Forward and inverse transformations between cartesian and channel-fitted coordinate systems for meandering rivers

Mathematical Geology

Volumn 38, Issue 8, 2006, Pages 927-958

  Legleiter, Carl J ^a,b   Kyriakidis, Phaedon C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Yellowstone Ecological Research Center   (United States)

Author keywords

Curvature; Orthogonal curvilinear coordinates; River channel; Spatial referencing

Indexed keywords

COMPUTATIONAL GEOMETRY; ENGINEERING GEOLOGY; FLOW PATTERNS; FLUID MECHANICS; RIVERS; VECTORS;

ALGORITHM; COORDINATE; CURVATURE; DIGITIZATION; FINITE DIFFERENCE METHOD; FLOW PATTERN; GEOSTATISTICS; INVERSE ANALYSIS; MEANDER; REFERENCE SAMPLE; RIVER CHANNEL; TRANSFORM;

EID: 34249818770     PISSN: 08828121     EISSN: 15738868     Source Type: Journal    
DOI: 10.1007/s11004-006-9056-6     Document Type: Article

References (43)

1. Barabas, N., Goovaerts, P., and Adriaens, P., 2001, Geostatistical assessment and validation of uncertainty for three-dimensional dioxin data from sediments in an estuarine river: Environ. Sci. Technol., v. 35, no. 16, p. 3294-3301.
2. Camporeale, C., Perona, P., Porporato, A., and Ridolfi, L., 2005, On the long-term behavior of meandering rivers: Water Resour. Res., v. 41, no. W12403, doi:10.1029/2005WR004109.
3. Chiles, J., and Delfiner, P., 1999, Geostatistics: Modeling spatial uncertainty: Wiley, New York, 695 p.
4. Cohen, E., Riesenfeld, R., and Elber, G., 2001, Geometric modeling with splines: An introduction: AK Peters, Natick, MA, 616 p.
5. Davis, J., 1986, Statistics and data analysis in geology: Wiley, New York, 646 p.
6. De Boor, C., 2001, A practical guide to splines: Springer-Verlag, New York, 372 p.
7. Deutsch, C. V., 2002, Geostatistical reservoir modeling: Oxford University Press, New York, 400 p.
8. Deutsch, C. V., and Tran, T., 2002, FLUVSIM: A program for object-based stochastic modeling of fluvial depositional systems: Comput. Geosci., v. 28, no. 4, p. 525-535.
9. Deutsch, C. V., and Wang, L. B., 1996, Hierarchical object-based stochastic modeling of fluvial reservoirs: Math. Geol., v. 28, no. 7, p. 857-880.
10. Dietrich, W. E., 1987, Mechanics of flow and sediment transport in river bends, in Richards, K. S., ed., River channels: Environment and process: Blackwell, New York, p. 179-227.
11. Dietrich, W. E., and Smith, D. J., 1983, Influence of the point bar on flow through curved channels: Water Resour. Res., v. 19, no. 5, p. 1173-1192.
12. Dietrich, W. E., and Smith, J. D., 1984, Bed-load transport in a river meander: Water Resour. Res., v. 20, no. 10, p. 1355-1380.
13. Environmental Systems Research Institute, 2004, ArcGIS 9 - Editing in ArcMap: ESRI Press, Redlands, CA, 504 p.
14. Fagherazzi, S., Gabet, E. J., and Furbish, D. J., 2004, The effect of bidirectional flow on tidal channel planforms: Earth Surf. Proc. Land., v. 29, no. 3, p. 295-309.
15. Ferguson, R. I., 1976, Disturbed periodic model for river meanders: Earth Surf. Proc. Land., v. 1, no. 4, p. 337-347.
16. Ganio, L. M., Torgersen, C. E., and Gresswell, R. E., 2005, A geostatistical approach for describing spatial pattern in stream networks: Front. Ecol. Environ., v. 3, no. 3, p. 138-144.
17. Gardner, B., and Sullivan, P. J., 2004, Spatial and temporal stream temperature prediction: Modeling nonstationary temporal covariance structures: Water Resour. Res., v. 40, no. W01102, doi:10.1029/ 2003WR002511.
18. Gardner, B., Sullivan, P. J., and Lembo, A. J., 2003, Predicting stream temperatures: Geostatistical model comparison using alternative distance metrics: Can. J. Fish. Aquat. Sci., v. 60, no. 3, p. 344-351.
19. Goff, J. A., and Nordfjord, S., 2004, Interpolation of fluvial morphology using channel-oriented coordinate transformation: A case study from the New Jersey shelf: Math. Geol., v. 36, no. 6, p. 643-658.
