Diffusion Wave Modeling of Distributed Catchment Dynamics
This article has a reply.
VIEW THE REPLYPublication: Journal of Hydrologic Engineering
Volume 1, Issue 3
Abstract
A diffusion wave model of distributed catchment dynamics is presented. The effects of catchment topography and river network structure on storm-flow response are incorporated by routing surface runoff in cascade throughout a digital elevation model (DEM) based conceptual transport network, where the Muskingum-Cunge scheme with variable parameters is used to describe surface runoff dynamics. Dynamic scaling of hydraulic geometry is also incorporated in the model by using the “at-a-station” and “downstream” relationships by Leopold and Maddock. Numerical experiments indicate that the model is more than 98% mass conservative for possible slope and roughness configurations, which may occur for hillslopes in a natural catchment. Fluctuations in the simulated discharge may occur in response to discontinuities in rainfall excess representation if Courant number Cu during the simulation exceeds a threshold of about 3. Catchment scale simulations with different temporal resolution show that the model response is independent of structural parameters (model consistency). Also, the overall accuracy is preserved for computationally inexpensive space-time discretizations (for which Cu > 3) because fluctuations that may occur at the local scale are dampened when propagating downstream. Comparison of model results with observed outlet hydrographs of the Rio Missiaga experimental catchment (Eastern Italian Alps) show this approach to be capable of describing both overland and channel phases of surface runoff in mountainous catchments.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Agnese, C., D'Asaro, F., and Giordano, G.(1988). “Estimation of the time scale of the geomorphologic instantaneous unit hydrograph from effective streamflow velocity.”Water Resour. Res., 24(7), 969–978.
2.
Band, L. E.(1986). “Topographic partition of watersheds with digital elevation models.”Water Resour. Res., 22(1), 15–24.
3.
Bathurst, J. C. (1986). “Physically-based distributed modelling of an upland catchment using the Système Hydrologique Européen.”J. Hydro., Amsterdam, The Netherlands, Vol. 87, 79–102.
4.
Beven, K.(1981). “Kinematic subsurface stormflow.”Water Resour. Res., 17(5), 1419–1424.
5.
Beven, K. J., and O'Connell, P. E. (1982). “On the role of distributed models in hydrology.”Rep. 81, Inst. of Hydro., Wallingford, England.
6.
Brandford, G. E., and Meadows, M. E.(1990). “Finite element simulation of nonlinear kinematic surface runoff.”J. Hydro., Amsterdam, The Netherlands, 119, 335–356.
7.
Bras, R. L. (1990). Hydrology: an introduction to hydrologic science . Addison-Wesley, Reading, Mass.
8.
Carlston, C. W. (1969). “Downstream variations in the hydraulic geometry of streams: special emphasis on mean velocity.”Am. J. Sci., Vol. 267, 499–509.
9.
Cunge, J. A.(1969). “On the subject of a flood propagation computation method (Muskingum method).”J. Hydr. Res., 7(2), 205–230.
10.
Emmett, W. W. (1978). “Overland flow.”Hillslope hydrology, M. J. Kirkby, ed., John Wiley & Sons, Inc., New York, N.Y., 145–176.
11.
Friz, C., Gatto, G., Villi, V., and Caleffa, G. (1983). “Groundwater resources of a typical catchment in the Dolomites area: The Rio Missiaga Catchment (Belluno, Italy).”Memorie Scienze Geologiche, Vol. 36, 293–315 (in Italian).
12.
Hayami, S. (1951). “On the propagation of flood waves.”Disaster Prevention Res. Inst. Bull. 1, Kyoto, Japan.
13.
Julien, P. Y., Saghafian, B., and Ogden, F. L.(1995). “Raster-based hydrologic modeling of spatially-varied surface runoff.”Water Resour. Bull., 31(3), 523–536.
14.
Kibler, D. F., and Woolhiser, D. A. (1972). “Mathematical properties of the kinematic cascade.”J. Hydro., Amsterdam, The Netherlands, Vol. 15, 131–147.
15.
