Errors in stratospheric bending angles retrieved from GPS radio occultations can be significantly reduced by using statistical optimization. In order for this technique to work optimally, the error covariance of the observations and the error covariance of the first guess must be known. This is generally not the case, and it is therefore common practice to assume that each of these errors is uncorrelated. In this study, it is shown that when this assumption is applied together with dynamical error estimation, it is important to account for the fact that first guess and the observation bending angle errors are not damped equally when refractivity profiles are computed through the Abel transform. It is demonstrated that this difference in damping can be accounted for by scaling the ratio of observation to first-guess bending angle error variances. It is shown that the scaling factor can be related to the ratio between the error correlation lengths of the observation errors and the first-guess errors. We present a simple procedure where both correlation lengths and variances are estimated dynamically and are scaled as described above. It is found that the relative errors can be reduced by up to 30% when compared to a standard statistical optimization scheme where the relative error in the first-guess bending angle profile is assumed to be 20%. However, it was also found that if the first guess is properly adjusted, the need for corrections is greatly reduced.
