EFFECTS OF FIRST-ORDER APPROXIMATIONS ON HEAD AND SPECIFIC DISCHARGE COVARIANCES IN HIGH-CONTRAST LOG CONDUCTIVITY

The hydraulic head and the specific discharge fluctuations depend nonl inearly on the hydraulic conductivity. However, the methods most commo nly used in the stochastic analysis of groundwater flow are based upon the linearization of these relations. In this paper we apply a numeri cal spectral approach to investigate the range of validity of the smal l perturbation approximation for head and specific discharge moments i n two-dimensional finite domains. We find that the small perturbation approximation tends to underestimate the variance of large-scale head and specific discharge fluctuations and error increases with increasin g log-conductivity variance and increasing domain size. The head fluct uations do not appear ergodic even when the small perturbation approxi mation predicts they will be ergodic. The specific discharge fluctuati ons, on the other hand, do appear ergodic. The small perturbation appr oximation performs well. in estimating specific discharge variance in the longitudinal direction but significantly underestimates transverse specific discharge variance.