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Groundwater quality in the St. Johns River Water Management District
Trend analysis of Floridan aquifer chloride data
Trend analysis statistical tests determine if observed water quality changes over time are due to random variability or statistically significant changes. Chloride concentration data for 293 Floridan aquifer wells with at least eight analyses over a minimum of two years were evaluated. Samples collected through October 2009 were used in the trend analysis. Of the 293 St. Johns River Water Management District Floridan aquifer monitoring wells evaluated, 35 wells had an increasing trend from the statistical tests. Of these 35 wells, 12 wells had a significantly increasing trend with a slope greater than 3.0 mg/L.
District staff hydrologists continually update various computer models to more accurately reflect groundwater flow conditions.
Nonparametric Mann-Kendall and Sen’s slope statistical tests were used to determine the significance of a trend and estimate the magnitude of the trend. The statistical tests were executed using S-Plus scripts, allowing user input for testing various scenarios. Nonparametric statistical methods are used because water quality data are generally not normally distributed and because of data variability issues. Data variability issues include seasonal or other cycles, missing values in the period of record, and outlier data. An assumption of the trend testing is that the observations are independent (not autocorrelated) and that the trends are monotonic; that is, they consistently increase, decrease or show no change with time. Lowess analysis was used for testing if non-monotonic time series had significant slope changes. Seasonality and autocorrelation are dealt with by data aggregation into years.
The null hypothesis (Ho) is that no change has occurred in the concentration of a variable over time, or that no trend is present. The alternate hypothesis (Ha) is that a significant change has occurred over time, or that an increasing or decreasing trend in the concentration of a variable is evident. The statistical tests determine the probability value (p-value) of the Mann-Kendall statistic and the slope of the trend line. The smaller the p-value, the greater the weight of evidence against Ho. The p-value can also be viewed as the probability that the slope of the trend line is zero.
The significance level (α) is the probability of concluding that there is a trend when none actually exists. The confidence level is (1 − α). A significance level of 0.20 corresponds to an 80 percent confidence level. A statistical test run with a significance level of 0.20 is more sensitive to detecting a possible trend than a test with a 0.05 significance level (95 percent confidence level). However, this higher significance level increases the chance of error that a possible trend is indicated, but where no change is actually occurring. A significance level of 0.20 is considered a conservative approach so that the analysis is sensitive to possible changes in water quality over time, thus identifying wells and areas that require continuing detailed examination.
A two-tailed test is used to detect either an increasing or a decreasing trend. If the p-value is less than 0.10 (half the 0.20 significance level), then Ho is rejected (a change has occurred over time); otherwise, Ho cannot be rejected. If Ho is rejected in favor of Ha, an increasing or decreasing trend in the concentration of a variable is evident. To test the Ho of no trend against the Ha of an increasing trend, Ho is rejected in favor of Ha if the Mann-Kendall statistic is positive and if the p-value is less than 0.10. Similarly, to test the Ho of no trend against the Ha of a decreasing trend, reject Ho and accept Ha if the Mann-Kendall statistic is negative and if the p-value is less than 0.10. If autocorrelation is present, the p-value of the column titled “AR Residuals p-value” in the trend results table is used. The column titled “AR Residuals Slope” is used to determine the direction and magnitude of the trend.
Sen’s slope is used with the Mann-Kendall test to estimate the magnitude of an apparent trend. The Sen’s slope test is a nonparametric, linear slope estimator that works most effectively on monotonic data. Unlike linear regression, it is not greatly affected by gross data errors, outliers or missing data. If the Mann-Kendall test indicates a trend, the slope of the trend line is used to determine the significance of the trend.
For wells with an increasing trend, a Sen’s slope of 3 milligrams per liter (mg/L) per year was used as a threshold for further evaluation. This threshold is based on laboratory analysis replication limits. If the Mann-Kendall test indicates an increasing trend with a slope greater than the threshold limit of 3.0 mg/L, the increasing trend is considered significant (critical). If the Mann-Kendall test indicates an increasing trend with a slope less than 3.0 mg/L, but greater than or equal to 1.0 mg/L, the trend is considered increasing, but not critical, and the chloride data for these wells will require close examination with additional data collection. If the Mann-Kendall test indicates an increasing trend with a slope less than 1.0 mg/L, the trend is considered increasing but insignificant. A well’s median chloride concentration and the location are also considered in this evaluation. For example, a well with a significantly increasing trend approaching 250 mg/L located near public supply wells is of greater concern than a well with an increasing trend and a median chloride concentration over 1,000 mg/L located in a Floridan aquifer discharge area.
Posted on 2-22-2013