1999 Annual Water Level Raw Data Report for Kansas
Prev Page--Acquisition Activity || Next Page--Conclusions
John C. Davis, Mathematical Geology Section
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 groundwater observation measurement program conducted by the Kansas Geological Survey, the geographic (latitude and longitude) coordinates of all wells were re-determined by GPS techniques. In subsequent measurement programs, all observation wells were again redetermined by GPS. The 1999 measurements are considered the most accurate for reasons discussed in Miller, Davis, and Olea (1998) and 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 122 wells, yielding a collection of 164 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 51 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 1999 and 1998 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 1999 and 1998 corrected depth measurements is abbreviated "'99-'98." If the water table is lower this year, the variable '99-'98 will be a positive number. Because seventeen wells measured in the current program were not measured in 1998, a total of 525 wells have the variable '99-'98.
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 wells formerly measured by the USGS. A comparison of results from 1999 with those from previous years shows that the quality control program is resulting in the desired improvements in the measurement program.
| Analysis of Variance Table for Initial Model | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 29 | 1225.9997 | 42.2759 | 2.4983 | >0.0001** |
| Measurer | 7 | 302.25694 | 43.17956 | 2.5517 | 0.0137** |
| Well Access | 1 | 2.71534 | 2.71534 | 0.1605 | 0.6889ns |
| Downhole Access | 1 | 0.46508 | 0.46508 | 0.0275 | 0.8684ns |
| Weighted Tape | 1 | 175.35171 | 175.35171 | 10.3625 | 0.0014** |
| Well Use | 3 | 178.91146 | 59.63710 | 3.5243 | 0.0149* |
| Oil on Water | 1 | 6.96890 | 6.96890 | 0.4118 | 0.5213ns |
| Chalk Cut Quality | 2 | 155.89459 | 77.94730 | 4.6064 | 0.0104** |
| Aquifer Code | 13 | 419.48970 | 32.26844 | 1.9069 | 0.0271* |
| Error | 512 | 8663.9109 | 16.9217 | ||
| Total | 541 | 9889.9106 | |||
| RSquare | 0.123965 | ||||
A revised model was run that combined aquifers into classes similar to those used in 1997 and 1998. This 5-part classification distinguishes between (1) alluvial aquifers, (2) alluvial aquifers plus other unconsolidated aquifers, (3) the High Plains aquifer, (4) bedrock aquifers, and (5) bedrock plus unconsolidated aquifers. This has the effect of reducing the degrees of freedom required for the model and thus increasing the sensitivity of the analysis.
| Analysis of Variance Table for Initial Model | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 20 | 1067.0404 | 53.3520 | 3.1505 | >0.0001** |
| Measurer | 7 | 296.64393 | 42.37770 | 2.5024 | 0.0155* |
| Well Access | 1 | 4.95300 | 4.95300 | 0.2925 | 0.5889ns |
| Downhole Access | 1 | 0.16717 | 0.16717 | 0.0099 | 0.9209ns |
| Weighted Tape | 1 | 224.30268 | 224.30268 | 13.2453 | 0.0003** |
| Well Use | 3 | 153.12923 | 51.04308 | 3.0141 | 0.0296* |
| Oil on Water | 1 | 8.93619 | 8.93619 | 0.5277 | 0.4679ns |
| Chalk Cut Quality | 2 | 147.72389 | 73.86194 | 4.3616 | 0.0132** |
| Aquifer Group | 4 | 260.53035 | 65.13259 | 3.8461 | 0.0043** |
| Error | 521 | 8822.8702 | 16.9345 | ||
| Total | 541 | 9889.9106 | |||
| RSquare | 0.107892 | ||||
Most of the components in the revised model are significant, in strong contrast with results obtained in 1998, when most components of the equivalent model were not significant. Unfortunately, past models are not directly comparable because there are different numbers of classes in Measurer and Aquifer Code, and the response variable has significantly different variances from year to year. It is important to note that the variance of the response variable in 1998 was unusually low; the variance of the response in 1999 is almost three times greater than last year, and is comparable to the variance in 1997. (Direct comparisons of responses from year to year are not possible because of the different numbers of wells, and possible differences in the behavior of the specific wells measured in each year.)
