KGS, Open-file Report 1999-11
by Ricardo A. Olea and John C. Davis
Kansas Geological Survey
KGS Open File Report 1999-11
The Kansas Geological Survey and the Division of Water Resources measured the depth to water in 1,402 observation wells in Kansas during January of 1999 as part of the annual water-level measurement program. Of the wells, 1,267 (90.4%) monitor water levels in the High Plains aquifer.
Statistical analysis, devoid of any geohydrological assumptions, determined that the 1999 measurements are likely to be free of measurement and recording errors, but did detect several wells whose fluctuations may not represent true variation in the water table under static conditions.
A map of the 1994-1999 change in water level elevation shows aquifer depletion is more critical in southwest Kansas, but some other areas show moderate reversals in the declining water level of the High Plains aquifer.
List of Plates
In 1999, the Kansas Geological Survey continued its program of measuring water levels in observation wells that formerly were measured by the United States Geological Survey (Miller and Davis, 1999). The Survey's activities were conducted in cooperation with the Kansas Division of Water Resources (DWR), who also measured water levels in observation wells that the Division has been monitoring for many years.
In 1998, the Kansas Geological Survey implemented WIZARD, a relational data base for storing all past and present groundwater information collected by any agency in Kansas (Hausberger and others, 1998). Information collected during the groundwater monitoring program in 1999 is contained in WIZARD, which the public can access through the KGS web site: http://www.kgs.ku.edu/Magellan/WaterLevels/index.html
The objective of this statistical study is to analyze and map the information collected in 1999 from the High Plains aquifer, the most important aquifer in the state of Kansas, for the purpose of detecting sampling errors that could compromise the quality of information going into the WIZARD database and hence any conclusions derived from the observations. The 1999 data are compared with equivalent measurements made in 1994 and 1998 as a check of the quality of information that has been gathered in the past.
The WIZARD data base includes historical records of water level measurements collected by many agencies for diverse purposes; the KGS cannot certify that these data are error-free. In addition, computer protocols for checking and extracting data from WIZARD are under continuing development. Although progress has been made in the ability to extract from the data base only those wells monitoring the High Plains aquifer, the operation of WIZARD is not yet completely automatic. For these reasons, repeated extractions from the data base were necessary in order to arrive at the final set of observations used here. During this process, numerous defects in the data (mostly in the form of missing codes and status flags) and erroneous procedures were corrected.
Observation wells in the WIZARD data base are coded 1 if they monitor the High Plains aquifer and 0 if they monitor another aquifer. Of the 1,402 observation wells, 91 are coded 0 and were deleted from this analysis; these wells are listed in Appendix B. The remaining 1,311 wells were posted on a map with the boundary of the High Plains aquifer as drawn by McClain and Buddemeier (1990). It was discovered that 34 wells were located outside the boundary of the aquifer; these wells outside the aquifer limits are shown on Plate 2 and listed in Appendix C. These wells may be misclassified Dakota aquifer wells, they may tap fluvial aquifers, or the boundary of the High Plains aquifer may be incorrectly mapped. Pending correction of the aquifer codes or modification of the aquifer boundary, these wells were removed from the analysis.
There are five pairs of duplicate wells (duplicate wells are two wells with identical or near-identical geographic locations) among the 1,277 wells tapping the High Plains aquifer. These wells are shown on Plate 3 and are listed in Appendix D. The kriging procedure in spatial analysis and mapping does not allow multiple measurements at one location, because this results in a singularity in the system of equations used for estimation. The second well in each pair of duplicates was arbitrarily discarded, except for the well pair at location 27S 07W 03ADC where the first well was deleted because it did not have a 1999 measurement. After discarding 5 wells from among the duplicate pairs, 1,272 wells remained.
Finally, 68 wells that tapped the nigh Plains aquifer could not be measured during the 1999 field season for mechanical or other reasons. The locations of these wells are posted on Plate 4 and listed in Appendix E. The remaining 1,204 wells are those which are unequivocably within the High Plains aquifer, are not duplicates, and which were measured in 1999; these are shown on Plate 1 and are listed in Appendix A. Table 1 summarizes the status of all observation wells in the network.
Table 1. Classification of observation wells measured in 1999.
|Not High Plains
Cross-validation is a geostatistical verification procedure based on kriging that takes advantage of the stochastic spatial continuity of surfaces such as water-table elevations (Miller, Davis, and Olea, 1997). The primary measure of spatial continuity in a surface is expressed in the semivariogram, a plot of distance between observations versus variance of the differences between values of the surface at the observation points. The experimental semivariogram, based on observations, usually is modeled by a theoretical semivariogram whose parameters are used in kriging, the estimation procedure of geostatistics. Calculating the semivariogram and estimating the appropriate form for a model requires that the surface be stationary, or free of any change in average value over long distances. The water table of the High Plains aquifer is not stationary, as it slopes downard to the east roughly parallel to the topographic surface. However, the surface can be leveled by subtracting a first degree trend; the semivariogram can then be computed from the residuals. The optimal semivariogram model for first degree residuals of the water-level elevation in the High Plains aquifer is Gaussian, with a nugget of 70 ft2, a sill of 7,910 ft2 and a range of 63,636 m (Olea, 1997).
