Computational Geodesy

Abstract

The observation of the dynamically changing system Earth is one major task in geodesy. To measure the temporal changes globally, observations collected by satellites are analyzed to highlight the changes with respect to some long term mean, for instance comparing the measurements to reference surfaces. Furthermore, reference surfaces are required for the realization of reference systems, e.g. the geoid for the definition of the vertical datum. Therefore, an accurate knowledge of these reference surfaces is important in geodesy and other geoscientific disciplines, such as oceanography or geophysics. <br/> This thesis covers the estimation of three different reference surfaces: the geoid - or more generally the Earth's gravity field, the Mean Dynamic ocean Topography (MDT), and the Mean Sea Surface (MSS). The basic idea for the determination of these reference surfaces is to formulate the problem as a (constrained) least squares parameter estimation problem. As a consequence of this design, a tailored parametric representation of the reference surface has to be established. In the framework of least squares estimation, it is immediately possible to account for the stochastic characteristics of the observations and to combine various complementary observation groups in a joint one-step estimation. The solution of the inverse problems becomes numerically and computationally demanding, as a large number of parameters (10⁵ to 10⁶) is required to adequately model the surfaces of interest. Furthermore, a huge number of (correlated) observations (10⁷ to 10⁸) has to be analyzed. Therefore, these challenges have to be solved utilizing specific numerical properties and High Performance Computing (HPC). In this context, the model design, the stochastic modelling and an efficient solution and implementation is referred to as <em>Computational Geodesy</em>. <br/> The first reference surface studied in this contribution is the geoid. The main focus is on the computation of a static global gravity field model from the observations taken by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite. While the general idea is inline with the time-wise GOCE-only models published previously, the improved EGM_TIM_RL06 model benefits from reprocessed gravity gradients and a refined stochastic model. The approach is summarized and the improvements of the new model are presented. Additionally, it is shown how EGM_TIM_RL06 is used as input in the GOCO06S satellite-only model and aspects for the combination with terrestrial gravity data are discussed. <br/> To estimate a geodetic MDT, a parametric least squares estimation approach is proposed and studied in different configurations. The proposed approach is used to jointly estimate the geoid and the MDT from altimetric Sea Surface Height (SSH) observations. A parameterization tailored to the characteristics of the MDT by a <em>C</em>¹-smooth linear combination of Finite Element (FE) basis functions is derived, which is used to approximate the unknown MDT surface. The approach enables to include information about the geoid as stochastic data sets and allows observations related to surface currents to be included (e.g. surface drifters or Synthetic Aperture Radar (SAR) derived Radial Surface Velocity (RSV)). It is shown with the help of simulated and real data experiments, that this kind of complementary observations strongly support the signal separation of the SSH into geoid and MDT. <br/> Similarly, an alternative estimation approach to estimate a parametric MSS model is proposed and numerically studied. Although basically 'just' the temporal average of altimetric SSHs in the analysis period has to be computed, this is challenging due to the spatial and temporal sampling characteristics of the different altimetry missions. Therefore, it is shown how the ocean variability can be coestimated as an additional Sea Level Anomalies (SLAs) model. For both model components, MSS and MDT, a tailored continuous <em>C</em>¹-smooth FE model function is derived. In case of the SLA, it is extended towards a spatio-temporal model using separable basis functions. Numerical real data studies are used to demonstrate the performance of the proposed approach. <br/> For all applications studied, it can be concluded that the parametric approaches accounting for the stochastic characteristics of the observations and using the developed parametric models are well suited and offer advantages compared to the existing (grid based) approaches.