Estimating Transmissivity from the Water Level Fluctuations of a Sinusoidally Forced Well

The water levels in wells are known to fluctuate in response to earth tides and changes in atmospheric pressure. These water level fluctuations can be analyzed to estimate transmissivity (T). A new method to estimate transmissivity, which assumes that the atmospheric pressure varies in a sinusoidal fashion, is presented. Data analysis for this simplified method involves using a set of type curves and estimating the ratio of the amplitudes of the well response over the atmospheric pressure. Type curves for this new method were generated based on a model for ground water flow between the well and aquifer developed by Cooper et al. (1965). Data analysis with this method confirmed these published results: (1) the amplitude ratio is a function of transmissivity, the well radius, and the frequency of the sinusoidal oscillation; and (2) the amplitude ratio is a weak function of storativity. Compared to other methods, the developed method involves simpler, more intuitive data analysis and allows shorter data sets to be analyzed. The effect of noise on estimating the amplitude ratio was evaluated and found to be more significant at lower T. For aquifers with low T, noise was shown to mask the water level fluctuations induced by atmospheric pressure changes. In addition, reducing the length of the data series did not affect the estimate of T, but the variance of the estimate was higher for the shorter series of noisy data.