1. Digital Terrain Model (DTM)

2. Idea of DTM
A digital terrain model (DTM) is a topographic model of the bare
earth that can be manipulated by computer program (Wikipedia)
Aim: height interpolation at any point based on
measured/known points
Interpolation method
Continuous interpolation preferred (0 order, 1st order, 2nd order continuity)
Good approximation of the surface of the earth
Digital Elevation Modeling Journal

3. Layout of base points Regular layout base points (tesselation/GRID)
Break lines
extremal points
Boundary restrictions
(e.g. lakes)
Irregular base points + +

4. Collection of elevation data
Topographic survey (irregular points and breaklines)
Leveling of grid points
Photogrammetry (grid, contours)
Contour line digitizing (contours + extremal points + breaklines)
Radar measurements (SRTM Shuttle Radar Topography Mission)
1” resolution (30 m) US only
3” resolution (100 m)
GTOPO30 30” resolution
Sample data

5. Creation of a DTM Regular layout (Rectangular Grid, DEM)
Interpolated points from irregular base points
Inverse Distance Weight (IDW)
Kriging
Surface interpolation (trends)
Triangulated Irregular Network (TIN)
Original base points are used
Optimal, non overlapping triangle network,
minimal sum of perimeters
Delaunay triangulation

6. IDW (Shepard 1968) w – weight f – function value at the base point
t – distance between base point and interpolated point
p – usual value is 2
Distance limit
Direction restriction (quarters)

7. Kriging (Krige 1951) Linear combination the elevation of base points
Conditions for the weight used:
Unbiased estimation
Estimate minimal standard deviation
Least squares method
Variograms (geostatistics)
h – distance from base point
Effective distance, (h) doesn’t change as h increased

8. Surface interpolation
Polynom interpolation
One continuous surface (global solution)
Dynamic surfaces (local, patchwork)
Spline interpolation
2nd order continuity between cubic polynoms
Sample
Sample 2

9. Delaunay triangulation (1934)
Minimize the sum of the perimeter of the non overlapping triangles
Algorithm (incremental):
Start from an optimal triangle contains all the base points
then add a new point and divide the triangle
Condition: no points in the inscribed
circle of the triangle
Sample

10. Voronoi cells Dual problem of Delaunay Triangulation.
Areas nearest to the base points.
DTM manipulation:
Add point
Add breakline
Add triangle or polygon
Erase part

11. Areas of DTM applications
Contour line interpolation
Watershed analysis
Cross sections
Flow directions
Viewshed analysis
Modeling (e.g. erosion)
Slope category map
Planning of roads, railways,
pipelines
Aspect (slope direction)
Visualization of the terrain
Volume calculation
Reduction (terrain correction) of gravity measurements
Rectification of airbone or
satellite photos
Hydrology example
3D view of DTM