0.41918 -0.00010 4.43474

68 1998 35991 C L 0.53425 -0.02429 4.42951

68 1998 36019 C L 0.61096 -0.07676 4.40623

68 1998 36061 C L 0.72603 -0.05664 4.40794

68 1999 36327 C L 1.45479 -0.00369 4.41992

68 2000 36700 C L 2.47671 -0.03785 4.41280

68 2001 37026 C L 3.36986 -0.00219 4.49502

68 2001 37140 C L 3.68219 -0.02276 4.42185

68 2001 37162 C L 3.74247 -0.01880 4.42628

68 2002 37370 C L 4.31233 0.06971 4.47187

68 2002 37491 C L 4.64384 0.17337 4.75935

69 1998 35942 C O 0.40000 -0.06328 4.75703

69 1998 35942 P O 0.40000 -0.06328 4.76661

69 1998 36026 C O 0.63014 0.02129 4.81324

69 1998 36026 P O 0.63014 0.02129 4.81608

69 1998 36040 C O 0.66849 0.00795 4.81080

69 2000 36747 C O 2.60548 -0.01108 4.82711

69 2001 37083 C O 3.52603 0.00151 4.80065

69 2002 37419 C O 4.44658 0.04281 4.77921

69 2002 37419 P O 4.44658 0.04281 4.80386

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 93

70 1998 35930 C O 0.36712 0.01237 4.90941

70 1998 35983 C O 0.51233 0.04637 4.91192

70 1998 36033 C O 0.64932 0.00592 4.85764

70 1999 36320 C O 1.43562 0.05971 4.93469

70 2000 36634 C O 2.29589 0.00216 4.93419

70 2000 36705 C O 2.49041 0.05294 4.93368

70 2000 36755 C O 2.62740 0.00346 4.94528

70 2001 37008 C O 3.32055 -0.07758 4.93087

70 2001 37105 C O 3.58630 -0.10280 5.16997

70 2002 37449 C O 4.52877 -0.00253 5.07636

72 1998 35948 C O 0.41644 -0.11268 3.85333

72 1998 35948 M O 0.41644 -0.11268 3.86849

72 1998 35992 C O 0.53699 0.00737 3.79863

72 1998 35992 M O 0.53699 0.00737 3.80622

72 1998 36041 C O 0.67123 -0.07947 3.76352

72 1998 36041 M O 0.67123 -0.07947 3.77574

72 1999 36355 C O 1.53151 -0.00170 3.80087

72 1999 36355 M O 1.53151 -0.00170 3.80466

72 2000 36719 C O 2.52877 -0.00218 3.78555

72 2000 36719 M O 2.52877 -0.00218 3.80243

72 2001 37070 C O 3.49041 0.03317 3.86556

72 2001 37070 M O 3.49041 0.03317 3.87577

72 2001 37140 C O 3.68219 0.06911 3.94526

72 2001 37140 M O 3.68219 0.06911 3.93339

72 2001 37161 C O 3.73973 0.08639 3.93789

72 2001 37161 M O 3.73973 0.08639 3.93730

74 1998 35935 C O 0.38082 -0.07054 4.49547

74 1998 35935 M O 0.38082 -0.07054 4.53614

74 1998 36004 C O 0.56986 -0.04915 4.43129

74 1998 36004 M O 0.56986 -0.04915 4.46338

74 1998 36048 C O 0.69041 -0.08808 4.42185

74 1998 36048 M O 0.69041 -0.08808 4.44547

74 2000 36686 C O 2.43836 0.03801 4.44136

74 2000 36686 M O 2.43836 0.03801 4.45829

74 2001 37007 C O 3.31781 0.18793 4.48852

74 2001 37007 M O 3.31781 0.18793 4.50701

74 2002 37454 C O 4.54247 -0.01816 4.42903

74 2002 37454 M O 4.54247 -0.01816 4.43592

75 1998 35914 C O 0.32329 0.05430 4.71411

75 1998 35914 M O 0.32329 0.05430 4.72597

75 1998 36004 C O 0.56986 -0.02450 4.66476

75 1998 36004 M O 0.56986 -0.02450 4.67386

75 1998 36041 C O 0.67123 -0.03010 4.66363

75 1998 36041 M O 0.67123 -0.03010 4.66589

75 2000 36720 C O 2.53151 0.00031 4.68878

75 2000 36720 M O 2.53151 0.00031 4.70565

77 1998 35997 C O 0.55068 -0.06278 4.61453

77 1998 35997 M O 0.55068 -0.06278 4.63967

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
94 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

77 1998 36005 C O 0.57260 -0.03646 4.62781

77 1998 36005 M O 0.57260 -0.03646 4.64535

77 1998 36040 C O 0.66849 0.06506 4.66419

77 1998 36040 M O 0.66849 0.06506 4.68000

77 1999 36363 C O 1.55342 0.03418 4.65738

77 1999 36363 M O 1.55342 0.03418 4.68167

80 1998 35907 C O 0.30411 -0.05807 4.25604

80 1998 35907 M O 0.30411 -0.05807 4.24420

80 1998 35907 P O 0.30411 -0.05807 4.28248

80 1998 35997 C O 0.55068 -0.03700 4.20886

80 1998 35997 M O 0.55068 -0.03700 4.20245

80 1998 36027 C O 0.63288 -0.02817 4.21818

80 1998 36027 M O 0.63288 -0.02817 4.20782

80 1999 36356 C O 1.53425 -0.06901 4.20738

80 1999 36356 M O 1.53425 -0.06901 4.18449

80 2000 36636 C O 2.30137 0.00173 4.27040

80 2000 36636 M O 2.30137 0.00173 4.28276

80 2000 36705 C O 2.49041 -0.02247 4.16620

80 2000 36705 M O 2.49041 -0.02247 4.18738

80 2000 36749 C O 2.61096 0.02117 4.19525

80 2000 36749 M O 2.61096 0.02117 4.19675

80 2002 37489 C O 4.63836 0.22085 4.30892

80 2002 37489 M O 4.63836 0.22085 4.27555

82 1998 35969 C L 0.47397 -0.16112 4.09134

82 1998 35993 C L 0.53973 -0.14613 4.20395

82 1998 36055 C L 0.70959 -0.08830 4.08210

82 2002 37419 C L 4.44658 0.18374 4.15261

82 2002 37504 C L 4.67945 0.20964 4.16713

85 1998 35928 C S 0.36164 -0.03246 5.40959

85 1998 35928 P S 0.36164 -0.03246 5.43638

85 1998 35970 C S 0.47671 -0.28981 5.43285

85 1998 35970 P S 0.47671 -0.28981 5.46506

85 1998 36024 C S 0.62466 0.01009 5.42107

85 1998 36024 P S 0.62466 0.01009 5.45074

85 1999 36356 C S 1.53425 -0.00230 5.43403

85 1999 36356 P S 1.53425 -0.00230 5.47332

85 2000 36685 C S 2.43562 0.00720 5.51072

85 2000 36685 P S 2.43562 0.00720 5.54806

85 2001 37055 C S 3.44932 0.30729 5.74079

85 2001 37055 P S 3.44932 0.30729 5.80236

86 1998 35920 C S 0.33973 -0.10908 5.24127

86 1998 35920 P S 0.33973 -0.10908 5.29586

86 1998 35976 C S 0.49315 0.02433 5.34506

86 1998 35976 P S 0.49315 0.02433 5.37667

86 1998 36021 C S 0.61644 0.05794 5.35969

86 1998 36021 P S 0.61644 0.05794 5.38555

86 1998 36062 C S 0.72877 0.05794 5.39345

86 1998 36062 P S 0.72877 0.05794 5.41921

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 95

86 1999 36333 C S 1.47123 0.00315 5.40205

86 1999 36333 P S 1.47123 0.00315 5.41938

86 1999 36370 C S 1.57260 0.05744 5.40524

86 1999 36370 P S 1.57260 0.05744 5.44393

86 2000 36686 C S 2.43836 0.11225 5.39345

86 2000 36686 P S 2.43836 0.11225 5.44605

86 2001 37055 C S 3.44932 0.03645 5.41093

86 2001 37055 P S 3.44932 0.03645 5.45775

86 2002 37378 C S 4.33425 -0.24043 5.41974

86 2002 37378 P S 4.33425 -0.24043 5.42279

87 1998 35920 C S 0.33973 -0.07827 5.41930

87 1998 35920 P S 0.33973 -0.07827 5.45865

87 1998 35964 C S 0.46027 -0.09757 5.42433

87 1998 35964 P S 0.46027 -0.09757 5.46527

87 1998 36026 C S 0.63014 -0.05233 5.41388

87 1998 36026 P S 0.63014 -0.05233 5.44536

87 1998 36062 C S 0.72877 -0.01113 5.42407

87 1998 36062 P S 0.72877 -0.01113 5.48600

87 1999 36370 C S 1.57260 -0.01065 5.39848

87 1999 36370 P S 1.57260 -0.01065 5.45618

87 2000 36657 C S 2.35890 0.00266 5.40191

87 2000 36657 P S 2.35890 0.00266 5.45579

87 2000 36735 C S 2.57260 0.02369 5.40304

87 2000 36735 P S 2.57260 0.02369 5.45506

87 2000 36782 C S 2.70137 0.03090 5.40466

87 2000 36782 P S 2.70137 0.03090 5.46226

87 2001 37070 C S 3.49041 0.04140 5.41245

87 2001 37070 P S 3.49041 0.04140 5.47834

87 2001 37113 C S 3.60822 0.04563 5.42036

87 2001 37113 P S 3.60822 0.04563 5.43660

87 2001 37140 C S 3.68219 0.05911 5.41978

87 2001 37140 P S 3.68219 0.05911 5.46231

87 2002 37379 C S 4.33699 0.04654 5.38893

87 2002 37379 P S 4.33699 0.04654 5.39658

89 1998 35920 C O 0.33973 -0.00449 4.38863

89 1998 35920 M O 0.33973 -0.00449 4.34186

89 1998 35950 C O 0.42192 0.05452 4.40085

89 1998 35950 M O 0.42192 0.05452 4.35607

89 1998 36048 C O 0.69041 0.09166 4.35876

89 1998 36048 M O 0.69041 0.09166 4.33624

89 1999 36322 C O 1.44110 0.03597 4.36767

89 1999 36322 M O 1.44110 0.03597 4.32863

89 1999 36370 C O 1.57260 -0.09735 4.33139

89 1999 36370 M O 1.57260 -0.09735 4.31695

89 2000 36720 C O 2.53151 -0.08030 4.34484

89 2000 36720 M O 2.53151 -0.08030 4.34160

90 1998 35922 C S 0.34521 -0.03911 5.45352

90 1998 35922 P S 0.34521 -0.03911 5.46574

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
96 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

90 1998 35977 C S 0.49589 -0.03659 5.48197

90 1998 35977 P S 0.49589 -0.03659 5.48687

90 1998 36021 C S 0.61644 -0.01203 5.45155

90 1998 36021 P S 0.61644 -0.01203 5.44458

90 1999 36356 C S 1.53425 -0.04012 5.50744

90 1999 36356 P S 1.53425 -0.04012 5.51625

90 2000 36686 C S 2.43836 0.04072 5.51428

90 2000 36686 P S 2.43836 0.04072 5.53682

90 2001 37055 C S 3.44932 0.06098 5.53165

90 2002 37379 C S 4.33699 0.05664 5.59091

90 2002 37379 P S 4.33699 0.05664 5.60701

92 1998 35920 C S 0.33973 -0.02916 5.92332

92 1998 35920 P S 0.33973 -0.02916 5.94916

92 1998 35964 C S 0.46027 -0.00023 5.84872

92 1998 35964 P S 0.46027 -0.00023 5.86141

92 1998 36053 C S 0.70411 -0.00319 5.86856

92 1998 36053 P S 0.70411 -0.00319 5.89735

92 1998 36060 C S 0.72329 -0.00274 5.86593

92 1998 36060 P S 0.72329 -0.00274 5.87796

92 1999 36333 C S 1.47123 -0.00148 5.87175

92 1999 36333 P S 1.47123 -0.00148 5.91193

92 1999 36370 C S 1.57260 0.01658 5.85019

92 1999 36370 P S 1.57260 0.01658 5.89402

92 2000 36643 C S 2.32055 -0.02134 5.88855

92 2000 36643 P S 2.32055 -0.02134 5.94587

92 2000 36719 C S 2.52877 0.00121 5.88020

92 2000 36719 P S 2.52877 0.00121 5.94584

92 2000 36782 C S 2.70137 -0.00148 5.88263

92 2000 36782 P S 2.70137 -0.00148 5.94235

92 2001 37012 C S 3.33151 -0.00391 5.89842

92 2001 37012 P S 3.33151 -0.00391 5.97668

92 2001 37126 C S 3.64384 0.01869 5.88524

92 2001 37126 P S 3.64384 0.01869 5.92484

92 2001 37168 C S 3.75890 0.02063 5.81506

92 2002 37386 C S 4.35616 0.01676 5.89465

92 2002 37386 P S 4.35616 0.01676 5.89316

95 1998 35921 C CL 0.34247 0.03804 4.47164

95 1998 35990 C CL 0.53151 -0.15220 4.42401

95 1998 35992 C CH 0.53699 0.11713 4.56934

95 1998 35992 P CH 0.53699 0.11713 4.62762

95 1998 36035 C CH 0.65479 0.01869 4.57780

95 1998 36035 P CH 0.65479 0.01869 4.72278

95 1998 36047 C CL 0.68767 0.03012 4.45423

95 1999 36319 C CL 1.43288 -0.19872 4.44441

95 2000 36635 C CL 2.29863 0.02633 4.46625

95 2000 36649 C CH 2.33699 0.05259 4.63103

95 2000 36719 C CH 2.52877 0.08896 4.64044

95 2001 36991 C CH 3.27397 -0.00457 4.63861

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 97

95 2001 37064 C CL 3.47397 -0.15220 4.47347

97 1998 35929 C CH 0.36438 0.01355 4.72384

97 1998 35929 C CL 0.36438 0.04902 4.60697

97 1998 35984 C CH 0.51507 -0.03129 4.66466

97 1998 35984 C CL 0.51507 0.00462 4.58129

97 1998 36029 C CH 0.63836 -0.05281 4.64928

97 1998 36029 C CL 0.63836 -0.02711 4.56132

97 1999 36369 C CH 1.56986 -0.05680 4.68951

97 1999 36369 C CH 1.56986 -0.03972 4.65167

97 2000 36692 C CL 2.45479 0.01355 4.64660

97 2001 37119 C CH 3.62466 0.01498 4.70329

97 2002 37448 C CL 4.52603 0.11201 4.64785

98 1998 35927 C CH 0.35890 -0.01967 4.87428

98 1998 35927 C CL 0.35890 0.01866 4.85857

98 1998 35984 C CL 0.51507 -0.04150 4.81259

98 1998 36047 C CH 0.68767 -0.06597 4.89575

98 1998 36047 C CL 0.68767 -0.03027 4.87939

98 1998 36056 C CL 0.71233 -0.02251 4.87604

98 1999 36320 C CH 1.43562 -0.01711 4.75841

98 2000 36651 C CH 2.34247 -0.00538 4.78206

98 2001 37011 C CL 3.32877 0.03947 4.81056

98 2001 37083 C CL 3.52603 0.01320 4.76958

98 2002 37356 C CL 4.27397 0.13109 4.82575

99 1998 35928 C CH 0.36164 -0.15822 5.00267

99 1998 35928 C CL 0.36164 -0.04642 4.81681

99 1998 35976 C CH 0.49315 -0.14916 5.00542

99 1998 35976 M CH 0.49315 -0.14916 5.00562

99 1998 35976 C CL 0.49315 -0.03581 4.81389

99 1998 35976 M CL 0.49315 -0.03581 4.81381

99 1998 36061 C CH 0.72603 -0.09323 4.98798

99 1998 36061 M CH 0.72603 -0.09323 4.99254

99 1998 36061 C CL 0.72603 -0.00223 4.80337

99 1998 36061 M CL 0.72603 -0.00223 4.80754

99 2000 36735 C CH 2.57260 0.00871 4.92500

99 2000 36735 M CH 2.57260 0.00871 4.94257

99 2001 37007 C CL 3.31781 0.21179 4.79991

99 2001 37007 M CL 3.31781 0.21179 4.81308

99 2002 37385 C CH 4.35342 0.16226 4.96606

99 2002 37385 M CH 4.35342 0.16226 4.96102

100 1998 35942 C CL 0.40000 -0.14704 4.15277

100 1998 35942 C CL 0.40000 -0.10075 4.15214

100 1998 35942 M CL 0.40000 -0.14704 4.16107

100 1998 35942 M CL 0.40000 -0.10075 4.15841

100 1998 35970 C CL 0.47671 -0.10249 4.13629

100 1998 35970 M CL 0.47671 -0.10249 4.13932

100 1998 36033 C CL 0.64932 -0.01095 4.11855

100 1998 36033 C CL 0.64932 0.02957 4.11790

100 1998 36033 M CL 0.64932 -0.01095 4.12568

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
98 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

100 1998 36033 M CL 0.64932 0.02957 4.12713

100 2001 36998 C CL 3.29315 0.05817 4.16231

100 2001 36998 M CL 3.29315 0.05817 4.18783

100 2001 37091 C CL 3.54795 0.10245 4.15904

100 2001 37091 M CL 3.54795 0.10245 4.16200

100 2001 37160 C CL 3.73699 0.13149 4.16154

100 2001 37160 M CL 3.73699 0.13149 4.15230

100 2002 37349 C CL 4.25479 0.09675 4.20320

100 2002 37349 M CL 4.25479 0.09675 4.20604

101 1998 35935 C CH 0.38082 0.02515 4.03300

101 1998 35935 M CH 0.38082 0.02515 4.04463

101 1998 35935 C CL 0.38082 0.02433 3.69362

101 1998 35935 M CL 0.38082 0.02433 3.71040

101 1998 35991 C CH 0.53425 0.03250 3.97819

101 1998 35991 M CH 0.53425 0.03250 3.98861

101 1998 35991 C CL 0.53425 0.03087 3.66254

101 1998 35991 M CL 0.53425 0.03087 3.67148

101 1998 36025 C CH 0.62740 0.09551 4.04006

101 1998 36025 M CH 0.62740 0.09551 4.05508

101 1998 36025 C CL 0.62740 0.09322 3.69387

101 1998 36025 M CL 0.62740 0.09322 3.70966

101 1999 36364 C CH 1.55616 -0.10686 4.03777

101 1999 36364 M CH 1.55616 -0.10686 4.03672

101 2000 36672 C CL 2.40000 -0.19472 4.18950

101 2000 36672 M CL 2.40000 -0.19472 4.20095

102 1998 35934 C CH 0.37808 -0.14907 4.89732

102 1998 35934 M CH 0.37808 -0.14907 4.91067

102 1998 35934 C CL 0.37808 -0.07080 4.72073

102 1998 35934 M CL 0.37808 -0.07080 4.73435

102 1998 35985 C CH 0.51781 0.03800 4.86268

102 1998 35985 C CL 0.51781 0.08683 4.69510

102 1998 36067 C CH 0.74247 0.03378 4.86020

102 1998 36067 C CL 0.74247 0.08107 4.69291

102 1999 36335 C CH 1.47671 -0.00448 4.85094

102 2000 36747 C CH 2.60548 0.06673 4.91317

102 2001 37105 C CH 3.58630 -0.09530 5.01103

102 2002 37420 C CL 4.44932 0.23311 4.71626

103 1998 35913 C CH 0.32055 0.01604 5.69864

103 1998 35913 P CH 0.32055 0.01604 5.71353

103 1998 35913 C CL 0.32055 0.04786 5.37560

103 1998 35913 P CL 0.32055 0.04786 5.38857

103 1998 35963 C CH 0.45753 -0.03188 5.58203

103 1998 35963 P CH 0.45753 -0.03188 5.57534

103 1998 35963 C CL 0.45753 0.02837 5.30767

103 1998 35963 P CL 0.45753 0.02837 5.30221

103 1998 36039 C CH 0.66575 -0.13043 5.58282

103 1998 36039 P CH 0.66575 -0.13043 5.57924

103 1998 36039 C CL 0.66575 -0.05099 5.29942

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
SUPPLEMENTAL INFORMATION 99

103 1998 36039 P CL 0.66575 -0.05099 5.29807

103 1999 36329 C CH 1.46027 -0.05825 5.63472

103 1999 36329 P CH 1.46027 -0.05825 5.66663

103 2000 36693 C CH 2.45753 -0.03801 5.53505

103 2000 36693 P CH 2.45753 -0.03801 5.55013

103 2001 37062 C CH 3.46849 0.04804 5.61877

103 2001 37062 P CH 3.46849 0.04804 5.60123

103 2002 37413 C CH 4.43014 0.16925 5.60370

103 2002 37413 P CH 4.43014 0.16925 5.59266

104 1998 35922 C CL 0.34521 0.01289 4.85593

104 1998 35922 C CL 0.34521 0.02153 4.86730

104 1998 35922 M CL 0.34521 0.01289 4.89866

104 1998 35922 M CL 0.34521 0.02153 4.90742

104 1998 35964 C CL 0.46027 0.02306 4.90030

104 1998 35964 C CL 0.46027 0.02554 4.88590

104 1998 35964 M CL 0.46027 0.02306 4.92341

104 1998 35964 M CL 0.46027 0.02554 4.91654

104 1998 36021 C CL 0.61644 -0.02184 4.90298

104 1998 36021 C CL 0.61644 0.00222 4.89268

104 1998 36021 M CL 0.61644 -0.02184 4.92064

104 1998 36021 M CL 0.61644 0.00222 4.91185

104 1999 36334 C CL 1.47397 0.00883 4.87482

104 1999 36334 M CL 1.47397 0.00883 4.88280

104 2000 36649 C CL 2.33699 0.02478 4.85101

104 2000 36649 M CL 2.33699 0.02478 4.88045

104 2001 37013 C CL 3.33425 0.04478 4.86607

104 2001 37013 M CL 3.33425 0.04478 4.87298

104 2002 37379 C CL 4.33699 -0.14178 4.88356

104 2002 37379 M CL 4.33699 -0.14178 4.93022

105 1998 35927 C CH 0.35890 -0.08941 5.83592

105 1998 35927 C CH 0.35890 0.02271 5.66632

105 1998 35992 C CH 0.53699 -0.02501 5.82219

105 1998 35992 C CH 0.53699 0.04987 5.65323

105 1998 35992 C CL 0.53699 0.05310 5.64368

105 1998 36042 C CH 0.67397 -0.02709 5.82641

105 1998 36042 C CL 0.67397 0.05109 5.61644

105 1999 36335 C CH 1.47671 -0.08399 5.77427

105 2000 36649 C CH 2.33699 -0.07304 5.74169

105 2001 37064 C CH 3.47397 -0.01758 5.73560

105 2002 37492 C CH 4.64658 0.13933 5.79140

106 1998 35955 C CL 0.43562 0.02125 4.79645

106 1998 36011 C CL 0.58904 0.00820 4.73427

106 1998 36055 C CL 0.70959 -0.03644 4.79975

106 1998 36055 C CL 0.70959 -0.02360 4.78891

106 2001 37162 C CL 3.74247 -0.14023 4.79240

106 2002 37372 C CL 4.31781 0.17082 4.73699

Table 12. Data used in the diffC model.—Continued

[C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high;

L, low-pressure; S, sprinkler; , log of pumping water level at time of measurement; , average log PWL for a

given site; diffC, log of power conversion coefficient]

Site Year Date Method Type t - diffC

w

w

w w
100 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

Table 13. Data used in the diffL model. 

