National Research Program

Statistical Analysis of Errors in Hydrologic Models

Uncertainty in application of physically based surface-water hydrologic models is a function of adequacy of the conceptualization of the processes involved and of the quantity and quality of data available to use as input to the model. In any type of modeling exercise, even if the physical processes are well understood, spatial heterogeneities make application of the model on a basin-wide scale problematic, and it is almost always necessary to use some form of spatial averaging to obtain "effective" input variables. The over-all goal of our research is to investigate: (1) Model output errors as a function of model complexity and uncertainty in model input; (2) Derivation of simplified yet physically based models that are appropriate to use with limited data; (3) Ways of evaluating and coping with uncertainty caused by spatial variability of input variables. This project seeks to develop unified approach to analyzing and partitioning errors in hydrologic modeling with particular attention to scale and spatial averaging problems; develop improvements to existing practices; and develop new approaches to managing error levels within the constraints of reduced budgets.


Mantilla, R.M., Gupta, V.K., and Troutman, B.M., 2012, Extending generalized Horton laws to test embedding algorithms for topologic river networks: Geomorphology, v. 151-152, p. 13-26. (on-line abstract of journal article)

Mantilla, R.M., Gupta, V.K., and Troutman, B.M., 2011, Scaling of peak flows with constant flow velocity in random self-similar networks: Nonlinear Processes in Geophysics, v. 18, no. 4, p. 489-502. (on-line abstract or on-line publication in pdf format, 7701 KB, open access journal of the European Geosciences Union)

Gupta, V.K., Mantilla, R., Troutman, B.M., Dawdy, D., and Krajewski, W.F., 2010, Generalizing a nonlinear geophysical flood theory to medium-sized river networks: Geophysical Research Letters, v. 37, no. 11, L11402. doi:10.1029/2009GL041540 (on-line abstract of journal article)

Mantilla, R., Troutman, B.M., and Gupta, .V.K., 2010, Testing statistical self-similarity in the topology of river networks, Journal of Geophysical Research, v. 115, F03038, doi:10.1029/2009JF001609 (on-line abstract of journal article)

Morin, R.H., LeBlanc D.R., and Troutman, B.M., 2010. The influence of topology on hydraulic conductivity in a sand-and-gravel aquifer: Ground Water, v. 48, no. 2, p.181-190. (on-line abstract or on-line journal article in pdf format, 876 KB, compiled by the National Ground Water Association)

Furey, P.R., and Troutman, B.M., 2008, A consistent framework for Horton regression statistics that leads to a modified Hack's law: Geomorphology, v. 102, no. 3-4, p. 603-614 . (on-line abstract of journal article)

Gupta, V.K., Troutman, B.M., and Dawdy, D.R., 2007, Towards a nonlinear geophysical theory of floods in river networks: An overview of 20 years of progress, Chapter 8 in Tsonis, A. and Elsner, J., eds., Nonlinear Dynamics in Geosciences: New York, Springer.

Troutman, B.M., 2005, Rainfall, landforms, and streamflow: Encyclopedia of Statistical Sciences, 2nd edition, New York, John Wiley, doi:10.1002/0471667196.ess5033 .

Troutman, B.M., 2005, Scaling of flow distance in random self-similar channel networks: Fractals - Complex Geometry, Patterns, and Scaling in Nature and Society, v. 13, no. 4, p. 265-282. (on-line abstract)

Troutman, B.M., Edelmann, P., and Dash, R.G., 2005, Variability of differences between two approaches for determining ground-water discharge and pumpage, including effects and trends, Lower Arkansas River Basin, Southwestern Colorado, 1998-2002: U.S. Geological Survey Scientific Investigations Report 2005-5063, 47 p. (on-line abstract or on-line report in pdf fomat, 2 MB)

Troutman, B.M., and Karlinger, M.R., 2003, Regional flood probabilities: Water Resources Research, v. 39, no. 4. (on-line abstract)

Veitzer, S.A., Troutman, B.M., and Gupta, V.K., 2003, Power-law tail probabilities of drainage areas in river basins: Physical Review E, v. 68, no. 1. (on-line abstract)

Brent M. Troutman
U.S. Geological Survey, P.O. Box 25046, ms418, Denver Federal Center, Lakewood, CO
Telephone: 303-236-5038

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