1. DIGITAL TERRAIN MODELS REQUIRE MODELLING 
"IT should see the garden far better”, 
satd Alice to herscolf, "Lf I-ooutd get 
to the top of that hill: und here ts a 
path that leads straight to it - at‘ least 
no, tt doesn't do that - but I suppose it 
will at last. But how curiously it twists! 
It's more Like a cork-skrew than a path! 
Well this turn goes to the hill, I sup 
pose - no it doesn't. This goes straight 
back to the housel Wet] then, I'!'LL try it 
the other way!" 
During the last decennium, Digital Terrain Models (DTM) became rather im- 
portant for various tasks of photogrammetry, such as orthophoto production, 
high accuracy processing of scanner data and others. The name Digital Ter- 
rain Model is however misleading. A DTM is a programme package consisting 
of routines for data storage, data retrieval, editing, interpolation and 
contouring. It is often a subsystem of a Land Information System, and is 
rather an Elevation Information System than a model. 
In order to properly understand the behaviour of the terrain forms and 
their Information Systems, a model of the terrain is necessary. But what 
is the concept of a model? According to the positivistic school of philo- 
sophy the complete understanding of the terrain form and its evolution is 
impossible for the human mind. We may well describe it with the help of a 
hypothesis, or a model. Such a model defines observable quantities and re- 
lationships between them (Weyl, 1949). The concept of a model allows de- 
ductions on the properties of the terrain and on the outcome of new obser- 
vations. These deductions may refer to the point density necessary for samp- 
ling, to the accuracy and .guality of interpolation and contouring, or to 
criteria for the detection of blunders in measurement. 
We may define many different models for the terrain. Their value is judged 
by the criteria of completeness, uniqueness and simplicity. A model should 
be complete, that is, it should enrich our understanding of the terrain as 
much as possible and it should not be easily disproveable by results of ex- 
periments. The model should be unique in that it allows unique deductions. 
Finally it should be simple: if two models behave otherwise equally well, 
the simpler model containing less hypothesis and less quantities is to be 
preferred. 
Models for the terrain have been defined in various sciences. Geography and 
its subscience Geomorphology supply a vast body of knowledge on terrain 
forms and - characterization. 
Geology and in particular Mathematical Geology, describes the geological 
processes and also their product, the terrain form. In Applied Mathematics 
and Statistics terrain is described by various concepts. The following 
sections give a short review of the major models in use and of their rela- 
tionship.