1. WFM 6202: Remote Sensing and GIS in Water Management
[Part-B: Geographic Information System (GIS)]
Lecture-7: Digital Terrain Model
Akm Saiful Islam
Institute of Water and Flood Management (IWFM)
Bangladesh University of Engineering and Technology (BUET)
January, 2008

2. DEM
A DEM (digital elevation model) is digital representation of topographic surface with the elevation or ground height above any geodetic datum. Followings are widely used DEM in GIS:

3. DTM
A DTM (digital terrain model) is digital representation of terrain features including elevation, slope, aspect, drainage and other terrain attributes.
Usually a DTM is derived from a DEM or elevation data.
several terrain features including the following DTMs.
Slope and Aspect
Drainage network
Catchment area
Shading
Shadow
Slope stability

4. Examples of DTM

5. 1. Slope and Aspect (i) Slope
The steepest slope (s) and the direction from the east () can be computed from 3 x 3 matrix.

6. Slope calculation

7. Slope calculation
Slope is defined by a plane tangent to a topographic surface, as modelled by the DEM at a point (Burrough, 1986).
Slope is classified as a vector; as such it has a quantity (gradient) and a direction (aspect).
Slope gradient is defined as the maximum rate of change in altitude (tan )

8. Example: Slope from elevation data

9. (ii) Aspect
The aspect that is, the slope faced to azimuth is 180° opposite to the direction of q

10. Figure 1. Slope components, note that slope gradient can be express in percent or in degrees

11. Aspect calculation
Aspect identifies the steepest downslope direction from each cell to its neighbors. It can be thought of as slope direction or the compass direction a hill faces.
It is measured clockwise in degrees from 0 (due north) to 360, (again due north, coming full circle). The value of each cell in an aspect dataset indicates the direction the cell's slope faces. Flat areas having no downslope direction are given a value of -1.

12. Example: aspect from the elevation data

13. 2. Drainage Network and Watershed
The lowest point out of the eight neighbors is compared with the height of the central point to determine the flow direction.

14. Surface Specific points
+ is assigned if the height of the central point is higher than the one of the eight neighbors and - if lower.
A peak can be detected if all the eight neighbors are lower.
A pit or sink is formed if all the eight neighbors are higher
A pass can be extracted if the + and - alternate around the central point with at least two complete cycle.

15. 4. Shade and 5.Shadow
Shade is defined as reduced reflection depending on the angle between the terrain surface and the incident light such as the sun.
Shadow is projected areas that the incident light cannot reach because of visual hindrance of objects on terrain relief

16. Hill Shading
The effect of hill shading on the assumption of an ideally diffused reflecting surface (called Lambertian surface) can be computed as follows:
Relative shading = cos  = |nxsx + nysy+ nzsz |≤ 1.0
where  : angle between incident light vector s and surface normal n

17. Altitude
The altitude is the slope or angle of the illumination source above the horizon. The units are in degrees, from 0 (on the horizon) to 90 degrees (overhead). The default is 45 degrees.

18. Azimuth
The azimuth is the angular direction of the sun, measured from north in clockwise degrees from 0 to 360. An azimuth of 90 is east. The default is 315 (NW).

19. Hill shading from elevation data
The hillshade below has an azimuth of 315 and an altitude of 45 degrees.

20. Examples: A slope and hillshade maps of Glacier National Park

21. Using hill shading for display
By placing an elevation raster on top of a created hillshade, then making the elevation raster transparent, you can create realistic images of the landscape.
Hillshade + elevation

22. Generation of Contour Lines
Contour lines are one of the terrain features which represent the relief of the terrain with the same height. There are two types of contour lines in visualizing GIS data:
Vector Line Drawing In case when the terrain points are given in grid, the simplest method is to divide the square cell into two triangles mechanically.
Raster Image Contour image with painted contour terraces, belts or lines instead of vector lines will be generated in raster form.

23. Interpolation of Elevation from Contours
Digital elevation model (DEM) is very often generated by measuring terrain points along contour lines using a digitizer. DEM with contour points should be provided with an algorithm interpolate elevation at arbitrary points. There are several interpolation methods as follows.
Profile Method A profile passing through the point to be interpolated will be generated and linear or spline curve applied.
Proportional Distance Method According to distance to two adjacent contour lines, the elevation is interpolated proportionally with respect to the distance ratio.
Window Method A circular window is set up around a point to be interpolated and adjacent terrain points are used to interpolate the value using second order or third order polynomials.
TIN Method TINs are generated using terrain points along contour lines.

24. Interpolation Methods

25. Examples: A Digital Elevation Model and associated contour map of Glacier Nat'l Park

26. Triangulated Irregular Network (TIN)
Triangulated irregular network or TIN is a DEM with a network of triangles at randomly located terrain points.
Contouring of TINs is based on the following procedure.
step 1: find the intersect of contour and a side.
step 2: assign the "reference point" with the symbol r to the vertex above the contour height and the "sub-point" with the symbol s to the vertex below the contour height.
step 3: shift over to the transversing to find the third vertex in the triangle by checking whether it is a reference point (r) or sub-point (s).

27. Example: TIN Creation

28. Automated Generation of DEM
Automated generation of DEM is achieved by photogrammetric methods based on stereo aerial photography and satellite stereo imagery.
Parallax is defined as difference between left and right photographs or image coordinates. The higher the elevation is, the bigger the parallax is. If the parallax is constant, equal elevation or contour lines will be produced.