Any new Geodetic Reference System should be mean-tide
Authors: Mäkinen Jaakko 
Published: February 2023

&lt;p&gt;By a Geodetic Reference System I here mean a system like the Geodetic Reference Systems GRS80: The ellipsoid of revolution provides the reference for geodetic 3-D coordinates and is the equipotential surface of the sum of two potentials - &amp;#160;the gravitational potential of the ellipsoidal masses and the centrifugal potential of the ellipsoid&#039;s/Earth&amp;#8217;s rotation (at the constant angular velocity &amp;#969;). The gravitational potential of the masses of the ellipsoid has the geocentric gravitational constant GM and the second-degree zonal coefficient J&lt;sub&gt;2&lt;/sub&gt;. In the Somigliana-Pizzetti theory four constants are needed. We could have (GM, J&lt;sub&gt;2&lt;/sub&gt;, &amp;#969;, a&lt;sub&gt;e&lt;/sub&gt;) where a&lt;sub&gt;e&lt;/sub&gt; is the semi-major axis of the ellipsoid, or (GM, J&lt;sub&gt;2&lt;/sub&gt;, &amp;#969;, U&lt;sub&gt;0&lt;/sub&gt;) where U&lt;sub&gt;0&lt;/sub&gt; is the normal potential (gravitation plus centrifugal) at the ellipsoid. All other relevant quantities can then be obtained from the theory.&lt;/p&gt;
&lt;p&gt;The adoption of a new GRS is often presented in terms of just updating the defining GM and J&lt;sub&gt;2&lt;/sub&gt; values of the GRS80 to current best estimates, and taking U&lt;sub&gt;0&lt;/sub&gt;=W&lt;sub&gt;0&lt;/sub&gt; where W&lt;sub&gt;0&lt;/sub&gt; is the conventional reference potential of the International Height Reference System IHRS adopted by the IAG in 2015. Obviously, using a new ellipsoid would create a huge disruption in practical geodesy by changing all ellipsoid-based coordinates. While the Cartesian 3-D coordinates of the ITRF would not be affected, in most applications even they are transformed to ellipsoidal coordinates using the GRS80 ellipsoid. Could any advantages from the new GRS outweigh the practical disadvantages of the disruption? The new ellipsoid and other new quantities like the new normal gravity formula might just remain ignored by the larger user community.&lt;/p&gt;
&lt;p&gt;The potential values in the IHRS include the permanent part of tide-generating potential, and the positions should be expressed in a mean-tide system. One of the purposes of the GRS is presumably to serve as an unifying reference in different fields of geodesy. For the new GRS now to serve such a purpose, its reference potential should include the mean tide. The ellipsoid would be the equipotential surface of the sum of three potentials, the permanent tide-generating potential added to the present two. Mean-tide gravity would be adopted, instead of the current zero-tide. As the new normal gravity formula would include the effect of the permanent tide, gravity anomalies would still be generated by the masses of the Earth only and classical theories with Stokes&#039; formula would apply. Such a framework has been shown to function by Vermeer and Poutanen (1997).&lt;/p&gt;
&lt;p&gt;One could imagine that in such a consistent combination of systems and of the new GRS the troublesome corrections between &quot;different systems of the permanent tide&amp;#8221; would soon become a memory only. However, while the International Terrestrial Reference System ITRS is defined as mean-tide, its realizations ITRFxx are (conventional) tide-free. Changing that would mean changing the 3-D Cartesian coordinates of the ITRF, and might cause the largest disruption of them all. The unifying influence of the new mean-tide GRS might therefore mostly remain in the theoretical realm.&lt;/p&gt;
&lt;p&gt;Reference: Vermeer M, Poutanen M (1997), IAG Symposia 117, pp 515&amp;#8211;522&lt;/p&gt;