Uncertainty propagation through wave optics retrieval of bending angles from GPS radio occultation: Theory and simulation results

The wave optical technique for bending angle retrieval in processing radio occultation observations is nowadays widely used by different data processing and assimilation groups and centers. This technique uses Fourier Integral Operators that map the observed records of the amplitude and phase into the impact parameter representation, which allows for the retrieval of bending angle as a function of impact parameter. We investigate the propagation of uncertainty in the observed amplitude and excess phase to the retrieved bending angle. We construct a simple linear approximation, where the excess phase uncertainty is mapped into the bending angle uncertainty. This results in a simple analytical expression for the final uncertainty. To verify our approximation, we perform numerical Monte Carlo simulations for three example occultation events (tropical, middle, and polar latitude profiles from an atmospheric analysis). We demonstrate that our approximation basically gives good results in all cases over the entire troposphere. Exception is the narrow area near the top of the sharp boundary layer, especially in tropics, where, due to nonlinear effects, a significant systematic error arises accompanied by increased uncertainty.