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

1 1998 O 0 -0.03652 4.35337

1 1999 O 1 -0.16764 4.40675

1 2000 O 2 -0.02808 4.37760

1 2001 O 3 0.08376 4.40732

1 2002 O 4 0.16065 4.44670

2 1998 CL 0 0.02769 4.37287

2 1999 CH 1 -0.06768 4.48512

2 2000 CL 2 -0.03567 4.46249

2 2001 CH 3 -0.00256 4.47577

2 2002 CH 4 0.09566 4.43039

3 1998 O 0 -0.06538 4.30802

3 1999 O 1 -0.09570 4.25977

3 2000 O 2 0.03971 4.24189

3 2001 O 3 0.05699 4.29083

3 2002 O 4 0.10651 4.40192

5 1998 CH 0 0.01021 5.56054

5 1999 CH 1 -0.05848 5.51983

5 2001 CL 3 -0.26612 5.44265

5 2002 CH 4 0.18916 5.46911

7 1998 CL 0 0.01310 4.82667

7 1999 CL 1 -0.13419 4.86791

7 2000 CH 2 -0.00066 4.88988

7 2002 CL 4 0.19045 4.93866

8 1998 L 0 -0.01912 4.28572

8 1999 L 1 -0.05916 4.23084

8 2000 L 2 -0.03969 4.28313

8 2002 L 4 0.14664 4.39942

9 1999 O 1 0.00268 4.05772

9 2000 O 2 -0.03148 4.04311

9 2001 O 3 0.08510 4.07977

11 1998 O 0 0.01381 4.36818

11 1999 O 1 -0.03748 4.36827

11 2000 O 2 -0.07850 4.34822

11 2001 O 3 0.05581 4.43966

12 1998 O 0 0.01321 4.21720

12 1999 O 1 -0.05828 4.19971

12 2000 O 2 -0.05982 4.22474

12 2001 O 3 0.07847 4.22760

14 1998 L 0 -0.01113 4.11853

14 1999 L 1 -0.03062 4.13586

14 2000 L 2 0.04175 4.17905

15 1998 O 0 0.03910 4.57411

15 1999 O 1 -0.07499 4.56517

15 2000 O 2 -0.01954 4.59487

15 2001 O 3 0.03280 4.74560

16 1998 CH 0 -0.04203 4.21422

16 1999 CL 1 -0.07418 4.21149

16 2001 CL 3 0.11364 4.34919

w w

w w
SUPPLEMENTAL INFORMATION 101

16 2002 CL 4 0.26246 4.55214

18 1998 L 0 -0.08549 4.13964

18 1999 L 1 -0.08186 4.13690

18 2000 L 2 -0.02694 4.14998

18 2002 L 4 0.18819 4.26619

19 1998 CH 0 -0.04126 4.27180

19 1999 CH 1 -0.09232 4.28652

19 2000 CH 2 0.07020 4.36300

19 2001 CH 3 0.05509 4.30633

20 1998 O 0 -0.03947 4.03298

20 1999 O 1 -0.10411 3.96069

20 2000 O 2 -0.00695 3.98000

20 2001 O 3 0.08794 3.97650

20 2002 O 4 0.24359 4.15830

22 1999 L 1 0.02889 4.81925

22 2000 L 2 0.07922 4.66617

22 2001 L 3 -0.12151 4.67903

22 2002 L 4 0.02326 4.53562

23 1998 O 0 0.03106 4.34270

23 1999 O 1 0.00811 4.35290

23 2000 O 2 -0.00722 4.40810

23 2001 O 3 -0.06794 4.57296

23 2002 O 4 -0.09093 4.74578

24 1998 O 0 -0.04273 4.78315

24 1999 O 1 -0.03590 4.88842

24 2001 O 3 0.05327 4.90857

24 2002 O 4 0.11082 5.04503

25 1998 O 0 -0.01005 4.32828

25 1999 O 1 -0.07009 4.35053

25 2000 O 2 0.02339 4.42622

27 1998 L 0 -0.15313 4.18959

27 1999 L 1 -0.01271 4.20032

27 2000 L 2 0.03482 4.29432

27 2001 L 3 0.06551 4.30247

28 1998 CH 0 -0.05465 4.71999

28 2000 CL 2 0.02876 4.73093

28 2001 CH 3 0.01294 4.72920

28 2002 CH 4 0.04533 4.74396

29 1998 O 0 -0.05279 4.22971

29 1999 O 1 -0.00881 4.27112

29 2000 O 2 0.01881 4.25621

29 2002 O 4 0.35833 4.38926

30 1998 O 0 0.04196 4.58768

30 1999 O 1 -0.13057 4.56735

30 2000 O 2 -0.15723 4.57188

30 2001 O 3 0.13200 4.58362

30 2002 O 4 0.01995 4.63538

32 1998 O 0 0.05187 4.60768

32 1999 O 1 -0.06786 4.62187

Table 13. Data used in the diffL model.—Continued

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

w w

w w
102 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

32 2000 O 2 -0.06310 4.61006

32 2001 O 3 0.04723 4.60986

32 2002 O 4 0.28564 4.67226

34 1998 O 0 0.00265 4.04397

34 1999 O 1 -0.14436 4.08005

34 2000 O 2 -0.05334 4.03010

34 2001 O 3 0.05496 4.03265

34 2002 O 4 0.23121 4.22470

35 1998 O 0 0.00202 5.42066

35 1999 O 1 0.00153 5.49202

35 2000 O 2 -0.00759 5.45742

36 1998 O 0 -0.04766 4.58330

36 1999 O 1 -0.03890 4.60517

36 2000 O 2 -0.02565 4.57262

36 2001 O 3 0.10568 4.61816

37 1998 O 0 -0.01563 4.17575

37 1999 O 1 -0.08090 4.13517

37 2001 O 3 0.04220 4.12734

37 2002 O 4 0.24112 4.24832

38 1998 O 0 -0.03129 4.67441

38 1999 O 1 -0.04404 4.59694

38 2000 O 2 0.01836 4.70381

38 2001 O 3 0.02963 4.69749

38 2002 O 4 0.07442 4.87583

39 1998 CH 0 -0.03989 4.66174

39 1999 CL 1 -0.04938 4.66527

39 2001 CL 3 0.08126 4.70747

39 2002 CL 4 0.14666 4.74839

40 1998 O 0 -0.01410 4.61600

40 1999 O 1 -0.02753 4.55862

40 2000 O 2 0.02793 4.66412

41 1998 O 0 0.05906 4.30354

41 1999 O 1 -0.32145 4.35085

41 2000 O 2 0.06409 4.33670

41 2001 O 3 0.04861 4.36320

43 1998 O 0 -0.04122 4.98466

43 1999 O 1 -0.00732 4.98103

43 2000 O 2 -0.01365 4.97827

43 2001 O 3 -0.02654 4.99655

43 2002 O 4 0.12969 4.96925

44 1998 S 0 -0.02554 5.76196

44 1999 S 1 -0.07764 5.74473

44 2000 S 2 0.02049 5.75457

44 2001 S 3 0.06185 5.78252

45 1998 S 0 0.01696 5.30766

45 1999 S 1 -0.04056 5.33901

45 2000 S 2 0.00488 5.26024

45 2001 S 3 -0.01443 5.31961

45 2002 S 4 -0.00777 5.29679

Table 13. Data used in the diffL model.—Continued

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

w w

w w
SUPPLEMENTAL INFORMATION 103

46 1998 O 0 0.02963 4.18864

46 1999 O 1 0.06353 4.22416

46 2000 O 2 -0.11986 4.19086

46 2001 O 3 0.07073 4.24569

46 2002 O 4 0.07035 4.32570

47 1998 O 0 -0.00251 4.49222

47 1999 O 1 0.06213 4.45571

47 2000 O 2 -0.14734 4.32087

47 2001 O 3 0.04031 4.33716

47 2002 O 4 0.16270 4.36067

48 1998 O 0 -0.00524 4.26310

48 1999 O 1 -0.02312 4.32487

48 2000 O 2 0.02589 4.29031

49 1998 CL 0 -0.05740 4.29623

49 2000 CH 2 0.03386 4.34530

49 2002 CH 4 0.15294 4.34135

50 1998 L 0 0.01057 4.38025

50 1999 L 1 -0.11431 4.27372

50 2000 L 2 -0.09818 4.33623

50 2001 L 3 0.17020 4.39261

51 1998 CL 0 -0.02623 4.77263

51 1999 CH 1 0.04632 4.82794

51 2000 CL 2 0.02002 4.74222

51 2001 CH 3 0.04404 4.77867

51 2002 CH 4 -0.07573 4.72823

52 1998 O 0 0.00202 4.48159

52 1999 O 1 -0.00354 4.50789

53 1998 O 0 0.08939 4.50908

53 1999 O 1 -0.16383 4.51881

53 2000 O 2 -0.03935 4.55175

53 2001 O 3 -0.04999 4.68884

53 2002 O 4 0.07778 4.66411

54 1998 L 0 0.00433 4.47196

54 1999 L 1 -0.01116 4.45788

54 2000 L 2 0.00460 4.47064

54 2002 L 4 -0.00418 4.47439

55 1998 O 0 -0.04325 4.37322

55 2000 O 2 -0.01625 4.38309

55 2002 O 4 0.07706 4.50494

56 1998 O 0 -0.07860 3.97001

56 2000 O 2 -0.08287 3.92072

56 2001 O 3 0.04657 4.04459

56 2002 O 4 0.21829 4.06530

58 1998 O 0 -0.11867 4.14652

58 1999 O 1 -0.16366 4.22673

58 2000 O 2 -0.11216 4.21261

58 2001 O 3 0.07900 4.24605

58 2002 O 4 0.18616 4.36401

59 1998 O 0 -0.08554 4.44924

Table 13. Data used in the diffL model.—Continued

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

w w

w w
104 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

59 1999 O 1 0.24237 4.39073

59 2000 O 2 -0.31367 4.29581

60 1998 O 0 -0.03682 4.32211

60 1999 O 1 -0.03365 4.30126

60 2000 O 2 -0.04055 4.29208

60 2001 O 3 0.07038 4.34002

60 2002 O 4 0.08932 4.41170

61 1998 O 0 0.01441 4.73484

61 1999 O 1 -0.04642 4.70667

61 2000 O 2 -0.16083 4.74416

61 2001 O 3 0.06110 4.83546

61 2002 O 4 0.10293 4.82919

62 1998 L 0 -0.09289 4.12126

62 1999 L 1 0.08093 4.43526

62 2000 L 2 0.00851 4.44434

62 2001 L 3 0.17524 4.43111

62 2002 L 4 0.04665 4.42754

63 1998 CL 0 -0.38284 4.24809

63 1999 CH 1 -0.35660 4.24976

63 2000 CL 2 0.22974 4.25535

63 2001 CH 3 0.29210 4.33234

63 2002 CH 4 -0.06041 4.38526

64 1998 O 0 -0.03887 4.41008

64 1999 O 1 -0.04071 4.43794

64 2000 O 2 0.11046 4.48320

64 2001 O 3 -0.02377 4.51556

64 2002 O 4 -0.02319 4.56067

65 1998 O 0 0.01852 4.49593

65 1999 O 1 -0.01704 4.43458

65 2000 O 2 -0.02001 4.50921

66 1998 O 0 -0.13334 4.17299

66 1999 O 1 -0.08258 4.12926

66 2000 O 2 -0.00827 4.15095

66 2001 O 3 0.02976 4.17164

66 2002 O 4 0.25036 4.25111

68 1998 L 0 -0.03945 4.43744

68 1999 L 1 -0.00369 4.44022

68 2000 L 2 -0.03785 4.43682

68 2001 L 3 -0.01458 4.45292

68 2002 L 4 0.12154 4.59470

69 1998 O 0 -0.01521 4.83315

69 2000 O 2 -0.01108 4.83350

69 2001 O 3 0.00151 4.80453

69 2002 O 4 0.04281 4.79066

70 1998 O 0 0.02155 4.85042

70 1999 O 1 0.05971 4.85510

70 2000 O 2 0.01952 4.90613

70 2001 O 3 -0.09019 5.03861

70 2002 O 4 -0.00253 4.91663

Table 13. Data used in the diffL model.—Continued

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

w w

w w
SUPPLEMENTAL INFORMATION 105

72 1998 O 0 -0.06159 3.80652

72 1999 O 1 -0.00170 3.81931

72 2000 O 2 -0.00218 3.82930

72 2001 O 3 0.06289 3.86247

74 1998 O 0 -0.06926 4.46541

74 2000 O 2 0.03801 4.50484

74 2001 O 3 0.18793 4.50789

74 2002 O 4 -0.01816 4.47514

75 1998 O 0 -0.00010 4.76369

75 2000 O 2 0.00031 4.92606

77 1998 O 0 -0.01139 4.68017

77 1999 O 1 0.03418 4.67134

80 1998 O 0 -0.04351 4.22263

80 1999 O 1 -0.06901 4.24005

80 2000 O 2 0.00014 4.22661

80 2002 O 4 0.22085 4.23781

82 1998 L 0 -0.13185 4.14375

82 2002 L 4 0.19669 3.86889

85 1998 S 0 -0.10406 5.42883

85 1999 S 1 -0.00230 5.44504

85 2000 S 2 0.00720 5.53837

85 2001 S 3 0.30729 5.87910

86 1998 S 0 0.00778 5.36851

86 1999 S 1 0.03029 5.38144

86 2000 S 2 0.11225 5.42202

86 2001 S 3 0.03645 5.40306

86 2002 S 4 -0.24043 5.47253

87 1998 S 0 -0.05983 5.41429

87 1999 S 1 -0.01065 5.39492

87 2000 S 2 0.01908 5.41361

87 2001 S 3 0.04872 5.42158

87 2002 S 4 0.04654 5.41786

89 1998 O 0 0.04723 4.33543

89 1999 O 1 -0.03069 4.33780

89 2000 O 2 -0.08030 4.34575

90 1998 S 0 -0.02924 5.47597

90 1999 S 1 -0.04012 5.51115

90 2000 S 2 0.04072 5.51195

90 2001 S 3 0.06098 5.51862

90 2002 S 4 0.05664 5.60768

92 1998 S 0 -0.00883 5.86743

92 1999 S 1 0.00755 5.85292

92 2000 S 2 -0.00721 5.84781

92 2001 S 3 0.01004 5.85243

92 2002 S 4 0.01676 5.86206

95 1998 CL 0 0.02680 4.52741

95 1999 CL 1 -0.19872 4.56977

95 2000 CL 2 0.05596 4.59436

95 2001 CH 3 -0.07838 4.62980

Table 13. Data used in the diffL model.—Continued

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

w w

w w
106 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

97 1998 CH 0 -0.00734 4.67159

97 1999 CH 1 -0.04826 4.65388

97 2000 CL 2 0.01355 4.69504

97 2001 CH 3 0.01498 4.74240

97 2002 CL 4 0.11201 4.80406

98 1998 CH 0 -0.02688 4.82442

98 1999 CH 1 -0.01711 4.77860

98 2000 CH 2 -0.00538 4.78745

98 2001 CL 3 0.02633 4.79147

98 2002 CL 4 0.13109 4.79738

99 1998 CH 0 -0.07655 4.70833

99 2000 CH 2 0.00871 4.69571

99 2001 CL 3 0.21179 4.64593

99 2002 CH 4 0.16226 4.93744

100 1998 CL 0 -0.06633 4.10179

100 2001 CL 3 0.09737 4.19458

100 2002 CL 4 0.09675 4.23120

101 1998 CH 0 0.05026 4.02671

101 1999 CH 1 -0.10686 3.98883

101 2000 CL 2 -0.19472 4.04425

102 1998 CH 0 -0.02501 4.81222

102 1999 CH 1 -0.00448 4.80453

102 2000 CH 2 0.06673 4.87831

102 2001 CH 3 -0.09530 5.03907

102 2002 CL 4 0.23311 4.83991

103 1998 CH 0 -0.02017 5.54507

103 1999 CH 1 -0.05825 5.57320

103 2000 CH 2 -0.03801 5.55009

103 2001 CH 3 0.04804 5.59023

103 2002 CH 4 0.16925 5.61110

104 1998 CL 0 0.01057 4.93108

104 1999 CL 1 0.00883 4.93744

104 2000 CL 2 0.02478 4.94723

104 2001 CL 3 0.04478 4.96598

104 2002 CL 4 -0.14178 4.96728

105 1998 CH 0 0.00504 5.72359

105 1999 CH 1 -0.08399 5.74714

105 2000 CH 2 -0.07304 5.71809

105 2001 CH 3 -0.01758 5.77068

105 2002 CH 4 0.13933 5.74954

106 1998 CL 0 -0.00765 4.86335

106 2001 CL 3 -0.14023 4.91179

106 2002 CL 4 0.17082 4.70504

Table 13. Data used in the diffL model.—Continued

[O, open; CL, complex low; CH, complex high; L, low-pressure; S, sprinkler; s, is time when power consumption at the well was 

used to estimate pumpage (in years, s=0 for 1998); , average log PWL for a given site in a given year; is average log of 

pumping water level for a given site]

Site Year Type s - diffL

w w

w w
Supplemental Information 107

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year. 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

1 1998 35950 C O -0.42188 -0.01289 0.05785

1 1998 35950 P O -0.42188 -0.01289 0.01333

1 1998 35989 C O -0.52881 -0.02053 0.01647

1 1998 35989 M O -0.52881 -0.02053 -0.03066

1 1998 35989 P O -0.52881 -0.02053 -0.04343

1 1998 36026 C O -0.63013 0.02912 -0.00744

1 1998 36026 M O -0.63013 0.02912 -0.01545

1 1998 36026 P O -0.63013 0.02912 -0.05213

1 1999 36343 C O -0.49866 -0.07621 0.10350

1 1999 36343 P O -0.49866 -0.07621 0.07615

1 1999 36369 C O -0.56982 0.01761 0.13189

1 1999 36369 P O -0.56982 0.01761 0.12000

1 1999 36397 C O -0.64661 0.05860 0.02685

1 1999 36397 P O -0.64661 0.05860 0.02173

1 2000 36650 C O -0.33972 -0.03940 0.02913

1 2000 36650 P O -0.33972 -0.03940 0.00134

1 2000 36727 C O -0.55066 0.00184 0.08468

1 2000 36727 P O -0.55066 0.00184 0.04542

1 2000 36752 C O -0.61914 0.03756 0.08372

1 2000 36752 P O -0.61914 0.03756 0.05373

1 2001 36990 C O -0.27124 -0.10029 -0.04085

1 2001 36990 P O -0.27124 -0.10029 -0.04621

1 2001 37084 C O -0.52881 0.06908 0.11112

1 2001 37084 P O -0.52881 0.06908 0.09063

1 2001 37111 C O -0.60278 0.03121 0.05498

1 2001 37111 P O -0.60278 0.03121 0.03610

1 2002 37351 C O -0.26025 -0.04304 0.03354

1 2002 37351 P O -0.26025 -0.04304 0.01220

1 2002 37449 C O -0.52881 0.01411 0.03124

1 2002 37449 P O -0.52881 0.01411 0.00511

1 2002 37476 C O -0.60278 0.02893 0.09449

1 2002 37476 P O -0.60278 0.02893 0.06043

2 1998 35936 C CL -0.38354 0.01708 0.02972

2 1998 35936 P CL -0.38354 0.01708 0.02959

2 1998 36048 C CL -0.69043 -0.01262 0.00102

2 1998 36048 P CL -0.69043 -0.01262 -0.02466

2 1998 36052 C CL -0.70142 -0.00446 -0.00728

2 1998 36052 P CL -0.70142 -0.00446 -0.03470

2 1999 36342 C CH -0.49585 0.04075 0.06471

2 1999 36342 P CH -0.49585 0.04075 0.05692

2 1999 36348 C CL -0.51233 -0.04075 0.12713

2 1999 36348 P CL -0.51233 -0.04075 0.09860

2 2000 36692 C CL -0.45483 0.00000 0.07374

2 2000 36692 P CL -0.45483 0.00000 0.13809

2 2001 37062 C CH -0.46851 0.06883 -0.09946

2 2001 37062 P CH -0.46851 0.06883 -0.07273

w w

w w
108 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

2 2001 37082 C CL -0.52332 -0.00982 -0.02304

2 2001 37082 P CL -0.52332 -0.00982 -0.01914

2 2001 37123 C CL -0.63562 -0.05901 0.07027

2 2001 37123 P CL -0.63562 -0.05901 0.08875

2 2002 37337 C CH -0.22192 0.00000 0.07458

2 2002 37337 P CH -0.22192 0.00000 -0.00837

3 1998 35975 C O -0.49036 -0.04265 0.02375

3 1998 35975 P O -0.49036 -0.04265 0.02914

3 1998 36000 C O -0.55896 -0.04405 0.02817

3 1998 36000 P O -0.55896 -0.04405 -0.06117

3 1998 36053 C O -0.70410 0.08670 -0.07275

3 1998 36053 P O -0.70410 0.08670 -0.12029

3 1999 36348 C O -0.51233 -0.02586 0.02104

3 1999 36348 P O -0.51233 -0.02586 -0.10001

3 1999 36367 C O -0.56433 0.02205 0.05792

3 1999 36367 P O -0.56433 0.02205 0.09668

3 1999 36395 C O -0.64111 0.00381 0.02393

3 1999 36395 P O -0.64111 0.00381 -0.07791

3 2000 36699 C O -0.47400 0.00419 -0.00646

3 2000 36720 C O -0.53149 -0.00628 0.02932

3 2000 36720 P O -0.53149 -0.00628 0.00417

3 2000 36739 C O -0.58362 0.00419 0.02725

3 2000 36739 P O -0.58362 0.00419 -0.18511

3 2001 36986 C O -0.26025 -0.06422 0.00752

3 2001 36986 P O -0.26025 -0.06422 0.03337

3 2001 37069 C O -0.48767 0.02147 0.11798

3 2001 37069 P O -0.48767 0.02147 -0.07418

3 2001 37104 C O -0.58362 0.04275 0.02365

3 2001 37104 P O -0.58362 0.04275 -0.09830

3 2002 37328 C O -0.19727 0.02471 0.10954

3 2002 37448 C O -0.52600 -0.00500 0.01540

3 2002 37448 P O -0.52600 -0.00500 -0.05301

3 2002 37449 C O -0.52881 -0.01471 0.04278

5 1998 35934 C CH -0.37805 -0.08457 0.26819

5 1998 35934 P CH -0.37805 -0.08457 -0.00639

5 1998 35975 C CH -0.49036 -0.10998 0.12826

5 1998 35975 P CH -0.49036 -0.10998 0.05606

5 1998 36038 C CH -0.66296 -0.07107 0.01873

5 1998 36038 P CH -0.66296 -0.07107 -0.02055

5 1998 36061 C CH -0.72607 0.26562 0.02534

5 1998 36061 P CH -0.72607 0.26562 -0.03413

5 1999 36333 C CH -0.47119 0.00000 -0.03739

5 1999 36333 P CH -0.47119 0.00000 -0.10419

5 2001 37057 C CL -0.45483 0.00000 0.10675

5 2001 37057 P CL -0.45483 0.00000 0.00696

5 2002 37385 C CH -0.35339 0.02449 0.01820

5 2002 37424 C CL -0.46033 -0.00020 0.02664

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 109

5 2002 37461 C CL -0.56165 -0.02430 0.00918

7 1998 35937 M CL -0.38635 -0.02896 -0.26401

7 1998 35937 P CL -0.38635 -0.02896 -0.25063

7 1998 35999 M CL -0.55615 -0.02367 -0.06518

7 1998 35999 P CL -0.55615 -0.02367 -0.10044

7 1998 36028 M CL -0.63562 0.05264 -0.07005

7 1998 36028 P CL -0.63562 0.05264 -0.06172

7 1999 36406 M CL -0.67126 0.00000 -0.12211

7 1999 36406 P CL -0.67126 0.00000 -0.13334

7 2000 36672 P CH -0.40002 0.00000 -0.18072

7 2002 37573 M CL -0.86853 0.00000 -0.23034

8 1998 35905 P L -0.29858 -0.09049 -0.04251

8 1998 35975 C L -0.49036 -0.01841 0.03636

8 1998 35975 P L -0.49036 -0.01841 -0.00980

8 1998 36031 C L -0.64380 0.06366 0.04353

8 1998 36031 P L -0.64380 0.06366 0.00572

8 1999 36299 C L -0.37805 0.00000 -0.00413

8 1999 36299 P L -0.37805 0.00000 -0.07227

8 2000 36713 C L -0.51233 0.00000 -0.02914

8 2000 36713 P L -0.51233 0.00000 -0.09727

8 2002 37379 C L -0.33704 0.00000 0.08340

8 2002 37379 P L -0.33704 0.00000 -0.03876

9 1999 36340 M O -0.49036 -0.00344 -0.12677

9 1999 36340 P O -0.49036 -0.00344 -0.15218

9 1999 36370 M O -0.57263 0.00344 -0.13481

9 1999 36370 P O -0.57263 0.00344 -0.15159

9 2000 36630 M O -0.28491 0.07847 -0.13894

9 2000 36734 M O -0.56982 -0.02727 -0.13848

9 2000 36790 M O -0.72327 -0.05120 -0.15544

9 2001 37063 M O -0.47119 0.00000 -0.19509

9 2001 37063 P O -0.47119 0.00000 -0.26078

11 1998 35947 M O -0.41370 0.01188 -0.07412

11 1998 35947 P O -0.41370 0.01188 -0.06881

11 1998 35998 M O -0.55347 -0.04474 -0.10048

11 1998 35998 P O -0.55347 -0.04474 -0.11063

11 1998 36020 M O -0.61365 0.03286 -0.04171

11 1998 36020 P O -0.61365 0.03286 -0.08081

11 1999 36355 M O -0.53149 0.00000 -0.01151

11 2000 36698 M O -0.47119 0.00000 -0.16264

11 2000 36698 P O -0.47119 0.00000 -0.10659

11 2001 36993 M O -0.27942 0.00000 -0.00781

11 2001 36993 P O -0.27942 0.00000 -0.01875

12 1998 35935 M O -0.38086 -0.00867 0.00005

12 1998 35935 P O -0.38086 -0.00867 -0.02095

12 1998 35982 M O -0.50964 -0.01526 -0.01226

12 1998 35982 P O -0.50964 -0.01526 0.01385

12 1998 36014 M O -0.59729 -0.00488 0.01865

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
110 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

12 1998 36061 M O -0.72607 0.05273 -0.04280

12 1999 36362 M O -0.55066 0.00000 0.00431

12 1999 36362 P O -0.55066 0.00000 -0.03034

12 2000 36630 M O -0.28491 0.00000 -0.01385

12 2000 36630 P O -0.28491 0.00000 -0.05512

12 2001 37025 M O -0.36707 0.02679 -0.00244

12 2001 37082 M O -0.52332 -0.02679 -0.05115

14 1998 35944 C L -0.40552 0.01449 -0.01455

14 1998 35944 P L -0.40552 0.01449 -0.01872

14 1998 35975 C L -0.49036 0.00051 -0.02461

14 1998 35975 P L -0.49036 0.00051 -0.01951

14 1998 36055 C L -0.70959 -0.01500 -0.05478

14 1998 36055 P L -0.70959 -0.01500 -0.05015

14 1999 36348 C L -0.51233 0.02358 -0.00917

14 1999 36348 P L -0.51233 0.02358 -0.01549

14 1999 36406 C L -0.67126 0.00919 -0.03436

14 1999 36406 P L -0.67126 0.00919 -0.03945

14 1999 36447 C L -0.78357 -0.03277 -0.07493

14 1999 36447 P L -0.78357 -0.03277 -0.09549

14 2000 36648 C L -0.33423 -0.00854 -0.10232

14 2000 36648 P L -0.33423 -0.00854 -0.16006

14 2000 36733 C L -0.56714 0.00592 -0.10205

14 2000 36733 P L -0.56714 0.00592 -0.13750

14 2000 36768 C L -0.66296 0.00262 -0.09190

14 2000 36768 P L -0.66296 0.00262 -0.13483

15 1998 35948 M O -0.41638 -0.00633 0.01729

15 1998 35948 P O -0.41638 -0.00633 0.01185

15 1998 35968 C O -0.47119 -0.01474 0.05319

15 1998 35968 M O -0.47119 -0.01474 0.04907

15 1998 36006 C O -0.57532 0.02107 0.04615

15 1998 36006 M O -0.57532 0.02107 0.04291

15 1999 36335 C O -0.47668 0.01931 0.05508

15 1999 36335 M O -0.47668 0.01931 0.05399

15 1999 36335 P O -0.47668 0.01931 0.02572

15 1999 36384 C O -0.61096 -0.07197 0.07205

15 1999 36384 M O -0.61096 -0.07197 0.06270

15 1999 36432 C O -0.74243 0.02867 0.10180

15 1999 36432 M O -0.74243 0.02867 0.09697

15 1999 36432 P O -0.74243 0.02867 0.08829

15 2000 36636 C O -0.30139 0.00173 0.07461

15 2000 36636 M O -0.30139 0.00173 0.05627

15 2000 36636 P O -0.30139 0.00173 0.04574

15 2000 36706 C O -0.49316 0.04189 0.11164

15 2000 36706 M O -0.49316 0.04189 0.07384

15 2000 36749 C O -0.61096 -0.04449 0.01913

15 2000 36749 M O -0.61096 -0.04449 0.01512

15 2001 37007 C O -0.31775 0.05371 0.16544

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 111

15 2001 37007 M O -0.31775 0.05371 0.15109

15 2001 37069 C O -0.48767 0.01477 0.13385

15 2001 37069 M O -0.48767 0.01477 0.11320

15 2001 37118 C O -0.62195 -0.06848 0.12024

15 2001 37118 M O -0.62195 -0.06848 0.12436

16 1998 35936 C CH -0.38354 -0.01867 -0.06370

16 1998 35936 P CH -0.38354 -0.01867 -0.06134

16 1998 35942 C CL -0.40002 -0.07082 -0.09174

16 1998 35942 P CL -0.40002 -0.07082 -0.10367

16 1998 35982 C CL -0.50964 0.06584 0.00105

16 1998 35982 P CL -0.50964 0.06584 -0.01101

16 1998 36017 C CL -0.60547 0.02696 -0.02032

16 1998 36017 P CL -0.60547 0.02696 -0.05015

16 1998 36056 C CH -0.71228 -0.00331 -0.04550

16 1998 36056 P CH -0.71228 -0.00331 -0.04973

16 1999 36321 C CL -0.43835 -0.05082 -0.06615

16 1999 36321 P CL -0.43835 -0.05082 -0.07554

16 1999 36357 C CH -0.53699 0.05082 -0.01505

16 1999 36357 P CH -0.53699 0.05082 -0.02652

16 2001 37097 C CL -0.56433 0.00486 0.01517

16 2001 37097 P CL -0.56433 0.00486 -0.01607

16 2001 37158 C CL -0.73157 -0.00486 -0.00918

16 2001 37158 P CL -0.73157 -0.00486 -0.05460

16 2002 37390 C CL -0.36707 0.00000 0.02084

18 1998 35947 P L -0.41370 -0.01918 0.06414

18 1998 35986 C L -0.52051 -0.01800 0.00080

18 1998 35986 P L -0.52051 -0.01800 -0.01768

18 1998 36020 C L -0.61365 0.02759 0.00929

18 1998 36020 P L -0.61365 0.02759 -0.01108

18 1999 36314 C L -0.41919 0.00000 -0.02914

18 1999 36314 P L -0.41919 0.00000 -0.06075

18 2000 36665 C L -0.38086 0.00152 -0.02886

18 2000 36665 P L -0.38086 0.00152 -0.09794

18 2000 36713 C L -0.51233 0.00266 -0.01591

18 2000 36713 P L -0.51233 0.00266 -0.08673

18 2000 36791 C L -0.72607 -0.00418 -0.06466

18 2000 36791 P L -0.72607 -0.00418 -0.18312

18 2002 37375 C L -0.32605 0.03910 0.02558

18 2002 37375 P L -0.32605 0.03910 -0.01933

18 2002 37522 C L -0.72876 -0.03910 -0.03855

18 2002 37522 P L -0.72876 -0.03910 -0.06442

19 1998 35964 C CH -0.46033 0.04402 -0.00861

19 1998 35964 P CH -0.46033 0.04402 -0.06497

19 1998 35999 C CH -0.55615 -0.07584 -0.07149

19 1998 36038 C CH -0.66296 -0.00610 -0.05167

19 1998 36038 P CH -0.66296 -0.00610 -0.12388

19 1999 36334 C CH -0.47400 0.00000 -0.01876

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
112 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

