Principles of variational assimilation of GNSS radio occultation data

The standard processing of the Global Navigation Satellite System (GNSS) based refractometric data performed by means of a space-borne GPS-receiver was based on the approximate derivation of the local vertical profiles of the atmospheric refractivity by means of the Abel transform. Being sufficient at the stage of a proof-of-concept experiment, this approach results in significant errors of the reconstruction of the tropospheric refractivity both due to its complicated spatial structure at heights below 10 km and due to the impossibility of separation of the effects of dry air and water vapor without use of additional information. As has been recognized, the most promising way of utilizing GNSS radio occultation data is their variational assimilation (3D/4DVar) into a Numerical Weather Prediction Model. Nevertheless practical implementation of variational assimilation of the radio occultation data has proved to be impossible without a careful theoretical investigation of the problem. The main difficulty arises due to the atmospheric refraction representing a complicated nonlinear integral functional of the global atmospheric fields. In this report, we describe the principles of the variational assimilation of GNSS data. The investigation of the problem is based on a model of radio occultation experiments that includes the physical model of the measurements, the model of the atmospheric refractivity, and the model of wave propagation in the atmosphere. The latter was designed in two variants: i) a model based on the scalar diffraction theory which allows for accurate simulation of the diffraction and multipath effects especially important in the lower troposphere; ii) a geometric optical model that allows for fast computations. Using the standard approach, we elaborate the linear tangent and linear adjoint model for the GNSS observations, creating thus all the necessary instrumentary for the implementation of variational data assimilation systems. This is complemented with a program for primary processing of the real measurements and preparation of the input data for their assimilation into a Numerical Weather Prediction Model. The algorithms are completed in the form of a working program code