Application of the convolution equation to stream‐aquifer relationships

Abstract

Flow and head variations in stationary linear stream‐aquifer systems are obtained through application of the convolution equation. Four highly idealized cases involving finite and semi‐infinite aquifers, with and without semipervious stream banks, are considered. Equations for the instantaneous unit impulse response function, the unit step response function, and the derivative of the unit step response function are given for each case. Head fluctuations in the aquifer due to an arbitrarily varying flood pulse are obtained for the cases involving a finite aquifer with and without a semipervious stream bank. Flow in and out of the aquifer at the stream bank is determined for the same cases and demonstrates the value of the convolution equation in evaluating the base flow. Head variations, and to a lesser extent flow variations, are apparently relatively insensitive to variations in aquifer diffusivity.

Longitudinal hydraulic analysis of river‐aquifer exchanges

“…The Boussinesq equation was derived for the general case of groundwater flow parallel to a underlying confining unit and can be solved by linearization in terms of h [e.g., Brutsaert, 1994] or h 2 for the steady state form [Crank, 1984]. For the analysis of river-aquifer exchanges, the Boussinesq equation is typically applied to calculate groundwater discharge for a valley cross section (i.e., is oriented perpendicular to the river channel) assuming horizontal flow where the river channel fully penetrates the aquifer and thus intercepts all groundwater flow [Cooper and Rorabaugh, 1963;Hornberger et al, 1970;Hall and Moench, 1972;Brutsaert and Nieber, 1997;Ostfeld et al, 1999;Troch et al, 2003]. Under these assumptions, solutions to the Boussinesq equation provide a theoretical basis for either linear or nonlinear exponential streamflow recession generated by a draining aquifer, which are characteristic of many rivers [Hall, 1968;Tallaksen, 1995].…”

Characterizing the Impact of River Barrage Construction on Stream-Aquifer Interactions, Korea

“…R refers to the sum of the retardation coefficient and the resistance effect by the partially penetrated river [26,40], and it is different from the retardation coefficient proposed by Hantush [41]. Singh [21] generalized R to the following cases: (1) R = 0 (i.e., a fully penetrating river without a semipervious bed) with a symmetrical floodwave response to linear variations of WL_R corresponding to the equations of Cooper and Rorabaugh [42] and Hantush [41,43]; (2) R = 0 for long-term sinusoidal variations of WL_R equivalent to a steady periodic solution [44,45]; and (3) R > 0 (i.e., a fully penetrating river and a semipervious bed) with a unit-step rise in WL_R equal to the solution of Hall and Moench [22,40]. The governing equation of stream-aquifer interactions in a semi-infinite homogeneous isotropic confined aquifer assuming the Boussinesq approximation can be expressed as…”

Transit losses and traveltimes for water-supply releases from Marion Lake during drought conditions, Cottonwood River, east-central Kansas

“…This type of model is called a diffusion-analogy model. The downstream hydrograph is computed by convoluting the upstream (inflow) hydrograph with the analytical solution for an instantaneous input (Hall and Moench, 1972;Keefer, 1974). 1 Withdrawal wells are within 0.5 mile of river and had been pumping for several months or years; rate of pumping was assumed to result in equal rate of reduction of gain to river.…”