19 1999 36334 P CH -0.47400 0.00000 -0.02616

19 2000 36643 C CH -0.32056 0.00000 -0.02451

19 2000 36643 P CH -0.32056 0.00000 -0.08400

19 2000 36732 C CL -0.56433 0.00000 0.03490

19 2000 36732 P CL -0.56433 0.00000 -0.03576

19 2001 36997 C CH -0.29041 0.00000 -0.11576

19 2001 36997 P CH -0.29041 0.00000 -0.15670

20 1998 35920 M O -0.33972 0.00222 -0.23924

20 1998 35920 P O -0.33972 0.00222 -0.22079

20 1998 36020 M O -0.61365 -0.01970 -0.09303

20 1998 36053 M O -0.70410 0.00763 -0.15456

20 1998 36053 P O -0.70410 0.00763 -0.14770

20 1999 36426 M O -0.72607 0.00000 -0.08901

20 1999 36426 P O -0.72607 0.00000 -0.10062

20 2000 36756 M O -0.63013 0.00000 -0.10480

20 2000 36756 P O -0.63013 0.00000 -0.12016

20 2001 37027 M O -0.37256 0.00000 -0.11901

20 2001 37027 P O -0.37256 0.00000 -0.11249

20 2002 37511 M O -0.69861 0.00000 -0.10902

22 1999 36361 C L -0.54797 0.06881 0.11260

22 1999 36361 P L -0.54797 0.06881 0.12827

22 1999 36406 C L -0.67126 -0.06881 0.30313

22 1999 36406 P L -0.67126 -0.06881 0.35208

22 2000 36664 P L -0.37805 0.03031 0.02863

22 2000 36754 P L -0.62463 -0.03031 0.10412

22 2001 37008 C L -0.32056 0.00990 -0.06808

22 2001 37084 C L -0.52881 -0.00200 -0.00920

22 2001 37159 C L -0.73425 -0.00790 -0.00819

22 2002 37396 C L -0.38354 -0.02565 0.06410

22 2002 37524 C L -0.73425 0.02565 0.01144

23 1998 35941 C O -0.39722 0.08816 -0.14244

23 1998 35972 C O -0.48218 -0.04036 -0.16794

23 1998 36013 C O -0.59448 -0.04470 -0.13611

23 1998 36013 P O -0.59448 -0.04470 -0.20959

23 1998 36056 C O -0.71228 0.04160 -0.13656

23 1999 36426 C O -0.72607 -0.01095 -0.14380

23 1999 36426 P O -0.72607 -0.01095 -0.19072

23 1999 36447 C O -0.78357 0.01095 -0.14023

23 1999 36447 P O -0.78357 0.01095 -0.17117

23 2000 36651 C O -0.34241 0.02063 -0.07309

23 2000 36651 P O -0.34241 0.02063 -0.22039

23 2000 36713 C O -0.51233 -0.01371 -0.11086

23 2000 36746 C O -0.60278 -0.02754 -0.09204

23 2001 37008 C O -0.32056 0.00000 -0.10034

23 2002 37476 C O -0.60278 0.00000 0.14331

24 1998 35913 C O -0.32056 -0.01688 -0.17682

24 1998 35913 P O -0.32056 -0.01688 -0.23014

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 113

24 1998 35991 C O -0.53430 -0.01457 -0.17169

24 1998 35991 P O -0.53430 -0.01457 -0.25432

24 1998 36040 C O -0.66846 0.03146 -0.08937

24 1998 36040 P O -0.66846 0.03146 -0.18805

24 1999 36369 C O -0.56982 0.00000 -0.07443

24 1999 36369 P O -0.56982 0.00000 -0.18676

24 2001 37082 C O -0.52332 0.00000 -0.14768

24 2001 37082 P O -0.52332 0.00000 -0.20847

24 2002 37449 C O -0.52881 0.00000 -0.12579

24 2002 37449 P O -0.52881 0.00000 -0.19502

25 1998 35927 C O -0.35889 -0.08039 -0.14838

25 1998 35978 C O -0.49866 -0.02322 -0.15110

25 1998 35978 M O -0.49866 -0.02322 -0.18741

25 1998 35978 P O -0.49866 -0.02322 -0.18324

25 1998 36017 C O -0.60547 0.05001 -0.11249

25 1998 36017 M O -0.60547 0.05001 -0.16931

25 1998 36017 P O -0.60547 0.05001 -0.14815

25 1999 36381 C O -0.60278 0.00000 -0.06771

25 1999 36381 P O -0.60278 0.00000 -0.13979

25 2000 36678 C O -0.41638 -0.01999 0.07440

25 2000 36678 M O -0.41638 -0.01999 -0.12259

25 2000 36678 P O -0.41638 -0.01999 -0.02405

25 2000 36713 C O -0.51233 -0.00605 -0.00078

25 2000 36713 M O -0.51233 -0.00605 -0.27653

25 2000 36713 P O -0.51233 -0.00605 -0.13906

25 2000 36734 C O -0.56982 0.02604 -0.08738

25 2000 36734 M O -0.56982 0.02604 -0.17092

25 2000 36734 P O -0.56982 0.02604 -0.14818

27 1998 36055 P L -0.70959 0.00000 -0.00490

27 1999 36335 P L -0.47668 0.00000 -0.06756

27 2000 36650 P L -0.33972 0.00000 -0.06354

27 2001 37005 P L -0.31238 -0.09502 -0.15165

27 2001 37104 P L -0.58362 0.09502 0.03655

28 1998 35963 C CH -0.45752 0.01288 -0.04815

28 1998 35963 M CH -0.45752 0.01288 -0.06516

28 1998 36003 C CH -0.56714 -0.00081 -0.01708

28 1998 36003 M CH -0.56714 -0.00081 -0.02023

28 1998 36038 C CH -0.66296 -0.01208 -0.02529

28 1998 36038 M CH -0.66296 -0.01208 -0.01577

28 2000 36658 C CL -0.36169 0.00964 -0.01990

28 2000 36658 M CL -0.36169 0.00964 0.00460

28 2000 36732 C CH -0.56433 0.02321 -0.00509

28 2000 36732 M CH -0.56433 0.02321 0.02311

28 2000 36763 C CH -0.64929 -0.03285 -0.03099

28 2000 36763 M CH -0.64929 -0.03285 0.01538

28 2001 37047 C CH -0.42737 0.01769 -0.00858

28 2001 37047 M CH -0.42737 0.01769 0.03639

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
114 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

28 2001 37089 C CH -0.54248 -0.01082 -0.00252

28 2001 37089 M CH -0.54248 -0.01082 0.00838

28 2001 37141 C CH -0.68494 -0.01375 -0.05236

28 2002 37375 C CH -0.32605 0.00000 -0.02825

28 2002 37375 M CH -0.32605 0.00000 0.01013

29 1998 35912 M O -0.31775 0.11481 0.04446

29 1998 35912 P O -0.31775 0.11481 0.02159

29 1998 35990 M O -0.53149 0.05681 0.10451

29 1998 35990 P O -0.53149 0.05681 0.07962

29 1998 35990 P O -0.53149 0.05681 0.09663

29 1998 36047 M O -0.68762 -0.20002 -0.06321

29 1998 36047 P O -0.68762 -0.20002 -0.10627

29 1999 36356 M O -0.53430 0.00598 -0.02969

29 1999 36356 P O -0.53430 0.00598 -0.06669

29 1999 36356 P O -0.53430 -0.01195 -0.02820

29 2000 36755 M O -0.62744 0.00000 -0.04691

29 2000 36755 P O -0.62744 0.00000 -0.10536

29 2002 37326 M O -0.19177 0.00000 -0.09419

30 1998 35913 C O -0.32056 -0.05477 0.09960

30 1998 35913 M O -0.32056 -0.05477 0.06589

30 1998 35971 C O -0.47949 0.13311 0.05648

30 1998 35971 M O -0.47949 0.13311 0.05562

30 1998 36041 C O -0.67126 -0.07834 0.08620

30 1998 36041 M O -0.67126 -0.07834 0.07869

30 1999 36425 C O -0.72327 0.00000 0.05759

30 1999 36425 M O -0.72327 0.00000 0.06965

30 2000 36699 C O -0.47400 0.00000 0.04058

30 2000 36699 M O -0.47400 0.00000 0.05107

30 2001 37112 C O -0.60547 0.00000 0.07067

30 2001 37112 M O -0.60547 0.00000 0.07397

30 2002 37379 C O -0.33704 -0.09327 0.09914

30 2002 37379 M O -0.33704 -0.09327 0.10042

30 2002 37531 M O -0.75342 0.18654 0.04320

32 1998 35893 M O -0.26575 -0.11699 -0.10948

32 1998 35893 P O -0.26575 -0.11699 -0.10050

32 1998 35977 M O -0.49585 0.04262 -0.04342

32 1998 35977 P O -0.49585 0.04262 -0.08091

32 1998 36026 M O -0.63013 0.07437 -0.07916

32 1998 36026 P O -0.63013 0.07437 -0.16951

32 1999 36333 M O -0.47119 -0.09069 -0.03523

32 1999 36333 P O -0.47119 -0.09069 -0.10295

32 1999 36370 M O -0.57263 0.03872 0.00408

32 1999 36370 P O -0.57263 0.03872 -0.05989

32 1999 36399 M O -0.65210 0.05197 0.00082

32 1999 36399 P O -0.65210 0.05197 -0.03533

32 2000 36690 M O -0.44934 -0.05263 -0.05668

32 2000 36690 P O -0.44934 -0.05263 -0.11102

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 115

32 2000 36720 M O -0.53149 0.04787 -0.01560

32 2000 36720 P O -0.53149 0.04787 -0.11227

32 2000 36747 M O -0.60547 0.00476 -0.02253

32 2000 36747 P O -0.60547 0.00476 -0.09477

32 2001 37064 M O -0.47400 0.02632 -0.03540

32 2001 37064 P O -0.47400 0.02632 -0.07689

32 2001 37111 M O -0.60278 -0.02632 -0.05415

32 2001 37111 P O -0.60278 -0.02632 -0.14287

32 2002 37455 M O -0.54517 0.00000 -0.04580

34 1998 35902 M O -0.29041 -0.09503 -0.09901

34 1998 35902 P O -0.29041 -0.09503 -0.09455

34 1998 35989 C O -0.52881 0.02633 -0.01112

34 1998 35989 P O -0.52881 0.02633 -0.03492

34 1998 36026 C O -0.63013 0.06869 0.01755

34 1998 36026 P O -0.63013 0.06869 -0.02966

34 1999 36368 C O -0.56714 -0.00347 0.09552

34 1999 36368 M O -0.56714 0.00694 0.05523

34 1999 36368 P O -0.56714 -0.00347 0.05095

34 2000 36690 C O -0.44934 -0.02966 -0.07880

34 2000 36690 M O -0.44934 -0.02966 -0.05604

34 2000 36690 P O -0.44934 -0.02966 -0.20762

34 2000 36752 C O -0.61914 0.02966 -0.05301

34 2000 36752 M O -0.61914 0.02966 -0.04097

34 2000 36752 P O -0.61914 0.02966 -0.12408

34 2001 36983 C O -0.25208 -0.05085 -0.13355

34 2001 36983 P O -0.25208 -0.05085 -0.12670

34 2001 37083 C O -0.52600 0.04689 -0.06602

34 2001 37083 P O -0.52600 0.04689 -0.08590

34 2001 37111 C O -0.60278 0.00793 -0.07806

34 2002 37445 C O -0.51782 0.00000 -0.05737

34 2002 37445 P O -0.51782 0.00000 -0.17210

35 1998 35920 P O -0.33972 -0.03974 -0.03731

35 1998 35970 P O -0.47668 -0.00226 0.13188

35 1998 36048 P O -0.69043 0.04201 -0.02228

35 1999 36333 P O -0.47119 0.00000 0.02400

35 2000 36692 P O -0.45483 0.00000 0.08473

36 1998 35915 M O -0.32605 0.01735 -0.03764

36 1998 35915 P O -0.32605 0.01735 -0.08362

36 1998 35985 M O -0.51782 0.03670 -0.04588

36 1998 35985 P O -0.51782 0.03670 -0.01645

36 1998 36054 M O -0.70691 -0.10810 -0.08212

36 1999 36339 M O -0.48767 0.00000 -0.01617

36 1999 36339 P O -0.48767 0.00000 0.07980

36 2000 36733 M O -0.56714 0.00000 -0.07963

36 2000 36733 P O -0.56714 0.00000 -0.08837

36 2001 37110 M O -0.59998 0.00000 -0.02998

37 1998 35915 M O -0.32605 -0.07468 -0.00980

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
116 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

37 1998 35915 P O -0.32605 -0.07468 -0.01481

37 1998 35977 C O -0.49585 0.00183 -0.00094

37 1998 35977 M O -0.49585 0.00183 0.02739

37 1998 35977 P O -0.49585 0.00183 0.00491

37 1998 36035 C O -0.65479 0.04796 -0.08834

37 1998 36035 M O -0.65479 0.04796 -0.03028

37 1998 36035 P O -0.65479 0.04796 -0.06601

37 1999 36395 C O -0.64111 0.00000 0.01857

37 1999 36395 M O -0.64111 0.00000 0.07231

37 1999 36395 P O -0.64111 0.00000 0.01955

37 2001 37134 C O -0.66577 0.00000 -0.00334

37 2001 37134 M O -0.66577 0.00000 -0.02134

37 2001 37134 P O -0.66577 0.00000 -0.04165

37 2002 37483 C O -0.62195 0.00000 0.00039

38 1998 35892 M O -0.26306 0.06542 -0.21692

38 1998 35892 P O -0.26306 0.06542 -0.17355

38 1998 35977 M O -0.49585 -0.02245 0.10011

38 1998 35977 P O -0.49585 -0.02245 0.14191

38 1998 36021 M O -0.61646 -0.04297 0.13037

38 1998 36021 P O -0.61646 -0.04297 0.17883

38 1999 36341 M O -0.49316 0.00388 0.07460

38 1999 36341 P O -0.49316 0.00388 0.09170

38 1999 36370 M O -0.57263 -0.01278 0.02202

38 1999 36370 P O -0.57263 -0.01278 0.06155

38 1999 36395 M O -0.64111 0.00890 -0.11601

38 1999 36395 P O -0.64111 0.00890 -0.07673

38 2000 36641 M O -0.31506 0.01498 -0.07464

38 2000 36641 P O -0.31506 0.01498 -0.06687

38 2000 36719 M O -0.52881 -0.01319 0.00260

38 2000 36719 P O -0.52881 -0.00901 0.04273

38 2000 36742 M O -0.59180 -0.00388 -0.01299

38 2000 36742 P O -0.59180 -0.00388 0.00006

38 2001 37012 M O -0.33154 -0.02864 -0.14204

38 2001 37012 P O -0.33154 -0.02864 -0.11518

38 2001 37104 M O -0.58362 0.02864 -0.03897

38 2001 37104 P O -0.58362 0.02864 -0.00426

38 2002 37350 M O -0.25757 0.01322 -0.00310

38 2002 37350 P O -0.25757 0.01322 0.03440

38 2002 37483 P O -0.62195 -0.02643 -0.15950

39 1998 36021 C CH -0.61646 -0.00043 0.02896

39 1998 36021 P CH -0.61646 -0.00043 -0.02777

39 1998 36028 C CH -0.63562 0.00043 0.00559

39 1998 36028 P CH -0.63562 0.00043 -0.02159

39 1999 36341 C CL -0.49316 0.02157 -0.00315

39 1999 36341 P CL -0.49316 0.02157 -0.02818

39 1999 36367 C CL -0.56433 -0.01337 0.00581

39 1999 36367 P CL -0.56433 -0.01337 -0.04543

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 117

39 1999 36433 C CL -0.74524 -0.00820 0.03444

39 1999 36433 P CL -0.74524 -0.00820 -0.00933

39 2001 37104 C CL -0.58362 -0.00763 0.00381

39 2001 37153 C CL -0.71777 0.00763 0.01146

39 2002 37326 C CL -0.19177 0.04646 0.13386

39 2002 37526 C CL -0.73975 -0.04646 -0.00149

40 1998 35919 M O -0.33704 -0.01414 0.03471

40 1998 35919 P O -0.33704 -0.01414 0.06507

40 1998 35944 M O -0.40552 0.03383 0.09063

40 1998 35944 P O -0.40552 0.03383 0.09704

40 1998 36010 M O -0.58630 -0.01969 -0.18277

40 1998 36010 P O -0.58630 -0.01969 -0.17033

40 1999 36341 M O -0.49316 0.00000 0.06751

40 1999 36341 P O -0.49316 0.00000 -0.01165

40 2000 36649 M O -0.33704 0.03876 0.00238

40 2000 36719 M O -0.52881 -0.00338 0.12477

40 2000 36719 P O -0.52881 -0.00338 0.12841

40 2000 36740 M O -0.58630 -0.01600 -0.06034

40 2000 36740 P O -0.58630 -0.01600 -0.02622

41 1998 35915 M O -0.32605 0.02071 -0.02982

41 1998 35915 P O -0.32605 0.02071 -0.05458

41 1998 36011 C O -0.58899 -0.01036 0.01720

41 1998 36011 C O -0.58899 -0.01036 0.03482

41 1998 36011 M O -0.58899 -0.01036 -0.06274

41 1998 36011 P O -0.58899 -0.01036 -0.08980

41 1999 36336 C O -0.47949 0.00000 0.05452

41 1999 36336 C O -0.47949 0.00000 0.06561

41 1999 36336 M O -0.47949 0.00000 -0.00085

41 2000 36656 C O -0.35620 0.00354 0.02081

41 2000 36656 C O -0.35620 0.00354 0.03195

41 2000 36656 M O -0.35620 0.00354 -0.03465

41 2000 36656 P O -0.35620 0.00354 -0.10889

41 2000 36740 C O -0.58630 -0.02858 -0.00983

41 2000 36740 M O -0.58630 -0.02858 -0.06010

41 2000 36763 C O -0.64929 0.02150 0.02014

41 2000 36763 M O -0.64929 0.02150 -0.02526

41 2001 37070 C O -0.49036 0.00000 0.04478

41 2001 37070 M O -0.49036 0.00000 -0.01243

43 1998 35958 C O -0.44385 -0.01942 -0.00373

43 1998 35958 M O -0.44385 -0.01942 0.01138

43 1998 35958 P O -0.44385 -0.01942 -0.00318

43 1998 36003 C O -0.56714 -0.00805 -0.01539

43 1998 36003 M O -0.56714 -0.00805 0.00841

43 1998 36003 P O -0.56714 -0.00805 -0.04630

43 1998 36053 C O -0.70410 0.04120 -0.02524

43 1998 36053 M O -0.70410 0.04120 0.00855

43 1999 36336 C O -0.47949 -0.03194 0.00595

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
118 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

43 1999 36336 P O -0.47949 -0.03194 -0.03194

43 1999 36399 C O -0.65210 0.02129 -0.00361

43 1999 36399 M O -0.65210 0.02129 0.00484

43 1999 36399 P O -0.65210 0.02129 -0.01578

43 2000 36657 C O -0.35889 -0.05540 -0.02305

43 2000 36657 M O -0.35889 -0.05540 -0.04686

43 2000 36657 P O -0.35889 -0.05540 -0.03316

43 2000 36720 C O -0.53149 -0.02303 -0.01739

43 2000 36720 M O -0.53149 -0.02303 -0.03230

43 2000 36720 P O -0.53149 -0.02303 -0.08559

43 2000 36747 C O -0.60547 0.07843 -0.00362

43 2000 36747 M O -0.60547 0.07843 -0.02083

43 2000 36747 P O -0.60547 0.07843 -0.08969

43 2001 36984 C O -0.25476 0.07041 -0.02819

43 2001 36984 M O -0.25476 0.07041 -0.06326

43 2001 36984 P O -0.25476 0.07041 -0.20355

43 2001 37103 C O -0.58081 -0.07041 -0.00518

43 2001 37103 M O -0.58081 -0.07041 -0.03839

43 2001 37103 P O -0.58081 -0.07041 -0.04701

43 2002 37419 C O -0.44653 0.01627 -0.03342

43 2002 37419 M O -0.44653 0.01627 -0.09081

43 2002 37419 P O -0.44653 0.01627 -0.14568

43 2002 37526 C O -0.73975 -0.02440 0.00159

43 2002 37526 M O -0.73975 -0.02440 -0.02437

44 1998 35906 C S -0.30139 -0.00953 0.02423

44 1998 35906 P S -0.30139 -0.00953 -0.03810

44 1998 35957 C S -0.44104 -0.01746 -0.04810

44 1998 35957 P S -0.44104 -0.01746 -0.08848

44 1998 36047 C S -0.68762 0.02699 -0.00811

44 1998 36047 P S -0.68762 0.02699 -0.00113

44 1999 36389 C S -0.62463 0.00000 -0.03169

44 1999 36389 P S -0.62463 0.00000 -0.05443

44 2000 36691 C S -0.45203 0.07634 -0.02543

44 2000 36691 P S -0.45203 0.07634 -0.03783

44 2000 36719 C S -0.52881 -0.05481 0.00060

44 2000 36719 P S -0.52881 -0.05481 -0.06587

44 2000 36740 C S -0.58630 -0.02153 0.02561

44 2000 36740 P S -0.58630 -0.02153 -0.07320

44 2001 37012 C S -0.33154 0.00490 0.32234

44 2001 37012 P S -0.33154 0.00490 0.22346

44 2001 37110 P S -0.59998 -0.00980 -0.00130

45 1998 35899 C S -0.28223 0.03772 0.00859

45 1998 35899 P S -0.28223 0.03772 -0.02733

45 1998 35942 C S -0.40002 -0.01882 0.05465

45 1998 35942 P S -0.40002 -0.01882 0.01189

45 1998 36054 P S -0.70691 -0.03779 0.00644

45 1999 36370 P S -0.57263 0.00000 0.00066

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 119

45 2000 36692 P S -0.45483 0.02498 -0.09011

45 2000 36720 P S -0.53149 -0.01910 -0.04506

45 2000 36755 P S -0.62744 -0.00589 -0.00478

45 2001 37012 P S -0.33154 -0.01948 0.01496

45 2001 37063 P S -0.47119 0.02613 0.00680

45 2001 37153 P S -0.71777 -0.00666 0.00764

45 2002 37418 P S -0.44385 0.00000 0.03586

45 2002 37418 P S -0.44385 0.00000 0.03586

46 1998 35892 C O -0.26306 -0.03669 -0.13999

46 1998 35892 M O -0.26306 -0.03669 -0.12578

46 1998 35892 P O -0.26306 -0.03669 -0.18447

46 1998 35915 C O -0.32605 -0.04534 -0.12538

46 1998 35915 M O -0.32605 -0.04534 -0.11691

46 1998 36000 C O -0.55896 0.04173 -0.05542

46 1998 36000 M O -0.55896 0.04173 -0.04937

46 1998 36038 C O -0.66296 0.05865 -0.08706

46 1998 36038 M O -0.66296 0.05865 -0.07657

46 1999 36241 C O -0.21924 0.00000 -0.09851

46 1999 36241 M O -0.21924 0.00000 -0.10631

46 2000 36683 C O -0.43018 0.21789 -0.07870

46 2000 36683 M O -0.43018 0.21789 -0.11213

46 2000 36683 P O -0.43018 0.21789 -0.16174

46 2000 36734 C O -0.56982 -0.13231 -0.02260

46 2000 36734 M O -0.56982 -0.13231 -0.07013

46 2000 36734 P O -0.56982 -0.13231 -0.10914

46 2000 36777 C O -0.68762 -0.12837 -0.06603

46 2000 36777 M O -0.68762 -0.12837 -0.07786

46 2001 36991 C O -0.27393 -0.05698 -0.00751

46 2001 36991 M O -0.27393 -0.05698 -0.02680

46 2001 36991 P O -0.27393 -0.05698 -0.03652

46 2001 37048 C O -0.43018 0.05698 -0.02583

46 2001 37048 M O -0.43018 0.05698 -0.02555

46 2001 37048 P O -0.43018 0.05698 -0.02806

46 2002 37335 C O -0.21643 0.00000 0.03511

46 2002 37335 M O -0.21643 0.00000 0.03470

47 1998 35951 M O -0.42468 -0.01181 -0.06639

47 1998 35951 P O -0.42468 -0.01181 -0.11804

47 1998 36000 M O -0.55896 0.01453 -0.04307

47 1998 36000 P O -0.55896 0.01453 -0.05257

47 1998 36031 M O -0.64380 -0.00272 -0.00693

47 1998 36031 P O -0.64380 -0.00272 -0.02532

47 1999 36241 M O -0.21924 0.00000 0.09185

47 2000 36683 M O -0.43018 0.23889 -0.00366

47 2000 36683 P O -0.43018 0.23889 -0.02320

47 2000 36734 M O -0.56982 -0.16302 0.04921

47 2000 36734 P O -0.56982 -0.16302 -0.01289

47 2000 36777 M O -0.68762 -0.15173 0.06073

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
120 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

