Elevations at individual points (commonly in systematic arrays or grids of geographic significance) as surveyed on the Earth’s surface, or calculated by stereoplotters, or digitized from existing maps can be expressed in digital numbers. The result is a Digital Elevation Model (DEM). This allows for production of a variety of maps that range from straight topographic ones to a variety of specialized displays such as shaded relief maps and perspective maps. The DEM database can also be "draped over" a remote sensing image (equivalent points registered) to produce views that give a 3-D appearance (usually from a perspective or oblique view) to the natural landscape or manmade features in an image.

### Digital Elevation Models (DEMs) and Viewing Modes

In recent years, contour values have been digitized allowing them to be manipulated into versatile displays of topographic data as digital elevation models or DEMs. Digital terrain models (DTMs) are variants that show additional landscape attributes. We can use existing maps as inputs by tracing contour lines on a digitizing tablet or table. The data are organized into cell arrays whose X-Y positions in the rectangular grid are related to map coordinates. Each cell has a single value representing the average elevation of the land surface within it. The finest-sized cells are 30 meters on a side, associated with the 7.5 minute topographic quadrangles mapped by the USGS using the Universal Transverse Mercator (UTM) coordinate system. Only a fraction of the maps at this scale have been digitized, as yet. This digitizing is also true for 15 and 30 minute maps. To date, all of the 50 U.S. states, except parts of Alaska, mapped at 1:250,000 scale (extending over 1 degree by 1 degree in eastern states and 1 degree by 2 degrees in western states) have now been digitized at a cell size of three arc seconds. They store the data in east-west profiles.

You can access a general review of the concepts and mechanics of producing DEMs at a site maintained by the Eros Data Center (EDC).

These DEM data sets have important applications. They allow for rapid reconstruction of contour maps and for plotting elevation profiles. Also, we can easily do various kinds of photogrammetric calculations with the numbers. Image processing systems can edit and filter these data to enhance the display products and merge data sets into larger maps. We can present surfaces as X-Y-Z plots, where the Z dimension appears as regularly spaced vertical lines whose lengths are proportional to elevation. These plot are available in several formats:

Shaded relief maps, in which we assign different shades of gray to slopes, depending on elevation, or a variant, in which we assign shadowing to selected slopes depending on their orientation (aspect) and on sun direction and azimuth. By shifting these parameters, we create different renditions that bring to light different surface features and trends.

Color density slices, in which we color-code elevations.

Perspective Views. Since we can readily calculate geometric variables, such as orientation and height from the digitized data, we can recreate the surfaces to look like oblique photos. We can easily examine such surfaces from different perspectives by rotating the view horizontally (along a vertical axis) or changing the look angle.

Draped Views. The ultimate display is usually one in which we register or "drape" a surface image, such as a Landsat scene, onto the DEM array (data cells match with pixels), causing that surface and the features on it to appear in some form of 3-D display (e.g., in a perspective view or by creating pseudo-stereo pairs as a stereo model). We can also convert various thematic maps, as for example, land use, urban structure, or geology into 3-D mode.

Examples of these DEM-based products abound on the Internet. Next, we show just a few that are typical:

Check first this gray level relief map, constructed from 1:250,000 DEM data, of the Susanville area in the Sierra Nevada Mountains:

11-14: Describe what you think you are seeing in the map. ANSWER

Next, examine the variant, in which shadow effects emphasize relief, by switching to a grand scale view of the entire conterminous U.S. Locate your home area.

An excellent example of a map, in which the elevations are color-coded, is this DEM version showing the state of Wyoming. The data source is a series of 30-second digitized maps. Lower areas are in green, and higher are in yellows, then brown.

11-15: Find the features in the Wyoming map in the topographic map of the entire U.S. ANSWER

Let's now peer at a spectacular scene, looking at the Grand Canyon, as shown in a perspective view developed from DEM data and artificially colorized to resemble the rock units. But first, to gain familiarity with this incredible "ditch," carved over millions of years by the Colorado River, examine this Landsat nearly full 1972 scene. The snow-covered area is the Kaibab Plateau, some 2000 feet higher than the South Rim.

Next, a later view (November 1,1993) taken by the Japanese JERS-1:

Now let's at the DEM rendition:

11-16: Try to locate the oblique perspective scene in the Landsat view. ANSWER

Primary Author: Nicholas M. Short, Sr. email: nmshort@ptd.net