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.