Technical Note: Spectral representation of spatial correlations in variational assimilation with grid point models and application to the Belgian Assimilation System for Chemical Observations (BASCOE)

Atmospheric Chemistry and Physics

Volumn 12, Issue 21, 2012, Pages 10015-10031

  Errera, Q ^a   Menard R ^b  

^a BELGIAN INSTITUTE FOR SPACE AERONOMY   (Belgium)

^b ENVIRONMENT CANADA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC CHEMISTRY; ERROR ANALYSIS; METEOROLOGY; MODELING; SPECTRAL ANALYSIS;

EID: 84868694614     PISSN: 16807316     EISSN: 16807324     Source Type: Journal    
DOI: 10.5194/acp-12-10015-2012     Document Type: Article

References (41)

1. Bannister, R. N.: A review of forecast error covariance statistics in atmospheric variational data assimilation. I: characteristics and measurements of forecast error covariances, Q. J. R. Meteorol. Soc., 134, 2008a.
2. Bannister, R. N.: A review of forecast error covariance statistics in atmospheric variational data assimilation. II: modelling the forecast error covariance statistics, Q. J. R. Meteorol. Soc., 134, 1971-1996, 2008b.
3. Bartello, P. and Mitchell, H. L.: A continuous three-dimensional model of short-range forecast error covariances, Tellus A, 44, 217, doi:10.1034/j.1600- 0870.1992.t01-2-00002.x, 1992.
4. Berre, L.: Estimation of synoptic and mesoscale forecast error co-variances in a limited-area model, Mon. Weather Rev., 128, 644, doi:10.1175/1520-0493(2000)1282.0.CO;2, 2000.
5. Boer, G. J.: Homogeneous and isotropic turbulence on the sphere, J. Atmos. Sci., 40, 154-163, 1983.
6. Boer, G. J. and Shepherd, T. G.: Large-scale two-dimensional turbulence in the atmosphere, J. Atmos. Sci., 40, 164-184, 1983.
7. Cortesi, U., Lambert, J. C., De Clercq, C., Bianchini, G., Blumen-stock, T., Bracher, A., Castelli, E., Catoire, V., Chance, K. V., De Mazière, M., Demoulin, P., Godin-Beekmann, S., Jones, N., Jucks, K., Keim, C., Kerzenmacher, T., Kuellmann, H., Kut-tippurath, J., Iarlori, M., Liu, G. Y., Liu, Y., McDermid, I. S., Meijer, Y. J., Mencaraglia, F., Mikuteit, S., Oelhaf, H., Piccolo, C., Pirre, M., Raspollini, P., Ravegnani, F., Reburn, W. J., Redaelli, G., Remedios, J. J., Sembhi, H., Smale, D., Steck, T., Taddei, A., Varotsos, C., Vigouroux, C., Waterfall, A., Wet-zel, G., and Wood, S.: Geophysical validation of MIPAS-ENVISAT operational ozone data, Atmos. Chem. Phys., 7, 4807-4867, doi:10.5194/acp-7-4807-2007, 2007. (Pubitemid 47469594)
8. Courtier, P., Andersson, E., Heckley, W., Vasiljevic, D., Ham-rud, M., Hollingsworth, A., Rabier, F., Fisher, M., and Pailleux, J.: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: formulation, Q. J. R. Mete-orol. Soc., 124, 1783-1807, doi:10.1002/qj. 49712455002, 1998. (Pubitemid 29007411)
9. Dee, D. P.: On-line estimation of error covariance parameters for atmospheric data assimilation, Mon. Weather Rev., 123, 1128, doi:10.1175/1520-0493(1995)1232.0.CO;2, 1995.
10. Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B., Hersbach, H., Hólm, E. V., Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N., and Vitart, F.: The ERA-Interim reanalysis: configuration and performance of the data assimilation system, Q. J. R. Meteorol. Soc., 137, 553-597, doi:10.1002/qj.828, 2011.
11. Derber, J. and Rosati, A.: A global oceanic data assimilation system, J. Phys. Oceanogr., 19, 1333-1347, doi:10.1175/1520-0485(1989)0192.0.CO;2, 1989.
12. Dethof, A. and Hólm, E. V.: Ozone assimilation in the ERA-40 reanalysis project, Q. J. R. Meteorol. Soc., 130, 2851-2872, doi:10.1256/qj.03.196, 2004. (Pubitemid 40015284)
13. Elbern, H., Schwinger, J., and Botchorishvili, R.: Chemical state estimation for the middle atmosphere by four-dimensional varia-tional data assimilation: system configuration, J. Geophys. Res., 115, D06302, doi:10.1029/2009JD011953, 2010.
14. Errera, Q., Daerden, F., Chabrillat, S., Lambert, J. C., Lahoz, W. A., Viscardy, S., Bonjean, S., and Fonteyn, D.: 4D-Var assimilation of MIPAS chemical observations: ozone and nitrogen dioxide analyses, Atmos. Chem. Phys., 8, 6169-6187, doi:10.5194/acp-8-6169-2008, 2008.
15. Fischer, H., Birk, M., Blom, C., Carli, B., Carlotti, M., von Clar-mann, T., Delbouille, L., Dudhia, A., Ehhalt, D., Endemann, M., Flaud, J. M., Gessner, R., Kleinert, A., Koopman, R., Langen, J., López-Puertas, M., Mosner, P., Nett, H., Oelhaf, H., Perron, G., Remedios, J., Ridolfi, M., Stiller, G., and Zander, R.: MIPAS: an instrument for atmospheric and climate research, Atmos. Chem. Phys., 8, 2151-2188, doi:10.5194/acp-8-2151-2008, 2008.
