A Ray-tracing operator and its adjoint for the use of GPS/MET refraction angle measurements

The development of small, high‐performance instruments to receive Global Positioning System (GPS) signals has created an opportunity for active remote sounding of the Earth's atmosphere by radio occultation techniques. A prototype demonstration of this capability has been provided by the GPS Meteorology (GPS/MET) experiment. Although it was shown that high vertical resolution profiles of atmospheric refractivity, temperature, and geopotential height of constant pressure levels can be derived from the GPS measurements, with high accuracy under many circumstances, many issues remain. These include the existence of multipath propagation, the ambiguity between water vapor and temperature in moist regions of the atmosphere, and the difficulty in retrieving an accurate refractivity profile from the GPS refraction angle measurements over regions where the horizontal gradient of the refractivity is large. The aim of this paper is to begin the development of a methodology for incorporating the GPS “raw” measurements (refraction angles) directly into numerical weather analysis and/or prediction systems in order to alleviate the above mentioned problems. First, a ray‐tracing observation operator that links the atmospheric state to the GPS refraction angle measurements is developed, the physics and numerics involved are described, and the simulated refraction angles, based on the NOAA National Centers for Environmental Prediction (NCEP) global analysis, are compared with the observed GPS/MET refraction angle measurements. Second, the tangent linear and adjoint of the ray‐tracing operator are developed. These three operators are required for the direct use of GPS refraction angle measurements in a variational data analysis system. A single observation experiment reveals that the direct use of GPS refraction angles in a variational analysis causes changes in the temperature and specific humidity fields that are not limited to the occultation location but in an elongated band of ±300 km in its occultation plane. On σ-levels, changes from the use of one GPS occultation occur in an area of about 600 km × 600 km large which is centered around the ray perigee point. Finally, the advantages and disadvantages are discussed for the use of the GPS refractivities versus refraction angles. Errors made by using local estimates of refractivity are also assessed.