Numerical Solutions for the Non-Linear Liouville Equation

The rotation of the Earth is affected by redistributions of masses in the atmosphere, the oceans and the Earth’s interior. In order to investigate its reaction on the combined effect of mass redistributions in these components a new gyroscopic model is being developed. The model is based on the balance of angular momentum, which can be described by the non-linear Liouville differential equation. Time-dependent circulation processes in atmosphere and oceans yield variations of the Earth’s tensor of inertia and relative angular momenta. The respective values are derived from both reanalysis data and model simulations. Some refinements concerning the shape of the Earth’s body and back-coupling mechanisms like rotational deformation are considered in the model. The results are derived numerically since the solution can not be given in analytical terms. Four different numerical solvers are tested to assess the reliability of the results. First results for polar motion and length of day variation are compared with the geodetic observations published in the series C04 by the International Earth Rotation Service (IERS).