ALBERT

Description: 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%.

Description: Water vapor plays an important role in meteorological applications; GeoForschungsZentrum (GFZ) therefore developed a tomographic system to derive 3-D distributions of the tropospheric water vapor above Germany using GPS data from about 300 ground stations. Input data for the tomographic reconstructions are generated by the Earth Parameter and Orbit determination System (EPOS) software of the GFZ, which provides zenith total delay (ZTD), integrated water vapor (IWV) and slant total delay (STD) data operationally with a temporal resolution of 2.5 min (STD) and 15 min (ZTD, IWV). The water vapor distribution in the atmosphere is derived by tomographic reconstruction techniques. The quality of the solution is dependent on many factors such as the spatial coverage of the atmosphere with slant paths, the spatial distribution of their intersections and the accuracy of the input observations. Independent observations are required to validate the tomographic reconstructions and to get precise information on the accuracy of the derived 3-D water vapor fields. To determine the quality of the GPS tomography, more than 8000 vertical water vapor profiles at 13 German radiosonde stations were used for the comparison. The radiosondes were launched twice a day (at 00:00 UTC and 12:00 UTC) in 2007. In this paper, parameters of the entire profiles such as the wet refractivity, and the zenith wet delay have been compared. Before the validation the temporal and spatial distribution of the slant paths, serving as a basis for tomographic reconstruction, as well as their angular distribution were studied. The mean wet refractivity differences between tomography and radiosonde data for all points vary from −1.3 to 0.3, and the root mean square is within the range of 6.5–9. About 32% of 6803 profiles match well, 23% match badly and 45% are difficult to classify as they match only in parts.