One way to improve the statistical analysis is to discard wells in which the exogenous variables make unusually high contributions to the total variance, arguing that the readings from such wells are atypical and likely erroneous. We can identify 24 wells which seem to make spurious contributions to the variance. Most of these wells were repeatedly measured, indicating that the measurers either had difficulty obtaining a reliable reading or that the initial depth to water was significantly out-of-trend. By removing fewer than 5% of the wells, the total variance can be reduced to one-fifth its original value. After removal, only Measurer, Weighted Tape, and Aquifer Group contribute significantly to the variance, a result that is comparable to results obtained in 1988.
| Analysis of Variance table for Grouped Aquifers After Removal of 24 Wells | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 20 | 303.6841 | 15.1842 | 4.6110 | <0.0001** |
| Measurer | 7 | 112.87320 | 16.12474 | 4.8967 | <0.0001** |
| Well Access | 1 | 0.62228 | 0.62228 | 0.1890 | 0.6640ns |
| Downhole Access | 1 | 4.45394 | 4.45394 | 1.3525 | 0.2454ns |
| Weighted Tape | 1 | 24.67192 | 24.67192 | 7.4922 | 0.0064** |
| Well Use | 3 | 20.62498 | 6.87499 | 2.0878 | 0.1009ns |
| Oil on Water | 1 | 1.05733 | 1.05733 | 0.3211 | 0.5712ns |
| Chalk Cut Quality | 2 | 12.83185 | 6.41593 | 1.9483 | 0.1436ns |
| Aquifer Group | 4 | 109.54708 | 27.38677 | 8.3166 | <0.0001** |
| Error | 497 | 1636.6263 | 3.2930 | ||
| Total | 517 | 1940.3103 | |||
| RSquare | 0.156513 | ||||
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 '99-'98 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 1999 than in 1998 (the water level has dropped 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 and for the data after removal of the 24 wells.
| Operator | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| DR | 0.1907 | 2.2155 |
| DRL | -1.8873 | 1.6487 |
| JCS | -0.0817 | 1.7368 |
| JDS | -0.6526 | 1.1995 |
| JMA | -1.6233 | 0.7093 |
| JMH | 0.5372 | 2.1048 |
| RB | -0.8102 | 0.7715 |
| RDM | -0.9056 | 1.3163 |
| Well Access | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| 0 | -0.4461 | 1.5382 |
| 1 | -0.8621 | 1.3873 |
| Downhole Access | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| 0 | -0.6816 | 1.6120 |
| 1 | -0.6266 | 1.3136 |
| Weighted Tape | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| 0 | -1.6258 | 1.1305 |
| 1 | 0.3176 | 1.7951 |
| Well Use | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| H | -1.0788 | 0.6683 |
| I | -0.9295 | 1.8822 |
| S | 1.2149 | 1.8468 |
| U | -1.8230 | 1.4539 |
| Oil on Water | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| 0 | -0.8358 | 1.5261 |
| 1 | -0.4724 | 1.3995 |
| Chalk Cut | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| 0 | -2.9156 | 2.1813 |
| 1 | 0.4336 | 1.1637 |
| 2 | 0.5197 | 1.0434 |
| Geologic Group | ||
|---|---|---|
| Level | Original Least Sq Mean | 24 Wells Removed Least Sq Mean |
| 1 (Cretaceous) | -2.8128 | 2.9674 |
| 2 (Alluvium) | -0.7249 | 0.4852 |
| 3 (Al. + Tert.) | -0.2074 | 0.8042 |
| 4 (Tertiary) | 0.0735 | 1.3210 |
| 5 (Tert. + K) | 0.4010 | 1.7362 |
Summary of the Analyses of Variance
Data collected in 1999 show significant variations attributable to Measurer, Downhole Access, Weighted Tape, and Chalk Cut, in addition to differences between the aquifer being tapped by the well. Most of the variation seems attributable to extreme changes in water level in a very few wells. The standard deviation of variable '99-'98 is 4.21 ft., almost twice the 2.48 ft. standard deviation of variable '98-'97. When the 24 troublesome wells discussed above are removed from the analysis, the standard deviation of variable '99-'98 is only 1.94 ft. The median decline in water level from 1998 to 1999 (0.72 ft.), although not large, is almost twice the median decline in the previous year; that is, from 1997 to 1998 (0.41 ft.). Removal of the 24 wells does not significantly change the median decline in water level (0.76 ft.). The fact that variation in the change in water table elevation shows a continuing reduction if certain wells are removed from the calculations suggests that quality control measures are successful in controlling exogenous variation but the improvement in data quality is being swamped by unreliable responses from a small number of wells. This is a strong argument for systematically replacing those wells in the network which yield unreliable values.
There are significant differences between the operators, particularly from JMH. (In addition, measurer DR is not part of the measurement team but is a DWR staff member who provided the water depth for a locked and hence inaccessible well.) These significant differences between measurers remain after removal of troublesome wells, showing that the differences are systematic and probably due to measurement techniques and not to the particular wells measured. There is little difference between wells with good access and poor access (an average difference of 0.4 foot, or 0.2 foot after removal of 24 wells) and the same small difference between wells with good downhole access and poor downhole access (0.4 foot and 0.3 foot). This similarity, coupled with measurer's informal comments, suggests that the field crews do not clearly distinguish between these two variables. The variable Well Access may be redundant; a better measure of this property may be extractable from the WaterWitch time log.
The water level measured without a weight on the tape tends to be almost 2 feet shallower than water levels measured in wells where the tape is weighted, but the difference drops to only 0.7 foot when the 24 wells are removed. By comparison, the difference between using or not using a weight on the tape was related to a difference in water level of only 0.4 feet in 1998, but more than 2.6 feet in 1997.