16. Fisher, M.: Background error covariance modelling, in: Seminar on Recent developments in data assimilation for atmosphere and ocean, 8-12 September 2003, edited by: ECMWF, Shinfield Park, Reading, 45-64, 2003.
17. Gaspari, G. and Cohn, S. E.: Construction of correlation functions in two and three dimensions, Q. J. R. Meteorol. Soc., 125, 723-757, 1999. (Pubitemid 29247364)
18. Gauthier, P., Courtier, P., and Moll, P.: Assimilation of simulated wind lidar data with a Kalman filter, Mon. Weather Rev., 121, 1803, doi:10.1175/1520-0493(1993)1212.0.CO;2, 1993.
19. Geer, A. J., Lahoz, W. A., Bekki, S., Bormann, N., Errera, Q., Es-kes, H. J., Fonteyn, D., Jackson, D. R., Juckes, M. N., Mas-sart, S., Peuch, V.-H., Rharmili, S., and Segers, A.: The ASSET intercomparison of ozone analyses: method and first results, Atmos. Chem. Phys., 6, 5445-5474, doi:10.5194/acp-6- 5445-2006, 2006. (Pubitemid 44887121)
20. Gilbert, J.-C. and Lemarechal, C.: Some numerical experiments with variable storage quasi-Newton algorithms, Math. Prog., 45, 407-435, 1989. (Pubitemid 20660312)
21. Jackson, J. D.: Classical Electrodynamics, 3rd edn., Wiley & Sons, 1998.
22. Krishnamurti, T. N., Bedi, H. S., Hardiker, V. M., and Ra-maswamy, L.: An Introduction to Global Spectral Modeling, 2nd revised and enlarged edition, Springer, 2006.
23. Lahoz, W. A., Errera, Q., Viscardy, S., and Manney, G. L.: The 2009 stratospheric major warming described from synergistic use of BASCOE water vapour analyses and MLS observations, Atmos. Chem. Phys., 11, 4689-4703, doi:10.5194/acp-11-4689-2011, 2011.
24. Lin, S.-J. and Rood, R. B.: Multidimensional flux-form semi-Lagrangian transport schemes, Mon. Weather Rev., 124, 2046-2070, 1996. (Pubitemid 126562396)
25. Machenhauer, B.: The spectral method, in: Numerical Methods used in Atmospheric Models, edited by: Kasahara, E. A., No. 17 in GARP Publication Series, WMO, 1979.
26. Machenhauer, B. and Daley, R.: A baroclinic primitive equation model with a spectral representation in three dimensions, Tech. Rep. 4, Institute for Theoritical Meteorology, Copenhagen University, 1972.
27. Monin, A. S. and Yaglom, A. M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1, The MIT Press, 1971.
28. Monin, A. S. and Yaglom, A. M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2, The MIT Press, 1975.
29. Panchev, S.: Random Functions and Turbulence, International Series of Monograph in Natural Philosophy, Pergamon Press, 1971.
30. Parrish, D. F. and Derber, J. C.: The National Meteorological Center's spectral statistical-interpolation analysis system, Mon. Weather Rev., 120, 1747-1763, 1992. (Pubitemid 23375504)
31. Phillips, N. A.: The spatial statistics of random geostrophic modes and first-guess errors, Tellus A, 38, 314, doi:10.1111/j.1600-0870.1986.tb00418.x, 1986.
32. Purser, R. J., Wu, W.-S., Parrish, D. F., and Roberts, N. M.: Numerical Aspects of the Application of Recursive Filters to Vari-ational Statistical Analysis. Part I: Spatially Homogeneous and Isotropic Gaussian Covariances, Mon. Weather Rev., 131, 1524-1535, 2003. (Pubitemid 37124286)
33. Satoh, M.: Atmospheric Circulation Dynamics and Circulation Models, ISBN 978-3-540-42638-7, Springer, 2004.
34. Schwinger, J. and Elbern, H.: Chemical state estimation for the middle atmosphere by four-dimensional variational data assimilation: a posteriori validation of error statistics in observation space, J. Geophys. Res., 115, D18307, doi:10.1029/2009JD013115, 2010.
35. Swarztrauber, P. N.: On the spectral approximation of discrete scalar and vector functions on the sphere, SIAM J. Numer. Anal., 16, 934-949, doi:10.1137/0716069, 1979.
36. Swarztrauber, P. N.: Discrete Fourier transforms and related topics, available at: http://www.cisl.ucar.edu/css/staff/pauls/tutorials/index.html, Lecture 1, 2003.
37. Swarztrauber, P. N.: Computing on the sphere: Part I, available at: http://www.cisl.ucar.edu/css/staff/pauls/tutorials/index. html, Lecture 2, 2003.
38. Swarztrauber, P. N. and Spotz, W. F.: Generalized discrete spherical harmonic transforms, J. Comp. Phys., 159, 213-230, 2000.
39. Talagrand, O.: Assimilation of observations, an introduction, J. Me-teorol. Soc. Jpn, 277, 191-209, 1997. (Pubitemid 127712496)
40. Viscardy, S., Errera, Q., Christophe, Y., Chabrillat, S., and Lambert, J.-C.: Evaluation of ozone analyses from UARS MLS assimilation by BASCOE between 1992 and 1997, IEEE J. Sel. Top. Appl., 3, 190-202, doi:10.1109/JSTARS.2010. 2040463, 2010.
41. Weaver, A. and Courtier, P.: Correlation modelling on the sphere using a generalized diffusion equation, Q. J. R. Meteorol. Soc., 127, 1815-1846, doi:10.1002/qj.49712757518, 2001. (Pubitemid 32752887)