Surface Analysis

Continuous fields have a number of characteristics not shared by discrete fields. Since the field changes continuously, we can talk of slope angle, slope aspect and concavity/convexity of the slope.

These notions are not applicable to discrete fields. The discussions in this subsection use terrain elevation as the prototype example of a continuous field, but all aspects discussed are equally applicable to other types of continuous fields. Nonetheless, we regularly refer to the continuous field representation as a DEM, to conform with the most common situation.

There are numerous examples that require more advanced computations on continuous field representations, such as:

• Slope angle calculation - the calculation of the slope steepness, expressed as an angle in degrees or percentages, for any or all locations.

• Calculating slope aspect - the calculation of the aspect (or orientation) of the slope in degrees (between 0 and 360^∘), for any or all locations.

• Slope convexity/concavity calculation - defined as the change of the slope (negative when the slope is concave and positive when the slope is convex)—can be calculated as the second derivative of the field.

• Slope length calculation - with the use of neighbourhood operations, it is possible to calculate for each cell the nearest distance to a watershed boundary (the upslope length) and to the nearest stream (the downslope length). This information is useful for hydrological modelling.

• Hillshading is used to portray relief difference and terrain morphology of hilly and mountainous areas. The application of a special filter to a DEM produces hillshading. The colour tones in a hillshading raster represent the amount of reflected light at each location, depending on its orientation relative to the illumination source. This illumination source is usually chosen to be to the northwest at an angle of 45^∘ above the horizon.

• Three-dimensional map display - with GIS software, three-dimensional views of a DEM can be constructed in which the location of the viewer, the angle under which he or she is looking, the zoom angle, and the amplification factor of relief exaggeration can be specified. Three-dimensional views can be constructed using only a predefined mesh, covering the surface, or using other rasters (e.g. a hillshading raster) or images (e.g. satellite images) that are draped over the DEM.

• Determination of change in elevation through time - the cut-and-fill volume of soil to be removed or to be brought in to make a site ready for construction can be computed by overlaying the DEM of the site before the work begins with the DEM of the expected modified topography. It is also possible to determine landslide effects by comparing DEMs of before and after a landslide event.

• Automatic catchment delineation - catchment boundaries or drainage lines can be automatically generated from a good quality DEM with the use of neighbourhood functions. The system will determine the lowest point in the DEM, which is considered to be the outlet of the catchment. From there, it will repeatedly search for the neighbouring pixels with the highest altitude. This process is repeated until the highest location (i.e. the cell with the highest value) is found; the path followed determines the catchment boundary. For delineating the drainage network, the process is reversed. Then the system will work from the watershed downwards, each time looking for the lowest neighbouring cells, which determines the direction of water flow (Flow Computation).

• Dynamic modelling - apart from the applications mentioned above, DEMs are increasingly used in GIS-based dynamic modelling, such as the computation of surface run-off and erosion, groundwater flow, the delineation of areas affected by pollution, the computation of areas that will be covered by processes such as flows of debris and lava. An example is (Diffusion).

• Visibility analysis - a viewshed is the area that can be “seen” (i.e. it is in the direct line-of-sight) from a specified target location. Visibility analysis can determine the area visible from a scenic lookout or the area that can be reached by a radar antenna, as well as assess how effectively a road or quarry will be hidden from view.