Embedding rivers in polyhedral terrains

Data conflation is a major issue in GIS: spatial data obtained from different sources, using different acquisition techniques, needs to be combined into one single consistent data set before the data can be analyzed. The most common occurrence for hydrological applications is conflation of a digital elevation model and rivers. We assume that a polyhedral terrain is given, and a subset of its edges are designated as river edges, each with a flow direction. The goal is to obtain a terrain where the rivers flow along valley edges, in the specified direction, while preserving the original terrain as much as possible. We study the problem of changing the elevations of the vertices to ensure that all the river edges become valley edges, while minimizing the total elevation change. We show that this problem can be solved using linear programming. However, several types of artifacts can occur in an optimal solution. We analyze which other criteria, relevant for hydrological applications, can be captured by linear constraints as well, in order to reduce such artifacts. We implemented and tested the approach on real terrain and river data, and describe the results obtained with different variants of the algorithm. Moreover, we give a polynomial-time algorithm for river embedding for the special case where only the elevations of the river vertices can be modified.

[1]  S. K. Jenson,et al.  Extracting topographic structure from digital elevation data for geographic information-system analysis , 1988 .

[2]  Maarten Löffler,et al.  Generating Realistic Terrains with Higher-Order Delaunay Triangulations , 2005, ESA.

[3]  Alan Saalfeld,et al.  Conflation Automated map compilation , 1988, Int. J. Geogr. Inf. Sci..

[4]  E. Nelson,et al.  Algorithm for Precise Drainage-Basin Delineation , 1994 .

[5]  J. Snoeyink,et al.  Extracting Consistent Watersheds From Digital River And Elevation Data , 1999 .

[6]  Nimrod Megiddo,et al.  Towards a Genuinely Polynomial Algorithm for Linear Programming , 1983, SIAM J. Comput..

[7]  René van Oostrum,et al.  Flooding Countries and Destroying dams , 2007, Int. J. Comput. Geom. Appl..

[8]  Craig A. Knoblock,et al.  Conflation of Geospatial Data , 2008, Encyclopedia of GIS.

[9]  L. Martz,et al.  An outlet breaching algorithm for the treatment of closed depressions in a raster DEM , 1999 .

[10]  Micha Sharir,et al.  A subexponential bound for linear programming , 1992, SCG '92.

[11]  J. N. Callow,et al.  How does modifying a DEM to reflect known hydrology affect subsequent terrain analysis , 2007 .

[12]  Michael F. Goodchild,et al.  GIS and hydrologic modeling. , 1993 .

[13]  Edith Cohen,et al.  Improved algorithms for linear inequalities with two variables per inequality , 1991, STOC '91.

[14]  Prosenjit Bose,et al.  The Complexity of Rivers in Triangulated Terrains , 1996, CCCG.

[15]  Jack Snoeyink,et al.  Flooding Triangulated Terrain , 2004, SDH.

[16]  Dara Entekhabi,et al.  Generation of triangulated irregular networks based on hydrological similarity , 2004 .

[17]  Gil Kalai,et al.  A subexponential randomized simplex algorithm (extended abstract) , 1992, STOC '92.

[18]  M. Goodchild,et al.  Environmental Modeling with GIS , 1994 .

[19]  M. Hutchinson A new procedure for gridding elevation and stream line data with automatic removal of spurious pits , 1989 .