A variational regularization of Abel transform for GPS radio occultation

Abstract

Abstract. In the Global Positioning System (GPS) radio occultation (RO) technique, the inverse Abel transform of measured bending angle (Abel inversion, hereafter AI) is the standard means of deriving the refractivity. While concise and straightforward to apply, the AI accumulates and propagates the measurement error downward. The measurement error propagation is detrimental to the refractivity in lower altitudes. In particular, it builds up negative refractivity bias in the tropical lower troposphere. An alternative to AI is the numerical inversion of the forward Abel transform, which does not incur the integration of error-possessing measurement and thus precludes the error propagation. The variational regularization (VR) proposed in this study approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement's considered accuracy. 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.

Initial Assessment of the COSMIC-2/FORMOSAT-7 Neutral Atmosphere Data Quality in NESDIS/STAR Using In Situ and Satellite Data

“…Because CDAAC COSMIC-2 wetPrf is only available before October 2019, we limited our comparisons to the same period in this study. CDAAC also provided another set of COSMIC-2 water vapor retrievals (i.e., wetPrf2, see [29]). Ref.…”

“…Ref. [29] stated that to reduce the refractivity bias impact to the retrievals due to the possible SR condition, the wetPrf2 water vapor profiles may substantially fit the background (for example, the ECMWF) below 2 km. Because wetProf2 retrievals may use more information from the background in the lower troposphere, which is hard to quantify, we do not use wetProf 2 in this study.…”

“…Studies ( [1,49]) demonstrated that RO derived water vapor results are highly accurate. The water vapor retrieval results may be weakly dependent on the a priori [1,29]. To examine how exactly COSMIC-2 refractivity biases would be improved when better SNR data are used in the inversion package, we compared the COSMIC-2 retrievals under different atmospheric conditions (dry and moisture troposphere in different latitudes) in this section.…”

COSMIC-2 radio occultation temperature, specific humidity, and precipitable water in Hurricane Dorian (2019)

“…In this study we obtain C2 soundings of temperature, moisture, and pressure using the most recent version (Wee 2018) of the CDAAC one-dimensional variational inversion algorithm (1D-Var). This version is an improved version of the original CDAAC algorithm that has been in use for many years.…”

“…These results, even though the hurricane sample size is small, indicate that the C2 1D-Var retrieves high quality temperature and water vapor soundings, even in the extreme cloud and precipitation atmosphere of an intense hurricane, as well as in the Northern Hemisphere tropics and subtropics. This is remarkable considering that the error covariance matrices used for the 1D-Var are based on climatological error statistics (Wee 2018) and are not tailored to such…”