47 2001 36991 M O -0.27393 -0.04164 0.11150

47 2001 36991 P O -0.27393 -0.04164 0.11398

47 2001 37057 M O -0.45483 0.02576 0.05344

47 2001 37152 M O -0.71509 0.02876 0.02341

47 2001 37152 P O -0.71509 0.02876 0.01276

47 2002 37335 M O -0.21643 0.09344 0.11375

47 2002 37477 M O -0.60547 -0.04672 0.01829

47 2002 37477 P O -0.60547 -0.04672 -0.01156

48 1998 35928 M O -0.36169 0.00651 -0.08227

48 1998 35928 P O -0.36169 0.00651 -0.09079

48 1998 35965 M O -0.46301 0.02731 -0.09605

48 1998 35965 P O -0.46301 0.02731 -0.09502

48 1998 36054 M O -0.70691 -0.03382 -0.11128

48 1998 36054 P O -0.70691 -0.03382 -0.14045

48 1999 36383 M O -0.60828 0.00000 0.02785

48 1999 36383 P O -0.60828 0.00000 0.01608

48 2000 36663 M O -0.37537 -0.01042 -0.11446

48 2000 36663 P O -0.37537 -0.01042 -0.08091

48 2000 36741 M O -0.58899 0.02083 -0.07902

49 1998 35912 P CL -0.31775 -0.14176 -0.01645

49 1998 35975 C CH -0.49036 -0.02570 0.03045

49 1998 35975 P CH -0.49036 -0.02570 -0.07335

49 1998 36035 C CH -0.65479 0.09658 0.06517

49 1998 36035 P CH -0.65479 0.09658 0.06969

49 2000 36763 C CH -0.64929 0.00000 0.05745

49 2002 37446 C CH -0.52051 0.00000 -0.01932

50 1998 35899 C L -0.28223 0.15796 0.08529

50 1998 35899 M L -0.28223 0.15796 0.06343

50 1998 35961 C L -0.45203 0.06397 0.10151

50 1998 35961 M L -0.45203 0.06397 0.07282

50 1998 36012 C L -0.59180 -0.09491 0.08774

50 1998 36012 M L -0.59180 -0.09491 0.06197

50 1998 36059 C L -0.72058 -0.12703 0.12748

50 1998 36059 M L -0.72058 -0.12703 0.09888

50 1999 36357 C L -0.53699 0.00000 0.02010

50 1999 36357 M L -0.53699 0.00000 -0.01014

50 2000 36662 C L -0.37256 0.00000 0.07850

50 2000 36662 M L -0.37256 0.00000 0.05666

50 2001 37023 C L -0.36169 0.01071 0.06517

50 2001 37118 C L -0.62195 -0.01071 0.06174

51 1998 35906 M CL -0.30139 0.00412 0.03731

51 1998 35906 P CL -0.30139 0.00412 -0.01419

51 1998 35972 M CH -0.48218 -0.05617 -0.05744

51 1998 35972 P CH -0.48218 -0.05617 -0.04982

51 1998 36020 M CH -0.61365 0.05205 0.08083

51 1998 36020 P CH -0.61365 0.05205 0.10009

51 1999 36241 M CH -0.21924 0.00000 0.05227

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 121

51 1999 36241 P CH -0.21924 0.00000 0.02860

51 2000 36678 M CL -0.41638 0.00000 -0.03345

51 2000 36678 P CL -0.41638 0.00000 -0.06131

51 2001 36991 M CH -0.27393 0.00701 -0.01181

51 2001 36991 P CH -0.27393 0.00701 -0.04314

51 2001 37048 M CH -0.43018 -0.00701 -0.02132

51 2001 37048 P CH -0.43018 -0.00701 -0.03733

51 2002 37421 M CH -0.45203 0.00000 -0.07342

51 2002 37421 P CH -0.45203 0.00000 -0.09423

52 1998 35965 C O -0.46301 0.03803 -0.06701

52 1998 35965 M O -0.46301 0.03803 -0.01454

52 1998 35965 P O -0.46301 0.03803 -0.11090

52 1998 35992 C O -0.53699 -0.05608 -0.07144

52 1998 35992 M O -0.53699 -0.05608 -0.03048

52 1998 36034 M O -0.65210 -0.00097 -0.01555

52 1998 36034 P O -0.65210 -0.00097 -0.04616

52 1999 36349 C O -0.51501 0.01640 0.01544

52 1999 36349 M O -0.51501 0.01640 0.01712

52 1999 36405 C O -0.66846 -0.01639 -0.03189

52 1999 36405 M O -0.66846 -0.01639 0.02015

53 1998 35949 M O -0.41919 0.00887 -0.02921

53 1998 35949 P O -0.41919 0.00887 -0.07915

53 1998 35991 C O -0.53430 -0.01463 -0.05392

53 1998 35991 M O -0.53430 -0.01463 -0.07569

53 1998 35991 P O -0.53430 -0.01463 -0.10078

53 1998 36035 C O -0.65479 0.01307 -0.05922

53 1998 36035 M O -0.65479 0.01307 -0.00584

53 1999 36319 C O -0.43286 0.00000 -0.01947

53 1999 36319 M O -0.43286 0.00000 0.00543

53 2000 36649 C O -0.33704 -0.17032 -0.05041

53 2000 36649 M O -0.33704 -0.17032 -0.08559

53 2000 36649 P O -0.33704 -0.17032 -0.14435

53 2000 36712 C O -0.50964 0.04719 -0.09628

53 2000 36712 M O -0.50964 0.04719 -0.12322

53 2000 36733 C O -0.56714 0.13887 -0.08762

53 2000 36733 M O -0.56714 0.13887 -0.09388

53 2000 36733 P O -0.56714 0.13887 -0.13932

53 2001 36982 C O -0.24927 0.18794 -0.03180

53 2001 36982 M O -0.24927 0.18794 -0.05304

53 2001 36982 P O -0.24927 0.18794 -0.13015

53 2001 37070 C O -0.49036 0.04484 0.00200

53 2001 37070 M O -0.49036 0.04484 -0.00067

53 2001 37070 P O -0.49036 0.04484 -0.05252

53 2001 37110 C O -0.59998 -0.23279 -0.01645

53 2001 37110 M O -0.59998 -0.23279 -0.02384

53 2001 37110 P O -0.59998 -0.23279 -0.07836

53 2002 37347 C O -0.24927 -0.12129 0.01196

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
122 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

53 2002 37347 M O -0.24927 -0.12129 -0.02071

53 2002 37445 C O -0.51782 -0.15668 -0.02237

53 2002 37445 M O -0.51782 -0.15668 -0.07524

53 2002 37504 C O -0.67944 0.27798 -0.02458

53 2002 37504 M O -0.67944 0.27798 -0.06998

54 1998 35963 C L -0.45752 0.00344 -0.08591

54 1998 35963 M L -0.45752 0.00344 0.00124

54 1998 36053 C L -0.70410 0.00052 -0.03306

54 1998 36056 C L -0.71228 -0.00741 -0.04055

54 1999 36362 C L -0.55066 0.00000 0.02208

54 1999 36362 M L -0.55066 0.00000 -0.07116

54 2000 36656 C L -0.35620 -0.00080 -0.00863

54 2000 36718 C L -0.52600 0.00080 -0.05343

54 2002 37349 C L -0.25476 0.00000 0.00413

55 1998 35956 C O -0.43835 -0.02975 -0.02357

55 1998 35956 M O -0.43835 -0.02975 -0.01776

55 1998 35998 C O -0.55347 -0.01930 0.00593

55 1998 35998 M O -0.55347 -0.01930 0.01178

55 1998 36035 C O -0.65479 0.04905 0.05321

55 1998 36035 M O -0.65479 0.04905 0.05254

55 2000 36769 C O -0.66577 0.00000 -0.03827

55 2000 36769 M O -0.66577 0.00000 -0.04701

55 2000 36769 P O -0.66577 0.00000 -0.10476

55 2002 37371 C O -0.31506 0.02637 0.06288

55 2002 37371 M O -0.31506 0.02637 0.05842

55 2002 37469 C O -0.58362 -0.02637 -0.27888

55 2002 37469 M O -0.58362 -0.02637 -0.29662

56 1998 35901 C O -0.28772 -0.00876 -0.04331

56 1998 35901 M O -0.28772 -0.00876 -0.04745

56 1998 35956 C O -0.43835 -0.02251 -0.12417

56 1998 35956 M O -0.43835 -0.02251 -0.00799

56 1998 35956 P O -0.43835 -0.02251 -0.08594

56 1998 36046 C O -0.68494 0.04253 0.03642

56 1998 36046 P O -0.68494 0.04253 0.01589

56 2000 36762 C O -0.64661 0.00000 -0.01502

56 2000 36762 M O -0.64661 0.00000 0.00490

56 2001 37036 C O -0.39722 0.17477 0.00858

56 2001 37036 M O -0.39722 0.17477 -0.00475

56 2001 37071 C O -0.49316 -0.09813 -0.05507

56 2001 37071 M O -0.49316 -0.09813 -0.06069

56 2001 37124 C O -0.63831 -0.07665 -0.04357

56 2001 37124 M O -0.63831 -0.07665 -0.04122

56 2002 37343 C O -0.23840 0.00000 -0.04934

56 2002 37343 M O -0.23840 0.00000 -0.03883

58 1998 35954 C O -0.43286 -0.06114 0.00243

58 1998 35990 C O -0.53149 0.00435 0.00195

58 1998 36020 C O -0.61365 0.05679 0.04553

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 123

58 1999 36378 C O -0.59448 -0.01364 0.02563

58 1999 36378 M O -0.59448 0.01364 0.00209

58 2000 36748 C O -0.60828 0.00000 0.05795

58 2001 36999 C O -0.29590 -0.07435 -0.13122

58 2001 37056 C O -0.45203 0.01607 -0.02211

58 2001 37103 C O -0.58081 0.05828 0.04449

58 2002 37335 C O -0.21643 0.01671 0.00935

58 2002 37414 C O -0.43286 0.02851 0.05657

58 2002 37515 C O -0.70959 -0.04522 0.00359

59 1998 35964 M O -0.46033 0.00000 -0.03659

59 1998 35964 P O -0.46033 0.00000 -0.02126

59 1999 36390 M O -0.62744 0.00000 -0.02134

59 1999 36390 P O -0.62744 0.00000 -0.00754

59 2000 36650 P O -0.33972 0.00000 -0.01941

60 1998 35901 C O -0.28772 -0.05101 -0.12792

60 1998 35901 M O -0.28772 -0.05101 -0.10632

60 1998 35901 P O -0.28772 -0.05101 -0.14391

60 1998 35978 C O -0.49866 -0.05830 -0.13664

60 1998 35978 M O -0.49866 -0.05830 -0.10858

60 1998 35978 P O -0.49866 -0.05830 -0.12699

60 1998 36046 C O -0.68494 0.10931 -0.05615

60 1998 36046 M O -0.68494 0.10931 -0.02726

60 1998 36046 P O -0.68494 0.10931 -0.05477

60 1999 36362 C O -0.55066 0.00184 -0.13396

60 1999 36362 C O -0.55066 -0.00551 -0.07437

60 1999 36362 M O -0.55066 0.00184 -0.12944

60 1999 36362 P O -0.55066 0.00184 -0.13821

60 2000 36691 C O -0.45203 0.01173 -0.11634

60 2000 36691 M O -0.45203 0.01173 -0.12156

60 2000 36691 P O -0.45203 0.01173 -0.12880

60 2000 36721 C O -0.53430 -0.00410 -0.10828

60 2000 36721 M O -0.53430 -0.00410 -0.11488

60 2000 36721 P O -0.53430 -0.00410 -0.13504

60 2000 36761 C O -0.64380 -0.00763 -0.14845

60 2000 36761 M O -0.64380 -0.00763 -0.12555

60 2000 36761 P O -0.64380 -0.00763 -0.17566

60 2001 37015 C O -0.33972 -0.02710 -0.05641

60 2001 37015 M O -0.33972 -0.02710 -0.08315

60 2001 37077 C O -0.50964 0.01383 -0.10110

60 2001 37077 M O -0.50964 0.01383 -0.13162

60 2001 37077 P O -0.50964 0.01383 -0.15355

60 2001 37111 C O -0.60278 0.00424 -0.09957

60 2001 37111 M O -0.60278 0.00424 -0.11189

60 2001 37111 P O -0.60278 0.00424 -0.18416

60 2002 37337 C O -0.22192 0.00000 -0.06881

60 2002 37337 M O -0.22192 0.00000 -0.07839

60 2002 37337 P O -0.22192 0.00000 -0.09254

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
124 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

61 1998 35957 C O -0.44104 0.06625 0.07556

61 1998 35957 M O -0.44104 0.06625 0.04864

61 1998 36004 C O -0.56982 -0.01713 0.04873

61 1998 36004 M O -0.56982 -0.01713 0.07527

61 1998 36042 C O -0.67395 -0.04912 0.09141

61 1998 36042 M O -0.67395 -0.04912 0.03882

61 1999 36383 C O -0.60828 0.00000 0.12518

61 1999 36383 M O -0.60828 0.00000 0.06276

61 2000 36691 C O -0.45203 0.00000 0.04196

61 2000 36691 M O -0.45203 0.00000 -0.13644

61 2001 37134 C O -0.66577 0.00000 0.06817

61 2001 37134 M O -0.66577 0.00000 -0.05398

61 2002 37349 C O -0.25476 0.00000 0.11921

61 2002 37349 M O -0.25476 0.00000 -0.05065

62 1998 35928 P L -0.36169 0.23606 0.07680

62 1998 35965 C L -0.46301 -0.04623 -0.07263

62 1998 35965 P L -0.46301 -0.05740 -0.02124

62 1998 36034 C L -0.65210 -0.06682 -0.09913

62 1998 36034 P L -0.65210 -0.06560 -0.04525

62 1999 36433 C L -0.74524 0.00000 -0.10591

62 1999 36433 P L -0.74524 0.00000 -0.03019

62 2000 36663 C L -0.37537 -0.02363 -0.11865

62 2000 36663 P L -0.37537 -0.02363 -0.08589

62 2000 36741 C L -0.58899 0.02363 -0.17355

62 2000 36741 P L -0.58899 0.02363 -0.09266

62 2001 37096 C L -0.56165 0.00000 -0.10514

62 2002 37505 C L -0.68225 0.00000 -0.12991

62 2002 37505 P L -0.68225 0.00000 -0.10086

63 1998 35902 C CL -0.29041 -0.00263 0.02286

63 1998 35949 C CL -0.41919 -0.00633 0.00633

63 1998 36047 C CH -0.68762 0.00897 0.04638

63 1999 36357 C CH -0.53699 0.00000 0.00070

63 2000 36684 C CL -0.43286 -0.03078 0.00315

63 2000 36728 C CL -0.55347 -0.03856 0.00429

63 2000 36761 C CH -0.64380 0.06934 0.01792

63 2001 36998 C CH -0.29309 -0.00652 0.02476

63 2001 37034 C CH -0.39172 -0.00380 0.01592

63 2001 37069 C CH -0.48767 0.01033 0.05193

63 2002 37356 C CH -0.27393 0.00000 -0.05350

64 1998 35921 C O -0.34241 0.00765 0.05196

64 1998 35949 C O -0.41919 -0.00098 -0.00912

64 1998 36047 C O -0.68762 0.00139 0.01860

64 1998 36054 C O -0.70691 -0.00806 0.00703

64 1999 36313 C O -0.41638 -0.00015 0.01297

64 1999 36369 C O -0.56982 0.00015 0.00201

64 2000 36684 C O -0.43286 -0.07952 0.10581

64 2000 36726 C O -0.54797 -0.09311 0.10871

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 125

64 2000 36781 C O -0.69861 0.17263 0.05013

64 2001 37035 C O -0.39453 -0.02652 0.10215

64 2001 37069 C O -0.48767 0.00527 0.10884

64 2002 37355 C O -0.27124 0.00000 -0.10088

65 1998 35900 C O -0.28491 0.06357 -0.00121

65 1998 35900 M O -0.28491 0.06357 0.00426

65 1998 35949 C O -0.41919 -0.24021 -0.02227

65 1998 35949 M O -0.41919 -0.24021 -0.02205

65 1998 36032 C O -0.64661 0.11660 0.00561

65 1998 36032 M O -0.64661 0.11660 0.01598

65 1998 36053 C O -0.70410 0.06004 0.02452

65 1998 36053 M O -0.70410 0.06004 0.03578

65 1999 36313 C O -0.41638 0.02404 0.00305

65 1999 36313 M O -0.41638 0.02404 0.00329

65 1999 36364 C O -0.55615 -0.02404 -0.04332

65 1999 36364 M O -0.55615 -0.02404 -0.04548

65 2000 36685 C O -0.43567 0.00797 0.01664

65 2000 36685 M O -0.43567 0.00797 0.00297

65 2000 36728 C O -0.55347 -0.00797 0.03483

65 2000 36728 M O -0.55347 -0.00797 0.04353

66 1998 35958 C O -0.44385 -0.03269 0.00493

66 1998 35958 M O -0.44385 -0.03269 -0.07850

66 1998 36005 C O -0.57263 -0.00921 0.00880

66 1998 36005 M O -0.57263 -0.00921 -0.03335

66 1998 36017 C O -0.60547 0.04190 0.08651

66 1998 36017 M O -0.60547 0.04190 0.06853

66 1999 36294 C O -0.36438 0.03125 0.00746

66 1999 36294 M O -0.36438 0.03125 -0.00527

66 1999 36362 C O -0.55066 -0.03125 0.00876

66 1999 36362 M O -0.55066 -0.03125 0.00035

66 2000 36665 C O -0.38086 0.02295 -0.00056

66 2000 36665 M O -0.38086 0.02295 0.00196

66 2000 36718 C O -0.52600 0.01046 0.00576

66 2000 36718 M O -0.52600 0.01046 0.01771

66 2000 36754 C O -0.62463 -0.03341 -0.01773

66 2000 36754 M O -0.62463 -0.03341 -0.00684

66 2001 37047 C O -0.42737 0.03410 0.01526

66 2001 37047 M O -0.42737 0.03410 0.00949

66 2001 37091 C O -0.54797 -0.00752 0.02803

66 2001 37091 M O -0.54797 -0.00752 0.03137

66 2001 37141 C O -0.68494 -0.02658 -0.01589

66 2001 37141 M O -0.68494 -0.02658 -0.10140

66 2002 37455 C O -0.54517 0.01357 0.00076

66 2002 37455 M O -0.54517 0.01357 0.00490

66 2002 37488 C O -0.63562 -0.01357 -0.01971

66 2002 37488 M O -0.63562 -0.01357 -0.03345

68 1998 35949 C L -0.41919 -0.03935 0.00270

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
126 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

68 1998 35991 C L -0.53430 -0.01516 0.00793

68 1998 36019 C L -0.61096 0.03731 0.03120

68 1998 36061 C L -0.72607 0.01719 0.02950

68 1999 36327 C L -0.45483 0.00000 0.02030

68 2000 36700 C L -0.47668 0.00000 0.02402

68 2001 37026 C L -0.36987 -0.01239 -0.04210

68 2001 37140 C L -0.68225 0.00818 0.03108

68 2001 37162 C L -0.74243 0.00421 0.02664

68 2002 37370 C L -0.31238 0.05183 0.12284

68 2002 37491 C L -0.64380 -0.05183 -0.16465

69 1998 35942 C O -0.40002 0.04807 0.07612

69 1998 35942 P O -0.40002 0.04807 0.06654

69 1998 36026 C O -0.63013 -0.03650 0.01991

69 1998 36026 P O -0.63013 -0.03650 0.01707

69 1998 36040 C O -0.66846 -0.02316 0.02235

69 2000 36747 C O -0.60547 0.00000 0.00638

69 2001 37083 C O -0.52600 0.00000 0.00388

69 2002 37419 C O -0.44653 0.00000 0.01145

69 2002 37419 P O -0.44653 0.00000 -0.01320

70 1998 35930 C O -0.36707 0.00918 -0.05899

70 1998 35983 C O -0.51233 -0.02482 -0.06150

70 1998 36033 C O -0.64929 0.01563 -0.00722

70 1999 36320 C O -0.43567 0.00000 -0.07959

70 2000 36634 C O -0.29590 0.01736 -0.02805

70 2000 36705 C O -0.49036 -0.03342 -0.02755

70 2000 36755 C O -0.62744 0.01606 -0.03915

70 2001 37008 C O -0.32056 -0.01261 0.10774

70 2001 37105 C O -0.58630 0.01261 -0.13136

70 2002 37449 C O -0.52881 0.00000 -0.15973

72 1998 35948 C O -0.41638 0.05108 -0.04681

72 1998 35948 M O -0.41638 0.05108 -0.06197

72 1998 35992 C O -0.53699 -0.06896 0.00789

72 1998 35992 M O -0.53699 -0.06896 0.00030

72 1998 36041 C O -0.67126 0.01788 0.04300

72 1998 36041 M O -0.67126 0.01788 0.03078

72 1999 36355 C O -0.53149 0.00000 0.01844

72 1999 36355 M O -0.53149 0.00000 0.01465

72 2000 36719 C O -0.52881 0.00000 0.04375

72 2000 36719 M O -0.52881 0.00000 0.02687

72 2001 37070 C O -0.49036 0.02972 -0.00309

72 2001 37070 M O -0.49036 0.02972 -0.01331

72 2001 37140 C O -0.68225 -0.00622 -0.08280

72 2001 37140 M O -0.68225 -0.00622 -0.07093

72 2001 37161 C O -0.73975 -0.02350 -0.07542

72 2001 37161 M O -0.73975 -0.02350 -0.07483

74 1998 35935 C O -0.38086 0.00128 -0.03006

74 1998 35935 M O -0.38086 0.00128 -0.07073

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 127

74 1998 36004 C O -0.56982 -0.02010 0.03412

74 1998 36004 M O -0.56982 -0.02010 0.00203

74 1998 36048 C O -0.69043 0.01883 0.04356

74 1998 36048 M O -0.69043 0.01883 0.01994

74 2000 36686 C O -0.43835 0.00000 0.06349

74 2000 36686 M O -0.43835 0.00000 0.04655

74 2001 37007 C O -0.31775 0.00000 0.01936

74 2001 37007 M O -0.31775 0.00000 0.00088

74 2002 37454 C O -0.54248 0.00000 0.04611

74 2002 37454 M O -0.54248 0.00000 0.03921

75 1998 35914 C O -0.32324 -0.05440 0.04958

75 1998 35914 M O -0.32324 -0.05440 0.03772

75 1998 36004 C O -0.56982 0.02440 0.09893

75 1998 36004 M O -0.56982 0.02440 0.08984

75 1998 36041 C O -0.67126 0.03000 0.10006

75 1998 36041 M O -0.67126 0.03000 0.09780

75 2000 36720 C O -0.53149 0.00000 0.23728

75 2000 36720 M O -0.53149 0.00000 0.22041

77 1998 35997 C O -0.55066 0.05138 0.06565

77 1998 35997 M O -0.55066 0.05138 0.04050

77 1998 36005 C O -0.57263 0.02507 0.05236

77 1998 36005 M O -0.57263 0.02507 0.03482

77 1998 36040 C O -0.66846 -0.07645 0.01598

77 1998 36040 M O -0.66846 -0.07645 0.00017

77 1999 36363 C O -0.55347 0.00000 0.01396

77 1999 36363 M O -0.55347 0.00000 -0.01032

80 1998 35907 C O -0.30408 0.01457 -0.03341

80 1998 35907 M O -0.30408 0.01457 -0.02157

80 1998 35907 P O -0.30408 0.01457 -0.05986

80 1998 35997 C O -0.55066 -0.00651 0.01376

80 1998 35997 M O -0.55066 -0.00651 0.02018

80 1998 36027 C O -0.63293 -0.01534 0.00444

80 1998 36027 M O -0.63293 -0.01534 0.01480

80 1999 36356 C O -0.53430 0.00000 0.03267

80 1999 36356 M O -0.53430 0.00000 0.05556

80 2000 36636 C O -0.30139 -0.00158 -0.04379

80 2000 36636 M O -0.30139 -0.00158 -0.05615

80 2000 36705 C O -0.49036 0.02261 0.06041

80 2000 36705 M O -0.49036 0.02261 0.03923

80 2000 36749 C O -0.61096 -0.02103 0.03136

80 2000 36749 M O -0.61096 -0.02103 0.02986

80 2002 37489 C O -0.63831 0.00000 -0.07111

80 2002 37489 M O -0.63831 0.00000 -0.03775

82 1998 35969 C L -0.47400 0.02927 0.05241

82 1998 35993 C L -0.53967 0.01428 -0.06019

82 1998 36055 C L -0.70959 -0.04355 0.06165

82 2002 37419 C L -0.44653 0.01295 -0.28372

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
128 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

