Geodetic Heights pp 117-138

# The Height Datum Problem

• Fernando Sansò
• Mirko Reguzzoni
• Riccardo Barzaghi
Chapter
Part of the Springer Geophysics book series (SPRINGERGEOPHYS)

## Abstract

Normal and orthometric heights are among the most widespread height coordinate systems in use for geodetic purposes. Yet in principle they can be determined only by ground gravimetric measurements combined with levelling so that $$W\left( \text {P}\right)$$ becomes available. Nevertheless, what the above measurements can really provide are at most potential differences, $$W\left( \text {P}_0\right) -W\left( \text {P}\right)$$, for instance with respect to an origin point $$\text {P}_0$$ of which however the absolute value $$W\left( \text {P}_0\right)$$ is unknown. When $$\text {P}_0$$ is a tide gauge, we know that we can assume $$W\left( \text {P}_0\right) \sim W_0$$ with an error $$\delta W_0$$ such that $$\displaystyle {\left| \frac{\delta W_0}{\gamma }\right| < 2\,\text {m}}$$ (cfr. Sect. 4.6); when $$\text {P}_0$$ is a point of known ellipsoidal height, e.g. a GNSS permanent station, we can always assume that $$h^* \cong \widetilde{h}^* = h - \displaystyle {\frac{T_b}{\gamma }}$$, where $$T_b$$ is some global model that has been computed with biases and so it has an error which however is almost surely included in the above range.

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© Springer Nature Switzerland AG 2019

## Authors and Affiliations

• Fernando Sansò
• 1
Email author
• Mirko Reguzzoni
• 1
• Riccardo Barzaghi
• 1
1. 1.Department of Civil and Environmental Engineering (DICA)Politecnico di MilanoMilanItaly