Based on this model, kriging was used to estimate the value of the water-level elevation at each observation well location, after each observed value has been removed from the data set. The estimate and the actual values were then compared; if the water-level surface exhibits the degree of smoothness and spatial continuity predicted by the semivariogram model, the estimate and the observed values should be very similar. If a water-level measurement is atypical for wells in the local area, there will tend to be a large difference between estimate and observation. This may indicate errors in water level measurement or erroneous locations of observation wells. For the first time since the Kansas Geological Survey began collecting and inspecting the observation well data for quality, cross-validation failed to detect any anomalous wells. The 1999 data for the High Plains aquifer can be considered to be "clean" and free of significant errors in depth to water, surface elevation, or well coordinates.
Plate 5 shows water-level elevations in the High Plains aquifer for 1999 in the form of a contour map. On casual inspection, the water level does not appear much different from the levels observed in the previous two years (Miller, Davis, and Olea, 1997; Miller, Davis, and Olea, 1998). However, the significant regional trend conceals small differences which become apparent only when examining maps of the differences in water level between years.
At each point where an estimate of the value of a surface is made by kriging, the standard deviation in the estimates can determined. This standard deviation is an estimate of the uncertainty or reliability in the estimated surface; the smaller the kriging standard deviation, the more reliable (less uncertain) is the individual estimate of the value of the surface. Just as kriging can be used to create a contour map of the water-level surface, it also can produce a map of the uncertainty in the water-level surface by contouring the kriging standard deviations. The resulting map will indicate areas where the uncertainty in the water-level map is relatively high because of a low density of observations.
Improving the reliability of the estimated water-level surface can be costly because reducing the kriging standard deviation requires increasing the number of samples inversely proportional to the fourth power of the sampling density (Olea, 1984). Because of this, the Kansas Geological Survey has not sought to significantly reduce the kriging standard deviation over the entire High Plains aquifer, but instead has decided to limit the kriging standard deviation to no more than ±10 ft (except near the edge of the aquifer). Areas meeting this criteria are shown in yellow on Plate 6, which is based on those observation wells where measurements were actually collected in the High Plains aquifer in 1999.
Plate 7 displays a hypothetical map of the reliability that would have been achieved in 1999 if water levels could have been measured in all observation wells shown on Plate 4. A comparison of Plates 6 and 7 shows that some of the measurements are more critical than others. Measurements from the following wells would have reduced the kriging standard deviation below 10 ft in the vicinity of the observation wells if these data could have been collected in the 1999 program.
|Location||Map Index No.|
|33S 32W 02AAC 01||65|
|32S 38W 11ADA 01||90|
|31S 39W 23BBB 01||106|
|24S 03W 14BBB 01||615|
|24S 08W 04AB 01||637|
|09S 27W 31ABB 01||1096|
|09S 28W 15CBA 01||1113|
|08S 27W 18DAA 01||1154|
|03S 35W 18CBB 01||1362|
|06S 28W 21BCD 01||1243|
The recommendations made in Open-File Report 98-39 (Olea, 1998) are still applicable for the purpose of reducing the kriging standard deviation below &plusmin;10 ft for all portions of the High Plains aquifer inside the boundaries of the aquifer.
Plate 8 is a contour map of changes in water-level elevation of the High Plains aquifer between January 1998, and January 1999. The map was produced by subtracting depth-to-water measurements made in 1999 from those made in 1998. Therefore, negative values indicate an increase in the depth to water, or a depletion in the groundwater level.
There are 1,175 observation wells in which the High Plains aquifer was measured in both 1998 and 1999. The observations consist of differences in water level and are moderately erratic with abrupt well-to-well discontinuities, resembling a Poisson (random) process in a plane. As a consequence, the semivariogram of the 1998-1999 differences consists of a pure nugget effect. The differences are more spatially continuous if the data are converted to normal scores. The best semivariogram model is exponential with a sill of 0.86 ft2, an effective range of 34,708 m, and a large nugget of 0.47 ft2.
The result of crossvalidation is relatively poor. The correlation between estimated differences and true differences is only r = 0.55 and there is pronounced smoothing as indicated by the slope of the regression between estimated and true values, which is only 0.34 (a perfect concidence between estimates and observations would produce a correlation of r = 1.00 and the regression would have a slope of 1.0). Highly anomalous wells that deserve scrutiny are listed in Table 2.