82 2002 37504 C L -0.67944 -0.01295 -0.29824

85 1998 35928 C S -0.36169 -0.07160 0.01924

85 1998 35928 P S -0.36169 -0.07160 -0.00755

85 1998 35970 C S -0.47668 0.18575 -0.00401

85 1998 35970 P S -0.47668 0.18575 -0.03623

85 1998 36024 C S -0.62463 -0.11415 0.00777

85 1998 36024 P S -0.62463 -0.11415 -0.02190

85 1999 36356 C S -0.53430 0.00000 0.01101

85 1999 36356 P S -0.53430 0.00000 -0.02829

85 2000 36685 C S -0.43567 0.00000 0.02764

85 2000 36685 P S -0.43567 0.00000 -0.00970

85 2001 37055 C S -0.44934 0.00000 0.13831

85 2001 37055 P S -0.44934 0.00000 0.07674

86 1998 35920 C S -0.33972 0.11686 0.12724

86 1998 35920 P S -0.33972 0.11686 0.07265

86 1998 35976 C S -0.49316 -0.01654 0.02345

86 1998 35976 P S -0.49316 -0.01654 -0.00815

86 1998 36021 C S -0.61646 -0.05016 0.00882

86 1998 36021 P S -0.61646 -0.05016 -0.01704

86 1998 36062 C S -0.72876 -0.05016 -0.02493

86 1998 36062 P S -0.72876 -0.05016 -0.05069

86 1999 36333 C S -0.47119 0.02715 -0.02060

86 1999 36333 P S -0.47119 0.02715 -0.03794

86 1999 36370 C S -0.57263 -0.02715 -0.02380

86 1999 36370 P S -0.57263 -0.02715 -0.06249

86 2000 36686 C S -0.43835 0.00000 0.02857

86 2000 36686 P S -0.43835 0.00000 -0.02403

86 2001 37055 C S -0.44934 0.00000 -0.00787

86 2001 37055 P S -0.44934 0.00000 -0.05470

86 2002 37378 C S -0.33423 0.00000 0.05279

86 2002 37378 P S -0.33423 0.00000 0.04974

87 1998 35920 C S -0.33972 0.01845 -0.00500

87 1998 35920 P S -0.33972 0.01845 -0.04436

87 1998 35964 C S -0.46033 0.03775 -0.01004

87 1998 35964 P S -0.46033 0.03775 -0.05098

87 1998 36026 C S -0.63013 -0.00749 0.00042

87 1998 36026 P S -0.63013 -0.00749 -0.03106

87 1998 36062 C S -0.72876 -0.04870 -0.00978

87 1998 36062 P S -0.72876 -0.04870 -0.07171

87 1999 36370 C S -0.57263 0.00000 -0.00356

87 1999 36370 P S -0.57263 0.00000 -0.06126

87 2000 36657 C S -0.35889 0.01642 0.01170

87 2000 36657 P S -0.35889 0.01642 -0.04218

87 2000 36735 C S -0.57263 -0.00460 0.01058

87 2000 36735 P S -0.57263 -0.00460 -0.04145

87 2000 36782 C S -0.70142 -0.01182 0.00896

87 2000 36782 P S -0.70142 -0.01182 -0.04865

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 129

87 2001 37070 C S -0.49036 0.00731 0.00913

87 2001 37070 P S -0.49036 0.00731 -0.05677

87 2001 37113 C S -0.60828 0.00308 0.00122

87 2001 37113 P S -0.60828 0.00308 -0.01502

87 2001 37140 C S -0.68225 -0.01039 0.00179

87 2001 37140 P S -0.68225 -0.01039 -0.04073

87 2002 37379 C S -0.33704 0.00000 0.02893

87 2002 37379 P S -0.33704 0.00000 0.02128

89 1998 35920 C O -0.33972 0.05172 -0.05320

89 1998 35920 M O -0.33972 0.05172 -0.00642

89 1998 35950 C O -0.42188 -0.00729 -0.06542

89 1998 35950 M O -0.42188 -0.00729 -0.02064

89 1998 36048 C O -0.69043 -0.04443 -0.02333

89 1998 36048 M O -0.69043 -0.04443 -0.00081

89 1999 36322 C O -0.44104 -0.06666 -0.02988

89 1999 36322 M O -0.44104 -0.06666 0.00917

89 1999 36370 C O -0.57263 0.06666 0.00641

89 1999 36370 M O -0.57263 0.06666 0.02084

89 2000 36720 C O -0.53149 0.00000 0.00091

89 2000 36720 M O -0.53149 0.00000 0.00416

90 1998 35922 C S -0.34521 0.00987 0.02245

90 1998 35922 P S -0.34521 0.00987 0.01024

90 1998 35977 C S -0.49585 0.00735 -0.00600

90 1998 35977 P S -0.49585 0.00735 -0.01090

90 1998 36021 C S -0.61646 -0.01721 0.02442

90 1998 36021 P S -0.61646 -0.01721 0.03139

90 1999 36356 C S -0.53430 0.00000 0.00370

90 1999 36356 P S -0.53430 0.00000 -0.00510

90 2000 36686 C S -0.43835 0.00000 -0.00233

90 2000 36686 P S -0.43835 0.00000 -0.02487

90 2001 37055 C S -0.44934 0.00000 -0.01303

90 2002 37379 C S -0.33704 0.00000 0.01676

90 2002 37379 P S -0.33704 0.00000 0.00066

92 1998 35920 C S -0.33972 0.02033 -0.05589

92 1998 35920 P S -0.33972 0.02033 -0.08173

92 1998 35964 C S -0.46033 -0.00860 0.01871

92 1998 35964 P S -0.46033 -0.00860 0.00602

92 1998 36053 C S -0.70410 -0.00564 -0.00113

92 1998 36053 P S -0.70410 -0.00564 -0.02991

92 1998 36060 C S -0.72327 -0.00609 0.00150

92 1998 36060 P S -0.72327 -0.00609 -0.01053

92 1999 36333 C S -0.47119 0.00903 -0.01883

92 1999 36333 P S -0.47119 0.00903 -0.05901

92 1999 36370 C S -0.57263 -0.00903 0.00273

92 1999 36370 P S -0.57263 -0.00903 -0.04109

92 2000 36643 C S -0.32056 0.01414 -0.04073

92 2000 36643 P S -0.32056 0.01414 -0.09805

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
130 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

92 2000 36719 C S -0.52881 -0.00841 -0.03239

92 2000 36719 P S -0.52881 -0.00841 -0.09803

92 2000 36782 C S -0.70142 -0.00572 -0.03481

92 2000 36782 P S -0.70142 -0.00572 -0.09454

92 2001 37012 C S -0.33154 0.01395 -0.04598

92 2001 37012 P S -0.33154 0.01395 -0.12425

92 2001 37126 C S -0.64380 -0.00866 -0.03281

92 2001 37126 P S -0.64380 -0.00866 -0.07241

92 2001 37168 C S -0.75891 -0.01059 0.03738

92 2002 37386 C S -0.35620 0.00000 -0.03259

92 2002 37386 P S -0.35620 0.00000 -0.03110

95 1998 35921 C CL -0.34241 -0.01124 0.05577

95 1998 35990 C CL -0.53149 0.17900 0.10340

95 1998 35992 C CH -0.53699 -0.09033 -0.04192

95 1998 35992 P CH -0.53699 -0.09033 -0.10021

95 1998 36035 C CH -0.65479 0.00811 -0.05039

95 1998 36035 P CH -0.65479 0.00811 -0.19536

95 1998 36047 C CL -0.68762 -0.00332 0.07318

95 1999 36319 C CL -0.43286 0.00000 0.12535

95 2000 36635 C CL -0.29858 0.02963 0.12811

95 2000 36649 C CH -0.33704 0.00337 -0.03667

95 2000 36719 C CH -0.52881 -0.03300 -0.04608

95 2001 36991 C CH -0.27393 -0.07382 -0.00880

95 2001 37064 C CL -0.47400 0.07382 0.15634

97 1998 35929 C CH -0.36438 -0.02088 -0.05226

97 1998 35929 C CL -0.36438 -0.05636 0.06462

97 1998 35984 C CH -0.51501 0.02396 0.00692

97 1998 35984 C CL -0.51501 -0.01196 0.09030

97 1998 36029 C CH -0.63831 0.04547 0.02230

97 1998 36029 C CL -0.63831 0.01977 0.11026

97 1999 36369 C CH -0.56982 0.00854 -0.03563

97 1999 36369 C CH -0.56982 -0.00854 0.00221

97 2000 36692 C CL -0.45483 0.00000 0.04844

97 2001 37119 C CH -0.62463 0.00000 0.03911

97 2002 37448 C CL -0.52600 0.00000 0.15621

98 1998 35927 C CH -0.35889 -0.00720 -0.04986

98 1998 35927 C CL -0.35889 -0.04553 -0.03415

98 1998 35984 C CL -0.51501 0.01463 0.01183

98 1998 36047 C CH -0.68762 0.03910 -0.07133

98 1998 36047 C CL -0.68762 0.00339 -0.05497

98 1998 36056 C CL -0.71228 -0.00437 -0.05162

98 1999 36320 C CH -0.43567 0.00000 0.02019

98 2000 36651 C CH -0.34241 0.00000 0.00539

98 2001 37011 C CL -0.32874 -0.01313 -0.01908

98 2001 37083 C CL -0.52600 0.01313 0.02189

98 2002 37356 C CL -0.27393 0.00000 -0.02837

99 1998 35928 C CH -0.36169 0.08167 -0.29434

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 131

99 1998 35928 C CL -0.36169 -0.03013 -0.10848

99 1998 35976 C CH -0.49316 0.07261 -0.29709

99 1998 35976 M CH -0.49316 0.07261 -0.29729

99 1998 35976 C CL -0.49316 -0.04074 -0.10556

99 1998 35976 M CL -0.49316 -0.04074 -0.10548

99 1998 36061 C CH -0.72607 0.01668 -0.27965

99 1998 36061 M CH -0.72607 0.01668 -0.28421

99 1998 36061 C CL -0.72607 -0.07432 -0.09503

99 1998 36061 M CL -0.72607 -0.07432 -0.09921

99 2000 36735 C CH -0.57263 0.00000 -0.22929

99 2000 36735 M CH -0.57263 0.00000 -0.24686

99 2001 37007 C CL -0.31775 0.00000 -0.15399

99 2001 37007 M CL -0.31775 0.00000 -0.16715

99 2002 37385 C CH -0.35339 0.00000 -0.02862

99 2002 37385 M CH -0.35339 0.00000 -0.02358

100 1998 35942 C CL -0.40002 0.08071 -0.05098

100 1998 35942 C CL -0.40002 0.03442 -0.05035

100 1998 35942 M CL -0.40002 0.08071 -0.05928

100 1998 35942 M CL -0.40002 0.03442 -0.05662

100 1998 35970 C CL -0.47668 0.03616 -0.03449

100 1998 35970 M CL -0.47668 0.03616 -0.03753

100 1998 36033 C CL -0.64929 -0.05538 -0.01676

100 1998 36033 C CL -0.64929 -0.09590 -0.01611

100 1998 36033 M CL -0.64929 -0.05538 -0.02389

100 1998 36033 M CL -0.64929 -0.09590 -0.02534

100 2001 36998 C CL -0.29309 0.03920 0.03226

100 2001 36998 M CL -0.29309 0.03920 0.00674

100 2001 37091 C CL -0.54797 -0.00508 0.03554

100 2001 37091 M CL -0.54797 -0.00508 0.03258

100 2001 37160 C CL -0.73694 -0.03412 0.03304

100 2001 37160 M CL -0.73694 -0.03412 0.04228

100 2002 37349 C CL -0.25476 0.00000 0.02800

100 2002 37349 M CL -0.25476 0.00000 0.02517

101 1998 35935 C CH -0.38086 0.02511 -0.00629

101 1998 35935 M CH -0.38086 0.02511 -0.01792

101 1998 35935 C CL -0.38086 0.02593 0.33309

101 1998 35935 M CL -0.38086 0.02593 0.31631

101 1998 35991 C CH -0.53430 0.01777 0.04852

101 1998 35991 M CH -0.53430 0.01777 0.03810

101 1998 35991 C CL -0.53430 0.01939 0.36417

101 1998 35991 M CL -0.53430 0.01939 0.35523

101 1998 36025 C CH -0.62744 -0.04525 -0.01336

101 1998 36025 M CH -0.62744 -0.04525 -0.02837

101 1998 36025 C CL -0.62744 -0.04295 0.33284

101 1998 36025 M CL -0.62744 -0.04295 0.31705

101 1999 36364 C CH -0.55615 0.00000 -0.04895

101 1999 36364 M CH -0.55615 0.00000 -0.04789

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
132 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

101 2000 36672 C CL -0.40002 0.00000 -0.14525

101 2000 36672 M CL -0.40002 0.00000 -0.15671

102 1998 35934 C CH -0.37805 0.12406 -0.08510

102 1998 35934 M CH -0.37805 0.12406 -0.09845

102 1998 35934 C CL -0.37805 0.04579 0.09149

102 1998 35934 M CL -0.37805 0.04579 0.07787

102 1998 35985 C CH -0.51782 -0.06301 -0.05045

102 1998 35985 C CL -0.51782 -0.11184 0.11712

102 1998 36067 C CH -0.74243 -0.05878 -0.04798

102 1998 36067 C CL -0.74243 -0.10608 0.11932

102 1999 36335 C CH -0.47668 0.00000 -0.04641

102 2000 36747 C CH -0.60547 0.00000 -0.03486

102 2001 37105 C CH -0.58630 0.00000 0.02804

102 2002 37420 C CL -0.44934 0.00000 0.12364

103 1998 35913 C CH -0.32056 -0.03622 -0.15357

103 1998 35913 P CH -0.32056 -0.03622 -0.16847

103 1998 35913 C CL -0.32056 -0.06803 0.16947

103 1998 35913 P CL -0.32056 -0.06803 0.15650

103 1998 35963 C CH -0.45752 0.01171 -0.03696

103 1998 35963 P CH -0.45752 0.01171 -0.03027

103 1998 35963 C CL -0.45752 -0.04854 0.23740

103 1998 35963 P CL -0.45752 -0.04854 0.24286

103 1998 36039 C CH -0.66577 0.11026 -0.03775

103 1998 36039 P CH -0.66577 0.11026 -0.03417

103 1998 36039 C CL -0.66577 0.03082 0.24565

103 1998 36039 P CL -0.66577 0.03082 0.24700

103 1999 36329 C CH -0.46033 0.00000 -0.06152

103 1999 36329 P CH -0.46033 0.00000 -0.09344

103 2000 36693 C CH -0.45752 0.00000 0.01504

103 2000 36693 P CH -0.45752 0.00000 -0.00004

103 2001 37062 C CH -0.46851 0.00000 -0.02854

103 2001 37062 P CH -0.46851 0.00000 -0.01100

103 2002 37413 C CH -0.43018 0.00000 0.00739

103 2002 37413 P CH -0.43018 0.00000 0.01843

104 1998 35922 C CL -0.34521 -0.00232 0.07515

104 1998 35922 C CL -0.34521 -0.01096 0.06378

104 1998 35922 M CL -0.34521 -0.00232 0.03242

104 1998 35922 M CL -0.34521 -0.01096 0.02366

104 1998 35964 C CL -0.46033 -0.01249 0.03078

104 1998 35964 C CL -0.46033 -0.01497 0.04518

104 1998 35964 M CL -0.46033 -0.01249 0.00768

104 1998 35964 M CL -0.46033 -0.01497 0.01454

104 1998 36021 C CL -0.61646 0.03241 0.02811

104 1998 36021 C CL -0.61646 0.00834 0.03840

104 1998 36021 M CL -0.61646 0.03241 0.01044

104 1998 36021 M CL -0.61646 0.00834 0.01924

104 1999 36334 C CL -0.47400 0.00000 0.06262

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w
Supplemental Information 133

104 1999 36334 M CL -0.47400 0.00000 0.05463

104 2000 36649 C CL -0.33704 0.00000 0.09621

104 2000 36649 M CL -0.33704 0.00000 0.06678

104 2001 37013 C CL -0.33423 0.00000 0.09991

104 2001 37013 M CL -0.33423 0.00000 0.09300

104 2002 37379 C CL -0.33704 0.00000 0.08372

104 2002 37379 M CL -0.33704 0.00000 0.03706

105 1998 35927 C CH -0.35889 0.09445 -0.11233

105 1998 35927 C CH -0.35889 -0.01767 0.05727

105 1998 35992 C CH -0.53699 0.03005 -0.09859

105 1998 35992 C CH -0.53699 -0.04483 0.07037

105 1998 35992 C CL -0.53699 -0.04806 0.07992

105 1998 36042 C CH -0.67395 0.03213 -0.10282

105 1998 36042 C CL -0.67395 -0.04605 0.10715

105 1999 36335 C CH -0.47668 0.00000 -0.02714

105 2000 36649 C CH -0.33704 0.00000 -0.02359

105 2001 37064 C CH -0.47400 0.00000 0.03508

105 2002 37492 C CH -0.64661 0.00000 -0.04185

106 1998 35955 C CL -0.43567 -0.02890 0.06690

106 1998 36011 C CL -0.58899 -0.01585 0.12908

106 1998 36055 C CL -0.70959 0.02880 0.06360

106 1998 36055 C CL -0.70959 0.01595 0.07444

106 2001 37162 C CL -0.74243 0.00000 0.11939

106 2002 37372 C CL -0.31775 0.00000 -0.03194

Table 14. Data used in the diffP model where PCC measurements and power consumption were made in 

the same year.—Continued 

[PCC, power conversion coefficient; Date, number of days from January 1, 1900; C, Collins flowmeter; 

P, Polysonic flowmeter; M, McCrometer flowmeter; O, open; CL, complex low; CH, complex high; L, low pressure; 

S, sprinkler; u, the diffP lag time; , average log pumping water level for a given site in a given year; , log of pumping 

water level at time of measurement; diffP, log total pumpage using PCC minus log total pumpage using totalizing flowmeter]

Site Year Date Method Type u - diffP

w w

w w

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years. 

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

1 1998 2002 35950 C O 3.57812 0.18427 0.15119

1 1998 2000 35950 P O 1.57812 -0.00445 0.03757

1 1998 2002 35989 C O 3.47119 0.17663 0.10980

1 1998 1999 35989 M O 0.47119 -0.15165 0.02273

1 1998 2002 35989 P O 3.47119 0.17663 0.04991

1 1998 2001 36026 C O 2.36987 0.14940 0.04652

1 1998 2000 36026 M O 1.36987 0.03756 0.00878

1 1998 1999 36026 P O 0.36987 -0.10199 0.00125

1 1999 2002 36343 C O 2.50134 0.25207 0.14345

w

w

w w
134 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

1 1999 2001 36343 P O 1.50134 0.17519 0.07672

1 1999 1998 36369 C O -1.56982 0.14873 0.07851

1 1999 2001 36369 P O 1.43018 0.26900 0.12056

1 1999 2001 36397 C O 1.35339 0.31000 0.02742

1 1999 2002 36397 P O 2.35339 0.38688 0.06168

1 2000 2002 36650 C O 1.66028 0.14933 0.09823

1 2000 2001 36650 P O 0.66028 0.07244 0.03106

1 2000 1999 36727 C O -1.55066 -0.13771 0.11383

1 2000 2001 36727 P O 0.44934 0.11368 0.07514

1 2000 1998 36752 C O -2.61914 0.02912 0.05949

1 2000 1999 36752 P O -1.61914 -0.10199 0.08288

1 2001 1998 36990 C O -3.27124 -0.22057 -0.09480

1 2001 2000 36990 P O -1.27124 -0.21214 -0.07594

1 2001 2002 37084 C O 0.47119 0.14597 0.15051

1 2001 2002 37084 P O 0.47119 0.14597 0.13001

1 2001 2002 37111 C O 0.39722 0.10810 0.09436

1 2001 1998 37111 P O -3.60278 -0.08906 -0.01785

1 2002 1999 37351 C O -3.26025 -0.37133 -0.00641

1 2002 1998 37351 P O -4.26025 -0.24021 -0.08113

1 2002 2001 37449 C O -1.52881 -0.06277 -0.00814

1 2002 2001 37449 P O -1.52881 -0.06277 -0.03427

1 2002 2000 37476 C O -2.60278 -0.15980 0.02539

1 2002 1998 37476 P O -4.60278 -0.16824 -0.03290

2 1998 2001 35936 C CL 2.61646 -0.01317 0.13261

2 1998 2001 35936 P CL 2.61646 -0.01317 0.13248

2 1998 2000 36048 C CL 1.30957 -0.07599 0.09064

2 1998 1999 36048 P CL 0.30957 -0.10800 0.08759

2 1998 1999 36052 C CL 0.29858 -0.09984 0.10497

2 1998 2000 36052 P CL 1.29858 -0.06782 0.05492

2 1999 2001 36342 C CH 1.50415 0.10587 0.05536

2 1999 2001 36342 P CH 1.50415 0.10587 0.04757

2 1999 1998 36348 C CL -1.51233 0.05463 0.01488

2 1999 2002 36348 P CL 2.48767 0.12260 0.04388

2 2000 1998 36692 C CL -2.45483 0.06336 -0.01588

2 2000 1999 36692 P CL -1.45483 -0.03201 0.16072

2 2001 2002 37062 C CH 0.53149 0.16705 -0.14483

2 2001 1998 37062 P CH -3.46851 0.09908 -0.17562

2 2001 2002 37082 C CL 0.47668 0.08841 -0.06842

2 2001 2000 37082 P CL -1.52332 -0.04293 -0.03242

2 2001 2000 37123 C CL -1.63562 -0.09212 0.05699

2 2001 2002 37123 P CL 0.36438 0.03922 0.04338

2 2002 1999 37337 C CH -3.22192 -0.16335 0.12931

2 2002 2000 37337 P CH -2.22192 -0.13134 0.02373

3 1998 2000 35975 C O 1.50964 0.06243 -0.04239

3 1998 2002 35975 P O 3.50964 0.12923 0.12303

3 1998 2002 36000 C O 3.44104 0.12784 0.12206

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 135

3 1998 2000 36000 P O 1.44104 0.06104 -0.12730

3 1998 2002 36053 C O 3.29590 0.25859 0.02114

3 1998 2000 36053 P O 1.29590 0.19179 -0.18642

3 1999 2001 36348 C O 1.48767 0.12683 0.05209

3 1999 2002 36348 P O 2.48767 0.17635 0.04214

3 1999 1998 36367 C O -1.56433 0.05238 0.10617

3 1999 2001 36367 P O 1.43567 0.17475 0.12774

3 1999 2001 36395 C O 1.35889 0.15651 0.05498

3 1999 1998 36395 P O -1.64111 0.03414 -0.02966

3 2000 2002 36699 C O 1.52600 0.07099 0.15357

3 2000 1998 36720 C O -2.53149 -0.11137 0.09545

3 2000 2002 36720 P O 1.46851 0.06052 0.16420

3 2000 2002 36739 C O 1.41638 0.07099 0.18728

3 2000 1998 36739 P O -2.58362 -0.10090 -0.11898

3 2001 1998 36986 C O -3.26025 -0.18659 0.02471

3 2001 2000 36986 P O -1.26025 -0.08151 -0.01556

3 2001 2002 37069 C O 0.51233 0.07099 0.22907

3 2001 2000 37069 P O -1.48767 0.00419 -0.12312

3 2001 2000 37104 C O -1.58362 0.02547 -0.02529

3 2001 1999 37104 P O -2.58362 -0.10995 -0.12936

3 2002 2001 37328 C O -1.19727 -0.02481 -0.00155

3 2002 1999 37448 C O -3.52600 -0.20721 -0.12675

3 2002 1999 37448 P O -3.52600 -0.20721 -0.19516

3 2002 2000 37449 C O -2.52881 -0.08151 -0.11725

5 1998 2001 35934 C CH 2.62195 -0.36090 0.15030

5 1998 2002 35934 P CH 3.62195 0.09438 -0.09783

5 1998 2001 35975 C CH 2.50964 -0.38631 0.01037

5 1998 2002 35975 P CH 3.50964 0.06897 -0.03537

5 1998 2002 36038 C CH 3.33704 0.10788 -0.07271

5 1998 1999 36038 P CH 0.33704 -0.13976 -0.06126

5 1998 1999 36061 C CH 0.27393 0.19693 -0.01538

5 1998 2002 36061 P CH 3.27393 0.44457 -0.12557

5 1999 2002 36333 C CH 2.52881 0.24764 -0.08811

5 1999 1998 36333 P CH -1.47119 0.06869 -0.06348

5 2001 1998 37057 C CL -3.45483 0.27633 0.22464

5 2001 1999 37057 P CL -2.45483 0.20764 0.08414

5 2002 2001 37385 C CH -1.35339 -0.43078 -0.00826

5 2002 1998 37424 C CL -4.46033 -0.17915 0.11808

5 2002 1999 37461 C CL -3.56165 -0.27193 0.05990

7 1998 1999 35937 M CL 0.61365 -0.17625 -0.22276

7 1998 2000 35937 P CL 1.61365 -0.04272 -0.18742

7 1998 1999 35999 M CL 0.44385 -0.17096 -0.02394

7 1998 2000 35999 P CL 1.44385 -0.03743 -0.03723

7 1998 2000 36028 M CL 1.36438 0.03888 -0.00684

7 1998 2000 36028 P CL 1.36438 0.03888 0.00149

7 1999 1998 36406 M CL -1.67126 0.14729 -0.16335

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
136 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

7 1999 2002 36406 P CL 2.32874 0.32464 -0.06260

7 2000 2002 36672 P CH 1.59998 0.19111 -0.13194

7 2002 2000 37573 M CL -2.86853 -0.19111 -0.27913

8 1998 2002 35905 P L 3.70142 0.07526 0.07119

8 1998 2002 35975 C L 3.50964 0.14734 0.15006

8 1998 2002 35975 P L 3.50964 0.14734 0.10390

8 1998 2002 36031 C L 3.35620 0.22941 0.15723

8 1998 1999 36031 P L 0.35620 0.02362 -0.04915

8 1999 2002 36299 C L 2.62195 0.20579 0.16444

8 1999 2000 36299 P L 0.62195 0.01947 -0.01999

8 2000 1998 36713 C L -2.51233 0.02058 -0.02656

8 2000 2002 36713 P L 1.48767 0.18633 0.01902

8 2002 1998 37379 C L -4.33704 -0.16575 -0.03030

8 2002 1999 37379 P L -3.33704 -0.20579 -0.20733

9 1999 2001 36340 M O 1.50964 0.07899 -0.10472

9 1999 2000 36340 P O 0.50964 -0.03760 -0.16679

9 1999 2001 36370 M O 1.42737 0.08586 -0.11276

9 1999 2001 36370 P O 1.42737 0.08586 -0.12953

9 2000 2001 36630 M O 0.71509 0.19506 -0.10228

9 2000 1999 36734 M O -1.56982 0.00689 -0.12387

9 2000 2001 36790 M O 0.27673 0.06538 -0.11878

9 2001 1999 37063 M O -2.47119 -0.08242 -0.21714

9 2001 1999 37063 P O -2.47119 -0.08242 -0.28283

11 1998 2000 35947 M O 1.58630 -0.08043 -0.09408

11 1998 2000 35947 P O 1.58630 -0.08043 -0.08877

11 1998 1999 35998 M O 0.44653 -0.09602 -0.10040

11 1998 1999 35998 P O 0.44653 -0.09602 -0.11055

11 1998 1999 36020 M O 0.38635 -0.01843 -0.04162

11 1998 2001 36020 P O 2.38635 0.07486 -0.00933

11 1999 2000 36355 M O 0.46851 -0.04102 -0.03156

11 2000 1999 36698 M O -1.47119 0.04102 -0.14259

11 2000 2001 36698 P O 0.52881 0.13431 -0.01516

11 2001 1998 36993 M O -3.27942 -0.04201 -0.07929

11 2001 1998 36993 P O -3.27942 -0.04201 -0.09023

12 1998 2001 35935 M O 2.61914 0.05659 0.01045

12 1998 2001 35935 P O 2.61914 0.05659 -0.01056

12 1998 2000 35982 M O 1.49036 -0.08829 -0.00472

12 1998 2001 35982 P O 2.49036 0.05000 0.02425

12 1998 2000 36014 M O 1.40271 -0.07791 0.02618

12 1998 2000 36061 M O 1.27393 -0.02031 -0.03526

12 1999 2000 36362 M O 0.44934 -0.00154 0.02934

12 1999 1998 36362 P O -1.55066 0.07150 -0.01284

12 2000 2001 36630 M O 0.71509 0.13829 -0.01099

12 2000 2001 36630 P O 0.71509 0.13829 -0.05226

12 2001 2000 37025 M O -1.36707 -0.11150 -0.00530

12 2001 2000 37082 M O -1.52332 -0.16508 -0.05401

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 137

14 1998 2000 35944 C L 1.59448 0.06738 0.04597

14 1998 2000 35944 P L 1.59448 0.06738 0.04181

14 1998 2000 35975 C L 1.50964 0.05339 0.03592

14 1998 2000 35975 P L 1.50964 0.05339 0.04101

14 1998 2000 36055 C L 1.29041 0.03789 0.00574

14 1998 1999 36055 P L 0.29041 -0.03448 -0.03281

14 1999 2000 36348 C L 0.48767 0.09595 0.03402

14 1999 1998 36348 P L -1.51233 0.04307 -0.03283

14 1999 2000 36406 C L 0.32874 0.08156 0.00883

14 1999 1998 36406 P L -1.67126 0.02868 -0.05678

14 1999 2000 36447 C L 0.21643 0.03960 -0.03174

14 1999 2000 36447 P L 0.21643 0.03960 -0.05229

14 2000 1999 36648 C L -1.33423 -0.08091 -0.14551

14 2000 1998 36648 P L -2.33423 -0.06142 -0.22059

14 2000 1999 36733 C L -1.56714 -0.06645 -0.14524

14 2000 1999 36733 P L -1.56714 -0.06645 -0.18069

14 2000 1999 36768 C L -1.66296 -0.06975 -0.13509

14 2000 1999 36768 P L -1.66296 -0.06975 -0.17802

15 1998 2001 35948 M O 2.58362 -0.01263 0.18878

15 1998 2001 35948 P O 2.58362 -0.01263 0.18334

15 1998 2001 35968 C O 2.52881 -0.02104 0.22468

15 1998 2001 35968 M O 2.52881 -0.02104 0.22056

15 1998 2001 36006 C O 2.42468 0.01477 0.21764

15 1998 1999 36006 M O 0.42468 -0.09302 0.03397

15 1999 1998 36335 C O -1.47668 0.13340 0.06402

15 1999 2001 36335 M O 1.52332 0.12710 0.23441

15 1999 2000 36335 P O 0.52332 0.07476 0.05541

15 1999 1998 36384 C O -1.61096 0.04212 0.08099

15 1999 2000 36384 M O 0.38904 -0.01652 0.09240

15 1999 2000 36432 C O 0.25757 0.08413 0.13150

15 1999 1998 36432 M O -1.74243 0.14277 0.10591

15 1999 1998 36432 P O -1.74243 0.14277 0.09723

15 2000 2001 36636 C O 0.69861 0.05407 0.22534

15 2000 1999 36636 M O -1.30139 -0.05372 0.02657

15 2000 1999 36636 P O -1.30139 -0.05372 0.01605

15 2000 1998 36706 C O -2.49316 0.10053 0.09088

15 2000 2001 36706 M O 0.50684 0.09423 0.22457

15 2000 2001 36749 C O 0.38904 0.00785 0.16986

15 2000 2001 36749 M O 0.38904 0.00785 0.16585

15 2001 2000 37007 C O -1.31775 0.00137 0.01471

15 2001 2000 37007 M O -1.31775 0.00137 0.00036

15 2001 2000 37069 C O -1.48767 -0.03757 -0.01688

15 2001 1999 37069 M O -2.48767 -0.09302 -0.06722

15 2001 2000 37118 C O -1.62195 -0.12081 -0.03049

15 2001 1999 37118 M O -2.62195 -0.17627 -0.05607

16 1998 2001 35936 C CH 2.61646 0.13700 0.07128

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
138 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

