Computing Representative Networks for Braided Rivers

Authors Maarten Kleinhans, Marc van Kreveld, Tim Ophelders, Willem Sonke, Bettina Speckmann, Kevin Verbeek

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Maarten Kleinhans
Marc van Kreveld
Tim Ophelders
Willem Sonke
Bettina Speckmann
Kevin Verbeek

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Maarten Kleinhans, Marc van Kreveld, Tim Ophelders, Willem Sonke, Bettina Speckmann, and Kevin Verbeek. Computing Representative Networks for Braided Rivers. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Drainage networks on terrains have been studied extensively from an algorithmic perspective. However, in drainage networks water flow cannot bifurcate and hence they do not model braided rivers (multiple channels which split and join, separated by sediment bars). We initiate the algorithmic study of braided rivers by employing the descending quasi Morse-Smale complex on the river bed (a polyhedral terrain), and extending it with a certain ordering of bars from the one river bank to the other. This allows us to compute a graph that models a representative channel network, consisting of lowest paths. To ensure that channels in this network are sufficiently different we define a sand function that represents the volume of sediment separating them. We show that in general the problem of computing a maximum network of non-crossing channels which are delta-different from each other (as measured by the sand function) is NP-hard. However, using our ordering between the river banks, we can compute a maximum delta-different network that respects this order in polynomial time. We implemented our approach and applied it to simulated and real-world braided rivers.
  • braided rivers
  • Morse-Smale complex
  • persistence
  • network extraction
  • polyhedral terrain


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  1. Pankaj Agarwal, Mark de Berg, Prosenjit Bose, Katrin Dobrint, Marc van Kreveld, Mark Overmars, Marko de Groot, Thomas Roos, Jack Snoeyink, and Sidi Yu. The complexity of rivers in triangulated terrains. In Proc. 8th Canadian Conference on Computational Geometry CCCG'96, pages 325-330, 1996. Google Scholar
  2. Lars Arge, Jeffrey S. Chase, Patrick Halpin, Laura Toma, Jeffrey S. Vitter, Dean Urban, and Rajiv Wickremesinghe. Efficient flow computation on massive grid terrain datasets. GeoInformatica, 7(4):283-313, 2003. Google Scholar
  3. Peter Ashmore. Channel morphology and bed load pulses in braided, gravel-bed streams. Geografiska Annaler: Series A, Physical Geography, 73(1):37-52, 1991. Google Scholar
  4. Mark de Berg, Otfried Cheong, Herman Haverkort, Jung-Gun Lim, and Laura Toma. The complexity of flow on fat terrains and its I/O-efficient computation. Computational Geometry, 43(4):331-356, 2010. Google Scholar
  5. Mark de Berg and Constantinos Tsirogiannis. Exact and approximate computations of watersheds on triangulated terrains. In Proc. 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 74-83. ACM, 2011. Google Scholar
  6. Walter Bertoldi, Luca Zanoni, and Marco Tubino. Planform dynamics of braided streams. Earth Surface Processes and Landforms, 34:547–557, 2009. Google Scholar
  7. Hamish Carr, Jack Snoeyink, and Ulrike Axen. Computing contour trees in all dimensions. Computational Geometry, 24(2):75-94, 2003. Google Scholar
  8. Yi-Jen Chiang, Tobias Lenz, Xiang Lu, and Günter Rote. Simple and optimal output-sensitive construction of contour trees using monotone paths. Computational Geometry, 30(2):165-195, 2005. Google Scholar
  9. Wout M. van Dijk, Wietse I. van de Lageweg, and Maarten G. Kleinhans. Formation of a cohesive floodplain in a dynamic experimental meandering river. Earth Surface Processes and Landforms, 38, 2013. Google Scholar
  10. Herbert Edelsbrunner, John Harer, and Afra Zomorodian. Hierarchical Morse complexes for piecewise linear 2-manifolds. In Proc. 17th Annual ACM Symposium on Computational Geometry, pages 70-79, 2001. Google Scholar
  11. D. Murray Hicks, Maurice J. Duncan, and Jeremy M. Walsh. New views of the morphodynamics of large braided rivers from high-resolution topographic surveys and time-lapse video. In The Structure, Function and Management Implications of Fluvial Sedimentary Systems (Proceedings), pages 373-380. IAHS Publ. no. 276, 2002. Google Scholar
  12. Alan D. Howard, Mary E. Keetch, and C. Linwood Vincent. Topological and geometrical properties of braided streams. Water Resources Research, 6(6), 1970. Google Scholar
  13. Maarten G. Kleinhans. Flow discharge and sediment transport models for estimating a minimum timescale of hydrological activity and channel and delta formation on Mars. Journal of Geophysical Research, 110, 2005. Google Scholar
  14. Maarten G. Kleinhans, Robert I. Ferguson, Stuart N. Lane, and Richard J. Hardy. Splitting rivers at their seams: bifurcations and avulsion. Earth Surface Processes and Landforms, 38(1):47-61, 2013. Google Scholar
  15. Thierry de Kok, Marc van Kreveld, and Maarten Löffler. Generating realistic terrains with higher-order Delaunay triangulations. Computational Geometry, 36(1):52-65, 2007. Google Scholar
  16. Marc van Kreveld and Rodrigo I. Silveira. Embedding rivers in triangulated irregular networks with linear programming. International Journal of Geographical Information Science, 25(4):615-631, 2011. Google Scholar
  17. Yuanxin Liu and Jack Snoeyink. Flooding triangulated terrain. In Developments in Spatial Data Handling, pages 137-148. Springer, 2005. Google Scholar
  18. Wouter A. Marra, Maarten G. Kleinhans, and Elisabeth A. Addink. Network concepts to describe channel importance and change in multichannel systems: test results for the Jamuna river, Bangladesh. Earth Surface Processes and Landforms, 39(6):766-778, 2014. Google Scholar
  19. Michael McAllister and Jack Snoeyink. Extracting consistent watersheds from digital river and elevation data. In Proc. ASPRS/ACSM Annu. Conf, volume 138, 1999. Google Scholar
  20. Gary Parker. On the cause and characteristic scales of meandering and braiding in rivers. Journal of Fluid Mechanics, 76(3):457-480, 1976. Google Scholar
  21. Günter Rote. Lexicographic Fréchet matchings. In Abstracts of the 30th European Workshop on Computational Geometry, 2014. Google Scholar
  22. Filip Schuurman, Maarten G. Kleinhans, and Hans Middelkoop. Network response to disturbances in large sand-bed braided rivers. Earth Surface Dynamics, 4(1):25-45, 2016. Google Scholar
  23. Filip Schuurman, Wouter A. Marra, and Maarten G. Kleinhans. Physics-based modeling of large braided sand-bed rivers: Bar pattern formation, dynamics, and sensitivity. Journal of Geophysical Research: Earth Surface, 118(4):2509-2527, 2013. Google Scholar
  24. Nithin Shivashankar, Senthilnathan M, and Vijay Natarajan. Parallel computation of 2D Morse-Smale complexes. IEEE Transactions on Visualization and Computer Graphics, 18(10):1757-1770, 2012. Google Scholar
  25. Rodrigo I. Silveira and René van Oostrum. Flooding countries and destroying dams. International Journal of Computational Geometry &Applications, 20(3):361-380, 2010. Google Scholar
  26. Sidi Yu, Marc van Kreveld, and Jack Snoeyink. Drainage queries in TINs: from local to global and back again. In Advances in GIS Research II: Proc. 7th International Symposium on Spatial Data Handling, pages 829-842, 1997. Google Scholar