1. Definition
In scientific literature there is no universal agreement about the usage of the terms:
digital elevation model (DEM)
digital terrain model (DTM)
digital surface model (DSM)
DEM is often used as synonimous of DTM, but in many cases it used as a generic term for both DTMs and DSMs.
The most common representation of a DEM is a raster, where the DNs correspond to the average elevation value of the area framed by the cell.

2. Uses Terrain analysis in geomorphology and physical geography
Modelling water flow for hydrology
Modelling soil erosion or mass movement
Creation of relief maps
Rendering of 3D visualizations
Rectification of aerial photography or satellite imagery
Climatology
Urban planning
Logistics and communications
Mining
...and many more other GIS applications

3. Sources of elevation data
Stereo photogrammetry from aerial surveys
traditional: manually by a trained photogrammetrist
contours of topographic maps, to be interpolated
modern: by automatic stereo-correlation
Stereo-correlation from optical satellite imagery
SPOT (off-track stereoscopy)
Aster DEM (along-track stereoscopy)
Interferometry from radar data
European Remote Sensing Satellite ERS (multi-pass)
Shuttle Radar Topography Mission SRTM (single-pass)
Lidar
interpolation of a matrix of xyz points obtained using a laser beam

4. Aspect
The rate of change in the x direction for cell 'e' is :
[dz/dx] = ((c + 2f + i) - (a + 2d + g)) / 8
The rate of change in the y direction for cell 'e' is :
[dz/dy] = ((g + 2h + i) - (a + 2b + c)) / 8
Taking the rate of change in both the x and y direction for cell 'e', aspect is calculated using:
aspect = * atan2 ([dz/dy], -[dz/dx])
The aspect value is converted to compass direction values (0–360 degrees, 0 and 360 indicate North)
The aspect image is generaly classified into 8 classes, i.e. N, NE, E, SE, S, SW, W, NW
NoData value is assigned to flat areas a b c d e f g h i
atan2

5. Slope a b c d e f g h i
Can be computed in different ways: like the aspect, it is usually calculated using a 3 x 3 matrix around each pixel
Horn’s algorithm:

6. When deriving aspect and slope information from a DEM, if the quality is poor, artefacts become visible specially in level or flat areas.
DEM aspect slope

7. Hillshading
Each pixel of the DEM is “artificially illuminated”, with the virtual sun positioned at a given azimuth and elevation (90° - zenith angle).
The max illumination is when the pixel slope is perpendicular to the sun direction, and the aspect coincides with the azimuth.
Pixel in shadow (not reachable by direct illumination) are set to 0. Usually algorithms calculate only direct shadows, and do not determine whether a surface is shadowed by another one.
As most software procedures assume that planar coordinates and elevation data are expressed with the same units (e.g. both easting, northing, and elevation are in meters), special care should be paid when using DEM in geographic coordinates.

8. Direction of Steepest Descent30 30 80 74 63 69 67 56 60 52 48 80 74 63 69 67 56 60 52 48
Slope:

9. Flow direction grid 9

10. The problem of the sink
A pixel is surrounded by points having a higher elevation.
If it is a DEM artifact, increase elevation of the pixel until the pit drains to a neighbor, or “carve” one of the neighbors.

11. Flow Accumulation Grid.3 2 11 1 15 5 24 3 2 2 11 1 1 15 2 5 24 1

12. Threshold Drainage Area3 2 2 1 11
Example:
5 cells 1 15 2 5 1 24

13. Stream segments 3 2 11 1 15 5 24

14. Convert stream segments into vectors
Drainage Lines are drawn through the centers of cells on the stream segment.
Drainage Points are located at the centers of the outlet cells of the catchments.

15. Catchments
For every stream segment, there is a corresponding catchment.
Also the catchments can be converted to vectors (polygons).

16. Catchments Subwatersheds Catchments Watershed
Catchments can be hyerarchically grouped into watersheds.
Watersheds are defined by their outlet points.

17. Sources of global DEM data
Aster Global Digital Elevation Model (GDEM)
Version 1 (2009)
30m
Version 2 (2011)
reduction of spikes and wells
improved elevation accuracy
Improved definition of water bodies and coastlines
Shuttle Radar Topographic Mission
Version 1 (2000 ->)
90m (3 arc-seconds), 30m (1 arc-second) for the USA
Version 2 (2005)
well-defined water bodies and coastlines
absence of spikes and wells
missing data ('voids') are still present
Version 3 (“SRTM Plus”, 2014)
void-filled (mostly using GDEM)
1 arc-second already released for most of Africa, other areas in the future