Home Reports Start

Preliminary Report on Statistical Quality Control for Year 2001 Water Well Measurements

John C. Davis

logo of Kansas Geological Survey Kansas Geological Survey

Report to the Director of the
Kansas Geological Survey
University of Kansas
Open-file Report No. 2001-2
Released Jan. 22, 2001, Electronic version created Jan. 2002


The Quality Control and Assurance Program for the year 2001 observation well measurement season followed the general outline for quality assurance developed during the preceding four years, as described in Miller, Davis, and Olea (1997). This discussion of procedures is taken primarily from that source.

The primary variable measured in the water well observation program is depth to water in an observation well. This primary variable is associated with three secondary variables; the ground elevation, east-west coordinate, and north-south coordinate of the well. The secondary variables serve to locate the primary variable in space, and make it possible to determine spatial relationships between observation wells, including mapping the water table and calculating changes in aquifer volume. Historically, the three location variables were determined initially by the U.S. Geological Survey for each well and not re-determined unless a serious error in the original coordinates was suspected. In the 1997 ground water observation measurement program conducted by the Kansas Geological Survey, the geographic (latitude and longitude) coordinates of all wells were redetermined by GPS techniques. In subsequent year's measurement programs, all observation wells were again re-determined by GPS. "Selective Availability," which limited the resolution of GPS measurements, was turned off by the Federal government in 2001, so locations determined this year have been substituted for previous determinations whenever possible. Otherwise, 1999 GPS measurements, which were previously considered the most accurate for reasons discussed in Miller, Davis, and Olea (1998), are used in this study.

In addition, several secondary characteristics of the observation wells and of the measurement procedure were noted in order to determine if these might influence the quality of the measurements being made (in statistical parlance, these extra measurements are called exogenous variables). As part of the quality control program, water level measurements were repeated two or more times on 71 wells, yielding a collection of 96 quality control observations. Because these data include replicates, they provide an additional check on estimates of the influence of well conditions or measuring techniques on water levels. A subsequent round of measurements resampled 48 wells selected at random from the original set for quality assurance purposes.

The primary variable, depth to water, varies with geographic location and differences in topography so much that these factors will overwhelm all other sources of variation. This means that any errors in location may have a profound effect on the water table elevation. To avoid the complications of simultaneously considering uncertainties in the secondary variables, this statistical quality control study is based on first differences (specifically, the difference between 2001 and 2000 depth-to-water measurements). The secondary variables cancel out, leaving only the difference in depth, which is numerically identical to the year's change in water level. In this statistical quality control study, the difference between 2001 and 2000 corrected depth measurements is abbreviated '01-'00. If the water. table is lower this year, the variable '01-'00 will be a positive number. Because all wells measured in the current program were also measured in 1999, there are a total of 494 wells having the variable '01-'00. This is fewer than the 548 wells measured in 2000, because DWR has assumed responsibility for measuring observation wells in Pawnee and Barton Counties.

The objective in our quality control study is to identify and assess possible sources of unwanted variation in water level measurements made by the KGS. The purpose of the analysis is to provide guidance to the KGS field measurement program, to suggest ways in which field measurements might be improved, and to provide information necessary to identify past or current measurements that are suspect. The statistical quality control and field measurement programs have been intimately intertwined from the outset when the KGS assumed responsibility in 1997 for measuring observation welts formerly measured by the USGS. A comparison of results from 2001 with those from previous years shows that the desired improvements in the measurement program are being achieved through quality control.

