Mathematical Modeling Principles

The development of models of hydrologic systems requires the description of individual processes in mathematical terms and the solution of sets of complex equations in differential form. This project is focused on developing mathematical descriptions of flow and water-quality processes that can be linked together to form such models. Research is needed on application of mathematical theory to the modeling of transport of sediments, including mudflows and hyperconcentrations such as occur after natural disasters such as volcanic eruptions or dam failures. This project is focused on developing mathematial description of flow and water-quality processes that can be linked together to form models of hydrologic systems and developing mathematical techniques for efficient solution of equations on digital computer techniques for studying sensitivity of parameters. For current information about work being done by this project, including investigations into hydrologic and erosional responses of burned watersheds, see project's home page.

REPORTS PUBLISHED 2000-2004

Yang, C.T., and Simões, F.J., 2004, Application of GSTARS to river sedimentation studies, , in Hu, C.-h, and Tan, Y., eds., Proceedings of the Ninth International Symposium on River Sedimentation, October 18-21, 2004, Yichang, China: Beijing, Tsinghua University Press, v. 1, p. 299-306.

Nelson, J.M., Bennett, J.P., and Wiele, S.M., 2003, Modeling flow, sediment transport, and bed evolution in channels, chapter 18, in Kondolph, M. and Piegay, H. Tools in Fluvial Geomorphology: Wiley, London.

Ruth, J.M., Petit, D.R., Sauer, J.R., Samuel, M.D. Johnson, F.A., Fornwall, M.D., Korschgen, C.E., and Bennett, J.P., 2003, Science for avian conservations - priorities for the new millennium: The Auk, v. 120, no. 1, p. 204-211. (on-line report)

Simões, F.J. and Yang, C.T., 2003, Numerical modeling of reservoir sedimentation using GSTARS 3.0: Proceedings of the XXXth IAHR (International Association for Hydraulic Research) Congress, Thessaloniki, Greece.

Yang, C.T., and Simoes, F.J., 2003, User's manual for GSTARS 3.0: U.S. Bureau of Reclamation, Technical Service Center, Denver, Colorado, December 2002.

Moody J.A., and Smith, J.D., 2002, Field measurements of Reynolds Stress near a riverbank: Proceedings EWRI and IAHR Hydraulic Measurement and Experimental Methods Conference, Estes Park, Colo., 29-31, July 2002 (CD).

Moody, J.A., and Troutman, B.M, 2002, Characterization of the spatial variability of channel morphology: Earth Surface Processes and Landforms, v. 27, no. 12, p. 1251-1266. (on-line abstract)

Yang, C.T., and Simoes, F.J., 2002, GSTARS 3.0: A numerical model for reservoir sedimentation: Proceedings from the 5th International Conference on Hydro-Science and Engineering (ICHE), Warsaw, Poland, Sep. 18-21, 2002.

Bennett, J.P., 2001, User's guide for mixed-size sediment transport model for networks of one-dimensional open channels: U.S. Geological Survey Water-Resources Investigations Report 01-4054, p.1-33.

Bennett, J.P., 2001, Mixed-size sediment transport model for networks of one-dimensional open channels: Proceedings of the Seventh Interagency Sedimentation Conference, v. 1, p. I -145 - I-152.

Martin, D.A., and Moody, J.A., 2001, The flux and particle size distribution of sediment collected in hillslope traps after a Colorado wildfire: Proceedings of the Seventh Interagency Sedimentation Conference, v. 1, p. III-I40 - III-I47.

Martin, D.A., and Moody, J.A., 2001, Comparison of soil infiltration rates in burned and unburned mountainous watersheds: Hydrological Processes, v. 15, no. 15, p. 2893-2903 (on-line abstract)

McDonald, R.R., Bennett, J.P., and Nelson, J.M., 2001, The USGS multi-dimensional surface water modeling system: Proceedings of the Seventh Interagency Sedimentation Conference, v. 1, p. I-161 - I-167.

Moody, J.A., 2001, Sediment transport regimes after a wildfire in steep mountainous terrain: Proceedings of the Seventh Interagency Sedimentation Conference, v. 2, p. X-41 - X-48.

Moody, J.A., and Martin, D.A., 2001, Initial hydrologic and geomorphic response following a wildfire in the Colorado Front Range: Earth Surface Processes and Landforms, v. 26, no. 10, p. 1049-1070 (on-line abstract)

Moody, J.A., and Martin, D.A., 2001, Post-fire, rainfall intensity-peak discharge relations for three mountainous watersheds in the western USA: Hydrological Processes: v. 15, no. 15, p. 2981-2993 (on-line abstract)

Moody, J.A., and Martin, D.A., 2001, Hydrologic and sedimentologic response of two burnded watersheds in Colorado: U.S. Geological Survey Water-Resources Investigations Report 01-4122, 138 p. (and data CD).

Schmeeckle, M.W., Nelson, J.M., Pitlick, J., and Bennett, J.P., 2001, Interparticle collisions of natural sediment grains in water: Water Resources Research, v. 37, no. 9, p. 2377-2391.

Wiele, S.M., and Franseen, M.A., 2001, Sand transport and bed evolution modeling applications in the Colorado River, Grand Canyon: Proceedings of the Seventh Federal Interagency Sedimentation Conference, v. 1, p. I-115-119.

Moody, J.A., Sullivan, J.F., and Taylor, H.E., 2000, Effects of the flood of 1993 on the chemical characteristics of bed sediments in the Upper Mississippi River: Water, Air, and Soil Pollution, v. 117, p. 329-351. (on-line abstract)

Moody, J.A., and Troutman, B.M., 2000, Quantitative model of the growth of flood plains by vertical accretion: Earth Surface Processes and Landforms, v. 25, p. 115-133. (on-line abstract)

Topping, D.J., Rubin, D.M., Nelson, J.M., Kinzel, P.J., III, and Corson, I.C., 2000, Colorado River sediment transport: Part 2: Systematic bed-elevation and grain-size effects of sand supply limitation: Water Resources Research, v. 36, p. 543-570. (on-line abstract)

Topping, D.J., Rubin, D.M., and Vierra, L.E., Jr., 2000, Colorado River sediment transport: Part 1: Natural sediment supply limitation and the influence of Glen Canyon Dam: Water Resources Research, v. 36, p. 515-542. (on-line abstract)

For information on additional projects in the National Research Program, see Indexes to NRP projects and bibliographies