2000 Annual Water Level Raw Data Report for Kansas
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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 year's measurement programs, all observation wells were again re-determined 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, except that year 2000 GPS measurements are used for wells that had no 1999 measurements.
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 120 wells, yielding a collection of 150 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 56 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 2000 and 1999 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 2000 and 1999 corrected depth measurements is abbreviated "'00-'99." If the water table is lower this year, the variable '00-'99 will be a positive number. Because all wells measured in the current program were also measured in 1999, there are a total of 548 wells having the variable '00-'99.
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 2000 with those from previous years shows that the desired improvements in the measurement program are being achieved through quality control.
| Analysis of Variance Table for Initial Model | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 26 | 586.8229 | 22.5701 | 3.4837 | <0.0001** |
| Measurer | 6 | 213.99124 | 35.66521 | 5.5050 | <0.0001** |
| Well Access | 1 | 9.98314 | 9.98314 | 1.5409 | 0.2150ns |
| Downhole Access | 1 | 0.00154 | 0.00154 | 0.0002 | 0.9877ns |
| Weighted Tape | 1 | 1.70515 | 1.70515 | 0.2632 | 0.6082ns |
| Well Use | 3 | 36.17535 | 12.05845 | 1.8612 | 0.1351ns |
| Oil on Water | 1 | 0.38886 | 0.38886 | 0.0600 | 0.8066ns |
| Chalk Cut Quality | 2 | 15.47985 | 7.73993 | 1.1947 | 0.3036ns |
| Aquifer Code | 11 | 364.23350 | 33.11214 | 5.1109 | <0.0001** |
| Error | 520 | 3368.9333 | 6.4787 | ||
| Total | 546 | 3955.7563 | |||
| RSquare | 0.148347 | ||||
A revised model was run that combined aquifers into classes similar to those used in 1997 through 1999. 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 Grouped Aquifers | |||||
|---|---|---|---|---|---|
| Source | DF | Sum of Squares | Mean Square | F Ratio | Prob>F |
| Model | 19 | 337.2486 | 17.7499 | 2.5851 | 0.0003** |
| Measurer | 7 | 168.27236 | 28.04539 | 4.0845 | 0.0005** |
| Well Access | 1 | 10.06818 | 10.06818 | 1.4663 | 0.2265ns |
| Downhole Access | 1 | 0.16162 | 0.16162 | 0.0239 | 0.8772ns |
| Weighted Tape | 1 | 0.04445 | 0.04445 | 0.0065 | 0.9359ns |
| Well Use | 3 | 35.01685 | 51.04308 | 11.6723 | 0.1660ns |
| Oil on Water | 1 | 1.65566 | 1.65566 | 0.2411 | 0.6236ns |
| Chalk Cut Quality | 2 | 20.52210 | 10.26105 | 1.4944 | 0.2253ns |
| Aquifer Group | 4 | 114.65918 | 28.664795 | 4.1747 | 0.0024** |
| Error | 527 | 3618.5076 | 6.8662 | ||
| Total | 546 | 3955.7563 | |||
| RSquare | 0.08526 | ||||
Most of the components in the revised model are not significant, in strong contrast with results obtained in 1999, when most components of the equivalent model 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. It is interesting to note that the variance of the response variable in 2000 is about one-third its value in 1999, which was about three times the variance measured in 1998, which in turn was about one-third the variance in 1997. 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. In 1999, we identified 24 wells that seemed to make spurious contributions to the variance. Most of these wells had been 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. These wells were deleted from the network in 2000; it is likely that their removal is responsible for the notable reduction in total variance in 2000.
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 '00-'99 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 2000 than in 1999 (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.
