Baseline Trend Analysis and Correction |
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Baseline Trend Analysis and Correction |
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Historic and baseline water level trends can impact the drawdown data you record during your pumping test. Surrounding pumping activities, or even surface disturbances such as trains, can effect the water level during the pumping test. It is important to identify all major disturbances (especially cyclic activities) which may impact the test data. Enough measurements have to be made to fully characterize the pre-pumping trends of these activities (Osborne, 1993). Therefore, the user must record water levels near or at the well, either before or after the test. (For example, daily water level measurements taken 1 week prior to the test, up to the day of the test, is a general recommendation from the EPA.) Using the measured trend data, AquiferTest performs a line fit to calculate a trend coefficient. The program will also run a “t-test”, to see if the trend is significant. If significant, the data is then corrected based on this trend.
NOTE: Baseline trend analysis and correction tools are only available in the AquiferTest Pro edition.
As an example, a trend analysis shows a trend of water levels rising 2 cm/hr due to surrounding activities. During the pumping test, for a water level recorded 3 hours after the test begins, you need to add 6 cm to the water level measurements in order to conduct a representative analysis of the aquifer.
If the data trend is already known (i.e. water level fluctuations due to tidal or ebb-flows), then the trend can be defined using a simple linear time-dependent correction. For more details, "Customized Water Level Trends".
A trend analysis generally involves the following steps:
1.Collect baseline trend data (time vs. water level) prior to, and after, the test; measurements should be recorded at a location that will not be influenced by the pumping test activities.
2.AquiferTest calculates a baseline trend, and trend coefficient. AquiferTest calculates the simple linear regression of the measured values and runs a t-test to determine if the trend is significant.
3.Apply the trend coefficient to the data collected during the pumping test (time vs. water level), resulting in “corrected drawdown” measurements.
4.Use the corrected drawdown values for the calculation of the aquifer parameters.
The general formula for a trend computation is a polynomial as a function of the time :
where:
Only the linear part of the trend is considered for hydrogeological observations (trend of 1st order):
Standard regression analysis is used in AquiferTest to calculate the values of and . To check the quality of the trend, compare the linear correlation coefficient with tabular values for the t-test, available in most statistical texts. A linear coefficient value is calculated that can be used to calculate corrected drawdown at the observation wells. AquiferTest calculates the change in water level based on the trend.
To check the trend for statistical significance, the Pearson correlation coefficient , is calculated as below:
The calculated value of is compared with the “critical value”. The critical values are available in tabular form, in most statistical reference books.
To calculate the critical value, first obtain the value of quantile of the test, .
There are two required parameters:
is the confidence interval
is the degrees of freedom, which is -2 (where is the number of data points)
The formula to calculate, is complex, and is not illustrated in this manual; however, it can be found in most reference books on statistics.
The confidence interval can be defined in AquiferTest in the main menu under Tools / Options, and under the Constants tab. The default value is 95%.
To obtain the critical value , the formula from Sachs (1974) is used:
•If the absolute value of the Pearson coefficient () is GREATER than the “critical value” then the trend is SIGNIFICANT.
•If the absolute value of the Pearson coefficient () is LESS than the “critical value” then the trend is NOT SIGNIFICANT.
Reference: Langguth & Voigt (1980), p413.
An example demonstrating a data trend analysis is available in Exercise 5: Adding Data Trend Correction.
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