The ray-tracing mapping operator in an asymmetric atmosphere

In a spherically symmetric atmosphere, the refractive index profile is retrieved from bending angle measurements through Abel integral transform. As horizontal refractivity inhomogeneity becomes significant in the moist low atmosphere, the error in refractivity profile obtained from Abel inversion reaches about 10%. One way to avoid this error is to directly assimilate bending angle profile into numerical weather models. This paper discusses the 2D ray-tracing mapping operator for bending angle in an asymmetric atmosphere. Through simulating computations, the retrieval error of the refractivity in horizontal inhomogeneity is assessed. The step length of 4 rank Runge-Kutta method is also tested.