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Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge


  • J. Jaime Gómez-Hernández,

  • Steven M. Gorelick


A stochastic simulation approach was used to inspect the influence of spatial variability in aquifer and recharge properties on effective (averaged) groundwater model parameters. A two-dimensional unconfined aquifer model was set up for an area similar to that near Livermore, California. Monte Carlo simulations were generated for different sets of spatial correlation structures assuming stationarity and an exponential semivariogram. For each Monte Carlo realization, groundwater flow was simulated, and estimates of the means and standard deviations of the hydraulic head were obtained. Nine different cases were studied involving different correlation lengths of hydraulic conductivity, conditional simulations, parameter zonation, and spatial recharge distributions. Results indicate that there is no single uniform value of the hydraulic conductivity that reproduces the expected head values. Spatial averaging to obtain effective values was based on the p norm (power norm) which ranges from 1 for the arithmetic mean to −1 for the harmonic mean, with 0 representing the geometric mean. For the unconditional case the −0.4 p norm seems to best reproduce the expected values. The −0.2 p norm gave the best result for the conditional simulation case. If the geometric mean were used instead, the heads would deviate from the expected heads by about 2 m near the wells. Some value between the arithmetic and the geometric means of riverbed leakance will give results close to the expected head values. The arithmetic mean of aerially distributed recharge produced results with small deviations from the expected head values. These particular results may only apply to this modeled system, as the pumping pattern and magnitudes exhibited strong influences on zones of maximum head deviation. The implication of this work is that if an effective hydraulic conductivity is used in a simulation model, it must be selected for a particular set of wells and pumping rates. In an aquifer with significant pumping centers the best effective value for a two-dimensional unconfined flow model is most likely between the geometric and harmonic mean. If the wells are turned off, the effective hydraulic conductivity for that flow model reverts to the geometric mean.

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