APPLICABILITY OF LINEARIZED BOUSSINESQ EQUATION FOR MODELING BANK STORAGE UNDER UNCERTAIN AQUIFER PARAMETERS

Boussinesq's equation is frequently employed to study the influence of flood-stage hydrographs in streams on bank storage effects. This equation is nonlinear and no analytical solutions are available for arbitrarily shaped stage hydrographs. Analytical solutions are presented for the linearized form of the equation, and expressions for the flow rate from the stream to the aquifer are developed. Results indicate that these analytical solutions may not be very accurate (as much as 10% error) when compared with numerical solution of the nonlinear equation. These deterministic analytical solutions lead to analytical expressions for the mean and variance of flux rates when the hydraulic properties of the aquifer are treated as random quantities. Monte-Carlo simulation results show that linearized analytical solutions are potentially useful for predicting mean flux rates when aquifer properties exhibit a large degree of variability.