A statistical F test for the natural attenuation of contaminants in groundwater

Natural attenuation (NA) is a catchall explanation for the overall decay and slowed movement of the contaminants in the subsurface. One direct support to NA is to demonstrate that contaminant concentrations from monitoring wells located near the source are decreasing over time. The decrease is summarily expressed in terms of an apparent half-life that is determined from the line best fitting the observed log-transformed concentration data and time. This simple (time-only) decay model assumes other factors are invariant, and so is flawed when complicating factors - such as a fluctuating water table - are present. A history of the water-table fluctuation can track changes in important NA factors like recharge, groundwater flow direction and velocity, as well as other non-NA factors like volume of water in and purged from the well before a sample is collected. When the trend in the concentrations is better associated with the water table rising or falling, any conclusion about degradation rate may be premature. We develop simple regressions to predict contaminant concentration (c) by two line models: one involving time (csimilar toc(t)), and another involving groundwater elevation (csimilar toc(z)). We develop a third model that includes both factors (csimilar toc(t, z)). Using an F-test to compare the fits to the models, we determine which model is statistically better in explaining the observed concentrations. We applied the test to sites where benzene degradation rates had previously been estimated. The F-test can be used to determine the suitability of applying non-parametric statistics, like the Mann-Kendall, to the concentration data, because the result from the F-test can indicate instability of the contaminant plume that may be masked when the water table fluctuates.