Analytical River Routing with Alternative Methods to Estimate Seepage

Main Article Content

Hubert J. Morel-Seytoux


Knowledge of flow exchange between surface and groundwater is of great importance for use of water resources. The determination of seepage between a stream and an underlying aquifer requires an accurate estimation of the river stage and of the head in the aquifer. An approach is presented to estimate analytically river flow and stage while using the SAFE conductance to calculate the seepage.  A major contribution of this article lies in the methodology for river routing with its use of a modified Linear Reservoir model.  The parameter C is related to discharge based on Manning’s equation. That relation breathes into an empirical model a dynamic character. A second major contribution is to show that it is possible to simultaneously calculate river stage and aquifer head in the aquifer cell that contains the river.  As a result iteration is not necessary to estimate that river cell head as river stage changes, as opposed to what is usually done in most numerical groundwater models.  Iteration is still needed for the adjacent cells to the river cell.  Because the influence of a change in the adjacent cell head on the river cell head is much delayed and attenuated the iteration is not sensitive to that change. A goal of this document is to show how that method can be used within a simple physically based routing procedure [1] to estimate the river stage that has a definite influence on seepage.

Stream-aquifer flow exchange, river routing, stream depletion, Leakance coefficient

Article Details

How to Cite
Morel-Seytoux, H. (2019). Analytical River Routing with Alternative Methods to Estimate Seepage. International Journal of Environment and Climate Change, 9(3), 167-192.
Original Research Article

Article Metrics


Morel-Seytoux HJ. Simple flow routing with discharge dependent celerity, fractional lag and bank overflow. Proceedings of 20th Annual AGU Hydrology Days, Hydroprose International Consulting, 684 Benicia Drive # 71, Santa Rosa, California, 95409. 2000;141-152.

Barlow PM, Leake SA. Streamflow depletion by wells—Understanding and managingthe effects of groundwater pumping on streamflow. U.S. Geological Survey Circular. 2012;1376:84.

Morel-Seytoux HJ, Illangasekare T, Bittinger MW, Evans NA. Potential use of a stream-aquifer model for management of a river basin: Case of the South Platte River in Colorado, proceedings of inter. Assoc. on Water Pollution Research Specialized Conference on "New Develop-ments in River Basin Management," Cincinnati, Ohio, U.S.A. 1980;1975-1987.

Bouwer H. Theory of seepage from open channels. Chapter in Advances in Hydroscience, V. T. Chow, Editor, Academic Press. 1969;5:121-172.

Bouwer H. Groundwater hydrology. McGrwaw-Hill Book company. New York. 1978;480.

Morel-Seytoux HJ, Peters G, Illangasekare T. Field verification of the concept of reach transmissivity. Proc. of the International Symposium on Hydrology of Areas of Low Precipitation, Canberra, Australia, December 10-13. 1979;355-359.

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.

Anderson EI. Modeling groundwater-surface water interaction using the Dupuit approximation. Adv. Water Resour. 2005;28:315-327.

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

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.

Glover RE, Balmer GG. River depletion resulting from pumping a well near a river. Trans. Am. Geophys. Union. 1954;35:487-493.

Woolfenden LR, Nishikawa T. editors. Simulation of groundwater and surface-water resources of the Santa Rosa plain watershed, Sonoma county, California. USGS Scientific Investigation Report. 2014;5052:241.

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.

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

Morel‐Seytoux HJ, Mehl S, Morgado K. Factors influencing the stream‐aquifer flow exchange coefficient. Groundwater. 2013; 52(5):775-781.

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, Calvin D. Miller Cinzia Miracapillo, Steffen Mehl. River Seepage Conductance in Large-Scale Regional Studies; 2016.

Gilcrest BR. Flood routing. Chapter X of Engineering Hydraulics, Hunter Rouse, editor. Wiley, inc. New York; 1950.

Chow VT, Maiden DR, Mays LW. Applied hydrology. McGraw-Hill Publishing Company, New York. 1988;572.

Morel-Seytoux HJ. The theory of the linear reservoir and practical relevance in hydrology. Proc. 13th Annual HYDROLOGY DAYS, Hydrology Days Public.,684 Benicia Drive Unit 71, CA. 1993;95409:390-406.

Morel-Seytoux HJ. Analytical solutions using integral formulations and their coupling with numerical approaches. National Ground Water Association; 2014.
DOI: 10.1111/gwat.12263

Cunge JA. On the subject of a flood propagation computation method (Muskingum method). J. Hydraul. Res. 1969;7(2):205-230.

Agricultural Research Service. Linear Theory of Hydrologic Systems. Technical Bulletin No. 1468.U.S. Government Printing Office, Washington D.C. 20402. 1973;327.

BCEOM-GrandsLacs de Seine. 1994. Etude d’optimisation de la gestioncoordonnée des barrages reservoirs du bassin de la Seine. Rapport d’étude. Tome 3. June. 1994;94.

Morel-Seytoux HJ. Optimal deterministic reservoir operations in continuous time. ASCE. Journal of Water Resources Planning and Management. 1999;125(3):126-134.

Box GE, Jenkins GM. Time series analysis, forecasting and control. Holden-Day, San Francisco. 1976;575.

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