Abstract. The bending angle observation operator (forward model) currently used to assimilate radio occultation (RO) data at the Met Office, ECMWF and other centres is the same as is included in the Radio Occultation Processing Package (ROPP), along with the corresponding tangent-linear and adjoint code. The functionality of this package is described in another paper in this issue. The mean bending angle innovations produced with this operator using Met Office background fields show a bias that oscillates with height and whose magnitude peaks between the model levels. These oscillations have been attributed to shortcomings in the assumption of exponentially varying refractivity between model levels. This is used directly in the refractivity operator, and indirectly to produce forward-modelled bending angles via the Abel transform. When the spacing between the model levels is small, this assumption is acceptable, but at stratospheric heights where the model level spacing is large, these biases can be significant, and can potentially degrade analyses. This paper provides physically-based improvements to the functional form of refractivity with height. These new assumptions considerably improve the oscillatory bias, and a number of approaches for practical implementation of the bending angle operator are provided.
Three paths toward the quantum angle operator