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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union

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https://doi.org/10.5194/amt-2017-228
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
26 Jul 2017
Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Atmospheric Measurement Techniques (AMT).
A variational regularization of Abel transform for GPS radio occultation
Tae-Kwon Wee University Corporation for Atmospheric Research, Boulder, Colorado, USA
Abstract. In the Radio Occultation (RO), the refractivity is generally obtained from the inverse Abel transform of measured bending angle, often called Abel inversion (AI). While concise and straightforward to apply, AI is susceptible to the error present in the bending angle. Aiming at reducing the adverse effects of the measurement error, this study proposes a new method for determining the refractivity through a variational regularization (VR). The method 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 optimal problem is then solved iteratively by means of the adjoint technique. VR incorporates the prior information about measurement characteristics and desired behaviour of the solution into the regularization via error covariance matrices. In contrast to variational data assimilations, VR holds the control variable in the measurement space. This makes VR particularly effective by allowing the method to benefit from the posterior height determination and to deal with model’s error in the impact parameter. The advantages are elaborated using a purposely corrupted synthetic sounding and with known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison with nearby radiosonde observations shows that VR is considerably smaller than AI in both random and systematic errors. It is concluded based on the results presented in this study that VR offers a definite advantage over AI in the quality of refractivity.

Citation: Wee, T.-K.: A variational regularization of Abel transform for GPS radio occultation, Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2017-228, in review, 2017.
Tae-Kwon Wee
Tae-Kwon Wee
Tae-Kwon Wee

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Short summary
The refractivity in the Radio Occultation (RO) is generally obtained from the inverse Abel transform (AI) of measured bending angle. While concise and mathematically exact, AI is susceptible to the error present in the measurement. Aiming at reducing the adverse effects of the measurement error, this study proposes a new method for determining the refractivity through a variational regularization (VR). Verification shows that VR offers a definite advantage over AI in the quality of refractivity.
The refractivity in the Radio Occultation (RO) is generally obtained from the inverse Abel...
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