usdasmall.gif (1686 bytes) Hillslope Erosion Model arslogo.gif (2004 bytes)
Engineered Information Systems for Natural Resources
USDA-ARS Southwest Watershed Research Center
Tucson, Arizona
eisnr2.gif (640 bytes)


Run the Model References
semiarid desert grassland


Hillslopes make up the landscape of much of the semiarid region of the Southwestern United States.  The hillslopes can be described by their profile shape, length, and slope.  Common hillslope shapes include convex, concave, straight, or complex.  Complex hillslopes are typically made up of several segments with various shapes.  Water induced soil erosion that drives hillslope evolution is impacted by several factors, including topography, vegetation, and soil surface characteristics. 
Vegetation and Bare Soil

Vegetation, such as grass, protects the soil .  A landscape view of seemingly uninterrupted grassland does not reveal the bare spaces between vegetation that provide flow paths for runoffA view from above reveals exposed, unprotected soil that is subject to erosion.
view of the grass from above


before the water  

Just Add Water

Water causes soil erosion. Soil particles detached by the impact of raindrops or flowing water may be transported or deposited downslope. Because flow rates change with time and position along the hillslope, soil detachment, transport, and deposition change with time and space. Steeper sections of hillslopes are subject to downcutting.  Eroded material is deposited in response to a reduction in slope.
erosion and deposition
Kinematic Wave Equations

Kinematic Wave Equations

Erosion/Sediment Yield Equations

Sediment Equations


A Mathematical Model to Simulate Hillslope Erosion and Sediment Yield

A mathematical model has been developed by scientists at the USDA-ARS Southwest Watershed Research Center in Tucson, Arizona to describe hillslope erosion processes. Given hillslope segment lengths, slopes, % canopy cover, % surface ground cover, runoff volume, and a soil erodibility value, the model will simulate erosion process along the hillslope and will return runoff volume, sediment yield, interrill detachment, rill detachment, rill deposition, and the mean concentration of sediment in the flow for each hillslope segment.

Sediment yield equations were developed for a single plane, and were extended to irregular slopes by approximating the irregular slopes as a cascade of planes.

Increasing sediment concentration in the downslope direction may indicate erosion along the hillslope. Deposition may be indicated by a decrease in sediment concentration in the downslope direction. Constant sediment concentration indicates an equilibrium.

Run the Model

Downloadable References

Additional detail regarding the Hillslope Erosion Model can be found in the following publications that are available in Adobe Acrobat Reader PDF format:

To view these files in PDF you will need the Adobe Acrobat Reader.  If you don't have the reader, please follow the Adobe Acrobat Reader link. Acrobat and the Acrobat logo are trademarks of Adobe Systems Incorporated.

Modeling Erosion on Hillslopes: Concepts, Theory, and Data (146 KB pdf file)
by L. J. Lane, M. H. Nichols, and G. B. Paige
In: Proceedings of the International Congress on Modelling and Simulation (MODSIM'95) (ed. by P. Binning, H. Bridgman, and B. Williams), November 27-30, 1995, Univ. of Newcastle, Newcastle, NSW, Australia, Uniprint, Perth, Australia, pp. 1-7.

Modelling Erosion on Hillslopes (126 KB pdf file)
by L. J. Lane, E. D. Shirley, and V. P. Singh
Chapter 10 In: Modelling Geomorphological Systems (ed. by M. G. Anderson). John Wiley and Sons, Chichester, 1988, pp. 287-308.

A Sediment Yield Equation From an Erosion Model (111 KB pdf file)
by E. D. Shirley and L. J. Lane
In: Hydrology and Water Resources in Arizona and the Southwest, 8, 90-96.10, 1978.

Processes Controlling Sediment Yield from Watersheds as Functions of Spatial Scale (249 KB pdf file)
by L. J. Lane, M. Hernandez, and M. H. Nichols
Journal of Environmental Modelling & Software, Vol. 12, No. 4, 1997, pp. 355-369.

Watershed Erosion and Sediment Yield Affecting Contaminant Transport (102 KB pdf file)
by L. J. Lane, T. Hakonson, and G. Foster
Proceedings of the Symposium on Environmental Research on Actinide Elements, November 1983, Hilton Head, SC, pp. 193-223.

Comments and Feedback


State of Technology Development Government Usage Policy Disclaimer Glossary of Terms

Engineered Information Systems for Natural Resources

Southwest Watershed Research Center
Tucson, Arizona

Last Modified 4/16/02