A refractive index mapping operator for assimilation of occultation data

This paper describes the details of a fast, linear, forward-inverse refractive index mapping operator that can be used for assimilation of occultation data of various kinds into NWP models. Basically, the mapping consists of the integration of the refractive index along finite straight lines, mimicking the observational geometry as well as the subsequent retrieval of a refractive index profile, assuming spherical symmetry. Line integrals are discretized such that the refractivity is evaluated along the horizontal at fixed levels that can be chosen to coincide with the pressure levels of an NWP model. Integration of the hydrostatic equation at a large number of locations is thereby avoided. The mapping operator is tested using an idealized model of a weather front with large horizontal gradients. Mapped refractivity profiles are compared with retrieved refractivity profiles obtained via accurate 3D ray tracing simulations of GPS radio occultation events with ray path tangent points near the weather front. The simulations indicate that the mapping is a good representation of occultation measurements, including the influence large horizontal gradients have on retrieved refractivity profiles. To further the results, a simple ad hoc modification is introduced to approximately account for the ray path bending near the tangent points. The forward-inverse mapping allows for the near cancellation of otherwise crude approximations-for example, straight-line propagation-and the general concept could perhaps be adapted for the development of fast and accurate observation operators for the assimilation of other types of remote sensing data.