Water levels from 25 wells were analyzed for trends (table 5). Some of the trends were then quantitatively or qualitatively correlated with potential factors causing these trends. The purpose of the trend analysis was to determine if a net upward or downward change in water level occurred during the selected period of record. The wells selected for trend analysis have multiple years of periodic water-level record. Most wells (19) have 5 years or more of record. In addition, 18 of the 25 wells include recent (1998) data. Water-level data used in the trend analysis are shown with filled symbols on plots in appendix 1. Data not used in the trend analysis consisted of some isolated data points, early water levels affected by well construction (except for well U-19bh), water levels affected by pumping, and anomalous levels. Additionally, water-level data computed from geophysical logs were not used for trend analysis because of the low precision of the data.

To test for a monotonic relation of water-level change with time, the slope of a Kendall-Theil robust line was calculated and tested for significance (Helsel and Hirsch, 1992, p. 266-74). The Kendall-Theil method was chosen as an alternative to simple linear regression because some of the data sets did not meet the test assumptions for linear regression (that is, the data were non-linear, or the residuals were non-normal, auto correlated, or the variance was not constant). The Kendall-Theil method is a non-parametric trend test that consists of two parts. The first part is a robust test that determines if a significant upward or downward change in water level has occurred over the period of record. The first part of the method does not imply anything about the magnitude of the change in water level or whether the change in water level is linear. The second part of the method gives an estimate of the best-fit robust line through the water-level data and represents the average linear change in water level for the period of record. The slope of the line is computed by calculating the slopes for all possible pairs of water levels and then selecting the median slope. In cases where a data set appeared non-linear, such as the hydrograph for well U-19v PS 1D, no best-fit line was estimated for the data. The Kendall-Theil method is slightly less powerful than simple linear regression when the data meet all assumptions of normality. However, when data are not normally distributed or are auto-correlated, the Kendall-Theil method gives a much better estimate of slope (Helsel and Hirsch, 1992, p. 268). Because the Kendall-Theil method is robust, each data point is given equal treatment. Where data are irregularly spaced in time (for example, see hydrograph for well U-19v PS 1D), specific time periods may be over-represented on the overall trend simply because they have more data points per unit time than other parts of the hydrograph. A 95-percent confidence level was used in the test for the statistical significance of an upward or downward change in water level. Additionally, for a statistically significant trend to be considered hydrologically significant, a minimum of 1 ft of water-level change over the period of record was required. This arbitrary criteria was used as a conservative measure to filter out changes in water levels that might be the result of measurement error resulting from the different accuracies of the measurement devices used.

Results of the trend analysis are shown in table 5. Thirteen wells had at least one hydrologically significant trend (figs. 8 and 9). The largest change in water levels occurred in well U-19v PS 1D (fig. 8) as a result of the Almendro nuclear test. Water, initially expelled from the test cavity by the detonation, rose 1,029 ft in 25 years as a result of slow infilling of water back into the test cavity. The rising trend in well U-19bh (fig. 8) may be an artifact of well construction; however, the trend also could be the result of some other factor such as the Inlet nuclear test that occurred in 1975 less than 0.5 mi to the southeast. Likely explanations for trends in the remaining 12 wells are changes in precipitation patterns that affect recharge rates to the ground-water system, pumping effects from water-supply well U-20 WW, or a combination of these two factors.

Well U-20 WW had a 27-ft decline in water level from 1985 to 1995 due to pumping followed by about a 5-ft rise in level from 1996 to 1998 during a period of no pumping (fig. 9). This water-level decline and subsequent rise are based on measurements made when the pump was off. Water levels in six observation wells show hydrologically significant water-level trends that may be influenced by pumping in well U-20 WW (fig. 9). These wells range from about 0.85 mi (UE-20n 1 and U-20n PS 1DD-H) to 1.8 mi (U-20be) from well U-20 WW. Two wells, U-20be and U-20bf, have less than 2 years of data; therefore, statistical correlations of this data with pumping in well U-20 WW were not attempted. The remaining four wells show declining water levels through 1995 or 1996 followed by stable or rising water levels. Spearman correlation coefficients (Helsel and Hirsch, 1992, p. 217-218) were used to correlate water levels in these four wells with pumping from water-supply well U-20 WW.

Water levels could not be correlated directly with monthly withdrawal rates because of relatively long periods of no pumping interspersed with periods of pumping. Therefore, to correlate water levels with pumping, a value of "+1" was assigned to each month withdrawals were made from well U-20 WW and a value of "-1" was assigned to each month with little (less than 0.75 million gallons) or no withdrawals. Then, the change in water level between two consecutive measurements was correlated with the sum of the months of pumping (+1) and no pumping (-1) between the two water-level measurements. For example, for a set of water levels that respond to pumping, one would expect a decline in water level between two measurements to correlate with a large sum (that is, the sum of many months of pumping which were assigned "+1") and a rise in water level between two measurements to correlate with a small sum. Water-level data sets were filtered to about two water levels per year. This was done to improve the correlation by allowing sufficient time between measurements for larger scale changes to occur that might be associated with pumping.

Water levels in wells U-20bg, U-20n PS 1DD-H, UE-20bh 1, and UE-20n 1 were correlated with each other and with pumping in well U-20 WW. Correlations of water levels between well pairs indicate that the four wells all are strongly correlated with each other (Spearman's rho greater than 0.90⁷), with the exception of the correlation between wells U-20bg and U-20n PS 1DD-H (Spearman's rho = 0.84). Water levels in well UE-20bh 1 correlate the strongest with pumping in well U-20 WW (Spearman's rho = 0.78). Water levels in U-20bg, U-20n PS 1DD-H, and UE-20n 1 had poorer correlations (Spearman's rho = 0.48-0.54, p = 0.02-0.04). The lack of strong statistical correlation between water levels and pumping, despite the appearance of a correlation in figure 9, may be due to small data sets, a possible lagged response between pumping and water-level change, and other factors simultaneously influencing water levels, such as changes in precipitation.

Small-magnitude changes in water level occurring over periods of several months to several years commonly are masked by the effects of cyclic changes in air pressure and Earth tides. These small-scale changes in water level, which are difficult to distinguish with periodic data, can sometimes be seen with continual water-level data. As an example, figure 10 shows periodic water levels in well PM-2, measured approximately monthly, from mid-1996 to late 1998. Changes occurring on a month-to-year scale are difficult to identify in the periodic water-level measurements primarily because of "barometric noise." Much of the short-term "noise" (hours to days) is removed from the water-level record by using hourly water-level data and calculating monthly means (fig. 10). However, to more adequately remove the effects of barometric pressure from the water-level record so that other influences can be seen, a barometric efficiency (the ratio of the change in water level to the change in barometric pressure) can be calculated. This efficiency, which was 0.41 for water levels in well PM-2, was used to remove the barometric effects from the hourly water-level record, as outlined by Brassington (1988, p. 81-84). These corrected water levels in well PM-2, when converted to monthly mean water levels (fig. 10), show a decline of about 0.2 ft from the end of 1996 to the end of 1997 and then a rise and decline of about 0.15 ft in 1998. These small-magnitude changes, apparent in the corrected monthly mean water-level record, may be caused by changes in recharge associated with seasonal differences in precipitation on Pahute Mesa or by seasonal changes in barometric pressure that were not removed from the water-level record.

⁷ The level of significance, p, is less than 0.01 for all correlations presented, unless otherwise specified.

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ANALYSIS OF WATER LEVELS