GIS and Remote Sensing

The presentation is going to introduce first the idea of a height system as a conglomerate of the reference surface, also known as a datum and properly defined heights. Then the kinds of height systems used in practice are going to be discussed. These are three: the geodetic system consisting of the reference ellipsoid as a datum and geodetic heights (also incorrectly often called “ellipsoidal heights”); the classical system that consists of the geoid as a datum and orthometric heights (above the sea level) and; the Molodensky system composed of the quasi-geoid as a datum and normal heights (referred to the quasi-geoid). The geodetic system is used when heights are being determined by satellites; classical system has been used throughout the world since individual nations introduced their national height systems and Molodensky’s system is now being used in Russia and several European countries. Further, the question of realization of a height system in practice will be discussed. This discussion is going to deal with mean sea level (MSL), sea surface topography (SST), the way observed heights and height differences are transformed into proper heights and height differences and the role of gravity in these transformations, the role of potential numbers and dynamic heights. Next, the properties of height systems that make them appropriate for practice will be shown: first and utmost, the system must be congruent, i.e., the datum and heights taken together must give us, as closely as possible, the Geodetic heights, the heights must be holonomic to allow us to adjust loops of height differences and the system must be useful in practice. The clear winner is the classical system. The geoid is a physically meaningful (equipotential) and convex surface whose shape best approximates the shape of MSL with the increased availability of gravity and topographical density data the geoid can be determined to an accuracy about 2.5 cm (standard deviation) except for high mountains. Rigorous orthometric heights are holonomic and can be computed with a quite high accuracy. Even though they are not physically meaningful (water can flow up the orthometric slope), orthometric heights are eometrically meaningful, yet they are close enough to dynamic heights to be useful in most applications in practice. The geodetic system is not useful in practice; for example, in this system the height of the sea shore varies between -100 and +100 metres which would make life very difficult for port builders as well as lots of other people. The Molodensky system became quite popular in Europe since about 1980’s as it is easy to work with, locally and regionally. Globally, its reference surface, the quasi-geoid, is a fairly complex surface with folds, sharp edges and other unfriendly features, utterly inapplicable as a reference system. In practice, the quasi-geoid is obtained as a byproduct of geoid computation, obtained by adding an approximate correction to the geoid. Hence, our vote must go against this system as well.