Temporal and spatial variation and scaling of groundwater levels in a bounded unconfined aquifer

Temporal and spatial variation and scaling of groundwater level (h) due to a white noise source in an unconfined aquifer bounded by a no-flow boundary and a river were investigated with non-stationary spectral analyses. Analytical solutions for the variance (image), covariance (Chh), and spectrum (Shh) of h described by a linearized Boussinesq equation were derived and verified by Monte Carlo simulations. It is found that in general the random process of h is temporally and spatially non-stationary and image, Chh, and Shh are functions of space and time. The effect of a constant-head boundary is to reduce the variance and covariance at late times or the spectrum power at low frequencies near the boundary and thus to create a crossover or break point in temporal scaling of h(x, t). The simulation results support the common practice of estimating scaling parameters from the spectrum of observed groundwater levels. The results obtained in this study are consistent with published theoretical analyses and provide more general theoretical basis for field observations.