Kouwen, N., and Li, R. M. (1980). “Biomechanics of vegetative channel linings.”J. Hydr. Div., ASCE, Vol. 106, 1085–1103.
16.
Leopold, L. B., and Maddock Jr., T. (1953). “The hydraulic geometry of steam channels and some physiographic implications.”Profl. Paper 252, U.S. Geol. Surv., Washington, D.C.
17.
Leopold, L. B., Wolman, M. G., and Miller, J. P. (1964). Fluvial processes in geomorphology . W. H. Freeman, San Francisco, Calif.
18.
Li, R. M., Ponce, V. M., and Simons, D. B.(1980). “Modeling rill density.”J. Irrig. and Drain. Div., ASCE, 106(1), 63–67.
19.
Montgomery, D. R., and Foufoula-Georgiou, E.(1993). “Channel network source representation using digital elevation models.”Water Resour. Res., 29(12), 3925–3934.
20.
Moore, I. D., and Grayson, R. B.(1991). “Terrain-based catchment partitioning and runoff prediction using vector elevation data.”Water Resour. Res., 27(6), 1177–1191.
21.
Mosley, M. P.(1979). “Streamflow generation in a forested watershed, New Zealand.”Water Resour. Res., 15(4), 795–806.
22.
Natural Environment Research Council (NERC). (1975). Flood Studies Rep., Flood Routing Studies III, Inst. of Hydro., Wallingford, England.
23.
Newson, M. D., and Harrison, J. G. (1978). “Channel studies in the Plynlimon experimental catchments.”Rep. 47, Inst. of Hydro., Wallingford, England.
24.
Orlandini, S. (1995). “Space-time dependence of catchment-scale hydrologic processes: comparison between physically based distributed models at different levels of conceptualization,” PhD thesis, DIIAR, Politecnico di Milano, Milano, Italy (in Italian).
25.
Pilgrim, D. H.(1977). “Isochrones of travel time and distribution of flood storage from a tracer study on a small watershed.”Water Resour. Res., 13(3), 587–595.
26.
Ponce, V. M.(1986). “Diffusion wave modeling of catchment dynamics.”J. Hydr. Engrg., ASCE, 112(8), 716–727.
27.
Ponce, V. M., and Theurer, F. D.(1982). “Accuracy criteria in diffusion routing.”J. Hydr. Div., ASCE, 108(6), 747–757.
28.
Ponce, V. M., and Yevjevich, V.(1978). “Muskingum-Cunge method with variable parameters.”J. Hydr. Div., ASCE, 104(12), 1663–1667.
29.
Rinaldo, A., Marani, A., and Rigon, R.(1991). “Geomorphological dispersion.”Water Resour. Res., 27(4), 513–525.
30.
Ross, B. B., Contractor, D. N., and Shanholtz, V.(1979). “A finite element model of overland flow and channel flow for assessing the hydrologic impact of land-use change.”J. Hydro., Amsterdam, The Netherlands, 41, 11–30.
31.
Sloan, P. G., and Moore, I. D.(1984). “Modelling subsurface stormflow on steeply sloping forested watersheds.”Water Resour. Res., 20(12), 1815–1822.
32.
Szymkiewicz, R. (1991). “Finite element method for the solution of the Saint Venant equations in an open channel network.”J. Hydro., Amsterdam, The Netherlands, Vol. 122, 275–287.
33.
Wooding, R. A. (1966a). “A hydraulic model for the catchment-stream problem. I: Kinematic wave theory.”J. Hydro., Amsterdam, The Netherlands, Vol. 3, 254–267.
34.
Wooding, R. A. (1966b). “A hydraulic model for the catchment-stream problem. II: Numerical solutions.”J. Hydro., Amsterdam, The Netherlands, Vol. 3, 268–282.
35.
Wooding, R. A. (1966c). “A hydraulic model for the catchment-stream problem. III: Comparison with runoff observation.”J. Hydro., Amsterdam, The Netherlands, Vol. 4, 21–37.
Information & Authors
Information
Published In
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jul 1, 1996
Published in print: Jul 1996
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.