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GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L07402, doi:10.1029/2006GL025747, 2006

Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography

Anders Wörman

Department of Biometry and Engineering, Swedish University of Agricultural Sciences, Uppsala, Sweden


Aaron I. Packman

Department of Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois, USA


Lars Marklund

Department of Biometry and Engineering, Swedish University of Agricultural Sciences, Uppsala, Sweden


Judson W. Harvey

U.S. Geological Survey, Reston, Virginia, USA


Susa H. Stone

Department of Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois, USA


Abstract

It has been long known that land surface topography governs both groundwater flow patterns at the regional-to-continental scale and on smaller scales such as in the hyporheic zone of streams. Here we show that the surface topography can be separated in a Fourier-series spectrum that provides an exact solution of the underlying three-dimensional groundwater flows. The new spectral solution offers a practical tool for fast calculation of subsurface flows in different hydrological applications and provides a theoretical platform for advancing conceptual understanding of the effect of landscape topography on subsurface flows. We also show how the spectrum of surface topography influences the residence time distribution for subsurface flows. The study indicates that the subsurface head variation decays exponentially with depth faster than it would with equivalent two-dimensional features, resulting in a shallower flow interaction.

Received 19 January 2006; accepted 1 March 2006; published 7 April 2006.

Index Terms: 1622 Global Change: Earth system modeling (1225); 1655 Global Change: Water cycles (1836); 1804 Hydrology: Catchment; 1839 Hydrology: Hydrologic scaling; 1860 Hydrology: Streamflow.

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Citation: Wörman, A., A. I. Packman, L. Marklund, J. W. Harvey, and S. H. Stone (2006), Exact three-dimensional spectral solution to surface-groundwater interactions with arbitrary surface topography, Geophys. Res. Lett., 33, L07402, doi:10.1029/2006GL025747.