M. Véronneau

Evaluation of topographical effects in precise geoid computation from densely sampled heights

In this paper we investigate the behaviour of Newtons kernel in the integration for topographical effects needed for solving the boundary value problem of geodesy. We follow the standard procedure and develop the kernel into a Taylor series in height and look at the convergence of this series when the integral is evaluated numerically on a geographical grid, as is always the case in practice. We show that the Taylor series converges very rapidly for the integration over the ”distant zone”, i.e., the zone well removed from the point of interest. We also show that the series diverges in the vicinity of the point of interest when the grid becomes too dense. Generally, when the grid step is smaller than either the height of the point of interest, or the difference between its height and those of the neighbouring points. Thus we claim that the Taylor series version of Newtons kernel cannot be used for evaluating topographical effects on too dense a topographical mesh.

Tilt of mean sea level along the Pacific coasts of North America and Japan

The tilt of coastal mean sea level with respect to an equipotential surface is estimated using two fundamentally different approaches. The geodetic approach is based on tide gauge and GPS observations, and a model of the geoid. The ocean approach uses a high-resolution, dynamically based ocean model to estimate mean dynamic topography. Along the Pacific coast of North America the two approaches give similar large-scale profiles with a minimum at about 40°N and a maximum in the northern part of the Gulf of Alaska. Along the Pacific coast of Japan the geodetically determined coastal sea levels indicate an eastward drop of about 20 cm along the south coast and a further northward drop across Tsugaru Strait. Both of these features are reproduced by the ocean models. An analysis of the alongshore momentum balance suggests that alongshore wind stress acting over the inner shelf is the primary driver of the mean sea level profile along the coast of North America. Several large-scale features are explained using arrested topographic wave theory. A similar momentum analysis, and an additional study of time variability of sea level and circulation, suggests that the Kuroshio is the main driver of the mean sea level tilt along the south coast of Japan. Discrepancies in the alongshore tilt of sea level estimated by the geodetic and ocean approaches along both coasts are discussed in terms of errors in the ocean and geoid models.

A Stokesian Approach for the Comparative Analysis of Satellite Gravity Models and Terrestrial Gravity Data

A Stokesian approach is formulated to update the geoid model for a specific spherical harmonic band by spectrally combining a GOCE-based satellite global geopotential model with terrestrial gravity data. A simulation test shows that the GOCE-based model can be combined into a geoid solution with an accuracy better than 3 mm for the band between degrees 90 and 180. A comparison of the GOCE-based model GOCO03S and the Canadian terrestrial gravity data for the spherical harmonic band between degrees 90 and 180 shows that the geoid update by GOCO03S reaches 1.6 cm in RMS in the Yukon Territory, 1.8 cm in northern British Columbia, and 1.6 cm in the Maritimes. This may suggest a slight improvement of the GOCE model over the Canadian gravity data considering the standard deviation of 1.0 cm given by GOCO03S. However the analysis indicates comparable accuracy between the terrestrial gravity data and GOCE models for the rest of Canada where topography is relatively flat. The comparisons at the GPS-levelling points suggest that GOCE has improved our existing knowledge of the Earth’s gravity field for wavelength components longer than 200 km over the Yukon Territory, northern British Columbia, the Maritimes, and Newfoundland.

Analysis of the GRAV-D Airborne Gravity Data for Geoid Modelling

In this study, airborne gravity data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project are compared with terrestrial gravity data in three survey blocks that cross the Canada-US border. One block (AN04) overlaps an area containing Alaska (USA) and the Yukon Territory (Canada) over a rough terrain while the other two blocks (EN05 and EN08) are within the Great Lakes-St-Lawrence River region with flat and moderate terrains. GRAV-D has an average flight altitude of about 6 km in the three blocks, in which each survey/cross line spans 240–700 km. The high flight altitude of GRAV-D puts forth a challenge for the comparisons. We have developed procedures to interpolate and continue the airborne and terrestrial gravity data to a mean flight height for each block. The remove-compute-restore Poisson method is used in the upward continuation of the terrestrial gravity data by removing and restoring the satellite-only geopotential model GOCO05S. The comparison between the datasets is done using Helmert gravity disturbances in order to satisfy the harmonic condition of the upward continuation. The comparisons show that differences between GRAV-D and terrestrial gravity data are 3.6 mGal for AN04, 1.8 mGal for EN05 and 2.3 mGal for EN08 in terms of Root Mean Square (RMS) at the mean flight height. The results can be improved for two blocks when applying a cross-over adjustment. The differences become 1.0 and 1.4 for EN05 and EN08, respectively.