Improvements to a GPS radio occultation ray-tracing model and their impacts on assimilation of bending angle

Several efforts are made to improve the accuracy and efficiency of a 2-D GPS radio occultation forward ray-tracing model. First, a large impact parameter offset existed in the forward model, caused by the inconsistency in the definition of the "occultation point'' between the forward model and the GPS/MET data. The forward model is modified to be consistent with the GPS/MET data. Second, the errors in the simulation of the impact parameter and the bending angle due to the original starting point scheme of the ray integration are examined and a new starting point scheme is introduced to reduce the forward modeling errors. Third, to more accurately simulate the GPS/MET bending angle data, a derivation of the bending angle from a Doppler shift measurement under the application of Snell's law is incorporated into the ray-tracing model. Fourth, a variable step size for the ray integration is proposed to the forward ray-tracing model to reduce its computational cost. Assessment of the impacts of these modifications to the forward modeling of the bending angle and to the data assimilation of the bending angle is carried out with simulated bending angles and impact parameters derived from an accurate 3-D ray-tracing model. The 3-D ray-tracing model simulates a total of 133 occultation profiles with the actual satellite positions and velocities taken from the 133 GPS/MET occultations observed on 11 October 1995. The NCEP analysis at T126L28 resolution is used to represent the "true'' refractivity field of the atmosphere. The bending angles and impact parameters in the 3-D ray-tracing model are derived following the same data processing procedure used in the GPS/MET experiment. All the input parameters (e.g., the tangent direction at the perigee point, etc.) required by the 2-D ray-tracing model are provided by the 3-D ray-tracing model. Numerical results with and without the above mentioned modifications to the 2-D ray-tracing model are examined and compared with the 3-D ray-tracing model results and the NCEP T126L28 analysis. It is shown that the modifications to the 2-D ray-tracing model significantly reduce the errors in the forward simulation of the bending angle and the impact parameter, and thus greatly improve the accuracy of the temperature, specific humidity, and surface pressure field analyses produced by GPS data assimilation, especially in middle and lower troposphere.