20. Gray, A., 1998: Modern differential geometry of curves and surfaces with Mathematica: CRC Press, Boca Raton, FL, 1053 p.
21. Hamming, R., 1983, Digital filters: Prentice Hall, Englewood Cliffs, NJ, 257 p.
22. Hooke, R., 1975, Distribution of sediment transport and shear-stress in a meander bend: J. Geol., v. 83, no. 5, p. 543-565.
23. Johannesson, H., and Parker, G., 1989, Linear theory of river meandering, in Ikeda, S., and Parker, G., eds., River meandering: American Geophysical Union, Washington, D.C., p. 181-214.
24. Keim, R. F., Skaugset, A. E., and ateman, D. S., 1999, Digital terrain modeling of small stream channels with a total-station theodolite: Adv. Water Resour., v. 23, no. 1, p. 41-48.
25. Lane, S. N., 1998, The use of digital terrain modelling in the understanding of dynamic river channel systems, in Lane, S. N., Richards, K., and Chandler, J. H., eds., Landform monitoring, modelling and analysis: John Wiley and Sons, New York, p. 311-342.
26. Langbein, W., and Leopold, L. B., 1966, River meanders - theory of minimum variance, U.S. Geological Survey Professional Paper 422H.
27. Little, L. S., Edwards, D., and Porter, D. E., 1997, Kriging in estuaries: As the crow flies, or as the fish swims?: J. Experimen. Mar. Biol. Ecol., v. 213, no. 1, p. 1-11.
28. Løland, A., and Høst, G., 2003, Spatial covariance modelling in a complex coastal domain by multidimensional scaling: Environmetrics, v. 14, no. 3, p. 307-321.
29. Longley, P. A., Goodchild, M. F., Maguire, D. J., and Rhind, D. W., 2001, Geographic information systems and science: Wiley, Chichester, UK, 454 p.
30. Merwade, V. M., Maidment, D. R., and Hodges, B. R., 2005, Geospatial representation of river channels: J. Hydrol. Eng., v. 10, no. 3, p. 243-251.
31. Monestiez, P., Bailly, J.-S., Lagacherie, P., and Voltz, M., 2005, Geostatistical modelling of spatial processes on directed trees: application to fluvisol extent: Geoderma, v. 128, no. 3-4, p. 179-191.
32. Nelson, J. M., Bennett, S. J., and Wiele, S. M., 2003, Flow and sediment transport modeling, in Kondolf, G. M., and Piegay, H., eds., Tools in fluvial geomorphology: Wiley, New York, p. 539-576.
33. Perucca, E., Camporeale, C., and Ridolfi, L., 2005, Nonlinear analysis of the geometry of meandering rivers: Geophys. Res. Lett., v. 32, no. L03402, doi:10.1029/2004GL021966.
34. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1994, Numerical recipes in FORTRAN: The art of scientific computing: Cambridge University Press, New York, 963 p.
35. Rathbun, S. L., 1998, Spatial modelling in irregularly shaped regions: kriging estuaries: Environmetrics, v. 9, no. 2, p. 109-129.
36. Sampson, P. D., and Guttorp, P., 1992, Nonparametric-estimation of nonstationary spatial covariance structure: J. Am. Stat. Assoc., v. 87, no. 417, p. 108-119.
37. Skoein, J., Merz, R., and Bloschl, G., 2005, Top-kriging - geostatistics on stream networks: Hydrol. Earth Syst. Sci., v. 2, no. 6, p. 2253-2286.
38. Smith, J. D., and McLean, S. R., 1984, A model for flow in meandering streams: Water Resour. Res., v. 20, no. 9, p. 1301-1315.
39. Sun, T., Meakin, P., and Jossang, T., 2001a, A computer model for meandering rivers with multiple bed load sediment sizes 1. theory: Water Resour. Res., v. 37, no. 8, p. 2227-2241.
40. Sun, T., Meakin, P., and Jossang, T., 2001b, A computer model for meandering rivers with multiple bed load sediment sizes 2. computer simulations: Water Resour. Res., v. 37, no. 8, p. 2243-2258.
41. Viseur, S., 2004, Turbidite reservoir characterization: Object-based stochastic simulation meandering channels: Bulletin de la Société Géologique de France, v. 175, no. 1, p. 11-20.
42. Whiting, P.J., and Dietrich, W.E., 1991, Convective accelerations and boundary shear-stress over a channel bar: Water Resour. Res., v. 27, no. 5, p. 783-796.
43. Williams, G.P., 1986, River meanders and channel size: J. Hydrol., v. 88, no. 1-2, p. 147-164.