Two-dimensional Analytical Derivation of Incipient Desaturation Criterion in Stream-aquifer Flow Exchange

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Hubert J. Morel-Seytoux


A criterion for incipient desaturation for a stream and an aquifer initially in saturated hydraulic connection is derived analytically. The riverbed acts as a clogging layer. Such a criterion cannot be derived using a one-dimensional analysis. At least a two-dimensional analysis is required. It applies for a variety of shape of cross-sections. The formulae are algebraic and show explicitly the various factors that affect the initiation of desaturation such as river width, thickness of the aquifer, thickness of the clogging layer, conductivities of the clogging layer and of the aquifer, (drainage) entry pressure of the aquifer, ponded depth over the riverbed and aquifer head at some distance from the river bank. It is shown also that neglecting the change in thickness of the capillary fringe due to flow, as opposed to its hydrostatic value, has little impact on the accuracy of the criteria for incipient desaturation.

Incipient desaturation, stream-aquifer interaction, desaturation criterion.

Article Details

How to Cite
Morel-Seytoux, H. J. (2019). Two-dimensional Analytical Derivation of Incipient Desaturation Criterion in Stream-aquifer Flow Exchange. Journal of Geography, Environment and Earth Science International, 23(4), 1-14.
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Bredehoeft JD, Kendy E. Strategies for offsetting seasonal impacts of pumping on a nearby stream. Groundwater. Tallahassee, Florida. 1990;46(1):23-29.

Dogrul EC. Integrated water flow model (IWFM v4.0): Theoretical documentation. Sacramento, (CA): Integrated Hydrological Models Development Unit, Modeling Support Branch, Bay Delta Office, California Department of Water Resources; 2012.

Foglia L, McNally A, Harter TJ. Coupling a spatiotemporally distributed soil water budget with stream-depletion functions to inform stakeholder-driven management of groundwater dependent ecosystems. Water Resour. Res. 2013;49: 7292–7310.

Harbaugh AW. MODFLOW-2005 - The U.S. Geological Survey modular ground-water model-The ground-water flow process. U.S. Geological Survey Techniques and Methods 6-A16. 2005;253.

Harter T, Morel-Seytoux H. Peer review of the IWFM, MODFLOW and HGS model codes: Potential for water management applications in California’s Central Valley and Other Irrigated Groundwater Basins. Final Report, California Water and Environmental Modeling Forum, Sacramento; 2013.

McDonald M, Harbaugh A. A modular three-dimensional finite-difference ground-water flow model: Techniques of Water-Resources Investigations of the United States Geological Survey, Book 6, Chapter A1. 1988;586.

Kumar M, Bhatt G, Duffy CJ. PIFM. An efficient domain decomposition framework for accurate representation of geodata in distributed hydrologic models. International Journal of Geographical Information Science. 2009;23(12):1569–1596.

Kinzelbach W, Rausch R. Grundwassermodellierung. Gebrüder Borntraeger Verlag, Berlin. 1995;283.

MIKE_SHE_Printed_V1.pdf. User Manual. User Guide. Particularly sections 7.6.2 to 7.6.6. 2013;202-212.
DOI: ORG/10.9734/IJECC/2019/V9I330106

Therrien R, McLaren RG, Sucdicky EA, Park YJ. HydroGeoSphere. A three-dimensional numerical model describing fully integrated subsurface and surface flow and solute transport. Université Laval and University of Waterloo. 2012;166.

Rushton K. Representation in regional models of saturated river-aquifer interaction for gaining/losing rivers. J. Hydrol. 2007;334:262-281.

Morel-Seytoux HJ. The turning factor in the estimation of stream-aquifer seepage. Groundwater. 2009;47(2):205-212.

Mehl S, Hill MC. Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interaction. Adv. Water Resour. 2010;33:430-442.

Morel-Seytoux HJ, Steffen Mehl, Kyle Morgado. Factors influencing the stream-aquifer flow exchange coefficient, Groundwater; 2013.
DOI: 10.1111/gwat.12112, 7

Miracapillo C, Morel-Seytoux HJ. Analytical solutions for stream-aquifer flow exchange under varying head asymmetry and river penetration: Comparison to numerical solutions and use in regional groundwater models, Water Resour. Res. 2014;50.

Morel-Seytoux HJ. MODFLOW’s River Package: Part 1: A Critique. Physical Science International Journal. PSIJ. 2019a;22(2):1-9.
Article no.PSIJ.49757
DOI: 10.9734/PSIJ/2019/v22i230129

Morel-Seytoux HJ. MODFLOW’s river package: Part 2: Correction, combining analytical and numerical approaches. Physical Science International Journal. 2019b;22(3):1-23.
Article no.PSIJ.49758
DOI: 10.9734/PSIJ/2019/v22i330131

Osman YZ, Michael P. Bruen. Modelling stream–aquifer seepage in an alluvial aquifer: An improved loosing-stream package for MODFLOW. Journal of Hydrology. 2002;264:69–86.

Fox, G. A., 2003. Improving MODFLOW’s RIVER Package for unsaturated stream/aquifer flow. Proc. Hydrology Days 2003, 56-67l

Bear J. Dynamics of Fluids in Porous Media. American Elsevier, New York, N.Y. 1972;764.

Fox GA, Gordji L. Consideration for unsaturated flow beneath a streambed during alluvial well Depletion; 2007.

Fox GA, Durnford DS. Unsaturated hyporheic zone flow in stream/aquifer conjunctive systems. Adv. Water Resour. 2003;26(9):989–1000.

Morel-Seytoux HJ. Introduction to flow of immiscible liquids in porous media. Chapter XI in Flow through Porous Media. R. deWiest, Editor, Academic Press. 1969;455-516.

Corey AT. Mechanics of heterogeneous fluids in porous media. Water Resources Publications. Fort Collins, Colorado. 1977; 259.

Smith A. The Wealth of Nations. W. Strahon and T. Cadell, London; 1776.

Haitjema H. Comparing a three-dimensional and a dupuit-forcheimer solution for a circular recharge area in a confined aquifer. J. Hydrol. 1987;91:83-101.

Morel-Seytoux HJ. Analytical solutions using integral formulations and their coupling with numerical approaches. Groundwater. 2014;9.

Morel-Seytoux HJ. Analytical river routing with alternative methods to estimate seepage. International Journal of Environment and Climate Change. 2019c;9 (3):167-190.