Geodetic Heights

This book provides the necessary background of geometry, mathematics and physical geodesy, useful to a rigorous approach to geodetic heights. The concept of height seems to be intuitive and immediate, but on the contrary it requires a good deal of scientific sharpness in the definition and use. As a matter of fact the geodetic, geographic and engineering practice has introduced many different heights to describe our Earth physical reality in terms of spatial position of points and surfaces. This has urged us to achieve a standard capability of transforming one system into the other. Often this is done in an approximate and clumsy way. This book solves the above practical problems in a rigorous way, showing what degree of approximation is used in approximate formulas. In addition the book gives a sound view on a matter that is presently occupying scientific associations, namely the unification of the global and regional height reference systems. It provides the mathematical background as well as the state of the art of its implementation. It will be particularly useful for professionals and national agencies.

Provides the definition of most height systems in use and to the relative transformations Gives rigorous observation equations for a classical technique like spirit leveling, showing that contrary to the geodetic practice it is natural to use normal heights instead of orthometric heights Acquaints the reader with an up-to-date problem, namely the definition and use of global and regional height reference systems

Contenu
Introduction.- General coordinates in R³.- The Earth gravity field: basics.- The anomalous potential and its determination.- Geodetic coordinate systems.- The relation between levelling, geodetic and other unholonomic heights.- The height datum problem.