Differences between the global geoid such as EGM2008 and the local geometrical geoid could reach more that 70 cm (here in Khartoum-Sudan). Now the question could we use the global geoid to guide the improvement of the local geoid such as modeling the trend and seasonality of the global geoid. I'm looking for ways other than the classical direct polynomial fitting of low cost implementation.
if you have a same points coordinates on the local and global geoid model can be used simple modeling the trend local geoid. but i think, on a small area can be applied.
In general, I don't think so. The spatial wavelength of the geoid represented by the global model is much more than the one of a local model with higher point density. However, the vertical difference is an interesting value itself. As a thumb rule, the gravitational origin of the longer wavelength components are deeper in the Earth than the shorter ones, it reflects to the local gravity anomalies, or, in other interpretation, to the isostatic character of the region. May I suggest and old abstract of ours:
https://www.researchgate.net/publication/259654104_Short-wavelength_component_of_the_geoid_a_possible_indicator_of_the_isostatic_character
Conference Paper Short-wavelength component of the geoid: a possible indicato...
I don't think so, I'm agree with Gábor, but if you have points with ellipsoidal height and geoid height, you can validate how EGM2008 model adjust on your country, before that, you need to do some corrections like tidal system
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