On the topographic bias in geoid determination by the external gravity field

AbstractFor many developing countries such as Uganda, precise gravimetric geoid determination is hindered by the low quantity and quality of the terrestrial gravity data. With only one gravity data point per 65 km2, gravimetric geoid determination in Uganda appears an impossible task. However, recent advances in geoid modelling techniques coupled with the gravity-field anomalies from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission have opened new avenues for geoid determination especially for areas with sparse terrestrial gravity. The present study therefore investigates the computation of a gravimetric geoid model overUganda (UGG2014) using the Least Squares Modification of Stokes formula with additive corrections. UGG2014 was derived from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second SRTM ver4.1 Digital Elevation Model from CGIAR-CSI and the GOCE-only global geopotential model GO_CONS_GCF_2_TIM_R5. To compensate for the missing gravity data in the target area, we used the surface gravity anomalies extracted from the World Gravity Map 2012. Using 10 Global Navigation Satellite System (GNSS)/levelling data points distributed over Uganda, the RMS fit of the gravimetric geoid model before and after a 4-parameter fit is 11 cm and 7 cm respectively. These results show that UGG2014 agrees considerably better with GNSS/levelling than any other recent regional/ global gravimetric geoid model. The results also emphasize the significant contribution of the GOCE satellite mission to the gravity field recovery, especially for areas with very limited terrestrial gravity data.With an RMS of 7 cm, UGG2014 is a significant step forward in the modelling of a “1-cm geoid” over Uganda despite the poor quality and quantity of the terrestrial gravity data used for its computation.

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Theoretical frame for the application of IOST in the downward continuation of GOCE SGG data

10.5194/egusphere-egu21-1968 ◽

2021 ◽

Author(s):

Ilias N. Tziavos ◽

Dimitrios A. Natsiopoulos ◽

Georgios S. Vergos ◽

Eleftherios A. Pitenis ◽

Elisavet G. Mamagiannou

Keyword(s):

Gravity Field ◽

Heterogeneous Data ◽

Theoretical Background ◽

Geoid Determination ◽

Downward Continuation ◽

Geopotential Model ◽

Correlated Errors ◽

Satellite Gravity ◽

The Earth ◽

Regional Gravity

<p>Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, one of the main goals is the investigation of downward continuation schemes for the GOCE Satellite Gravity Gradiometry (SGG) data. It is well known that once the original SGG observations have been filtered to the GOCE Measurement Band Width (MBW), in order to remove noise and long-wavelength correlated errors, a crucial point for gravity field and geoid determination refers to the combination of GOCE data with local gravity field information. One possible way to exploit GOCE data is to use them in a Spherical Harmonic Synthesis (SHS) to derive a GOCE-only and/or a combined Global Geopotential Model. Our aim is to overcome the inherent smoothing of SHS and use directly the SGG data in order to investigate their contribution to regional gravity field and geoid determination. For that, methods based on the input-output-system-theory (IOST) are used for the combination of heterogeneous data at the Earth&#8217;s surface and at the satellite altitude or a mean sphere. The GOCE Level 2 gradients are first processed, transformed and reduced to a mean orbit using the IOST methods and then are downward continued to the Earth&#8217;s surface with an iterative Monte Carlo method (simulated annealing - SA). In this work we present the theoretical background of the proposed methodology and key-concepts for its implementation.</p>

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The topographic bias in Stokes’ formula vs. the error of analytical continuation by an Earth Gravitational Model - are they the same?

Journal of Geodetic Science ◽

10.1515/jogs-2015-0017 ◽

2015 ◽

Vol 5 (1) ◽

Cited By ~ 2

Author(s):

L. E. Sjöberg

Keyword(s):

Gravity Anomaly ◽

Spherical Harmonics ◽

Analytical Continuation ◽

Geoid Determination ◽

Disturbing Potential ◽

Solid Spherical Harmonics ◽

Topographic Bias ◽

Gravitational Model ◽

Stokes Formula ◽

Original Formula

AbstractGeoid determination below the topographic surface in continental areas using analytical continuation of gravity anomaly and/or an external type of solid spherical harmonics determined by an Earth GravitationalModel (EGM) inevitably leads to a topographic bias, as the true disturbing potential at the geoid is not harmonic in contrast to its estimates. We show that this bias differs for the geoid heights represented by Stokes’ formula, an EGMand for the modified Stokes formula. The differences are due to the fact that the EGM suffers from truncation and divergence errors in addition to the topographic bias in Stokes’ original formula.

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The topographic bias in gravimetric geoid determination revisited

Journal of Geodetic Science ◽

10.1515/jogs-2019-0007 ◽

2019 ◽

Vol 9 (1) ◽

pp. 59-64

Author(s):

Lars E. Sjöberg

Keyword(s):

Density Distribution ◽

Geoid Determination ◽

The Other ◽

Harmonic Potential ◽

Gravimetric Geoid ◽

Potential Bias ◽

Computation Point ◽

Density Distributions ◽

Topographic Bias ◽

Topographic Potential

Abstract The topographic potential bias at geoid level is the error of the analytically continued geopotential from or above the Earth’s surface to the geoid. We show that the topographic potential can be expressed as the sum of two Bouguer shell components, where the density distribution of one is spherical symmetric and the other is harmonic at any point along the normal to a sphere through the computation point. As a harmonic potential does not affect the bias, the resulting topographic bias is that of the first component, i.e. the spherical symmetric Bouguer shell. This implies that the so-called terrain potential is not likely to contribute significantly to the bias. We present three examples of the geoid bias for different topographic density distributions.

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Quality Estimates in Geoid Computation by EGM08

Journal of Geodetic Science ◽

10.2478/v10156-011-0014-y ◽

2011 ◽

Vol 1 (4) ◽

pp. 361-366 ◽

Cited By ~ 5

Author(s):

L. Sjüberg

Keyword(s):

Geoid Determination ◽

Commission Error ◽

Mean Square ◽

Terrestrial Gravity ◽

Topographic Bias ◽

Gravitational Model ◽

High Degree ◽

Harmonic Representation ◽

Mean Gravity ◽

Geoid Computation

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.

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