A variational regularization of Abel transform for GPS radio occultation

The optimization problem is then solved iteratively by means of the adjoint technique. VR is formulated with error covariance matrices, which permit a rigorous incorporation of prior information on measurement error characteristics and the solution's desired behavior into the regularization. VR holds the control variable in the measurement space to take advantage of the posterior height determination and to negate the measurement error due to the mismodeling of the refractional radius.

The advantages of having the solution and the measurement in the same space are elaborated using a purposely corrupted synthetic sounding with a known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison to nearby radiosonde observations shows that VR attains considerably smaller random and systematic errors compared to AI.

A noteworthy finding is that in the heights and areas that the measurement bias is supposedly small, VR follows AI very closely in the mean refractivity deserting the first guess. In the lowest few kilometers that AI produces large negative refractivity bias, VR reduces the refractivity bias substantially with the aid of the background, which in this study is the operational forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF).

It is concluded based on the results presented in this study that VR offers a definite advantage over AI in the quality of refractivity.