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Analysis of DWR Water Well Measurements

John C. Davis

Supplement to OFR 2003-8, Released Feb. 19, 2003, Electronic version created Jan. 2005


In 2003, field crews from the Division of Water Resources (DWR) were equipped with devices for digitally capturing observation well measurements in the field. Although lacking the on-screen navigation capabilities of lap-top computers running the WaterWitch software used by KGS personnel, the DWR's Personal Digital Assistants (PDA's) and attached GPS devices possess the same data-collection functionality. The PDA software, called WaterBug, is a subset of WaterWitch and produces records that are similar in format.

For the first time, information has been collected by DWR personnel that is comparable to that routinely gathered by KGS field operators and which can be used to statistically assess the significance of extraneous influences on the water level measurements. This supplement to OFR2003-8 provides a statistical quality control analysis similar to that performed annually on KGS measurements of observation wells. The initial data base of DWR measurements contained 805 rows representing 787 observation wells. Of these, 26 observation wells could not be used because there was no measurement of depth to water for 2002, and hence no annual change in water level, variable '03-'02. The usable data base therefore contains 761 wells. Nine of these wells failed a preliminary threshold screening that checks for extreme values of '03-'02. Of these, three wells reported previous year's depths to water that were significantly deeper than expected from past trends, resulting in values of '03-'02 that are extreme and negative. Depths to water in the other six wells are much deeper in 2003 than expected from past trends so that '03-'02 is extreme and positive. However, these may reflect true depletions over the past year, which has been exceptionally dry in western Kansas. Under KGS operating procedures, these nine wells would have been remeasured in a subsequent quality control step and the remeasurements used for statistical analyses. The original measurements, listed below, are included in analyses that follow.

Well Location '03-'02
22S 17W 05BBC 02 -23.12
18S 38W 23BAB 01 -10.93
28S 08W 26ABC 01 -10.23
29S 43W 33CDB 01 23.13
29S 37W 29BBA 01 20.35
27S 39W 27BBA 01 19.71
09S 28W 15CBA 01 17.67
27S 42W 17CCC 01 16.95
O1S 29W 03DDB 01 12.82

Statistical Procedures

The measurements of 761 wells made by DWR are included in the statistical analysis, which is an unbalanced analysis of variance (ANOVA) procedure designed to estimate the influence of different well characteristics and procedural differences on variable '03-'02. The same variables have been recorded for each DWR well as for KGS wells. However, the variable Well Use contains the additional categories N = industrial, and P = public, and the variable Aquifer Code does not include the category KN = Cretaceous Niobrara aquifer. Of course, all of the categories of Measurer are different.

The statistical model fitted to the DWR measurements includes all exogenous variables recorded during the quality control study that might add to the variability in the response, '03-'02, plus the variables Well Use and Aquifer Code. In contrast to the KGS measurement program, the exogenous variable Weighted Tape contributed significantly to the total variance. As expected there also was a significant operator effect measured by the variable Measurer. The only other significant contribution to total variance came from Aquifer Code.

Analysis of Variance table for DWR model
Source DF Sum of Squares Mean Square F Ratio Prob>F
Model 35 1095.5336 31.3010 5.4018 <0.0001
Measurer 12 609.5943 50.7995 8.7667 <0.0001**
Well Access 1 5.9545 5.9545 1.0276 0.3111ns
Weighted Tape 1 26.4051 26.4051 4.5569 0.0331*
Well Use 6 46.8101 7.8017 1.3464 0.2341ns
Oil on Water 1 3.2523 3.2523 0.5613 0.454Qns
Chalk Cut Quality 2 24.0394 12.0197 2.0743 0.1264ns
Aquifer Code 12 225.1937 18.7661 3.2386 0.0001**
Error 725 4201.0792 5.7946    
Total 760 5296.6128      
RSquare 0.21
ns = Not significant; * = Significant; ** = Highly significant

Because this is possibly the only year that statistical quality control data will be collected from DWR wells, additional analyses such as those routinely run on KGS wells grouped by aquifer type were not performed.

One way to improve the statistical results of the measurement program is to discard wells in which exogenous variables make unusually high contributions to the total variance, arguing that the readings from such wells are atypical and likely erroneous. In addition to the nine wells flagged in the initial examination, there are 14 more wells which were rated "poor" on Well Access and "no weight used" on Weighted Tape. Based on prior experience by KGS measurers, these wells should be considered for replacement by DWR.

