Pascal Gegout

Global atmospheric loading and gravity

Abstract The purpose of this paper is to model atmospheric pressure effects on surface gravity. Pressure corrections are usually done with the help of an empirical trans fer function called barometric admittance between pressure and gravity both measured locally. We show the validity of this local approach with the help of spectral coherency between air pressure and gravity residuals after subtraction from the superconducting gravimeter observations in Strasbourg (France) of luni-solar tides, polar motion and instrumental drift contributions. We compute the atmospheric surface loading effects using a Greens function formalism and global surface pressure data provided by the European Centre for Medium Range Weather Forecasts (ECMWF). We model a specific oceanic response to atmospheric loading which incorporates interactions between ocean, atmosphere and solid Earth and differs from the classical inverted or non-inverted barometer hypotheses. We investigate the contribution of this global pressure correction in a 3000 day (1987–1996) tidal analysis of the French superconducting gravimeter.

Are the free core nutation parameters variable in time

Abstract The Free Core Nutation (FCN) is a normal mode of the Earth which induces resonance in the diurnal tides as well as in the nutations. This is particularly true for frequencies near the resonance frequency, i.e., for the retrograde annual nutation and the ψ1 tide. The paper aims at analyzing Very Long Baseline Interferometry (VLBI) data and superconducting gravimeter (SG) data in order to gain more information on the FCN period, damping, resonance strength and free mode amplitude. Section 2 deals with the variability as seen in precise tidal gravimetric observations from consecutive subsets of an SG located near Strasbourg (France). We will show that the apparent variations appearing in the eigenperiod, quality factor and strength are related to a variable noise level in the tidal gravimetric data. Section 3 is devoted to the analysis of the time variability of the VLBI series. In particular we show that the amplitude variations found in the forced nutational response of the Earth are not real but rather induced by a variable free mode excitation. We show that the eigenperiod is stable within a range of 3 days.

Influence of atmospheric pressure on the Free Core Nutation, precession and some forced nutational motions of the Earth

Abstract The atmospheric pressure effects on the Earths Free Core Nutation (FCN) and some forced nutations are evaluated numerically from the global pressure field provided by the European Center for Medium Range Weather Forecast (ECMWF) on the Earths solid surface using a 12-year long pressure data set sampled every 6 h on a (1.125°×1.125°) grid. Our model incorporates both the pressure and gravitational torques from the atmosphere as well as the elastic deformational effects induced by atmospheric loading. The pressure torque is computed from the surface pressure field acting on the Earths topography and the antagonist gravitational torque is also dependent on this pressure field but acting on the gravitational equipotential surface (assuming vertical hydrostatic equilibrium between density and pressure). The response of the oceans to pressure excitation is approximated by the static ocean model which is different from the classical non-inverted barometer (NIBO) and the inverted barometer (IBO) hypotheses and depends on the degree of the spherical harmonic decomposition of the pressure field. The most efficient term in perturbing the nutations is the S1 solar barometric tide of thermal origin which induces a contribution to the prograde annual nutation of gravitational origin. Seasonal modulations of S1 also appear clearly which cause perturbations to other nutations. We show that the contributions to the nutation values are ranging from a few tenths of a milliarcsecond up to the milliarcsecond for the annual prograde term and therefore are close to the lower bounds of the values from a previous calculation by Dehant et al. [Dehant, V., Bizouard, Ch., Hinderer, J., Legros, H., Lefftz, M., 1996. On atmospheric pressure perturbation on precession and nutations. Phys. Earth Planet. Interiors 96, 25–39.] based on the 20-yr-old S1 pressure field from Haurwitz and Cowley [Haurwitz, B., Cowley, A.D., 1973. The diurnal and semidiurnal barometric oscillations, global distribution and annual variation. Pageoph. 102, 193–222.] and speculations on its amplitude modulation. These effects are therefore not negligible and this study points out the importance of atmospheric pressure corrections on the gravitational nutations of lunisolar origin. We also estimate the excitation power available from the atmospheric pressure, gravitational torques and elastic surface loading to explain the mean observed FCN amplitude as derived from VLBI (Very Long Baseline Interferometry) observations. It is suggested that the atmosphere is a good candidate for randomly exciting this free rotational mode.