In 1999, the classification (P) was combined with (H) because only one public well was measured. Usage from all wells of unknown (?) classification was resolved using field photographs and notes. Eliminating these two classes of well usage removed what had been a major source of variance in previous years. Only unused or monitoring wells (U) are significantly different than other classes, measuring over 1.8 ft. shallower. With removal of the 24 wells, differences attributable to well usage is no longer significant. Household wells (H) deviate most from other classes of usage (0.8 ft. deeper than average), but the difference is not statistically significant.
If the quality of the chalk cut on the measuring tape is "poor," the reading tends to be over 2.9 foot shallower than in 1998; if the cut is "good" or "excellent," the reading tends to be about a half-foot deeper than the preceding year. If the 24 wells are removed from the data set, the differences attributable to chalk cut quality are no longer statistically significant.
Water levels in exclusively Cretaceous aquifers (1) tend to be almost 2.8 feet shallower than in 1997 (3.0 feet after removal of 24 wells). The Ogallala aquifer (4) tends to be about the same (1.3 feet deeper after removal of 24 wells) as last year. Measurements made in wells tapping alluvial aquifers (2) or alluvial plus other sources (3) tend to be about a half-foot shallower. Water levels in wells tapping Cretaceous aquifers plus Quaternary and/or Tertiary aquifers (5) tend to be about 0.4 feet deeper (1.7 feet after removal of 24 wells) this year. Unlike measurements made in 1998, the differences in annual changes of water level for different aquifers are highly significant, and remain significant after deletion of the 24 troublesome wells.
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. Four wells have been identified by this process. These wells show rises in water level between 1998 and 1999 that are far outside the range expected; each well was measured repeatedly (usually by different individuals) and the measurements proved to be reproducible. These well measurements may be correct and reflect highly unusual changes in aquifer level; the wrong wells may have been measured in 1998 or 1999; or changes in well construction or other factors may have altered the measurability of a well (field notes indicate measurement difficulties with all four wells). The four wells are:
| 375958099530101 | 24S 23W 06AAB 01 | |
| 374421101490901 | 26S 41W 32DDB 01 | |
| 373228100595701 | 29S 34W 11ADD 01 | |
| 372200100214001 | 31S 28W 10BCB 01 |
All of these wells are contained in the set of 24 wells that were identified by their extreme expected values and excluded from the second Analysis of Variance.
Quality Assurance (Remeasure) Program
The 1999 Quality Assurance program of random remeasurements showed that the QA data contained statistically significant sources of variation, in contrast to 1998 when no significant sources of variation were detected among the QA wells. This is in conformity with characteristics observed in the main 1999 measurements, which are much more variable than in 1998. Fifty-one randomly selected QA wells were remeasured during the late January supplementary data collection period. Combined with measurements made during the regular collection period, 132 measurements were available for statistical quality control. In spite of the additional control provided by replication, significant contributions from exogenous variables were detected. As expected, the variance among the QA replicates is much lower, approximately half, that of the complete data set. The most extreme value of '99-'98 among the QA wells is only 14.7, compared to an extreme of -54.4 in the complete data set. The most extreme well in the QA data set is:
| 374035099500101 | 27S 23W 28AAA 01 |
Within the QA data set, there are significant contributions due to Measurer, mostly attributable to DRL and to a lesser extent to RDM. Wells in the QA set measured by DRL show a change (decline in water level) in '99-'98 of about 2 feet, double the average change for the QA data. Downhole Access is a highly significant source of variation; much of this is attributable to a single well, 27S 23W 28AAA 01, but Downhole Access remains a significant source of variation even after this well is removed. Wells with poor downhole access tend to measure about 3 feet deeper than wells with good downhole access, possibly the result of tape deflections and hang-ups in the wells. There are significant effects attributable to Oil on Water, but these are due almost entirely to one well, 25S 35W 25BBB 03, which has an average decline of -5.65 ft. with a very small variance over 4 repeated measurements. There are significant differences attributable to use of Weighted Tape; unweighted measurements tend to be about 1.1 ft. deeper than expected. Well Usage is anticipated to be a significant source of variation, and this is confirmed in the QA data. However, only household use appears to be significantly different than other uses, resulting in measurements that are 2 to 3 ft. deeper than expected. Quality of the Chalk Cut has a significant effect; a poor cut tends to be about 2.5 ft. deeper than an excellent cut, or 4 ft. deeper than a good cut. Although there are significant effects attributable to Geological Unit, these are unreliable because of the small number of measurements per unit. Geological Groups, which are aggregations of Geological Units, show no significant differences 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 numerous spurious values, both in the measured data and in the historical data, resulting in a much "cleaner" data base than otherwise would have been the case. 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 data will be progressively improved with time.
Prev Page--Acquisition Activity || Next Page--Conclusions