16 1998 1999 35936 P CH 0.61646 -0.05082 -0.06407

16 1998 2001 35942 C CL 2.59998 0.08485 0.04324

16 1998 2002 35942 P CL 3.59998 0.23367 0.23426

16 1998 1999 35982 C CL 0.49036 0.03369 -0.00168

16 1998 2002 35982 P CL 3.49036 0.37034 0.32692

16 1998 1999 36017 C CL 0.39453 -0.00519 -0.02305

16 1998 1999 36017 P CL 0.39453 -0.00519 -0.05288

16 1998 2001 36056 C CH 2.28772 0.15236 0.08947

16 1998 2002 36056 P CH 3.28772 0.30118 0.28820

16 1999 2002 36321 C CL 2.56165 0.28582 0.27451

16 1999 2002 36321 P CL 2.56165 0.28582 0.26511

16 1999 1998 36357 C CH -1.53699 0.08298 -0.01232

16 1999 2001 36357 P CH 1.46301 0.23865 0.11118

16 2001 1998 37097 C CL -3.56433 -0.15081 -0.11980

16 2001 1999 37097 P CL -2.56433 -0.18296 -0.15377

16 2001 1998 37158 C CL -3.73157 -0.16053 -0.14416

16 2001 1998 37158 P CL -3.73157 -0.16053 -0.18957

16 2002 2001 37390 C CL -1.36707 -0.14882 -0.18212

18 1998 2002 35947 P L 3.58630 0.25450 0.19068

18 1998 1999 35986 C L 0.47949 -0.01436 -0.00194

18 1998 1999 35986 P L 0.47949 -0.01436 -0.02042

18 1998 2000 36020 C L 1.38635 0.08614 0.01963

18 1998 2000 36020 P L 1.38635 0.08614 -0.00074

18 1999 2000 36314 C L 0.58081 0.05492 -0.01606

18 1999 2000 36314 P L 0.58081 0.05492 -0.04767

18 2000 1999 36665 C L -1.38086 -0.05340 -0.04193

18 2000 2002 36665 P L 1.61914 0.21665 0.01826

18 2000 1999 36713 C L -1.51233 -0.05226 -0.02899

18 2000 2002 36713 P L 1.48767 0.21779 0.02947

18 2000 1998 36791 C L -2.72607 -0.06273 -0.07500

18 2000 1998 36791 P L -2.72607 -0.06273 -0.19346

18 2002 1998 37375 C L -4.32605 -0.23458 -0.10097

18 2002 1998 37375 P L -4.32605 -0.23458 -0.14587

18 2002 2000 37522 C L -2.72876 -0.25423 -0.15476

18 2002 2000 37522 P L -2.72876 -0.25423 -0.18062

19 1998 2000 35964 C CH 1.53967 0.15548 0.08259

19 1998 2001 35964 P CH 2.53967 0.14037 -0.03044

19 1998 1999 35999 C CH 0.44385 -0.12689 -0.05677

19 1998 1999 36038 C CH 0.33704 -0.05716 -0.03695

19 1998 2001 36038 P CH 2.33704 0.09025 -0.08935

19 1999 2001 36334 C CH 1.52600 0.14741 0.00105

19 1999 1998 36334 P CH -1.47400 0.05106 -0.04088

19 2000 1999 36643 C CH -1.32056 -0.16252 -0.10099

19 2000 1999 36643 P CH -1.32056 -0.16252 -0.16048

19 2000 1998 36732 C CL -2.56433 -0.11146 -0.05630

19 2000 1998 36732 P CL -2.56433 -0.11146 -0.12696

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 139

19 2001 2000 36997 C CH -1.29041 0.01511 -0.05909

19 2001 1999 36997 P CH -2.29041 -0.14741 -0.17651

20 1998 2000 35920 M O 1.66028 0.03474 -0.29222

20 1998 2001 35920 P O 2.66028 0.12963 -0.27726

20 1998 1999 36020 M O 0.38635 -0.08435 -0.16532

20 1998 2000 36053 M O 1.29590 0.04015 -0.20754

20 1998 1999 36053 P O 0.29590 -0.05702 -0.21999

20 1999 1998 36426 M O -1.72607 0.06465 -0.01672

20 1999 1998 36426 P O -1.72607 0.06465 -0.02833

20 2000 1998 36756 M O -2.63013 -0.03252 -0.05182

20 2000 1999 36756 P O -1.63013 -0.09716 -0.13947

20 2001 1998 37027 M O -3.37256 -0.12741 -0.06254

20 2001 1999 37027 P O -2.37256 -0.19205 -0.12831

20 2002 2001 37511 M O -1.69861 -0.15565 -0.29081

22 1999 2000 36361 C L 0.45203 0.11914 -0.04047

22 1999 2000 36361 P L 0.45203 0.11914 -0.02481

22 1999 2001 36406 C L 1.32874 -0.21921 0.16290

22 1999 2000 36406 P L 0.32874 -0.01848 0.19900

22 2000 2001 36664 P L 0.62195 -0.17042 0.04148

22 2000 2002 36754 P L 1.37537 -0.08627 -0.02643

22 2001 2002 37008 C L 0.67944 0.15468 -0.21148

22 2001 2000 37084 C L -1.52881 0.19873 -0.02205

22 2001 2002 37159 C L 0.26575 0.13687 -0.15159

22 2002 1999 37396 C L -3.38354 -0.02002 0.34772

22 2002 2000 37524 C L -2.73425 0.08161 0.14199

23 1998 2001 35941 C O 2.60278 -0.01085 0.08781

23 1998 2000 35972 C O 1.51782 -0.07865 -0.10254

23 1998 2001 36013 C O 2.40552 -0.14371 0.09415

23 1998 2001 36013 P O 2.40552 -0.14371 0.02066

23 1998 2001 36056 C O 2.28772 -0.05741 0.09369

23 1999 2002 36426 C O 2.27393 -0.11000 0.24908

23 1999 1998 36426 P O -1.72607 0.01200 -0.20091

23 1999 2001 36447 C O 1.21643 -0.06511 0.07984

23 1999 1998 36447 P O -1.78357 0.03390 -0.18136

23 2000 1999 36651 C O -1.34241 0.03596 -0.12830

23 2000 1998 36651 P O -2.34241 0.05891 -0.28579

23 2000 2002 36713 C O 1.48767 -0.09742 0.22682

23 2000 2001 36746 C O 0.39722 -0.08826 0.07282

23 2001 2002 37008 C O 0.67944 -0.02299 0.07248

23 2002 1999 37476 C O -3.60278 0.09905 -0.24957

24 1998 2001 35913 C O 2.67944 0.07911 -0.05140

24 1998 2002 35913 P O 3.67944 0.13667 0.03173

24 1998 2002 35991 C O 3.46570 0.13898 0.09019

24 1998 2002 35991 P O 3.46570 0.13898 0.00756

24 1998 2001 36040 C O 2.33154 0.12746 0.03605

24 1998 2002 36040 P O 3.33154 0.18501 0.07383

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
140 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

24 1999 2002 36369 C O 2.43018 0.14672 0.08219

24 1999 2002 36369 P O 2.43018 0.14672 -0.03014

24 2001 1999 37082 C O -2.52332 -0.08917 -0.16783

24 2001 1999 37082 P O -2.52332 -0.08917 -0.22862

24 2002 1999 37449 C O -3.52881 -0.14672 -0.28241

24 2002 1999 37449 P O -3.52881 -0.14672 -0.35163

25 1998 2000 35927 C O 1.64111 -0.04696 -0.05043

25 1998 2000 35978 C O 1.50134 0.01022 -0.05316

25 1998 2000 35978 M O 1.50134 0.01022 -0.08946

25 1998 2000 35978 P O 1.50134 0.01022 -0.08530

25 1998 2000 36017 C O 1.39453 0.08345 -0.01455

25 1998 1999 36017 M O 0.39453 -0.01003 -0.14706

25 1998 2000 36017 P O 1.39453 0.08345 -0.05021

25 1999 2000 36381 C O 0.39722 0.09348 0.00798

25 1999 2000 36381 P O 0.39722 0.09348 -0.06410

25 2000 1998 36678 C O -2.41638 -0.05343 -0.02355

25 2000 1999 36678 M O -1.41638 -0.11347 -0.19828

25 2000 1998 36678 P O -2.41638 -0.05343 -0.12199

25 2000 1999 36713 C O -1.51233 -0.09953 -0.07647

25 2000 1999 36713 M O -1.51233 -0.09953 -0.35222

25 2000 1998 36713 P O -2.51233 -0.03949 -0.23701

25 2000 1998 36734 C O -2.56982 -0.00740 -0.18533

25 2000 1999 36734 M O -1.56982 -0.06744 -0.24661

25 2000 1999 36734 P O -1.56982 -0.06744 -0.22387

27 1998 2000 36055 P L 1.29041 0.18794 0.09983

27 1999 1998 36335 P L -1.47668 -0.14042 -0.07829

27 2000 1998 36650 P L -2.33972 -0.18794 -0.16827

27 2001 1999 37005 P L -2.31238 -0.17324 -0.25380

27 2001 2000 37104 P L -1.58362 0.06433 0.02841

28 1998 2001 35963 C CH 2.54248 0.08048 -0.03894

28 1998 2001 35963 M CH 2.54248 0.08048 -0.05596

28 1998 2002 36003 C CH 3.43286 0.09918 0.00688

28 1998 2001 36003 M CH 2.43286 0.06678 -0.01103

28 1998 2000 36038 C CH 1.33704 0.07134 -0.01435

28 1998 2001 36038 M CH 2.33704 0.05551 -0.00656

28 2000 2001 36658 C CL 0.63831 -0.00619 -0.02163

28 2000 2002 36658 M CL 1.63831 0.02620 0.01763

28 2000 2002 36732 C CH 1.43567 0.03978 0.00794

28 2000 1998 36732 M CH -2.56433 -0.06020 0.01217

28 2000 2001 36763 C CH 0.35071 -0.04868 -0.03272

28 2000 1998 36763 M CH -2.64929 -0.11627 0.00444

28 2001 2002 37047 C CH 0.57263 0.05008 0.00618

28 2001 2002 37047 M CH 0.57263 0.05008 0.05114

28 2001 2002 37089 C CH 0.45752 0.02158 0.01224

28 2001 2000 37089 M CH -1.54248 0.00501 0.01011

28 2001 2000 37141 C CH -1.68494 0.00208 -0.05063

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 141

28 2002 2001 37375 C CH -1.32605 -0.03239 -0.04301

28 2002 1998 37375 M CH -4.32605 -0.09998 -0.01384

29 1998 2002 35912 M O 3.68225 0.52593 0.20401

29 1998 2000 35912 P O 1.68225 0.18641 0.04809

29 1998 2000 35990 M O 1.46851 0.12841 0.13101

29 1998 2002 35990 P O 3.46851 0.46793 0.23917

29 1998 2000 35990 P O 1.46851 0.12841 0.12312

29 1998 2000 36047 M O 1.31238 -0.12842 -0.03672

29 1998 2002 36047 P O 3.31238 0.21111 0.05328

29 1999 2000 36356 M O 0.46570 0.03360 -0.04461

29 1999 2000 36356 P O 0.46570 0.03360 -0.08161

29 1999 2002 36356 P O 2.46570 0.35519 0.08994

29 2000 2002 36755 M O 1.37256 0.33952 0.08614

29 2000 1998 36755 P O -2.62744 -0.07160 -0.13186

29 2002 1998 37326 M O -4.19177 -0.41112 -0.25374

30 1998 2002 35913 C O 3.67944 -0.07679 0.14731

30 1998 2002 35913 M O 3.67944 -0.07679 0.11360

30 1998 2002 35971 C O 3.52051 0.11109 0.10418

30 1998 2002 35971 M O 3.52051 0.11109 0.10332

30 1998 2000 36041 C O 1.32874 -0.27754 0.07041

30 1998 2000 36041 M O 1.32874 -0.27754 0.06289

30 1999 1998 36425 C O -1.72327 0.17254 0.07792

30 1999 2002 36425 M O 2.27673 0.15052 0.13769

30 2000 2002 36699 C O 1.52600 0.17718 0.10408

30 2000 1998 36699 M O -2.47400 0.19920 0.06687

30 2001 2000 37112 C O -1.60547 -0.28923 0.05894

30 2001 2002 37112 M O 0.39453 -0.11205 0.12573

30 2002 2000 37379 C O -2.33704 -0.27045 0.03564

30 2002 1999 37379 M O -3.33704 -0.24379 0.03239

30 2002 1998 37531 M O -4.75342 0.20856 -0.00451

32 1998 2002 35893 M O 3.73425 0.11678 -0.04490

32 1998 2000 35893 P O 1.73425 -0.23196 -0.09812

32 1998 2002 35977 M O 3.50415 0.27639 0.02116

32 1998 2001 35977 P O 2.50415 0.03797 -0.07873

32 1998 2002 36026 M O 3.36987 0.30814 -0.01459

32 1998 2002 36026 P O 3.36987 0.30814 -0.10493

32 1999 2000 36333 M O 0.52881 -0.08594 -0.04704

32 1999 2002 36333 P O 2.52881 0.26281 -0.05256

32 1999 2001 36370 M O 1.42737 0.15380 -0.00793

32 1999 2001 36370 P O 1.42737 0.15380 -0.07190

32 1999 2001 36399 M O 1.34790 0.16705 -0.01118

32 1999 2001 36399 P O 1.34790 0.16705 -0.04733

32 2000 1999 36690 M O -1.44934 -0.05739 -0.04487

32 2000 1998 36690 P O -2.44934 0.06234 -0.11341

32 2000 2002 36720 M O 1.46851 0.39662 0.04660

32 2000 1998 36720 P O -2.53149 0.16285 -0.11465

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
142 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

32 2000 2002 36747 M O 1.39453 0.35351 0.03967

32 2000 2002 36747 P O 1.39453 0.35351 -0.03258

32 2001 2002 37064 M O 0.52600 0.26474 0.02700

32 2001 1998 37064 P O -3.47400 0.03097 -0.07907

32 2001 2000 37111 M O -1.60278 -0.13665 -0.05394

32 2001 1999 37111 P O -2.60278 -0.14140 -0.13086

32 2002 2001 37455 M O -1.54517 -0.23842 -0.10819

34 1998 1999 35902 M O 0.70959 -0.24204 -0.06293

34 1998 2001 35902 P O 2.70959 -0.04272 -0.10587

34 1998 2002 35989 C O 3.47119 0.25489 0.16961

34 1998 2000 35989 P O 1.47119 -0.02966 -0.04879

34 1998 2001 36026 C O 2.36987 0.12100 0.00623

34 1998 1999 36026 P O 0.36987 -0.07832 0.00642

34 1999 2000 36368 C O 0.43286 0.08754 0.04557

34 1999 2000 36368 M O 0.43286 0.09796 0.00529

34 1999 1998 36368 P O -1.56714 0.14354 0.01487

34 2000 1999 36690 C O -1.44934 -0.12068 -0.02886

34 2000 1999 36690 M O -1.44934 -0.12068 -0.00610

34 2000 1999 36690 P O -1.44934 -0.12068 -0.15768

34 2000 1998 36752 C O -2.61914 0.08566 -0.03915

34 2000 1998 36752 M O -2.61914 0.08566 -0.02711

34 2000 2002 36752 P O 1.38086 0.31422 0.07051

34 2001 2002 36983 C O 0.74792 0.12540 0.05850

34 2001 1999 36983 P O -2.25208 -0.25017 -0.07930

34 2001 1998 37083 C O -3.52600 -0.00541 -0.05470

34 2001 2002 37083 P O 0.47400 0.22314 0.10615

34 2001 1999 37111 C O -2.60278 -0.19139 -0.03066

34 2002 2001 37445 C O -1.51782 -0.17625 -0.24942

34 2002 1998 37445 P O -4.51782 -0.22856 -0.35282

35 1998 1999 35920 P O 0.66028 -0.04024 0.03405

35 1998 2000 35970 P O 1.52332 -0.01188 0.16864

35 1998 1999 36048 P O 0.30957 0.04151 0.04908

35 1999 1998 36333 P O -1.47119 0.00049 -0.04736

35 2000 1998 36692 P O -2.45483 0.00962 0.04797

36 1998 2000 35915 M O 1.67395 0.03936 -0.04833

36 1998 2001 35915 P O 2.67395 0.17070 -0.04877

36 1998 2000 35985 M O 1.48218 0.05871 -0.05656

36 1998 2000 35985 P O 1.48218 0.05871 -0.02714

36 1998 1999 36054 M O 0.29309 -0.09934 -0.06025

36 1999 1998 36339 M O -1.48767 -0.00876 -0.03804

36 1999 2000 36339 P O 0.51233 0.01325 0.04725

36 2000 1999 36733 M O -1.56714 -0.01325 -0.04707

36 2000 1998 36733 P O -2.56714 -0.02201 -0.07768

36 2001 1999 37110 M O -2.59998 -0.14458 -0.04296

37 1998 2001 35915 M O 2.67395 -0.01685 -0.05822

37 1998 1999 35915 P O 0.67395 -0.13995 -0.05540

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 143

37 1998 2001 35977 C O 2.50415 0.05966 -0.04936

37 1998 2001 35977 M O 2.50415 0.05966 -0.02102

37 1998 2002 35977 P O 3.50415 0.25857 0.07747

37 1998 2002 36035 C O 3.34521 0.30470 -0.01577

37 1998 2002 36035 M O 3.34521 0.30470 0.04228

37 1998 1999 36035 P O 0.34521 -0.01732 -0.10659

37 1999 2002 36395 C O 2.35889 0.32202 0.13172

37 1999 1998 36395 M O -1.64111 0.06527 0.11290

37 1999 2002 36395 P O 2.35889 0.32202 0.13270

37 2001 1999 37134 C O -2.66577 -0.12311 0.00449

37 2001 2002 37134 M O 0.33423 0.19891 0.09964

37 2001 2002 37134 P O 0.33423 0.19891 0.07933

37 2002 1999 37483 C O -3.62195 -0.32202 -0.11276

38 1998 1999 35892 M O 0.73694 0.05267 -0.29439

38 1998 2000 35892 P O 1.73694 0.11507 -0.14415

38 1998 2000 35977 M O 1.50415 0.02720 0.12951

38 1998 2001 35977 P O 2.50415 0.03847 0.16500

38 1998 2001 36021 M O 2.38354 0.01796 0.15345

38 1998 2002 36021 P O 3.38354 0.06274 0.38025

38 1999 2002 36341 M O 2.50684 0.12233 0.35350

38 1999 2002 36341 P O 2.50684 0.12233 0.37059

38 1999 2002 36370 M O 2.42737 0.10568 0.30091

38 1999 2001 36370 P O 1.42737 0.06090 0.16210

38 1999 2000 36395 M O 0.35889 0.07130 -0.00914

38 1999 2000 36395 P O 0.35889 0.07130 0.03014

38 2000 1999 36641 M O -1.31506 -0.04742 -0.18151

38 2000 2002 36641 P O 1.68494 0.07104 0.10514

38 2000 2002 36719 M O 1.47119 0.04287 0.17462

38 2000 2001 36719 P O 0.47119 0.00226 0.03642

38 2000 2002 36742 M O 1.40820 0.05217 0.15903

38 2000 2002 36742 P O 1.40820 0.05217 0.17208

38 2001 1998 37012 M O -3.33154 -0.08956 -0.16512

38 2001 1998 37012 P O -3.33154 -0.08956 -0.13827

38 2001 2000 37104 M O -1.58362 0.01737 -0.03265

38 2001 2000 37104 P O -1.58362 0.01737 0.00206

38 2002 1999 37350 M O -3.25757 -0.10524 -0.28199

38 2002 1999 37350 P O -3.25757 -0.10524 -0.24449

38 2002 2000 37483 P O -2.62195 -0.08249 -0.33152

39 1998 1999 36021 C CH 0.38354 -0.00993 0.03249

39 1998 2001 36021 P CH 2.38354 0.12072 0.01796

39 1998 2001 36028 C CH 2.36438 0.12158 0.05132

39 1998 1999 36028 P CH 0.36438 -0.00907 -0.01806

39 1999 2002 36341 C CL 2.50684 0.21761 0.07996

39 1999 2002 36341 P CL 2.50684 0.21761 0.05494

39 1999 1998 36367 C CL -1.56433 -0.00387 0.00227

39 1999 2002 36367 P CL 2.43567 0.18267 0.03769

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
144 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

39 1999 2001 36433 C CL 1.25476 0.12244 0.07663

39 1999 1998 36433 P CL -1.74524 0.00129 -0.01286

39 2001 1998 37104 C CL -3.58362 -0.12878 -0.04192

39 2001 1998 37153 C CL -3.71777 -0.11351 -0.03428

39 2002 1999 37326 C CL -3.19177 -0.14958 0.05075

39 2002 1999 37526 C CL -3.73975 -0.24250 -0.08460

40 1998 1999 35919 M O 0.66296 -0.02756 -0.02267

40 1998 2000 35919 P O 1.66296 0.02790 0.11319

40 1998 2000 35944 M O 1.59448 0.07587 0.13875

40 1998 1999 35944 P O 0.59448 0.02041 0.03966

40 1998 1999 36010 M O 0.41370 -0.03312 -0.24015

40 1998 2000 36010 P O 1.41370 0.02234 -0.12220

40 1999 2000 36341 M O 0.50684 0.05546 0.17302

40 1999 1998 36341 P O -1.49316 0.01342 0.04573

40 2000 1998 36649 M O -2.33704 -0.00327 -0.04574

40 2000 1999 36719 M O -1.52881 -0.05884 0.01927

40 2000 1999 36719 P O -1.52881 -0.05884 0.02290

40 2000 1998 36740 M O -2.58630 -0.05804 -0.10847

40 2000 1999 36740 P O -1.58630 -0.07146 -0.13172

41 1998 2000 35915 M O 1.67395 0.02574 0.00333

41 1998 1999 35915 P O 0.67395 -0.35980 -0.00727

41 1998 2000 36011 C O 1.41101 -0.00532 0.05035

41 1998 1999 36011 C O 0.41101 -0.39087 0.08213

41 1998 2000 36011 M O 1.41101 -0.00532 -0.02958

41 1998 2001 36011 P O 2.41101 -0.02080 -0.03014

41 1999 1998 36336 C O -1.47949 0.38051 0.00721

41 1999 2001 36336 C O 1.52051 0.37006 0.07796

41 1999 2001 36336 M O 1.52051 0.37006 0.01150

41 2000 1999 36656 C O -1.35620 -0.38200 0.03496

41 2000 1999 36656 C O -1.35620 -0.38200 0.04611

41 2000 2001 36656 M O 0.64380 -0.01194 -0.00814

41 2000 1999 36656 P O -1.35620 -0.38200 -0.09474

41 2000 2001 36740 C O 0.41370 -0.04406 0.01667

41 2000 1998 36740 M O -2.58630 -0.03361 -0.09325

41 2000 2001 36763 C O 0.35071 0.00602 0.04665

41 2000 1998 36763 M O -2.64929 0.01647 -0.05841

41 2001 1999 37070 C O -2.49036 -0.37006 0.03243

41 2001 1998 37070 M O -3.49036 0.01045 -0.07209

43 1998 1999 35958 C O 0.55615 0.01448 -0.00736

43 1998 1999 35958 M O 0.55615 0.01448 0.00775

43 1998 2002 35958 P O 3.55615 0.15149 -0.01859

43 1998 1999 36003 C O 0.43286 0.02586 -0.01902

43 1998 2002 36003 M O 3.43286 0.16287 -0.00700

43 1998 1999 36003 P O 0.43286 0.02586 -0.04993

43 1998 1999 36053 C O 0.29590 0.07510 -0.02888

43 1998 2002 36053 M O 3.29590 0.21212 -0.00686

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 145

43 1999 2002 36336 C O 2.52051 0.10507 -0.00583

43 1999 2000 36336 P O 0.52051 -0.03827 -0.03469

43 1999 1998 36399 C O -1.65210 -0.01261 0.00003

43 1999 2001 36399 M O 1.34790 0.00207 0.02037

43 1999 2002 36399 P O 2.34790 0.15830 -0.02756

43 2000 2002 36657 C O 1.64111 0.08794 -0.03207

43 2000 2002 36657 M O 1.64111 0.08794 -0.05588

43 2000 2001 36657 P O 0.64111 -0.06829 -0.01489

43 2000 2001 36720 C O 0.46851 -0.03592 0.00089

43 2000 2001 36720 M O 0.46851 -0.03592 -0.01402

43 2000 1999 36720 P O -1.53149 -0.01670 -0.08283

43 2000 1998 36747 C O -2.60547 0.05086 0.00277

43 2000 1999 36747 M O -1.60547 0.08477 -0.01808

43 2000 1999 36747 P O -1.60547 0.08477 -0.08693

43 2001 2002 36984 C O 0.74524 0.22664 -0.05548

43 2001 1998 36984 M O -3.25476 0.05573 -0.07515

43 2001 1999 36984 P O -2.25476 0.08963 -0.21907

43 2001 1999 37103 C O -2.58081 -0.05119 -0.02070

43 2001 1998 37103 M O -3.58081 -0.08509 -0.05028

43 2001 1998 37103 P O -3.58081 -0.08509 -0.05889

43 2002 2000 37419 C O -2.44653 -0.12708 -0.02440

43 2002 2001 37419 M O -1.44653 -0.13997 -0.06351

43 2002 1999 37419 P O -3.44653 -0.12075 -0.13391

43 2002 2000 37526 C O -2.73975 -0.16774 0.01061

43 2002 1999 37526 M O -3.73975 -0.16141 -0.01260

44 1998 2001 35906 C S 2.69861 0.07787 0.04479

44 1998 1999 35906 P S 0.69861 -0.06162 -0.05534

44 1998 1999 35957 C S 0.55896 -0.06956 -0.06534

44 1998 1999 35957 P S 0.55896 -0.06956 -0.10572

44 1998 1999 36047 C S 0.31238 -0.02511 -0.02534

44 1998 2000 36047 P S 1.31238 0.07303 -0.00852

44 1999 1998 36389 C S -1.62463 0.05209 -0.01445

44 1999 2000 36389 P S 0.37537 0.09813 -0.04458

44 2000 2001 36691 C S 0.54797 0.11770 0.00252

44 2000 2001 36691 P S 0.54797 0.11770 -0.00988

44 2000 1998 36719 C S -2.52881 -0.10084 0.00799

44 2000 1998 36719 P S -2.52881 -0.10084 -0.05848

44 2000 1999 36740 C S -1.58630 -0.11966 0.01576

44 2000 1999 36740 P S -1.58630 -0.11966 -0.08304

44 2001 2000 37012 C S -1.33154 -0.03646 0.29439

44 2001 1998 37012 P S -3.33154 -0.08250 0.20290

44 2001 1998 37110 P S -3.59998 -0.09720 -0.02186

45 1998 2002 35899 C S 3.71777 0.01299 -0.00228

45 1998 2002 35899 P S 3.71777 0.01299 -0.03820

45 1998 1999 35942 C S 0.59998 -0.07634 0.08601

45 1998 2001 35942 P S 2.59998 -0.05021 0.02385

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
146 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

