System modelling of the interaction between surface and ground waters in problems of hydrology

Abstract

The objective of the paper is to give a survey of the mathematical (quantitative) modelling of the interaction between surface water and groundwater. Besides describing the existing approach to such modelling and the main difficulties in its realization, the paper presents a brief review of the principal works on the subject under consideration including Soviet ones. The construction of such coupled models requires the development of methods of conjunction between models which represent surface and subsurface flows, which describe the different processes of water transfer and transformation, constituting the hydrological cycle, and which include the different components of hydrological, hydrogeological and water management systems (water bodies, streams, aquifers, etc.). Such models are of different complexities and have different dimensionality in space variables. The characteristic time-scales of transient processes for surface water and groundwater differ greatly, and this is of profound importance in the numerical modelling of their interconnected motion.

On the Coupling Between Channel Level and Surface Ground-Water Flows

“…Vertical filtration in a porous ground. By applying the Darcy law, it is well known that (see ABBOTT et al, 1986;PHILIP, 1969;VASILIEV, 1987) if we denote by 0 to the volumetric moisture content and by w to the pressure of the soil moisture then we arrive at the so-called Richards equation…”

“…Horizontal plane filtration equations for the levels of ground waters. By using the socalled Boussinesq and Shchelkachev equations, it is well known (KUCHMENT et al, 1983;MILES, 1985;PHILIP, 1969;POLUBARINOVA-KOCHINA, 1977;VASILIEV, 1987) that if we denote by H(x, t) and H 1 (x, t), respectively, to the elevation of the ground-water free surface in the upper layer and the piezometric head in the lower layer, then we arrive at the coupled system of…”

“…1), f X is a source function (see VASILIEV, 1987). Here the div operator must be understood only in the spatial variable.…”

“…Water level flow in open channels. By applying a diffusion wave approximation to the Saint-Venant equations, it is well known ANTONTSEV, and MEIRMANOV, 1977b;DALUZ VIEIRA, 1983;EPIKHOV, 1985;KUCHMENT et al, 1983;VASILIEV, 1987 and their references) that if we denote by u(s, t) to the water level in the channel stream, by x to the cross-sectional area (x u = qx/qu = B is the width) and to s to the channel curvilinear length variably measured along its axial cross section, then we arrive at the nonlinear parabolic equation where w(s,u) = Cx R 2/3 is the discharge modulus, C is the coefficient Chezy, R is the hydraulic radius, f P is a source function,…”

Estimate of river seepage by conditioning downward groundwater flow in the Toyohira River alluvial fan, Japan

“…One might require river seepage to be estimated throughout one hydrologic cycle, including focused recharge by snow melting and precipitation events. Water loss transiently varies during shorter events such as floods, generally increasing with water discharge (Vasiliev 1987, Frei et al 2009). The regional-scale model is not suitable for such diverse discharge conditions for limited head data in the deep aquifer.…”