Picture from Chase p.108.
The first use of terrain models was due to military purposes. The relief model allows a quick overview of a certain area. Time is in war an absolute crucial point. This means, that the relief of the interesting area must be prepared before a probable conflict. But nowadays the computer based production of terrain models allows production even in very short time, assumed the needed raw data inclusive digital terrain model already exists. A model of the landscape enables to memorise the details much better than a map and minimises the risk of incorrect reading of a map. In addition the field of vision from each point is easily to detect, something very important in war and not so easy to find out from a map. It is also possible to easy evaluate the coverage of a fire position.
Picture from Roux p.68.