Analyses of uncertainties and scaling of groundwater level fluctuations

Abstract. Analytical solutions were derived 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. It was found that in a typical aquifer, the error in h(x, t) at an early point in time is mainly caused by the random initial condition, and the error reduces as time progresses to reach a constant error at a later time. The duration for which the effect of the random initial condition is significant may be a few hundred days in most aquifers. The constant error in h(x, t) at a 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 to 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 parts of a low permeable aquifer whose horizontal length is much larger than its thickness, caused by the temporal fluctuations of areal source/sink.