Abstract
Earth Gravitational Models (EGMs) describe the Earth’s gravity field including the geoid, except for its zero-degree harmonic, which is a scaling parameter that needs a known geometric distance for its calibration. Today this scale can be provided by the absolute geoid height as estimated from satellite altimetry at sea. On the contrary, the above technique cannot be used to determine the geometric parameters of the Mean Earth Ellipsoidal (MEE), as this problem needs global data of both satellite altimetry and gravimetric geoid models, and the standard technique used today leads to a bias for the unknown zero-degree harmonic of the gravimetric geoid height model. Here we present a new method that eliminates this problem and simultaneously determines the potential of the geoid (W0) and the MEE axes. As the resulting equations are non-linear, the linearized observation equations are also presented.
Highlights
The level surface of the Earth’s gravity field defined by the undisturbed sea level is the Gauss-Listing definition of the geoid (Gauss 1828; Listing 1873)
The above technique cannot be used to determine the geometric parameters of the Mean Earth Ellipsoidal (MEE), as this problem needs global data of both satellite altimetry and gravimetric geoid models, and the standard technique used today leads to a bias for the unknown zero-degree harmonic of the gravimetric geoid height model
This leads to Approach I below, which implies a direct integration of satellite altimetry derived sea surface topography (SST; frequently denoted Dynamic Ocean Topography) combined with the potential of an Earth Gravitational Model (EGM) all over the oceans
Summary
The geometric approach to determine W0 will be presented under the assumption that the mean angular velocity of the Earth’s daily rotation (ω) is known, and the problem is to estimate both the dimensions [i.e., semi-major and -minor axes a and b (or eccentricity e) of the globally best fitting ellipsoid (= MEE)] as well as the geoid potential W0 in a joint adjustment from the available geoid surface estimates derived from satellite altimetry and an EGM. Sanchez 2012), the fixing of GM to the best known value may improve W0 by adjusting just for the ellipsoidal geometry parameters by the following geometric approach. Once the ellipsoidal parameters a and e of the MEE have been fixed by solving Eq (19a), the normal potential at the MEE, i.e. U0 of Eq (15), can be computed, provided that GM is ( sufficiently well) known, and this value should be the estimate for the geopotential value at the geoid, i.e. one problem with this approach is that the present-day uncertainty in GM contributes to about 20% of the uncertainty in W0 (see Groten 2004). This implies that a, e and ∆W0 are determined in a combined adjustment
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