A methodology to compute GPS slant total delays in a numerical weather model

A numerical algorithm based on Fermat's Principle was developed to simulate the propagation of Global Positioning System (GPS) radio signals in the refractivity field of a numerical weather model. The unique in the proposed algorithm is that the ray‐trajectory automatically involves the location of the ground‐based receiver and the satellite, i.e. the posed two‐point boundary value problem is solved by an implicit finite difference scheme. This feature of the algorithm allows the fast and accurate computation of the signal travel‐time delay, referred to as Slant Total Delay (STD), between a satellite and a ground‐based receiver. We provide a technical description of the algorithm and estimate the uncertainty of STDs due to simplifying assumptions in the algorithm and due to the uncertainty of the refractivity field. In a first application, we compare STDs retrieved from GPS phase‐observations at the German Research Centre for Geosciences Potsdam (GFZ STDs) with STDs derived from the European Center for Medium‐Range Weather Forecasts analyses (ECMWF STDs). The statistical comparison for one month (August 2007) for a large and continuously operating network of ground‐based receivers in Germany indicates good agreement between GFZ STDs and ECMWF STDs; the standard deviation is 0.5% and the mean deviation is 0.1%.