by
John C. Davis
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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 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.
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 | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 28 | 912.5326 | 32.5904 | 4.0504 | <0.0001 |
| Measurer | 6 | 312.7253 | 52.1209 | 6.4776 | <0.0001** |
| Well Access | 1 | 16.4361 | 16.4361 | 2.0427 | 0.1536ns |
| Weighted Tape | 1 | 17.2125 | 17.2125 | 2.1392 | 0.1443ns |
| Well Use | 4 | 158.5998 | 39.6500 | 4.9277 | 0.0007** |
| Oil on Water | 1 | 26.4498 | 26.4498 | 3.2872 | 0.0705ns |
| Chalk Cut Quality | 2 | 142.1722 | 71.0861 | 8.8346 | 0.0002** |
| Aquifer Code | 13 | 369.0623 | 28.3894 | 3.5283 | <0.0001** |
| Error | 464 | 3733.4864 | 8.0463 | ||
| Total | 492 | 4646.0190 | |||
| RSquare | 0.1964 | ||||
| Analysis of Variance table for Grouped Aquifers | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 20 | 749.1091 | 37.4555 | 4.5367 | <.0001** |
| Measurer | 6 | 293.4023 | 48.9004 | 5.9229 | <.0001** |
| Well Access | 1 | 19.1931 | 19.1931 | 2.3247 | 0.1280ns |
| Weighted Tape | 1 | 22.7335 | 22.7335 | 2.7535 | 0.0977ns |
| Well Use | 4 | 193.2591 | 48.3148 | 5.8520 | 0.0001** |
| Oil on Water | 1 | 22.6530 | 22.6530 | 2.7438 | 0.0983ns |
| Chalk Cut Quality | 2 | 121.8222 | 60.9111 | 7.3776 | 0.0007** |
| Aquifer Group | 5 | 205.6389 | 41.1278 | 4.9815 | 0.0002** |
| Error | 472 | 3896.9098 | 8.2562 | ||
| Total | 492 | 4646.0190 | |||
| RSquare | 0.1612 | ||||
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.
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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 ID | Residual, ft. |
|---|---|
| 24S 33W 18BDB 02 | 21.8 |
| 33S 37W 35ACD 01 | 19.4 |
| 30S 32W 31BAB 01 | 19.3 |
| 24S 33W 19DBB 02 | 13.7 |
| 27S 25W 25BBB 01 | 10.4 |
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.
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 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, 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]