The Uncertainties and Temporal Scaling of Groundwater Level Fluctuations in a bounded aquifer.

Abstract:

Analytical solutions for the variance, covariance, and spectrum of groundwater level, h(x, t), in an unconfined aquifer described by a linearized Boussinesq equation with random source/sink and initial and boundary conditions were derived. It was found that in a typical aquifer the error in h(x, t) in early time is mainly caused by the random initial condition and the error reduces as time progresses to reach a constant error in later time. The duration during which the effect of the random initial condition is significant may last a few hundred days in most aquifers. The constant error in h(x, t) in later time is due to the combined effects of the uncertainties in the source/sink and flux boundary: the closer to the flux boundary, the larger the error. The error caused by the uncertain head boundary is limited in a narrow zone near the boundary and remains more or less constant over time. The aquifer system behaves as a low-pass filter which filters out high-frequency noises and keeps low-frequency variations. Temporal scaling of groundwater level fluctuations exists in most part of a low permeable aquifer whose horizontal length is much larger than its thickness caused by the temporal fluctuations of areal source/sink.