Table 2. 1998-1999 water-level differences most likely to be in error, as determined by crossvalidation.
|35S 39W 10CAD 01||7||2.14|
|32S 36W 21AAC 01||78||6.49|
|32S 39W 14DDD 01||80||2.54|
|31S 28W 10BCB 01||113||25.85|
|29S 34W 11ADD 01||218||25.80|
|27S 23W 28AAA 01||330||-14.66|
|25S 33W 16DCC 01||518||1.60|
|23S 02W 34DCC 01||645||-18.07|
|17S 40W 31BBA 01||929||-14.81|
|17S 40W 17BBA 01||952||3.37|
|10S 35W 09ABB 01||1090||-27.42|
|09S 35W 32DAA 01||1094||1.98|
|09S 27W 12CCC 01||1119||-7.23|
|09S 30W 03AAB 02||1129||11.62|
|08S 27W 35CBB 01||1133||14.44|
|07S 27W 22DAC 01||1192||-24.46|
|06S 27W 05CBB 01||1272||-7.60|
|05S 37W 15DBB 01||1193||6.99|
|05S 28W 14ADD 01||1295||19.58|
|01S 29W 03DDB 01||1402||10.81|
As expected, the 5-year differences in water level between 1994 and 1999 are more pronounced and systematic, and result in a better crossvalidation. The semivariogram model for 5-year differences is exponential in form, with a nugget of 0.32 ft2, a sill of 1.18 ft2 and an effective range of 186,225 m. The points determined to be most likely in error are listed in Table 3.
Table 3. 1994-1999 differences in water level most likely to be in error, as determined by crossvalidation.
|32S 40W 21ADB 01||77||5.50|
|31S 28W 10BCB 01||113||15.01|
|30S 39W 23BBB 01||146||2.42|
|29S 29W 10ABB 01||223||2.55|
|29S 25W 03ADA 01||228||6.90|
|28S 15W 23CCD 01||258||-9.97|
|27S 24W 03CDD 01||373||16.14|
|27S 24W 03BBD 01||381||-12.47|
|26S 28W 06DDB 01||463||4.95|
|25S 30W 20BCB 01||510||9.48|
|23S 02W 34DCC 01||645||-17.83|
|18S 37W 21BBB 01||905||22.57|
|11S 28W 08AAA 01||1059||7.15|
|10S 35W 09ABB 01||1090||-26.71|
|09S 35W 32DAA 01||1094||9.28|
|08S 27W 35CBB 01||1133||16.29|
|07S 34W 26DBD 01||1182||9.17|
|07S 27W 22DAC 01||1192||-24.53|
|05S 28W 14ADD 01||1295||13.62|
|03S 36W 21DBC 01||1354||6.01|
The crossvalidation correlation between true 5-year differences and estimated 5-year differences is r = 0.75, which is much higher than the equivalent correlation for crossvalidation of 1-year differences. The slope of the regression line between observed and estimated 5-year differences is 0.56. This indicates that there is significant smoothing in the map of 5-year differences, but not so pronounced as in the map of 1-year differences. The smoothing, in 1-year differences, which results in part from the high nugget effect, is so pronounced that abnormal differences in water-level elevation do not produce observable features in the contour lines in Plate 8.
Several conclusions can be drawn from geostatistical analyses of the water-level observations, based on the spatial continuity of the attributes. These conclusions, and the suggestions that follow as a consequence, do not require any presumptions about hydrological or geological conditions.
1. The 1999 observation wells can be classified into four categories: 1272 wells monitor the elevation of the water level in the High Plains aquifer; 68 wells have no recorded elevation of the water level for 1999; 34 wells tap aquifers outside the mapped boundary of the High Plains aquifer; and 5 wells are too close to an adjacent well to be used for geostatistical analyses.
2. It would be much easier to differentiate wells in alluvium inside the High Plains aquifer from wells outside the boundary of the aquifer if those outside were assigned a different aquifer code.
3. The recommendation made in 1998 that 50 observation wells be added to the network in order to achieve more uniform coverage of the High Plains aquifer remains valid.
4. Crossvalidation of water-level elevations measured in 1999 does not indicate any wells that are likely to be in error in depth-to-water, surface elevation, or well location.
5. Crossvalidation of water-level differences detects numerous wells with abnormal values, suggesting errors in the depth-to-water in one or both of the years compared, the effects of coning in some wells, or adverse mechanical conditions in some wells that have resulted in erratic measurements for one or both of the years.
Hausberger, G., and others, 1998, WIZARD, Water Information Storage and Retrieval Database: Kansas Geological Survey, Open-File Report No. 98-13, 59 p.
McClain, T.J., and R. Buddemeier, 1990, Major Kansas Aquifers (Preliminary): Kansas Geological Survey, Open-File Report No. 90-7, 1 map, scale 1:500,000.
Miller, R.D., and J.C. Davis, 1999, 1999 Annual Water Level Raw Data Report for Kansas: Kansas Geological, Survey Open-File Report No. 99-5, 262 p., 1 compact disk.
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.
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
Olea, R.A., 1984, Sampling Design Optimization for Spatial Functions: Mathematical Geology, vol. 16, no. 4, p. 369-392.
Olea, R.A., 1997, Sampling Analysis of the Annual Observation Water-Level Wells in Kansas: Kansas Geological Survey, Open-File Report No. 97-73, 44 p.
Olea, R.A., 1998, Proposed Expansion of the High Plains Aquifer Observation Network for Reliability Enhancement: Kansas Geological Survey, Open-File Report No. 99-39, 2 p.
Next Page--Appendix A