High-resolution global gravity field modelling by the finite volume method

We discuss the parallel computational solution to the modified fixed gravimetric boundary-value problem (MFGBVP). In our approach, the computational domain is a finite space bounded by two spatial boundaries. The boundaries represent an approximation of the Earth's surface and an approximation of the chosen satellite orbit. Then the MFGBVP consists of the Laplace equation for unknown disturbing potential with the Neumann and Dirichlet boundary conditions. Solution of such elliptic boundary-value problem is understood in a weak sense, so it always exists and is unique. As a numerical method for our parallel approach, the finite volume method (FVM) has been designed and implemented. The FVM is a method for solving elliptic equations and it leads to a solution of the sparse linear system of equations with an appropriate structure for parallel implementation concerning memory costs. The parallel implementation of FVM algorithms using MPI and NUMA procedures is also described. Several numerical experiments are discussed. In the first testing experiment, we show that the proposed approach is second-order accurate. Then we test a convergence of the FVM solution to the EGM2008 Earth gravitational model when refining the grid. In this case all boundary conditions (BCs) are generated from this model. Finally we present high-resolution global gravity field modelling using input data generated from the DTU10 gravity field model and the GOCO03S satellite-only geopotential model. It combines information from the GRACE and GOCE satellite misions prescribed on the upper boundary with the altimetryderived and terrestrial gravity data available on the Earth's surface. The obtained global gravity field model is compared with the EGM2008.