| Operator | |
|---|---|
| Level | Original Least Sq Mean |
| DRL | -1.8798 |
| JBE | -1.3370 |
| JLT | -2.1814 |
| JMA | -0.6825 |
| MWF | -0.4329 |
| RCB | -1.3735 |
| RDM | -1.3543 |
| Well Access | |
|---|---|
| Level | Original Least Sq Mean |
| 0 | -1.0065 |
| 1 | -1.6339 |
| Downhole Access | |
|---|---|
| Level | Original Least Sq Mean |
| 0 | -1.2921 |
| 1 | -1.3482 |
| Weighted Tape | |
|---|---|
| Level | Original Least Sq Mean |
| 0 | -1.3431 |
| 1 | -1.2973 |
| Well Use | |
|---|---|
| Level | Original Least Sq Mean |
| H | -2.3343 |
| I | -1.0086 |
| S | -0.4431 |
| U | -1.4948 |
| Oil on Water | |
|---|---|
| Level | Original Least Sq Mean |
| 0 | -1.2293 |
| 1 | -1.4111 |
| Chalk Cut | |
|---|---|
| Level | Original Least Sq Mean |
| 0 | -1.3202 |
| 1 | -0.2109 |
| 2 | -0.1182 |
| Geologic Group | |
|---|---|
| Level | Original Least Sq Mean |
| 1 (Cretaceous) | -1.6449 |
| 2 (Alluvium) | -1.4135 |
| 3 (Al. + Tert.) | -1.2447 |
| 4 (Tertiary) | -0.3446 |
| 5 (Tert. + K) | -1.9532 |
Summary of the Analyses of Variance
Data collected in 2000 show significant variations attributable to Measurer in addition to differences between the aquifer being tapped by the well. The standard deviation of variable '00-'99 is 2.69 ft., about half the standard deviation of variable '99-'98 (4.21 ft.) and about the same as the 2.48 ft. standard deviation of variable '98-'97. The median decline in water level from 1999 to 2000 is 0.31 ft., which is less than half the decline noted from 1998 to 1999 (0.72 ft.). (The decline between 1997 to 1998 was 0.41 ft.)
There are significant differences between the operators, particularly JLT and MWF. (Note that measurer MLA was not part of the measurement team but a visiting administrator who measured the water depth on a single well. To avoid inflating degrees of freedom in the model, this operator and this specific well have been removed from the data set prior to analysis.)
Water levels measured in 2000 in exclusively Cretaceous aquifers (1) tend to be unchanged from those measured in 1999. The Ogallala aquifer (4) tends to be almost a half-foot deeper than last year. Measurements made in wells tapping alluvial aquifers (2) or alluvial plus other sources (3) tend to be unchanged or slightly shallower. Water levels in wells tapping Cretaceous aquifers plus Quaternary and/or Tertiary aquifers (5) tend to be about 0.7 feet shallower this year. There are highly significant differences of the annual change in water level among aquifers, but these are due in part to an extreme decline (over 32 ft.) in well 27S 38W 15BBB 01.
In the year 2000, there were no other statistically significant contributors to total variance among the variables recorded by the field crew.
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. Three wells have been identified by this process. These wells show changes in water level between 1999 and 2000 that are outside the range expected. These well measurements may be correct and reflect highly unusual changes in aquifer level; the wrong wells may have been measured in 1999; or changes in well construction or other factors may have altered the measurability of a well. The three wells, with their residuals, are:
| Well ID | Residual, ft. |
|---|---|
| 27S 38W 15BBB 01 | -25.8 |
| 23S 22W 07DAA 01 | +15.0 |
| 24S 33W 18BDB 02 | -10.8 |
An additional five wells were flagged because their residuals depart significantly from that expected in a normal distribution of errors. Although the residuals for these wells are less extreme than those listed above, they also may be candidates for replacement in the network.
| Well ID | Residual, ft. |
|---|---|
| 29S 34W 11ADD 01 | +10.0 |
| 25S 36W 28CBD 01 | -9.9 |
| 24S 33W 18BDB 02 | -9.2 |
| 24S 23W 06AAB 01 | -8.6 |
| 27S 37W 04ABB 01 | -7.5 |
Quality Assurance (Remeasure) Program
The year 2000 Quality Assurance program of random remeasurements showed that the QA data contained only one statistically significant source of variation. Fifty-six randomly selected QA wells were remeasured during the late January supplementary data collection period. Combined with measurements made during the regular collection period, 131 measurements were available for statistical quality control. In spite of the additional control provided by replication, a significant contribution from only one exogenous variable, well access, was detected. As expected, the variance among the QA replicates is about 11% lower than the variance of the complete data set. The most extreme value of '00-'99 among the QA wells is only 8.1 feet, compared to an extreme of -32.2 feet in the complete data set.
Within the QA data set, there are no significant contributions due to Measurer, although the mean difference between readings by MWF and other measurers is nearly significant. Wells in the QA set measured by MWF show a change (decline in water level) in '00-'99 of over 2 feet, more than three times the average change for the QA data. It should be noted that 2000 is the first year that has MWF measured groundwater levels so this difference probably is attributable to lack of experience. Well Access is a highly significant source of variation; much of this is attributable to two wells, 23S 24W 11DAA 01 and 35S 39W 10CAD 01, because Well Access becomes insignificant as a source of variation when these wells are removed from the data set. Wells with poor access tend to measure about 3 feet deeper than wells with good access, possibly the result of tape deflections and hang-ups in the wells. An identical difference was noted in the 1999 QA measurements. No other exogenous 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 database 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.
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