Use of discrete Fourier transforms in the 1D-Var retrieval problem

Quarterly Journal of the Royal Meteorological Society

Volumn 131, Issue 605, 2005, Pages 63-72

  Healy, Sean B ^a,b   White, A A ^a  

^a MET OFFICE   (United Kingdom)

^b EUROPEAN CENTRE FOR MEDIUM RANGE WEATHER FORECASTS   (United Kingdom)

Author keywords

Satellite observations; Variational analysis

Indexed keywords

ERROR ANALYSIS; INFORMATION ANALYSIS; MATRIX ALGEBRA; MEASUREMENT THEORY; PROBLEM SOLVING; VECTORS;

CIRCULANT MATRIX; ERROR COVARIANCE; MATRIX PRODUCTS;

FOURIER TRANSFORMS;

FOURIER TRANSFORM; METEOROLOGY; SATELLITE DATA;

EID: 23044469177     PISSN: 00359009     EISSN: None     Source Type: Journal    
DOI: 10.1256/qj.03.193     Document Type: Article

References (16)

1. Amato, U., de Canditiis, D. and Serio, C. 1998 Effect of apodisation on the retrieval of geophysical parameters from Fourier-transform spectrometers. Appl. Optics, 37, 6537-6543
2. Bunch, J. R. 1985 Stability of methods for solving Toeplitz systems of equations. SIAM J. Sci. Stat. Comp., 6, 349-364
3. Conan, J., Mugnier, L. M., Fusco, T., Michau, V. and Rousset, G. 1998 Myopic deconvolution of adaptive optics images by use of object and point-spread function power spectra. Appl. Optics, 37, 4614-4622
4. Demoment, G. 1989 Image reconstruction and restoration: Overview of common estimation structures and problems. IEEE Trans. on Acoust., Speech, Signal Processing, 37, 2024-2036
5. Golub, G. H. and Van Loan, C. H. 1996 Matrix computations (third edition). Johns Hopkins University Press, Baltimore, USA
6. Gray, R. M. 2002 Toeplitz and circulant matrices: A review. Available at http://www-ee.stanford.edu/~gray/toeplitz.pdf
7. Liu, Z.-Q. and Rabier, F. 2002 The interaction between model resolution, observation resolution and observation density in data assimilation: A one-dimensional study. Q. J. R. Meteorol. Soc., 128, 1367-1386
8. Preisendorfer, R. W. 1988 Principal component analysis in meteorology and oceanography. Elsevier, New York and Amsterdam
9. Rabier, F., Fourrié, N., Chafaï, D. and Prunet, P. 2002 Channel selection methods for Infrared Atmospheric Sounding Interferometer radiances. Q. J. R. Meteorol. Soc., 128, 1011-1027
10. Rino, C. L. 1970 The inversion of covariance matrices by finite Fourier Transforms. IEEE Trans. on Information Theory, 16, 230-232
11. Rodgers, C. D. 2000 Inverse methods for atmospheric sounding: theory and practice. World Scientific Publishing
12. Sherlock, V. J. 2000 'Results from the first UKMO IASI radiative transfer model intercomparison'. Numerical Weather Prediction Branch Technical Note no. 287, Met Office, Exeter, UK
13. Strang, G. 1986 Introduction to applied mathematics. Wellesley-Cambridge Press, Wellesley, USA
14. Watts, P. D. and McNally, A. P. 1988 'The sensitivity of a minimum variance retrieval scheme to the value of its principal parameters'. Pp. 399-407 of Technical Proceedings of the Fourth International TOVS Study Conference, 16-22 March, Igls, Austria. University of Wisconsin, Madison, USA
15. White, A. A. and Healy, S. B. 2004a 'Error covariance matrices having sinusoidal eigenvectors. I: cyclic domains'. Forecasting Research Tech. Report 446, Met Office, Exeter, UK
16. White, A. A. and Healy, S. B. 2004b 'Error covariance matrices having sinusoidal eigenvectors. II: non-cyclic and mixed domains'. Forecasting Research Tech. Report 447, Met Office, Exeter, UK