On regularized time varying gravity field models based on grace data and their comparison with hydrological models

Determination of spherical harmonic coefficients of the Earth’s gravity field is often an ill-posed problem and leads to solving an ill-conditioned system of equations. Inversion of such a system is critical, as small errors of data will yield large variations in the result. Regularization is a method to solve such an unstable system of equations. In this study, direct methods of Tikhonov, truncated and damped singular value decomposition and iterative methods of ν, algebraic reconstruction technique, range restricted generalized minimum residual and conjugate gradient are used to solve the normal equations constructed based on range rate data of the gravity field and climate experiment (GRACE) for specific periods. Numerical studies show that the Tikhonov regularization and damped singular value decomposition methods for which the regularization parameter is estimated using quasioptimal criterion deliver the smoothest solutions. Each regularized solution is compared to the global land data assimilation system (GLDAS) hydrological model. The Tikhonov regularization with L-curve delivers a solution with high correlation with this model and a relatively small standard deviation over oceans. Among iterative methods, conjugate gradient is the most suited one for the same reasons and it has the shortest computation time.

Ray-Tracing of GNSS Signal Through the Atmosphere Powered by CUDA, HMPP and GPUs Technologies

The ray-tracing of signals emitted by the Global Navigation Satellite Systems (GNSS) is implemented on Graphics Processing Units (GPU) by two parallel programming techniques: the “Compute Unified Device Architecture” (CUDA) C-language and the directives for “Hybrid Multicore Parallel Programming” (HMPP) developed by CAPS Entreprise. The signal propagation is obtained by the numerical integration of the differential system derived from the eikonal equation by the Runge-Kutta method. The computation of atmospheric delays on GPU has to preserve the millimeter accuracy using the double precision arithmetic. Four versions describe how the ray-tracing of 8,100 rays was optimized for the Fermi architecture. As referring to a single-core single-threaded CPU version, accelerations ranging from 20 to 50 times are progressively obtained when the software enhancements gradually harness the hardware capabilities. The versions HMPP and CUDA provide exactly the same accelerations. HMPP further provides an easy implementation for multiple kind of GPU cards. A speed-up of 75 times versus the CPU version is finally reached when the ray-tracing algorithm is applied to 130,000 rays.

Rigorous Interpolation of Atmospheric State Parameters for Ray-Traced Tropospheric Delays

The transformation between European Center for Medium-range Weather Forecast (ECMWF) model level assimilations and the refractivity at any given point of the neutral atmosphere has been investigated. We first present the IFS interpolations and extrapolations of each physical parameter done in operations at ECMWF. These formulae are used to compute, for example, pressure levels from model levels at ECMWF. We use this formulation to compute the pressure levels, the large majority of which are found similar to the pressure levels provided by ECMWF with an appropriate accuracy for ray-tracing. The IFS-based scheme (IFS-BS) is then presented. It is an adaptation of the interpolations and extrapolations done at ECMWF for troposphere delay computation by ray-tracing. This scheme ensures the coherence with the ECMWF meteorological model and is used in our software Horizon designed to compute the Adaptive Mapping Functions (AMF). In the IFS-BS, vertical interpolations are adapted for each thermodynamic parameter necessary to precisely rebuild the refractivity along the ray path according to the physical laws. In order to take into account the atmospheric part between the lowest model level and the Earth’s topography during the ray-tracing, extrapolation of physical parameters below the lowest model level are included. The proposed scheme is expected to be relevant for applications where accuracy of refractivity is important as troposphere delay modelling for high-accuracy geodesy.

Methodological Investigation of the Processing of Absolute Gravity Data

This paper is devoted to the influence of several parameters (modelling of solid and ocean tides, air pressure, vertical gradient, site conditions) affecting the determination of the value of the absolute gravity. The confidence in the results relies on the dependence of the gravity (mean value and time-varying residues) on small changes in these parameters and the way we can constrain our choice of them. With the help of data sets obtained from absolute gravimeter (AG) FG5#206 at different stations, we will thus study the influence of i) the modelling of solid tides by the use of several models based on recent tidal developments, ii) the modelling of the oceanic loading tides including models derived from satellite altimetry, iii) the modelling of the pressure correction by the use of a local barometric admittance value versus a global loading computation, iv) the vertical gradient (do we have to measure it each time or is it better to use always the same value even if it is a theoretical one?). A methodological investigation of the consequences of these corrections will help answering the fundamental question of the duration which is needed in order to achieve convergence in the mean g value. We will also show the impact on the gravity residues of these parameters.