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

Autorentext

Fernando Sansò is professor emeritus at the Polytechnic University of Milan and a Honorary President of the International Association of Geoscience (IAG). He established the International Geoid Service in 1992 and served as its President until 2011. He is a full member of the Accademia dei Lincei, a fellow of the Royal Astronomical Society (UK), and the president of Geomatics and Research Development (GReD), which he founded in 2012. His research areas include gravity field modelling, boundary value problems, statistics, generalized random fields, and GNSS theory. Sansò has received numerous accolades, including the Bomford Prize for Geodesy in 1979 and the Feltrinelli Award for Astronomy, Geodesy, Geophysics, and Applications in 1986. He holds honorary doctorates from the University of Copenhagen, the University of Thessaloniki, and the University of Stuttgart. Throughout his career, he has (co)-authored over 500 works. Alberta Albertella is Associate Professor of Geodesy at Politecnico di Milano. She earned her Ph.D in Geodetic, Surveying, and Photogrammetric Sciences from the Politecnico of Turin, Italy, in 1993. She has conducted extensive research in satellite geodesy, specializing in satellite gradiometry and gravity field determination. She contributed to multiple European and Italian satellite missions,. From 2005 to 2012, she was a research partner in the German project GEOTOP, which focused on ocean circulation using geodetic observations. Her expertise includes statistical and numerical data analysis for physical geodesy, geoid estimation, Bayesian methods, and remote sensing. She has also worked on digital mapping, GIS applications, and contributed to Citizen Science projects.

Inhalt
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.