45 1998 1999 36054 P S 0.29309 -0.09531 0.03780

45 1999 2000 36370 P S 0.42737 0.04544 -0.07812

45 2000 1999 36692 P S -1.45483 -0.02046 -0.01133

45 2000 1999 36720 P S -1.53149 -0.06454 0.03372

45 2000 1999 36755 P S -1.62744 -0.05133 0.07400

45 2001 2002 37012 P S 0.66846 -0.01282 -0.00786

45 2001 2002 37063 P S 0.52881 0.03279 -0.01602

45 2001 1998 37153 P S -3.71777 0.02473 -0.00432

45 2002 2001 37418 P S -1.44385 -0.00666 0.05868

45 2002 2001 37418 P S -1.44385 -0.00666 0.05868

46 1998 2000 35892 C O 1.73694 -0.18618 -0.13777

46 1998 1999 35892 M O 0.73694 -0.00280 -0.09026

46 1998 1999 35892 P O 0.73694 -0.00280 -0.14895

46 1998 2002 35915 C O 3.67395 -0.00463 0.01169

46 1998 2000 35915 M O 1.67395 -0.19484 -0.11469

46 1998 2001 36000 C O 2.44104 0.08283 0.00163

46 1998 2001 36000 M O 2.44104 0.08283 0.00768

46 1998 2001 36038 C O 2.33704 0.09975 -0.03000

46 1998 2000 36038 M O 1.33704 -0.09084 -0.07435

46 1999 2000 36241 C O 0.78076 -0.18339 -0.13182

46 1999 2000 36241 M O 0.78076 -0.18339 -0.13961

46 2000 1999 36683 C O -1.43018 0.40127 -0.04540

46 2000 2002 36683 M O 1.56982 0.40810 0.02272

46 2000 1998 36683 P O -2.43018 0.36738 -0.16396

46 2000 2002 36734 C O 1.43018 0.05790 0.11224

46 2000 1999 36734 M O -1.56982 0.05108 -0.03683

46 2000 1999 36734 P O -1.56982 0.05108 -0.07584

46 2000 1999 36777 C O -1.68762 0.05502 -0.03273

46 2000 2001 36777 M O 0.31238 0.06223 -0.02303

46 2001 1998 36991 C O -3.27393 -0.09808 -0.06456

46 2001 1999 36991 M O -2.27393 -0.06419 -0.04833

46 2001 1999 36991 P O -2.27393 -0.06419 -0.05805

46 2001 2000 37048 C O -1.43018 -0.13362 -0.08066

46 2001 1999 37048 M O -2.43018 0.04977 -0.04707

46 2001 2002 37048 P O 0.56982 0.05659 0.05196

46 2002 2001 37335 C O -1.21643 0.00039 -0.04491

46 2002 2001 37335 M O -1.21643 0.00039 -0.04532

47 1998 1999 35951 M O 0.57532 0.05284 -0.10289

47 1998 2000 35951 P O 1.57532 -0.15664 -0.28939

47 1998 1999 36000 M O 0.44104 0.07918 -0.07957

47 1998 2002 36000 P O 3.44104 0.17974 -0.18411

47 1998 2001 36031 M O 2.35620 0.04010 -0.16198

47 1998 2001 36031 P O 2.35620 0.04010 -0.18038

47 1999 2000 36241 M O 0.78076 -0.20948 -0.04300

47 2000 1999 36683 M O -1.43018 0.44837 0.13118

47 2000 2002 36683 P O 1.56982 0.54893 0.01660

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 147

47 2000 1998 36734 M O -2.56982 -0.01819 0.22056

47 2000 1998 36734 P O -2.56982 -0.01819 0.15846

47 2000 1998 36777 M O -2.68762 -0.00690 0.23207

47 2001 1998 36991 M O -3.27393 -0.08446 0.26655

47 2001 2000 36991 P O -1.27393 -0.22929 0.09769

47 2001 2000 37057 M O -1.45483 -0.16190 0.03714

47 2001 1999 37152 M O -2.71509 0.05058 0.14197

47 2001 1999 37152 P O -2.71509 0.05058 0.13132

47 2002 1998 37335 M O -4.21643 -0.07177 0.24529

47 2002 1998 37477 M O -4.60547 -0.21193 0.14984

47 2002 2000 37477 P O -2.60547 -0.35676 -0.05136

48 1998 1999 35928 M O 0.63831 -0.01136 -0.02049

48 1998 1999 35928 P O 0.63831 -0.01136 -0.02902

48 1998 2000 35965 M O 1.53699 0.05844 -0.06884

48 1998 1999 35965 P O 0.53699 0.00943 -0.03325

48 1998 2000 36054 M O 1.29309 -0.00270 -0.08407

48 1998 1999 36054 P O 0.29309 -0.05170 -0.07868

48 1999 2000 36383 M O 0.39172 0.04901 -0.00671

48 1999 2000 36383 P O 0.39172 0.04901 -0.01848

48 2000 1999 36663 M O -1.37537 -0.05942 -0.07990

48 2000 1999 36663 P O -1.37537 -0.05942 -0.04635

48 2000 1998 36741 M O -2.58899 -0.01029 -0.10623

49 1998 2000 35912 P CL 1.68225 -0.05050 0.03263

49 1998 2000 35975 C CH 1.50964 0.06557 0.07953

49 1998 2002 35975 P CH 3.50964 0.18464 -0.02822

49 1998 2000 36035 C CH 1.34521 0.18784 0.11425

49 1998 2002 36035 P CH 3.34521 0.30692 0.11481

49 2000 1998 36763 C CH -2.64929 -0.09126 0.00837

49 2002 1998 37446 C CH -4.52051 -0.21034 -0.06445

50 1998 2001 35899 C L 2.71777 0.31759 0.09764

50 1998 2000 35899 M L 1.71777 0.04921 0.01941

50 1998 2001 35961 C L 2.54797 0.22360 0.11386

50 1998 2001 35961 M L 2.54797 0.22360 0.08517

50 1998 2001 36012 C L 2.40820 0.06472 0.10010

50 1998 2000 36012 M L 1.40820 -0.20366 0.01795

50 1998 2000 36059 C L 1.27942 -0.23578 0.08346

50 1998 1999 36059 M L 0.27942 -0.25192 -0.00765

50 1999 2000 36357 C L 0.46301 0.01614 0.08261

50 1999 2001 36357 M L 1.46301 0.28451 0.10875

50 2000 1998 36662 C L -2.37256 0.10875 0.12252

50 2000 1998 36662 M L -2.37256 0.10875 0.10068

50 2001 1998 37023 C L -3.36169 -0.14892 0.05282

50 2001 1998 37118 C L -3.62195 -0.17033 0.04939

51 1998 2001 35906 M CL 2.69861 0.07440 0.04335

51 1998 2000 35906 P CL 1.69861 0.05038 -0.04461

51 1998 2001 35972 M CH 2.51782 0.01410 -0.05140

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
148 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

51 1998 2002 35972 P CH 3.51782 -0.10567 -0.09423

51 1998 2001 36020 M CH 2.38635 0.12232 0.08687

51 1998 1999 36020 P CH 0.38635 0.12461 0.15539

51 1999 2000 36241 M CH 0.78076 -0.02630 -0.03345

51 1999 2002 36241 P CH 2.78076 -0.12205 -0.07111

51 2000 2001 36678 M CL 0.58362 0.02402 0.00300

51 2000 2002 36678 P CL 1.58362 -0.09575 -0.07530

51 2001 1999 36991 M CH -2.27393 0.00930 0.03746

51 2001 2000 36991 P CH -1.27393 -0.01700 -0.07960

51 2001 2000 37048 M CH -1.43018 -0.03103 -0.05778

51 2001 1998 37048 P CH -3.43018 -0.07729 -0.04336

51 2002 1998 37421 M CH -4.45203 0.04949 -0.02901

51 2002 2000 37421 P CH -2.45203 0.09575 -0.08024

52 1998 1999 35965 C O 0.53699 0.03247 -0.04071

52 1998 1999 35965 M O 0.53699 0.03247 0.01175

52 1998 1999 35965 P O 0.53699 0.03247 -0.08460

52 1998 1999 35992 C O 0.46301 -0.06164 -0.04515

52 1998 1999 35992 M O 0.46301 -0.06164 -0.00418

52 1998 1999 36034 M O 0.34790 -0.00653 0.01075

52 1998 1999 36034 P O 0.34790 -0.00653 -0.01986

52 1999 1998 36349 C O -1.51501 0.02196 -0.01086

52 1999 1998 36349 M O -1.51501 0.02196 -0.00918

52 1999 1998 36405 C O -1.66846 -0.01083 -0.05819

52 1999 1998 36405 M O -1.66846 -0.01083 -0.00615

53 1998 2000 35949 M O 1.58081 -0.11987 0.01347

53 1998 2001 35949 P O 2.58081 -0.13051 0.10061

53 1998 1999 35991 C O 0.46570 -0.26784 -0.04418

53 1998 2001 35991 M O 2.46570 -0.15401 0.10408

53 1998 2000 35991 P O 1.46570 -0.14337 -0.05810

53 1998 2000 36035 C O 1.34521 -0.11566 -0.01654

53 1998 2000 36035 M O 1.34521 -0.11566 0.03684

53 1999 2001 36319 C O 1.56714 0.11384 0.15056

53 1999 2001 36319 M O 1.56714 0.11384 0.17546

53 2000 2001 36649 C O 0.66296 -0.18096 0.08667

53 2000 2002 36649 M O 1.66296 -0.05319 0.02676

53 2000 2002 36649 P O 1.66296 -0.05319 -0.03200

53 2000 1998 36712 C O -2.50964 0.17592 -0.13896

53 2000 1998 36712 M O -2.50964 0.17592 -0.16590

53 2000 2002 36733 C O 1.43286 0.25600 0.02473

53 2000 2002 36733 M O 1.43286 0.25600 0.01847

53 2000 1999 36733 P O -1.56714 0.01439 -0.17226

53 2001 1998 36982 C O -3.24927 0.32732 -0.21156

53 2001 1999 36982 M O -2.24927 0.07411 -0.22307

53 2001 2002 36982 P O 0.75073 0.31572 -0.15488

53 2001 1999 37070 C O -2.49036 -0.06899 -0.16803

53 2001 2000 37070 M O -1.49036 0.05548 -0.13776

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 149

53 2001 2002 37070 P O 0.50964 0.17262 -0.07725

53 2001 2002 37110 C O 0.40002 -0.10501 -0.04118

53 2001 1999 37110 M O -2.59998 -0.34662 -0.19387

53 2001 2000 37110 P O -1.59998 -0.22215 -0.21545

53 2002 1998 37347 C O -4.24927 -0.10969 -0.14307

53 2002 2000 37347 M O -2.24927 -0.23843 -0.13306

53 2002 1998 37445 C O -4.51782 -0.14508 -0.17740

53 2002 1999 37445 M O -3.51782 -0.39830 -0.22054

53 2002 1998 37504 C O -4.67944 0.28958 -0.17961

53 2002 2000 37504 M O -2.67944 0.16084 -0.18234

54 1998 2002 35963 C L 3.54248 -0.00507 -0.08348

54 1998 1999 35963 M L 0.54248 -0.01204 -0.01284

54 1998 1999 36053 C L 0.29590 -0.01497 -0.04713

54 1998 2000 36056 C L 1.28772 -0.00713 -0.03811

54 1999 2000 36362 C L 0.44934 0.01576 0.03859

54 1999 2002 36362 M L 2.44934 0.00698 -0.05465

54 2000 1998 36656 C L -2.35620 -0.00107 -0.00731

54 2000 2002 36718 C L 1.47400 -0.00799 -0.04968

54 2002 1999 37349 C L -3.25476 -0.00698 -0.01238

55 1998 2000 35956 C O 1.56165 -0.00275 -0.01370

55 1998 2002 35956 M O 3.56165 0.09056 0.11396

55 1998 2002 35998 C O 3.44653 0.10101 0.13765

55 1998 2002 35998 M O 3.44653 0.10101 0.14350

55 1998 2000 36035 C O 1.34521 0.07604 0.06308

55 1998 2002 36035 M O 3.34521 0.16936 0.18426

55 2000 2002 36769 C O 1.33423 0.09332 0.08358

55 2000 1998 36769 M O -2.66577 -0.02699 -0.05688

55 2000 1998 36769 P O -2.66577 -0.02699 -0.11463

55 2002 2000 37371 C O -2.31506 -0.06695 -0.05897

55 2002 1998 37371 M O -4.31506 -0.09394 -0.07330

55 2002 2000 37469 C O -2.58362 -0.11969 -0.40072

55 2002 1998 37469 M O -4.58362 -0.14668 -0.42834

56 1998 2002 35901 C O 3.71228 0.28813 0.05198

56 1998 2000 35901 M O 1.71228 -0.01303 -0.09674

56 1998 2000 35956 C O 1.56165 -0.02678 -0.17346

56 1998 2000 35956 M O 1.56165 -0.02678 -0.05728

56 1998 2001 35956 P O 2.56165 0.10266 -0.01136

56 1998 2001 36046 C O 2.31506 0.16770 0.11100

56 1998 2000 36046 P O 1.31506 0.03826 -0.03340

56 2000 2002 36762 C O 1.35339 0.30116 0.12956

56 2000 2001 36762 M O 0.35339 0.12944 0.12878

56 2001 2002 37036 C O 0.60278 0.34650 0.02929

56 2001 2000 37036 M O -1.39722 0.04534 -0.12863

56 2001 2000 37071 C O -1.49316 -0.22757 -0.17894

56 2001 1998 37071 M O -3.49316 -0.22330 -0.13527

56 2001 1998 37124 C O -3.63831 -0.20182 -0.11815

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
150 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

56 2001 2002 37124 M O 0.36169 0.09508 -0.02051

56 2002 2000 37343 C O -2.23840 -0.30116 -0.19392

56 2002 2001 37343 M O -1.23840 -0.17172 -0.05954

58 1998 1999 35954 C O 0.56714 -0.10614 0.08265

58 1998 1999 35990 C O 0.46851 -0.04064 0.08217

58 1998 1999 36020 C O 0.38635 0.01180 0.12574

58 1999 2000 36378 C O 0.40552 0.03786 0.01150

58 1999 2001 36378 M O 1.40552 0.25631 0.02140

58 2000 2002 36748 C O 1.39172 0.29832 0.20935

58 2001 1999 36999 C O -2.29590 -0.31702 -0.15053

58 2001 2002 37056 C O 0.54797 0.12323 0.09585

58 2001 2002 37103 C O 0.41919 0.16544 0.16245

58 2002 1998 37335 C O -4.21643 -0.28812 -0.20814

58 2002 1999 37414 C O -3.43286 -0.32131 -0.08070

58 2002 1999 37515 C O -3.70959 -0.39504 -0.13369

59 1998 2000 35964 M O 1.53967 -0.22813 -0.19001

59 1998 2000 35964 P O 1.53967 -0.22813 -0.17468

59 1999 1998 36390 M O -1.62744 -0.32791 0.03716

59 1999 2000 36390 P O 0.37256 -0.55604 -0.10246

59 2000 1998 36650 P O -2.33972 0.22813 0.13402

60 1998 2002 35901 C O 3.71228 0.07513 -0.03833

60 1998 1999 35901 M O 0.71228 -0.04784 -0.12718

60 1998 2002 35901 P O 3.71228 0.07513 -0.05432

60 1998 2002 35978 C O 3.50134 0.06784 -0.04705

60 1998 2002 35978 M O 3.50134 0.06784 -0.01900

60 1998 2000 35978 P O 1.50134 -0.06203 -0.15702

60 1998 2002 36046 C O 3.31506 0.23545 0.03343

60 1998 2000 36046 M O 1.31506 0.10558 -0.05729

60 1998 2002 36046 P O 3.31506 0.23545 0.03481

60 1999 2000 36362 C O 0.44934 -0.00507 -0.14313

60 1999 1998 36362 C O -1.55066 -0.00867 -0.05352

60 1999 2000 36362 M O 0.44934 -0.00507 -0.13862

60 1999 2002 36362 P O 2.44934 0.12480 -0.02777

60 2000 1999 36691 C O -1.45203 0.01863 -0.10717

60 2000 2001 36691 M O 0.54797 0.12267 -0.07363

60 2000 2001 36691 P O 0.54797 0.12267 -0.08087

60 2000 1998 36721 C O -2.53430 -0.00037 -0.07824

60 2000 2001 36721 M O 0.46570 0.10683 -0.06695

60 2000 1999 36721 P O -1.53430 0.00280 -0.12586

60 2000 1999 36761 C O -1.64380 -0.00072 -0.13928

60 2000 1999 36761 M O -1.64380 -0.00072 -0.11638

60 2000 1998 36761 P O -2.64380 -0.00389 -0.14563

60 2001 2000 37015 C O -1.33972 -0.13804 -0.10434

60 2001 2002 37015 M O 0.66028 -0.00817 -0.01147

60 2001 2000 37077 C O -1.50964 -0.09711 -0.14904

60 2001 1999 37077 M O -2.50964 -0.09021 -0.17038

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 151

60 2001 1999 37077 P O -2.50964 -0.09021 -0.19231

60 2001 2002 37111 C O 0.39722 0.02317 -0.02789

60 2001 1999 37111 M O -2.60278 -0.09980 -0.15065

60 2001 2000 37111 P O -1.60278 -0.10670 -0.23210

60 2002 2001 37337 C O -1.22192 -0.01893 -0.14050

60 2002 1998 37337 M O -4.22192 -0.12614 -0.16798

60 2002 2000 37337 P O -2.22192 -0.12987 -0.21216

61 1998 2002 35957 C O 3.55896 0.15477 0.16991

61 1998 1999 35957 M O 0.55896 0.00542 0.02048

61 1998 2002 36004 C O 3.43018 0.07139 0.14308

61 1998 2002 36004 M O 3.43018 0.07139 0.16962

61 1998 2001 36042 C O 2.32605 -0.00242 0.19203

61 1998 2001 36042 M O 2.32605 -0.00242 0.13945

61 1999 2000 36383 C O 0.39172 -0.11441 0.16267

61 1999 2001 36383 M O 1.39172 0.10752 0.19155

61 2000 1998 36691 C O -2.45203 0.17524 0.03263

61 2000 1999 36691 M O -1.45203 0.11441 -0.17393

61 2001 1999 37134 C O -2.66577 -0.10752 -0.06062

61 2001 2000 37134 M O -1.66577 -0.22193 -0.14528

61 2002 2000 37349 C O -2.25476 -0.26376 0.03418

61 2002 2001 37349 M O -1.25476 -0.04183 -0.04438

62 1998 2000 35928 P L 1.63831 0.33745 0.39989

62 1998 1999 35965 C L 0.53699 0.12758 0.24137

62 1998 2000 35965 P L 1.53699 0.04399 0.30184

62 1998 2000 36034 C L 1.34790 0.03457 0.22395

62 1998 2001 36034 P L 2.34790 0.20252 0.26460

62 1999 1998 36433 C L -1.74524 -0.17381 -0.41991

62 1999 2002 36433 P L 2.25476 -0.03428 -0.03791

62 2000 1998 36663 C L -2.37537 -0.12502 -0.44174

62 2000 2002 36663 P L 1.62463 0.01451 -0.10269

62 2000 2002 36741 C L 1.41101 0.06176 -0.19035

62 2000 1999 36741 P L -1.58899 0.09604 -0.10174

62 2001 1998 37096 C L -3.56165 -0.26812 -0.41499

62 2002 2001 37505 C L -1.68225 0.12859 -0.12634

62 2002 1998 37505 P L -4.68225 -0.13953 -0.40714

63 1998 2002 35902 C CL 3.70959 0.31980 0.16004

63 1998 2001 35949 C CL 2.58081 0.66861 0.09058

63 1998 2001 36047 C CH 2.31238 0.68391 0.13063

63 1999 2000 36357 C CH 0.46301 0.58634 0.00629

63 2000 1999 36684 C CL -1.43286 -0.61712 -0.00244

63 2000 2001 36728 C CL 0.44653 0.02380 0.08127

63 2000 2001 36761 C CH 0.35620 0.13170 0.09490

63 2001 1999 36998 C CH -2.29309 -0.65523 -0.05781

63 2001 2002 37034 C CH 0.60828 -0.35632 0.06884

63 2001 1999 37069 C CH -2.48767 -0.63838 -0.03064

63 2002 2000 37356 C CH -2.27393 0.29015 -0.18341

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
152 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

64 1998 2000 35921 C O 1.65759 0.15698 0.12509

64 1998 2000 35949 C O 1.58081 0.14835 0.06400

64 1998 2002 36047 C O 3.31238 0.01707 0.16919

64 1998 2002 36054 C O 3.29309 0.00762 0.15762

64 1999 1998 36313 C O -1.41638 0.00169 -0.01489

64 1999 2002 36369 C O 2.43018 0.01767 0.12475

64 2000 1999 36684 C O -1.43286 -0.23069 0.06054

64 2000 2002 36726 C O 1.45203 -0.22676 0.18617

64 2000 2001 36781 C O 0.30139 0.03840 0.08248

64 2001 2002 37035 C O 0.60547 -0.02593 0.14727

64 2001 2000 37069 C O -1.48767 0.13950 0.07649

64 2002 1998 37355 C O -4.27124 -0.01568 -0.25147

65 1998 1999 35900 C O 0.71509 0.02800 -0.06256

65 1998 2000 35900 M O 1.71509 0.02504 0.01754

65 1998 2000 35949 C O 1.58081 -0.27874 -0.00899

65 1998 1999 35949 M O 0.58081 -0.27577 -0.08340

65 1998 1999 36032 C O 0.35339 0.08104 -0.05574

65 1998 2000 36032 M O 1.35339 0.07808 0.02926

65 1998 2000 36053 C O 1.29590 0.02151 0.03780

65 1998 2000 36053 M O 1.29590 0.02151 0.04906

65 1999 1998 36313 C O -1.41638 0.05960 0.06440

65 1999 2000 36313 M O 0.58362 0.02107 0.07791

65 1999 1998 36364 C O -1.55615 0.01152 0.01802

65 1999 2000 36364 M O 0.44385 -0.02701 0.02915

65 2000 1998 36685 C O -2.43567 0.04649 0.00337

65 2000 1999 36685 M O -1.43567 0.01093 -0.07165

65 2000 1999 36728 C O -1.55347 -0.00500 -0.03980

65 2000 1999 36728 M O -1.55347 -0.00500 -0.03110

66 1998 2002 35958 C O 3.55615 0.35101 0.08305

66 1998 1999 35958 M O 0.55615 0.01806 -0.12223

66 1998 2002 36005 C O 3.42737 0.37449 0.08692

66 1998 2002 36005 M O 3.42737 0.37449 0.04477

66 1998 2001 36017 C O 2.39453 0.20500 0.08516

66 1998 2001 36017 M O 2.39453 0.20500 0.06718

66 1999 2002 36294 C O 2.63562 0.36420 0.12931

66 1999 2002 36294 M O 2.63562 0.36420 0.11658

66 1999 2000 36362 C O 0.44934 0.04306 0.03045

66 1999 2000 36362 M O 0.44934 0.04306 0.02204

66 2000 1998 36665 C O -2.38086 -0.10211 0.02147

66 2000 2002 36665 M O 1.61914 0.28159 0.10212

66 2000 2001 36718 C O 0.47400 0.04849 0.02645

66 2000 2002 36718 M O 1.47400 0.26909 0.11786

66 2000 1998 36754 C O -2.62463 -0.15847 0.00431

66 2000 1999 36754 M O -1.62463 -0.10772 -0.02853

66 2001 2000 37047 C O -1.42737 -0.00393 -0.00543

66 2001 2000 37047 M O -1.42737 -0.00393 -0.01121

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 153

66 2001 1998 37091 C O -3.54797 -0.17062 0.02938

66 2001 2000 37091 M O -1.54797 -0.04555 0.01068

66 2001 1998 37141 C O -3.68494 -0.18968 -0.01454

66 2001 1998 37141 M O -3.68494 -0.18968 -0.10006

66 2002 1998 37455 C O -4.54517 -0.37013 -0.07736

66 2002 2001 37455 M O -1.54517 -0.20703 -0.07456

66 2002 2000 37488 C O -2.63562 -0.27221 -0.11986

66 2002 1999 37488 M O -3.63562 -0.34652 -0.15529

68 1998 2001 35949 C L 2.58081 -0.01448 0.01819

68 1998 2001 35991 C L 2.46570 0.00971 0.02342

68 1998 1999 36019 C L 0.38904 0.07307 0.03399

68 1998 2000 36061 C L 1.27393 0.01879 0.02888

68 1999 1998 36327 C L -1.45483 -0.03576 0.01751

68 2000 2001 36700 C L 0.52332 0.02327 0.04013

68 2001 1999 37026 C L -2.36987 -0.00150 -0.05480

68 2001 2002 37140 C L 0.31775 0.14430 0.17286

68 2001 1998 37162 C L -3.74243 -0.02065 0.01115

68 2002 2001 37370 C L -1.31238 -0.08429 -0.01894

68 2002 1998 37491 C L -4.64380 -0.21282 -0.32191

69 1998 2001 35942 C O 2.59998 0.06479 0.04750

69 1998 2001 35942 P O 2.59998 0.06479 0.03793

69 1998 2002 36026 C O 3.36987 0.02152 -0.02258

69 1998 2000 36026 P O 1.36987 -0.03236 0.01742

69 1998 2001 36040 C O 2.33154 -0.00643 -0.00627

69 2000 1998 36747 C O -2.60547 -0.00413 0.00604

69 2001 1998 37083 C O -3.52600 -0.01672 0.03250

69 2002 2001 37419 C O -1.44653 -0.04130 0.02533

69 2002 2000 37419 P O -2.44653 -0.05388 0.02964

70 1998 2002 35930 C O 3.63293 -0.01490 0.00722

70 1998 2000 35983 C O 1.48767 -0.02685 -0.00579

70 1998 2001 36033 C O 2.35071 -0.09611 0.18097

70 1999 2000 36320 C O 0.56433 -0.04019 -0.02856

70 2000 2001 36634 C O 0.70410 -0.09235 0.10443

70 2000 2001 36705 C O 0.50964 -0.14313 0.10493

70 2000 1999 36755 C O -1.62744 0.05625 -0.09018

70 2001 1998 37008 C O -3.32056 0.09913 -0.08045

70 2001 2000 37105 C O -1.58630 0.12232 -0.26384

70 2002 2001 37449 C O -1.52881 -0.08766 -0.03775

72 1998 2000 35948 C O 1.58362 0.11049 -0.02403

72 1998 2000 35948 M O 1.58362 0.11049 -0.03919

72 1998 2000 35992 C O 1.46301 -0.00955 0.03067

72 1998 2001 35992 M O 2.46301 0.05552 0.05625

72 1998 1999 36041 C O 0.32874 0.07777 0.05578

72 1998 1999 36041 M O 0.32874 0.07777 0.04356

72 1999 2000 36355 C O 0.46851 -0.00048 0.02843

72 1999 1998 36355 M O -1.53149 -0.05989 0.00186

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
154 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

