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Improving the Bias Characteristics of the Ropp Refractivity and Bending Angle Operators : Volume 7, Issue 10 (09/10/2014)

By Burrows, C. P.

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Book Id: WPLBN0003999495
Format Type: PDF Article :
File Size: Pages 14
Reproduction Date: 2015

Title: Improving the Bias Characteristics of the Ropp Refractivity and Bending Angle Operators : Volume 7, Issue 10 (09/10/2014)  
Author: Burrows, C. P.
Volume: Vol. 7, Issue 10
Language: English
Subject: Science, Atmospheric, Measurement
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Healy, S. B., Culverwell, I. D., & Burrows, C. P. (2014). Improving the Bias Characteristics of the Ropp Refractivity and Bending Angle Operators : Volume 7, Issue 10 (09/10/2014). Retrieved from

Description: Met Office, Exeter, UK. The bending angle observation operator (forward model) currently used to assimilate radio occultation (RO) data at the Met Office, the European Centre for Medium-Range Weather Forecasts (ECMWF) and other centres is the same as is included in the Radio Occultation Processing Package (ROPP), along with the corresponding tangent-linear and adjoint code. The functionality of this package will be described in another paper in this issue. The mean bending angle innovations produced with this operator using Met Office background fields show a bias that oscillates with height and whose magnitude peaks between the model levels. These oscillations have been attributed to shortcomings in the assumption of exponentially varying refractivity between model levels. This is used directly in the refractivity operator, and indirectly to produce forward-modelled bending angles via the Abel transform. When the spacing between the model levels is small, this assumption is acceptable, but at stratospheric heights where the model level spacing is large, these biases can be significant, and can potentially degrade analyses. This paper provides physically based improvements to the functional form of refractivity with height. These new assumptions considerably improve the oscillatory bias, and a number of approaches for practical implementation of the bending angle operator are provided.

Improving the bias characteristics of the ROPP refractivity and bending angle operators

Abramowitz, M. and Stegun, I. A. (Eds.): Handbook of mathematical functions, Dover, 1965.; Cucurull, L., Derber, J. C., and Purser, R. J.: A bending angle forward operator for global positioning system radio occultation measurements, J. Geophys. Res. Atmo., 118, 14–28, 2013.; Davies, T., Cullen, M. J. P., Malcolm, A. J., Mawson, M. H., Staniforth, A., White, A. A., and Wood, N.: A new dynamical core for the Met Offices global and regional modelling of the atmosphere, Q. J. Roy. Meteorol. Soc., 131, 1759–1782, 2005.; ECMWF: IFS Documentation – Cy38r1. P}art III: Dynamics and numerical procedures, {IFS documentation, ECMWF, available at: (last access: 3 October 2014), 2007.; Healy, S. B. and Thepaut, J.-N.: Assimilation experiments with CHAMP GPS radio occultation measurements, Q. J. Roy. Meteorol. Soc., 132, 605–623, 2006.; Fjeldbo, G., Kliore, G. A., and Eshleman, V. R.: The neutral atmosphere of V}enus as studied with the Mariner {V radio occultation experiments, Astron. J., 76, 123–140, 1971.; Healy, S. B.: Assimilation of GPS radio occultation measurements at ECMWF, in: Proceedings of GRAS SAF Workshop on Applications of GPS radio occultation measurements, ECMWF, Reading, 99–109, 2008.; Healy, S. B. and Eyre, J. R.: Retrieving temperature, water vapor and surface pressure information from refractive–index profiles derived by radio occultation: A simulation study, Q. J. Roy. Meteorol. Soc., 126, 1661–1683, 2000.; Kursinski, E. R., Hajj, G. A., Schofield, J. T., Linfield, R. P., and Hardy, K. R.: Observing earth's atmosphere with radio occultation measurements using the Global Positioning System, J. Geophys. Res., 102, 23429–23465, 1997.; Melbourne, W. G., Davis, E. S., Duncan, C. B., Hajj, G. A., Hardy, K. R., Kursinski, E. R., Meehan, T. K., and Young, L. E.: The application of spaceborne GPS to atmospheric limb sounding and global change monitoring, Publication 94–18, Jet Propulsion Laboratory, Pasadena, Calif., 1994.; Poli, P., Healy, S. B., and Dee, D. P.: Assimilation of Global Positioning System radio occultation data in the ECMWF ERA-Interim reanalysis, Q. J. Roy. Meteorol. Soc., 136, 1972–1990, 2010.; Rennie, M. P.: The impact of GPS radio occultation assimilation at the Met Office, Q. J. Roy. Meteorol. Soc., 136, 116–131, 2010.; Smith, E. K. and Weintraub, S.: The constants in the equation for atmospheric refractivity index at radio frequencies, Proceedings of the IRE, 41, 1035–1037, 1953.


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