The range differences between the high- and low-altitude reflectors help quantify relative differences in the path delay.Figure 1.Observation geometry.Another interesting side effect is that the average scene height in both configurations is close to the midpoint between the two reflector altitudes. Additional meteorological data (temperature, water vapour pressure, air pressure) from weather stations near Meiringen, Interlaken and Jungfraujoch provided further reference information for accurate modeling of the refractive index and atmospheric path delays.Though they play only a minor role in this case, ionospheric path delays observed during the data takes and at the corresponding locations were estimated using the total electron content (TEC) along the ray path.

TEC measurements were obtained from global vertical TEC maps with bi-hourly temporal resolution. The TEC maps can be downloaded in the IONosphere map EXchange format (IONEX) from the Center for Orbit Determination in Europe (CODE) [10].3.?Models and MeasurementsThe following sections provide a brief description of two models used: (a) Raytracer, and (b) height-dependent. In addition, the measurements made for the estimation of the atmospheric path delays are described. While the raytracer uses weather data for an estimation of the path delays with mm accuracy the altitude-dependent approach should provide a simplified model to correct path delays with cm accuracy.3.1. RaytracerThe tropospheric delay is estimated on the basis of data provided by a numerical weather model [11].

Using this information, the raytracing algorithm integrates through the refractivity field along the path between the satellite and the point on the surface of the Earth.The non-hydrostatic local area model COSMO-2 is used as a numerical weather model. It is operated by the Swiss Federal Office of Meteorology and Climatology GSK-3 and covers central Europe. It has a resolution of about 2 km and consists of 60 layers. The bottom layer follows the terrain, while the top boundary ends at 23589 m above the reference ellipsoid (WGS84). The model is used for the determination of the refractivity.The raytracer assumes that the path followed by the ray is equivalent to the shortest geometrical path between the satellite and the point of interest. It is therefore only determined by the satellite position and the point of interest, but not by the refractivity field.

This permits a simple computation of the ray paths. Since the refractivity field and its variability decreases with altitude, the length of the integration steps can be enlarged at upper levels without significantly reducing the accuracy, saving computation time. The integration method used is Newton-Cotes quadrature. However, this method has a fixed integration step length. To overcome this constraint, the atmosphere is subdivided into layers, each with a characteristic integration step size.