Statistical Procedures

A preliminary examination showed that one well, 30S 31W 26ABB 01, deviated from last year's measurement by almost 100 feet. Field notes indicate that this well has been plugged and water in the well is perched on top of the clay plug. This well has been removed from the data base. In addition, all repeated measurements are excluded from this analysis to avoid inflating the total variance. 493 observations are included in the initial statistical analyis, which is an unbalanced analysis of variance (ANOVA) procedure designed to estimate the influence of different well characteristics and procedural differences on variable '01-'00. The following variables have been recorded for each well.
1. Depth to water
2. GPS longitude
3. GPS latitude
4. Date
5. Measurer's initials
6. Well Access
1 = good
0 = poor
7. Weighted Tape
1 = yes
0 = no
8. Oil on Water
1 = yes
0 = no
9. Chalk Cut Quality
2 = excellent
1 = good
0 = poor
The variable downhole access was removed from the list of recorded varibles in 2001 because previous years' analyses have shown that measurers did not consistently distinguish between this variable and the variable well access. In instructions to field measurers this year, the two were effectively combined. In addition, each well has a unique USGS ID number and KGS ID designation, a surface elevation, a legal description of the well location, a decimal latitude and longitude (obtained by LEO conversion of the legal description), and the purpose for which water from the well is used. The variable Aquifer Code describes the primary source of water in the well; the manner in which aquifer code values were assigned is summarized in Miller, Davis, and Olea (1997). The additional variables taken from the historical records are:
10. Well Use
H = household water supply
S = stock water supply
I = irrigation
U = unused observation
Z = animal disposal
11. Aquifer Code
KD = Cretaceous Dakota aquifer
KJ = undifferentiated Cretaceous/Jurassic aquifer
KN = Cretaceous Niobrara aquifer
KU = undifferentiated Cretaceous aquifer
QA = Quaternary alluvium aquifer
QAQU = Quaternary alluvium and undifferentiated aquifers
QAQUTO = Quaternary alluvium and undifferentiated aquifers and Tertiary Ogallala aquifer
QATO = Quaternary alluvium and Tertiary Ogallala aquifers
QU = Quaternary undifferentiated aquifer
QUTO = Quaternary undifferentiated and Tertiary Ogallala aquifers
QUTOKJ = Quaternary undifferentiated, Tertiary Ogallala, and Cretaceous/ Jurassic aquifers
QUKD = Quaternary undifferentiated and Cretaceous Dakota aquifers
TO = Tertiary Ogallala aquifer
TOKD = Tertiary Ogallala and Cretaceous Dakota aquifers
TOKJ = Tertiary Ogallala and undifferentiated Cretaceous/Jurassic aquifers

The initial statistical model includes all exogenous variables recorded during the quality control study that may contribute to the variability in the response, '01-'00, plus the variables Well Use and Aquifer Code. As in the 2000 measurement program, no exogenous variables contribute significantly to the total variance except for a significant operator effect as measured by the variable Measurer and a sgnificant effect of Chalk Cut Quality. As in earlier years, there are significant contributions to total variance from Well Use and Aquifer Code.

Analysis of Variance Table for Initial Model
SourceDFSum of Squares Mean SquareF RatioProb>F
Well Access116.436116.43612.04270.1536ns
Weighted Tape117.212517.21252.13920.1443ns
Well Use4158.599839.65004.92770.0007**
Oil on Water126.449826.44983.28720.0705ns
Chalk Cut Quality2142.172271.08618.83460.0002**
Aquifer Code13369.062328.38943.5283<0.0001**
A revised model was run that combined aquifers into classes similar to those used in 1997 through 2000. This 5-part classification distinguishes between (1) wells that tap alluvial aquifers, (2) wells that tap both alluvial aquifers and other unconsolidated aquifers, (3) wells drawing from the High Plains aquifer, (4) wells into bedrock aquifers, and (5) wells that draw from both bedrock and unconsolidated aquifers. This has the effect of reducing the degrees of freedom required for the model and thus increasing the sensitivity of the analysis for detecting other influences.

Analysis of Variance table for Grouped Aquifers
SourceDFSum of Squares Mean SquareF RatioProb>F
Well Access119.193119.19312.32470.1280ns
Weighted Tape122.733522.73352.75350.0977ns
Well Use4193.259148.31485.85200.0001**
Oil on Water122.653022.65302.74380.0983ns
Chalk Cut Quality2121.822260.91117.37760.0007**
Aquifer Group5205.638941.12784.98150.0002**

Measurer, Well Use, Chalk Cut Quality, and Aquifer Group are signficant sources of variation in the revised model, in contrast to last year when only Measurer and Aquifer Group were significant. Unfortunately, past models are not directly comparable because there are different numbers of degrees of freedom assigned to some variables, and the response (annual change in water level) has significantly different variances from year to year. Last year it was noted that the variance of the response variable seems to alternate in magnitude every other year; this pattern continues in 2001 which has a significantly higher variance than measurements made in 2000. Although the year-to-year changes in total variance are highly significant, the cause is speculative.

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. Twenty-four wells were deleted from the network in 2000; this year, only six wells exhibit extreme behavior, and one of these has been deleted from the network because it is plugged and cannot be measured in the future.

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 '01-'00 for a specified state of a variable, while holding all other variables at their average value. (In statistical parlance, 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 2001 than in 2000 (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 Group
Least Sq Mean
1 (Cretaceous)-3.5029
2 (Alluvium)-0.1388
3 (Al. + Tert.)1.0707
4 (Tertiary)1.6145
5 (Tert. + K)0.7837

Summary of the Analyses of Variance

Data collected in 2001 show significant variations attributable to Measurer, Well Use, and Chalk Cut in addition to differences between the aquifer being tapped by the well. The standard deviation of variable '01-'00 is 3.07 ft., greater than the standard deviation of variable '00-'99 (2.69 ft.), but less than the standard deviation of variable '99-'98 (4.21 ft.). The median decline in water level from 2000 to 2001 is 1.39ft., much greater than the 1999 to 2000 decline of 0.31 ft., the 1998 to 1999 decline (0.72 ft.) or the decline between 1997 to 1998 (0.41 ft.).

