Global Eustatic Sea-Level Variations for the Approximation of Geocenter Motion from Grace

Global degree-1 coefficients are derived by means of the method by Swenson et al. (2008) from a model of ocean mass variability and RL05 GRACE monthly mean gravity fields. Since an ocean model consistent with the GRACE GSM fields is required to solely include eustatic sea-level variability which can be safely assumed to be globally homogeneous, it can be empirically derived from GRACE aswell, thereby allowing to approximate geocenter motion entirely out of the GRACE monthly mean gravity fields. Numerical experiments with a decade-long model time-series reveal that the methodology is generally robust both with respect to potential errors in the atmospheric part of AOD1B and assumptions on global degree-1 coefficients for the eustatic sea-level model. Good correspondence of the GRACE RL05-based geocenter estimates with independent results let us conclude that this approximate method for the geocenter motion is well suited to be used for oceanographic and hydrological applications of regional mass variability from GRACE,where otherwise an important part of the signal would be omitted.

DISCUSSION ON THE ORTHOMETRIC HEIGHT REALIZATION

In the theory of the orthometric height, the mean value of gravity along the plumbline between the geoid and the earth's surface is defined as the integral mean. To determine the mean gravity from the gravity observations realized at the physical surface of the earth, the actual topographical density distribution and vertical change of gravity with depth have to be known. In Helmert's (1890) definition of the orthometric height, the assumption of the linear change of normal gravity is used adopting the constant topographical density distribution. The mean value of gravity is then approximately evaluated so that the observed gravity of a point at the earth's surface is reduced to the mid-point of the plumbline by Poincaré-Prey's gravity gradient. To avoid the problems related to the determination of mean gravity, Molodensky (1945) formulated the different concept. In his theory of the normal height, the mean value of the normal gravity along the ellipsoidal normal between the ellipsoid surface and telluroid is considered. The mean normal gravity is then evaluated explicitly without any hypothesis about the topographical density distribution and vertical gradient of actual gravity. In this paper, the corrections to Helmert's orthometric height are formulated based on the comparison of the integral mean of gravity and Poincaré-Prey's gravity reduction. As follows from the results of the numerical investigation, the orthometric heights can also be determined with a reasonable accuracy if the sufficient information about topographical density and gravity are available.

Quality Estimates in Geoid Computation by EGM08

Quality Estimates in Geoid Computation by EGM08The high-degree Earth Gravitational Model EGM08 allows for geoid determination with a resolution of the order of 5'. Using this model for estimating the quasigeoid height, we estimate the global root mean square (rms) commission error to 5 and 11 cm, based on the assumptions that terrestrial gravity contributes to the model with an rms standard error of 5 mGal and correlation length 0:01° and 0:1°, respectively. The omission error is estimated to—0:7Δg [mm], where Δg is the regional mean gravity anomaly in units of mGal.In case of geoid determination by EGM08, the topographic bias must also be considered. This is because the Earth's gravitational potential, in contrast to its spherical harmonic representation by EGM08, is not a harmonic function at the geoid inside the topography. If a correction is applied for the bias, the main uncertainty that remains is that from the uncertainty in the topographic density, which will still contribute to the overall geoid error.