Well Location '03-'02
26S 16W 18CAC 01 4.1
30S 35W 19BCD 01 9.63
28S 09W 01BCC 01 -0.45
17S 28W 15BBC 01 1.85
17S 28W 26ABB 01 0.39
17S 28W 34CBB 01 0.09
17S 30W 20BBB 01 6.22
35S 41W 16CCD 01 -9.7
28S 13W 02DDC 01 0.22
25S lOW 19ABD 01 3.62
17S 32W 16BBB 01 3.33
20S 33W 36CAD 01 5.58
24S 11W 17DDB 01 1.44
30S 40W 33CCB 01 0.76

Importance of contributing variables

We can determine the relative contributions of each category of the contributing variables by examining the least-squares means (averages) of '03-'02 for a specified state of a variable, while holding all other variables at their average value. (In statistical terms, these averages are referred to as the expected values of the variables.) A positive value indicates the average depth to water in a well is greater in 2003 than in 2002 (the water level has declined from last year's measurement). That is, the elevation of the water level in the well is lower than it was previously. The following list gives the least-squares means for the complete data set.

Least Sq Mean
Well Access
Least Sq Mean

Weighted Tape
Least Sq Mean
Well Use
Least Sq Mean
Oil on Water
Least Sq Mean
Chalk Cut
Least Sq Mean
Geologic Unit
Least Sq Mean

Summary of the Analysis of Variance

DWR Year 2003 measurements show significant or highly significant variations attributable to Measurer and Weighted Tape in addition to differences between the aquifer being tapped by the well. The standard deviation of variable '03-'02 of DWR wells is 2.64 ft., which is less than the standard deviation of variable '03-'02 of KGS wells (3.86 ft.). The median decline in water level from 2002 to 2003 in DWR wells is 1.21 ft., in constrast to the median decline in water level from 2002 to 2003 in KGS wells which is 2.50 ft.

The significant differences between measurers are mostly attributable to operator DWA (who tended to produce deeper than expected measurements) and DWZ (who tended to produce shallower than expected measurements). In addition, operators DB, PHD, and SB all tended to produce values that were shallower than expected, although not so extreme as DWZ.

The ANOVA equation can be used to create an expected value and residual (difference between observed and expected value) for each well. The distribution of residuals should be approximately normal. Examination of the residual outliers will reveal any well measurements which cannot be explained by extreme combinations of the different sources of variation. The residual plot is more peaked than normal and skewed toward negative values. As a consequence, outliers or extreme values are those measurements which differ from their expected values by an amount that is greater for positive residuals than for negative residuals. The approximate upper and lower limits are +10 ft. and -5 ft. Nineteen wells have been identified by this process. These wells show changes in water level between 2002 and 2003 that are outside the range expected. These well measurements may be correct and reflect unusual changes in aquifer level; the wrong wells may have been measured in one year or the other; or changes in well construction or other factors may have altered the measurability of a well. The 19 wells, with their residuals, are:

Well ID Residual, ft.
01S 29W 03DDB 01 11.28
13S 27W 16CA 02 -5.49
29S 37W 29BBA 01 14.64
30S 32W 22BBB 01 13.04
16S 40W 15ACC 01 -6.99
28S 08W 26ABC 01 -12.26
35S 41W 16CCD 01 -9.04
22S 17W 05BBC 02 -22.09
09S 28W 15CBA 01 15.75
27S 39W 27BBA 01 13.60
27S 42W 17CCC 01 10.47
28S 41W 02CCC 01 -7.66
29S 42W 27DAD 01 -4.47
29S 43W 33CDB 01 14.38
30S 42W 12ACC 01 -6.21
30S 43W 36BB 01 -4.53
06S 35W 26ACB 01 -6.15
10S 31W 29AAB 01 -6.07
18S 38W 23BAB 01 -11.25

A positive residual indicates that the 2003 water level is lower than predicted in a well with a declining water level, or is not as high as predicted in a well with an increasing water level. A negative residual indicates that the 2003 water level has declined less than predicted in a well with a declining water level, or has risen more than predicted in a well with a rising water table. These wells, along with wells previously identified by other criteria and DWR wells showing anomalous geostatistical characteristics (identified in Olea and Davis, 2003) should be scrutinized closely during the next field measurement season to determine if they should be replaced in the network.

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Updated Jan. 5, 2005
Available online at URL = http://www.kgs.ku.edu/Magellan/WaterLevels/CD/Reports/OFR03_8/rep01.htm