University of Illinois at Urbana-Champaign

Copyright © 1998 Helena Mitasova, GMS Laboratory, University of Illinois at Urbana-Champaign

For requests to use this material or its parts please contact: helena@gis.uiuc.edu

References: Mitasova, H., L. Mitas, 1993, Interpolation by regularized spline with tension : I. Theory and implementation. Mathematical Geology 25, p. 641-655.

Mitasova, H., J. Hofierka, 1993, Interpolation by regularized spline with tension : II. Application to terrain modeling and surface geometry analysis. Mathematical Geology 25, p. 657-669.

Topographic parameters representing the geometric properties of terrain surface are important for many applications related to environmental modeling and land use management. GRASS programs s.surf.tps, v.surf.tps and r.resample.tps allow users to compute several topographic parameters simultaneously with interpolation from point, vector or raster elevation data. The program computes a mathematical model of the surface and its first and second order derivatives using regularized spline with tension . Derivatives are then used in the programs for computation of slope, aspect, profile, tangential and mean curvature as described in Mitasova and Hofierka 1993 . The following images show an example of results from s.surf.tps.

  • Elevation surface
  • Slope angle is a measure of gradient magnitude and influences e.g. flow velocity.
  • Aspect angle represents gradient direction and e.g. direction of flow.
  • Profile curvature indicates areas of accelerated flow (convex) and areas with decreasing flow velocity (concave).
  • Tangential curvature represents areas of convergent (concave) and divergent (convex) flow.

  • Flow related topographic parameters needed for hillslope erosion modeling are computed by flow tracing program r.flow, the combined grid-vector flowtracing algorithm used in this program is described in Mitasova and Hofierka 1993 and Mitasova, Mitas et al. 1995).

  • Upslope flowlines shows terrain with flowlines generated uphill and flow path length draped as color.
  • Downslope flowlines shows terrain with flowlines generated downhill and upslope contributing area (flowline density or potential water flux) draped as color.

  • Topographic potential of landscape for erosion/deposition can be computed based on the unit stream power theory as a change in sediment transport capacity (see Mitasova, Hofierka et al. 1995).

  • Topographic potential for net erosion/deposition visualized as color mapped values draped over terrain.
  • Erosion/deposition draped over sediment transport capacity surface, providing more quantitative visual information about relative differences in erosion potential.

  • Flow (movie - 68,164 bytes)

    animated gif

    This animation created by r.flow and SG3d, shows a simple simulation of water flow as it changes during a rainfall event. For simplicity, the distribution and rate of rainfall remains constant. The depth of water is visualized as a surface.

    Sediment transport capacity (movie - 252,876 bytes)

    animated gif

    This animation shows how sediment transport capacity changes over time due to changes in water flux during a rainfall event. Again, the distribution and rate of rainfall is kept constant and the sediment transport capacity is visualized as a surface for better quantitative comparisons.

    Lake Filling(movie - 36,138 bytes)

    animated gif

    This simple animation created by r.reclass and SG3d, shows how the landscape will be changing when a proposed water reservoir is filling with water.

    insolation during the summer solstice(animated gif)

    insolation during the winter solstice(animated gif)

    The animation created by r.sun (developed by Jaro Hofierka) and SG3d shows dynamics of insolation during the summer and winter.

    Images and animations for this document were created using the GRASS4.1 program SG3d. Programming, computations and visualization for this project was done by Environmental modeling and visualization group at U.S.Army CERL (H. Mitasova, W. Brown, D.P. Gerdes, T. Baker, I. Kosinovsky), interpolation methods were designed by Lubos Mitas at NCSA, flowtracing program was developed by Jaro Hofierka, Maros Zlocha from Comenius University, Bratislava, Slovakia, and Joshua Caplan from University of Illinois, data are courtesy Illinois Natural History Survey (Dr. Louis Iverson).

    This work was partially supported by DOD Strategic Environmental Research and Development Program ( SERDP ), Conservation Pillar, project: Digital Elevation Modeling and Erosion Simulation.

    GMSL_VIZ_ICON GMSL Modeling & Visualization
    Home Page