72 2000 1999 36719 C O -1.52881 0.00048 0.03375

72 2000 1998 36719 M O -2.52881 -0.05941 0.00409

72 2001 1999 37070 C O -2.49036 -0.03488 -0.04625

72 2001 1999 37070 M O -2.49036 -0.03488 -0.05647

72 2001 2000 37140 C O -1.68225 -0.07129 -0.11596

72 2001 1998 37140 M O -3.68225 -0.13070 -0.12687

72 2001 2000 37161 C O -1.73975 -0.08857 -0.10858

72 2001 2000 37161 M O -1.73975 -0.08857 -0.10800

74 1998 2001 35935 C O 2.61914 0.25846 0.01242

74 1998 2002 35935 M O 3.61914 0.05237 -0.06101

74 1998 2000 36004 C O 1.43018 0.08716 0.07355

74 1998 2002 36004 M O 3.43018 0.03099 0.01176

74 1998 2000 36048 C O 1.30957 0.12609 0.08300

74 1998 2001 36048 M O 2.30957 0.27601 0.06242

74 2000 2001 36686 C O 0.56165 0.14992 0.06653

74 2000 2002 36686 M O 1.56165 -0.05617 0.01684

74 2001 2000 37007 C O -1.31775 -0.14992 0.01632

74 2001 1998 37007 M O -3.31775 -0.25719 -0.04160

74 2002 2001 37454 C O -1.54248 0.20609 0.07886

74 2002 1998 37454 M O -4.54248 -0.05110 0.02949

75 1998 2000 35914 C O 1.67676 -0.05400 0.21194

75 1998 2000 35914 M O 1.67676 -0.05400 0.20009

75 1998 2000 36004 C O 1.43018 0.02481 0.26130

75 1998 2000 36004 M O 1.43018 0.02481 0.25220

75 1998 2000 36041 C O 1.32874 0.03041 0.26243

75 1998 2000 36041 M O 1.32874 0.03041 0.26017

75 2000 1998 36720 C O -2.53149 -0.00041 0.07492

75 2000 1998 36720 M O -2.53149 -0.00041 0.05804

77 1998 1999 35997 C O 0.44934 0.09696 0.05682

77 1998 1999 35997 M O 0.44934 0.09696 0.03168

77 1998 1999 36005 C O 0.42737 0.07064 0.04353

77 1998 1999 36005 M O 0.42737 0.07064 0.02599

77 1998 1999 36040 C O 0.33154 -0.03087 0.00715

77 1998 1999 36040 M O 0.33154 -0.03087 -0.00866

77 1999 1998 36363 C O -1.55347 -0.04558 0.02279

77 1999 1998 36363 M O -1.55347 -0.04558 -0.00149

80 1998 2002 35907 C O 3.69592 0.27892 -0.01823

80 1998 1999 35907 M O 0.69592 -0.01093 -0.00415

80 1998 1999 35907 P O 0.69592 -0.01093 -0.04243

80 1998 1999 35997 C O 0.44934 -0.03201 0.03119

80 1998 2002 35997 M O 3.44934 0.25785 0.03536

80 1998 2002 36027 C O 3.36707 0.24902 0.01962

80 1998 2000 36027 M O 1.36707 0.02831 0.01879

80 1999 2000 36356 C O 0.46570 0.06915 0.01923

80 1999 1998 36356 M O -1.53430 0.02550 0.03814

80 2000 2002 36636 C O 1.69861 0.21912 -0.03259

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 155

80 2000 1999 36636 M O -1.30139 -0.07073 -0.04271

80 2000 2002 36705 C O 1.50964 0.24331 0.07161

80 2000 2002 36705 M O 1.50964 0.24331 0.05043

80 2000 2002 36749 C O 1.38904 0.19968 0.04256

80 2000 1998 36749 M O -2.61096 -0.06468 0.02588

80 2002 1999 37489 C O -3.63831 -0.28986 -0.06887

80 2002 1999 37489 M O -3.63831 -0.28986 -0.03550

82 1998 2002 35969 C L 3.52600 0.35781 -0.22245

82 1998 2002 35993 C L 3.46033 0.34281 -0.33505

82 1998 2002 36055 C L 3.29041 0.28499 -0.21321

82 2002 1998 37419 C L -4.44653 -0.31559 -0.00886

82 2002 1998 37504 C L -4.67944 -0.34149 -0.02338

85 1998 2000 35928 C S 1.63831 0.03966 0.12878

85 1998 2001 35928 P S 2.63831 0.33975 0.44272

85 1998 1999 35970 C S 0.52332 0.28751 0.01219

85 1998 2000 35970 P S 1.52332 0.29701 0.07331

85 1998 1999 36024 C S 0.37537 -0.01239 0.02397

85 1998 2000 36024 P S 1.37537 -0.00289 0.08763

85 1999 1998 36356 C S -1.53430 -0.10176 -0.00519

85 1999 2000 36356 P S 0.46570 0.00950 0.06505

85 2000 2001 36685 C S 0.56433 0.30009 0.36838

85 2000 2001 36685 P S 0.56433 0.30009 0.33104

85 2001 1998 37055 C S -3.44934 -0.41135 -0.31196

85 2001 2000 37055 P S -1.44934 -0.30009 -0.26399

86 1998 2001 35920 C S 2.66028 0.14553 0.16179

86 1998 2001 35920 P S 2.66028 0.14553 0.10719

86 1998 2001 35976 C S 2.50684 0.01212 0.05800

86 1998 2001 35976 P S 2.50684 0.01212 0.02639

86 1998 1999 36021 C S 0.38354 -0.02765 0.02175

86 1998 1999 36021 P S 0.38354 -0.02765 -0.00410

86 1998 2002 36062 C S 3.27124 -0.29837 0.07908

86 1998 2002 36062 P S 3.27124 -0.29837 0.05332

86 1999 2000 36333 C S 0.52881 0.10911 0.01997

86 1999 2001 36333 P S 1.52881 0.03330 -0.01633

86 1999 1998 36370 C S -1.57263 -0.04966 -0.03673

86 1999 2000 36370 P S 0.42737 0.05481 -0.02191

86 2000 2002 36686 C S 1.56165 -0.35268 0.07908

86 2000 2001 36686 P S 0.56165 -0.07580 -0.04299

86 2001 2000 37055 C S -1.44934 0.07580 0.01109

86 2001 2002 37055 P S 0.55066 -0.27688 0.01478

86 2002 1998 37378 C S -4.33423 0.24821 -0.05123

86 2002 2000 37378 P S -2.33423 0.35268 -0.00077

87 1998 1999 35920 C S 0.66028 0.06763 -0.02438

87 1998 2002 35920 P S 3.66028 0.12481 -0.04079

87 1998 2000 35964 C S 1.53967 0.11665 -0.01072

87 1998 2002 35964 P S 3.53967 0.14411 -0.04741

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
156 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

87 1998 2002 36026 C S 3.36987 0.09887 0.00399

87 1998 2001 36026 P S 2.36987 0.10105 -0.02378

87 1998 2000 36062 C S 1.27124 0.03021 -0.01045

87 1998 2001 36062 P S 2.27124 0.05984 -0.06442

87 1999 2002 36370 C S 2.42737 0.05719 0.01938

87 1999 2001 36370 P S 1.42737 0.05936 -0.03460

87 2000 1998 36657 C S -2.35889 -0.06249 0.01238

87 2000 2001 36657 P S 0.64111 0.04606 -0.03421

87 2000 2002 36735 C S 1.42737 0.02285 0.01482

87 2000 2002 36735 P S 1.42737 0.02285 -0.03720

87 2000 2001 36782 C S 0.29858 0.01781 0.01692

87 2000 1999 36782 P S -1.70142 -0.04155 -0.06734

87 2001 2000 37070 C S -1.49036 -0.02232 0.00117

87 2001 1999 37070 P S -2.49036 -0.05205 -0.08343

87 2001 1998 37113 C S -3.60828 -0.10546 -0.00606

87 2001 2002 37113 P S 0.39172 0.00090 -0.01874

87 2001 2000 37140 C S -1.68225 -0.04003 -0.00617

87 2001 1999 37140 P S -2.68225 -0.06976 -0.06739

87 2002 2001 37379 C S -1.33704 0.00218 0.03264

87 2002 1998 37379 P S -4.33704 -0.10636 0.01772

89 1998 2000 35920 C O 1.66028 -0.07581 -0.04288

89 1998 2000 35920 M O 1.66028 -0.07581 0.00390

89 1998 2000 35950 C O 1.57812 -0.13482 -0.05510

89 1998 1999 35950 M O 0.57812 -0.08521 -0.01827

89 1998 1999 36048 C O 0.30957 -0.12235 -0.02096

89 1998 2000 36048 M O 1.30957 -0.17196 0.00951

89 1999 1998 36322 C O -1.44104 0.01126 -0.03224

89 1999 1998 36322 M O -1.44104 0.01126 0.00680

89 1999 1998 36370 C O -1.57263 0.14458 0.00404

89 1999 1998 36370 M O -1.57263 0.14458 0.01848

89 2000 1998 36720 C O -2.53149 0.12753 -0.00941

89 2000 1999 36720 M O -1.53149 0.04961 -0.00380

90 1998 1999 35922 C S 0.65479 -0.00101 0.05762

90 1998 2000 35922 P S 1.65479 0.07983 0.04621

90 1998 1999 35977 C S 0.50415 -0.00352 0.02918

90 1998 2002 35977 P S 3.50415 0.09323 0.12081

90 1998 2002 36021 C S 3.38354 0.06867 0.15612

90 1998 2001 36021 P S 2.38354 0.07300 0.07404

90 1999 1998 36356 C S -1.53430 0.01087 -0.03147

90 1999 2000 36356 P S 0.46570 0.08084 -0.00430

90 2000 1999 36686 C S -1.43835 -0.08084 -0.00313

90 2000 2001 36686 P S 0.56165 0.02025 -0.01821

90 2001 1998 37055 C S -3.44934 -0.09022 -0.05568

90 2002 1998 37379 C S -4.33704 -0.08588 -0.11494

90 2002 1999 37379 P S -3.33704 -0.09675 -0.09587

92 1998 2000 35920 C S 1.66028 0.02195 -0.07551

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 157

92 1998 2000 35920 P S 1.66028 0.02195 -0.10135

92 1998 2000 35964 C S 1.53967 -0.00698 -0.00091

92 1998 2000 35964 P S 1.53967 -0.00698 -0.01360

92 1998 2001 36053 C S 2.29590 0.01323 -0.01613

92 1998 2000 36053 P S 1.29590 -0.00402 -0.04953

92 1998 2000 36060 C S 1.27673 -0.00447 -0.01812

92 1998 1999 36060 P S 0.27673 0.01029 -0.02504

92 1999 2001 36333 C S 1.52881 0.01152 -0.01932

92 1999 2001 36333 P S 1.52881 0.01152 -0.05950

92 1999 2002 36370 C S 2.42737 0.00018 0.01188

92 1999 2000 36370 P S 0.42737 -0.02379 -0.04621

92 2000 1999 36643 C S -1.32056 0.02889 -0.03562

92 2000 2002 36643 P S 1.67944 0.03810 -0.08380

92 2000 2002 36719 C S 1.47119 0.01555 -0.01813

92 2000 1999 36719 P S -1.52881 0.00634 -0.09292

92 2000 2002 36782 C S 1.29858 0.01824 -0.02056

92 2000 2001 36782 P S 0.29858 0.01152 -0.08992

92 2001 2000 37012 C S -1.33154 -0.00330 -0.05060

92 2001 2000 37012 P S -1.33154 -0.00330 -0.12887

92 2001 1998 37126 C S -3.64380 -0.02752 -0.01781

92 2001 2002 37126 P S 0.35620 -0.00194 -0.06278

92 2001 2000 37168 C S -1.75891 -0.02783 0.03276

92 2002 2000 37386 C S -2.35620 -0.02396 -0.04684

92 2002 2001 37386 P S -1.35620 -0.00672 -0.04073

95 1998 2001 35921 C CL 2.65759 -0.11643 0.15816

95 1998 1999 35990 C CL 0.46851 -0.04652 0.14576

95 1998 1999 35992 C CH 0.46301 -0.31585 0.00043

95 1998 2001 35992 P CH 2.46301 -0.19551 0.00219

95 1998 2000 36035 C CH 1.34521 0.03727 0.01656

95 1998 2001 36035 P CH 2.34521 -0.09707 -0.09297

95 1998 2001 36047 C CL 2.31238 -0.10850 0.17557

95 1999 2000 36319 C CL 0.56714 0.25468 0.14995

95 2000 1999 36635 C CL -1.29858 -0.22505 0.10352

95 2000 2001 36649 C CH 0.66296 -0.13098 -0.00123

95 2000 1999 36719 C CH -1.52881 -0.28768 -0.07067

95 2001 2000 36991 C CH -1.27393 0.06053 -0.04424

95 2001 2000 37064 C CL -1.47400 0.20816 0.12089

97 1998 2002 35929 C CH 3.63562 0.09846 0.08022

97 1998 2002 35929 C CL 3.63562 0.06298 0.19709

97 1998 2000 35984 C CH 1.48499 0.04484 0.03037

97 1998 2002 35984 C CL 3.48499 0.10738 0.22277

97 1998 2000 36029 C CH 1.36169 0.06636 0.04575

97 1998 2000 36029 C CL 1.36169 0.04065 0.13371

97 1999 1998 36369 C CH -1.56982 0.04946 -0.01793

97 1999 2001 36369 C CH 1.43018 0.05470 0.09073

97 2000 1998 36692 C CL -2.45483 -0.02088 0.02498

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
158 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

97 2001 1999 37119 C CH -2.62463 -0.06324 -0.04941

97 2002 1998 37448 C CL -4.52600 -0.11934 0.02374

98 1998 1999 35927 C CH 0.64111 0.00257 -0.09568

98 1998 2002 35927 C CL 3.64111 0.11244 -0.06119

98 1998 1999 35984 C CL 0.48499 0.02440 -0.03399

98 1998 1999 36047 C CH 0.31238 0.04887 -0.11715

98 1998 2000 36047 C CL 1.31238 0.02489 -0.09194

98 1998 2000 36056 C CL 1.28772 0.01712 -0.08859

98 1999 1998 36320 C CH -1.43567 -0.00977 0.06601

98 2000 1999 36651 C CH -1.34241 -0.01173 -0.00346

98 2001 1999 37011 C CL -2.32874 -0.05657 -0.03196

98 2001 1999 37083 C CL -2.52600 -0.03031 0.00902

98 2002 1998 37356 C CL -4.27393 -0.15797 -0.00133

99 1998 2001 35928 C CH 2.63831 0.37002 -0.35674

99 1998 2002 35928 C CL 3.63831 0.20867 0.12063

99 1998 2001 35976 C CH 2.50684 0.36096 -0.35949

99 1998 2002 35976 M CH 3.50684 0.31142 -0.06818

99 1998 2001 35976 C CL 2.50684 0.24761 -0.16796

99 1998 2001 35976 M CL 2.50684 0.24761 -0.16788

99 1998 2000 36061 C CH 1.27393 0.10194 -0.29227

99 1998 2002 36061 M CH 3.27393 0.25549 -0.05510

99 1998 2001 36061 C CL 2.27393 0.21403 -0.15744

99 1998 2002 36061 M CL 3.27393 0.16449 0.12990

99 2000 2002 36735 C CH 1.42737 0.15354 0.01243

99 2000 1998 36735 M CH -2.57263 -0.08526 -0.23424

99 2001 2002 37007 C CL 0.68225 -0.04954 0.13753

99 2001 1998 37007 M CL -3.31775 -0.28835 -0.10475

99 2002 2000 37385 C CH -2.35339 -0.15354 -0.27034

99 2002 2001 37385 M CH -1.35339 0.04954 -0.31510

100 1998 2002 35942 C CL 3.59998 0.24379 0.07843

100 1998 2002 35942 C CL 3.59998 0.19750 0.07906

100 1998 2002 35942 M CL 3.59998 0.24379 0.07013

100 1998 2001 35942 M CL 2.59998 0.19812 0.03616

100 1998 2001 35970 C CL 2.52332 0.19986 0.05829

100 1998 2001 35970 M CL 2.52332 0.19986 0.05526

100 1998 2002 36033 C CL 3.35071 0.10770 0.11265

100 1998 2001 36033 C CL 2.35071 0.06780 0.07668

100 1998 2001 36033 M CL 2.35071 0.10832 0.06890

100 1998 2001 36033 M CL 2.35071 0.06780 0.06744

100 2001 2002 36998 C CL 0.70691 0.03858 0.06889

100 2001 2002 36998 M CL 0.70691 0.03858 0.04337

100 2001 1998 37091 C CL -3.54797 -0.16878 -0.05725

100 2001 1998 37091 M CL -3.54797 -0.16878 -0.06021

100 2001 2002 37160 C CL 0.26306 -0.03473 0.06967

100 2001 1998 37160 M CL -3.73694 -0.19782 -0.05051

100 2002 1998 37349 C CL -4.25476 -0.16309 -0.10141

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
Supplemental Information 159

100 2002 1998 37349 M CL -4.25476 -0.16309 -0.10424

101 1998 1999 35935 C CH 0.61914 -0.13201 -0.04417

101 1998 1999 35935 M CH 0.61914 -0.13201 -0.05580

101 1998 2000 35935 C CL 1.61914 -0.21905 0.35063

101 1998 2000 35935 M CL 1.61914 -0.21905 0.33385

101 1998 2000 35991 C CH 1.46570 -0.22722 0.06606

101 1998 1999 35991 M CH 0.46570 -0.13936 0.00021

101 1998 2000 35991 C CL 1.46570 -0.22559 0.38171

101 1998 2000 35991 M CL 1.46570 -0.22559 0.37277

101 1998 1999 36025 C CH 0.37256 -0.20237 -0.05124

101 1998 1999 36025 M CH 0.37256 -0.20237 -0.06626

101 1998 1999 36025 C CL 0.37256 -0.20008 0.29496

101 1998 1999 36025 M CL 0.37256 -0.20008 0.27917

101 1999 2000 36364 C CH 0.44385 -0.08786 0.00647

101 1999 1998 36364 M CH -1.55615 0.15712 -0.01001

101 2000 1998 36672 C CL -2.40002 0.24498 -0.16279

101 2000 1998 36672 M CL -2.40002 0.24498 -0.17425

102 1998 2001 35934 C CH 2.62195 0.05377 0.14176

102 1998 2000 35934 M CH 1.62195 0.21580 -0.03236

102 1998 2001 35934 C CL 2.62195 -0.02450 0.31835

102 1998 2000 35934 M CL 1.62195 0.13753 0.14396

102 1998 2002 35985 C CH 3.48218 0.19510 -0.02277

102 1998 2002 35985 C CL 3.48218 0.14627 0.14481

102 1998 2001 36067 C CH 2.25757 -0.12907 0.17887

102 1998 2002 36067 C CL 3.25757 0.15203 0.14700

102 1999 2000 36335 C CH 0.52332 0.07121 0.02737

102 2000 2002 36747 C CH 1.39453 0.16638 -0.07326

102 2001 2000 37105 C CH -1.58630 0.16203 -0.13273

102 2002 1998 37420 C CL -4.44934 -0.25811 0.09596

103 1998 2001 35913 C CH 2.67944 0.03200 -0.10841

103 1998 2002 35913 P CH 3.67944 0.15321 -0.10244

103 1998 2001 35913 C CL 2.67944 0.00018 0.21463

103 1998 2002 35913 P CL 3.67944 0.12140 0.22253

103 1998 2001 35963 C CH 2.54248 0.07992 0.00820

103 1998 2002 35963 P CH 3.54248 0.20114 0.03576

103 1998 1999 35963 C CL 0.54248 -0.08662 0.26552

103 1998 2002 35963 P CL 3.54248 0.14088 0.30889

103 1998 2000 36039 C CH 1.33423 0.09242 -0.03273

103 1998 1999 36039 P CH 0.33423 0.07218 -0.00604

103 1998 2002 36039 C CL 3.33423 0.22025 0.31168

103 1998 2001 36039 P CL 2.33423 0.09903 0.29216

103 1999 2002 36329 C CH 2.53967 0.22751 -0.02362

103 1999 2002 36329 P CH 2.53967 0.22751 -0.05554

103 2000 2001 36693 C CH 0.54248 0.08605 0.05518

103 2000 2001 36693 P CH 0.54248 0.08605 0.04010

103 2001 2000 37062 C CH -1.46851 -0.08605 -0.06868

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w
160 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

103 2001 1999 37062 P CH -2.46851 -0.10629 -0.02803

103 2002 1998 37413 C CH -4.43018 -0.18943 -0.05863

103 2002 2000 37413 P CH -2.43018 -0.20727 -0.04257

104 1998 1999 35922 C CL 0.65479 -0.00406 0.08151

104 1998 1999 35922 C CL 0.65479 -0.01270 0.07013

104 1998 2002 35922 M CL 3.65479 -0.15467 0.06861

104 1998 2001 35922 M CL 2.65479 0.02325 0.05856

104 1998 2002 35964 C CL 3.53967 -0.16484 0.06698

104 1998 1999 35964 C CL 0.53967 -0.01671 0.05153

104 1998 2001 35964 M CL 2.53967 0.02172 0.04257

104 1998 2002 35964 M CL 3.53967 -0.16731 0.05073

104 1998 2001 36021 C CL 2.38354 0.06662 0.06300

104 1998 2001 36021 C CL 2.38354 0.04255 0.07330

104 1998 2002 36021 M CL 3.38354 -0.11993 0.04664

104 1998 1999 36021 M CL 0.38354 0.00661 0.02559

104 1999 2001 36334 C CL 1.52600 0.03595 0.09117

104 1999 1998 36334 M CL -1.47400 0.00174 0.04828

104 2000 1999 36649 C CL -1.33704 -0.01594 0.08642

104 2000 2001 36649 M CL 0.66296 0.02000 0.08553

104 2001 2000 37013 C CL -1.33423 -0.02000 0.08116

104 2001 1999 37013 M CL -2.33423 -0.03595 0.06445

104 2002 2000 37379 C CL -2.33704 0.16655 0.06367

104 2002 1998 37379 M CL -4.33704 0.15234 0.00086

105 1998 2001 35927 C CH 2.64111 0.07183 -0.06524

105 1998 2002 35927 C CH 3.64111 0.11662 0.08322

105 1998 1999 35992 C CH 0.46301 -0.05898 -0.07505

105 1998 1999 35992 C CH 0.46301 -0.13386 0.09391

105 1998 1999 35992 C CL 0.46301 -0.13709 0.10346

105 1998 2000 36042 C CH 1.32605 -0.04595 -0.10832

105 1998 1999 36042 C CL 0.32605 -0.13508 0.13069

105 1999 1998 36335 C CH -1.47668 0.08903 -0.05068

105 2000 1999 36649 C CH -1.33704 -0.01095 0.00545

105 2001 1999 37064 C CH -2.47400 -0.06641 0.01153

105 2002 2001 37492 C CH -1.64661 -0.15692 -0.02071

106 1998 2001 35955 C CL 2.56433 -0.16149 0.11534

106 1998 2001 36011 C CL 2.41101 -0.14844 0.17752

106 1998 2002 36055 C CL 3.29041 0.20726 -0.09471

106 1998 2002 36055 C CL 3.29041 0.19441 -0.08386

106 2001 1998 37162 C CL -3.74243 0.13259 0.07095

106 2002 1998 37372 C CL -4.31775 -0.17846 0.12636

 Table 15. Data used in the diffP model where PCC measurements and pumpage estimates were made in different 

years.—Continued

[Year-PCC, year that PCC was measured; PCC, power conversion coefficient; Year-pump, year that power consumption was used

to estimate pumpage; Date, number of days from January 1, 1900; C, Collins flowmeter; P, Polysonic flowmeter; M, McCrometer flowmeter;

O, open; CL, complex low; CH, complex high; L, low pressure; S, sprinkler; u, the diffP lag time; , average log pumping water level for a 

given site in a given year; , log of pumping water level at time of measurement; diffP, log total pumpage using PCC minus log total 

pumpage using totalizing flowmeter]

Site Yearpcc

Yearpump Date Method Type u - diffP

w

w

w w