There are significant differences between measurers, almost all attributable to PAM and RDM. It should be noted that RDM is the "clean-up" person responsible for remeasuring wells which proved difficult for others to measure.

Water levels measured in 2001 in exclusively Cretaceous aquifers (Group 1) show declines of over 3.5 ft. from 2000. The water level in the Ogalalla aquifer (Group 4) tends to be over 1.6 ft. deeper than last year. Measurements made in wells tapping alluvial aquifers (Group 2) show a slight increase in water level. Wells in alluvial plus other sources (Group 3) show a decline in water level of slightly over 1 ft. Water levels in wells tapping Cretaceous aquifers plus Quaternary and/or Tertiary aquifers (Group 5) tend to be a little over 0.7 feet deeper this year. There are highly significant differences of the annual change in water level among aquifers, mostly due to the behavior of Cretaceous wells. (Statistics for 2001 are not comparable in detail with those from previous years because of the change in responsibility for wells in two counties.)

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. Five wells have been identified by this process. These wells show changes in water level between 2000 and 2001 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 2000; or changes in well construction or other factors may have altered the measurability of a well. The five wells, with their residuals, are:

Well IDResidual, ft.
24S 33W 18BDB 0221.8
33S 37W 35ACD 0119.4
30S 32W 31BAB 0119.3
24S 33W 19DBB 0213.7
27S 25W 25BBB 0110.4

This list does not include well 30S 31W 26ABB 01, which has already been removed from the analysis because it was plugged after the 2000 measurement season and can no longer be measured. Although the five wells listed above deviate signficantly from their expected values, two of them were measured by a person with no prior field experience and the measurements may not be reliable, two are Cretaceous aquifer wells that have a history of erratic measurments, and the fifth has such a limited prior history that no conclusions can be drawn as to how consistent its 2001 measurement might be. Because so few wells have questionable measurements, the decision was made not to have a post-season remeasurement program in 2001.

Quality Assurance (remeasure) Program

The year 2001 Quality Assurance program of random remeasurements showed that the QA data contained only one statistically significant sources of variation. Forty-eight randomly selected QA wells were remeasured by experienced personnel during the period when the regular field measurement program was underway. These were combined with data from the regular measurement program, to yield 106 measurements for statistical quality control. In spite of the additional control provided by replication, a significant contribution from only one exogenous variable, well use, was detected. As expected, the variance among the QA replicates is about 40% lower than the variance of the complete data set. The most extreme value of '01-'00 among the QA wells is only 8.7 feet, compared to an extreme of 28.8 feet in the complete data set.

Within the QA data set alone, there are significant contributions due to Measurer, mostly attributable to JMA and MWF. No other erogenous variables, including Geological Units, show any significant differences between levels in the QA data set.


The purpose of the Quality Control and Assurance Program is to identify wells and procedural conditions that may contribute significantly to the variance of Depth to Water measured in observation wells, and which does not reflect true changes in the water table elevation. Gathering Quality Control information requires little additional effort by the field crews, emphasizes the importance of procedural consistency, and certifies performance. Quality Control for the year 2001 field season is remarkably free of inconsistencies compared to previous field seasons. The results can be interpreted as reinforcing the need for training and the desirability of deleting troublesome wells from the monitoring program. The QA process continues to identify specific wells as troublesome, and flags well locations which require verification before being permanently incorporated into the WIZARD data base.

The Quality Control program has achieved its objectives of identifying and quantifying sources of unwanted variation in observation well data collection, and in flagging wells whose measurements required verification. It detected a small number of spurious values, confirming the benefits of "cleaning" the data base in past years. As the Quality Control process is routinely applied to KGS observation well measurements in the future, and particularly if it is applied to the entire Kansas observation well network, the quality of the groundwater measurement data will continue to be progressively improved with time.


Miller, R.D., J.C. Davis, and R.A. Olea, 1997, Acquisition Activity, Statistical Quality Control, and Spatial Quality Control for 1997 Annual Water Level Data Acquired by the Kansas Geological Survey: Kansas Geological Survey Open-File Report No. 97-33, 45 p. [Available Online]

Miller, R.D., J.C. Davis, and R.A. Olea, 1998, 1998 Annual Water Level Raw Data Report for Kansas: Kansas Geological Survey Open-File Report No. 98-7, 275 p., 6 plates, and 1 compact disk. [Available Online]

Next Page--Appendix A

Kansas Geological Survey, Water Level CD-ROM
Send comments and/or suggestions to webadmin@kgs.ku.edu
Updated Jan. 11, 2002
Available online at URL = http://www.kgs.ku.edu/Magellan/WaterLevels/CD/Reports/OFR01_2/rep00.htm