G.I. Marchuk - Academic of RAS A.I. Chavro - Dr. Sc. (Phys.-Math.), Professor, Institute of Numerical Mathematics RAS (Moscow). E-mail: chavro@ inm.ras.ru N.V. Uvarov - Ph. D. (Phys.-Math.), Institute for Metal Physics NASU (Ukraine). E-mail: uvarov@gmail.com A.A. Sokolov - Ph. D. (Phys.-Math.), Laboratorie de Physico-Chimie de I - Atmosphere (LPCA, ULCO) (France). E-mail: msaa@mail.ru

The number of used narrow-band spectral channels increased in satellites instruments to hundreds and even thousands, due to resent developments of technologies satellite meteorology. They are measuring radiation in wide area of ranges: from ultra-violet to distant infra-red. The comparison of various approaches for selection of the most «informative» channels represents a certain scientific and practical interest. In our work the techniques an optimum of choice are considered for spectral channels with the fixed and variable widths. Practically all known methods of the solution of inverse problems of satellite meteorology use certain a-priori information on required parameters. For the variety of methods the statistical information is available for vectors of restored parameters, such as noise characteristics of the satellite radiometer. The following methods of the optimal planning were employed for a remote sensing satellites experiments: DRM(analysis of Data resolution Matrix), Jacobians, Iterations(selection of the satellite channels is defined by Entropy Reduction), pseudo channel technique (spectral channel with variable width - based on maximizing determinant of Fisher-s information matrix). For the solving inverse problem the method of the best linear linear estimate and variational technique were used. The proposed technique was employed for remote sensing of atmosphere and surface parameters.

 

1. Kondratev K.JA. Radiacionnye faktory sovremennykh izmerenijj globalnogo klimata // L.: Gidrometeoizdat. 1980. 279 s.
2. Marchuk G.I. Uravnenie dlja cennosti informacii s meteorologicheskikh sputnikov i postanovka obratnykh zadach // Kosmicheskie issledovanija. 1964. T. 2. № 3. S. 462−477.
3. Marchuk G.I., Chavro A.I. On the Statement and Solution of Inverse Problems in Satellite Meteorology// Russ. J. Numer. Anal. Math. Modelling. 1998. V. 13. № 6. P. 501−515.
4. Hadamard J. Le probleme de Cany et les equations aux derivees partielles lineaires huperboliques. P.: Hermann. 1932.
5. Tikhonov A.N., Arsenin V.JA. Metody reshenija nekorrektnykh zadach. M.: Nauka. 1986. 288 s.
6. Lavrentev M.M. O nekotorykh nekorrektnykh zadachakh matematicheskojj fiziki. M.: SO AN SSSR. 1962. S. 92.
7. Marchuk G.I. O postanovke nekotorykh obratnykh zadach // DAN SSSR. 1964. T. 156. № 3. S. 503−506.
8. Uspenskijj A.B. Obratnye zadachi matematicheskojj fiziki - analiz i planirovanie ehksperimentov // Matematicheskie metody planirovanija ehksperimenta. Novosibirsk: Nauka: 1981. S. 199−242.
9. Rodgers C.D. Retrieval of Atmospheric Temperature and Composition From Remote Measurements of Thermal Radiation // Reviews of Geophysics and Space Physics. November 1976. V. 14. № 4. P. 409−424.
10. Turchin V.F., Kozlov V.P., Malkevich M.S. Ispolzovanie metodov matematicheskojj statistiki dlja reshenija nekorrektnykh zadach // UFN. 1970. T. 102. № 3. S. 33−55.
11. Kondratev K.JA., Timofeev JU.M. Meteorologicheskoe zondirovanie atmosfery iz kosmosa. L.: Gidrometeoizdat. 1978. 280 s.
12. Rogers C.D. Characterization and Error Analysis of Profiles Retrieved From Remote Sounding Measurements // Journal of Geophysical Research. 990. ol.95. o. D5. P. 5587−5597.
13. CHavro A.I., Uvarov N.V., Sokolov A.A. Nelinejjnye metody reshenija obratnykh zadach sputnikovojj meteorologii v IK-oblasti spektra // Trudy Mezhdunar. simpoziuma stran SNG po atmosfernojj radiacii (MSAR-2004). 22−25 ijunja 2004 g. S.-Peterburg. S. 108.
14. Faddeev D.K // Tr. MIAN SSSR. 1959. T. 53. S. 387.
15. Faddeev D.K., Fadeeva V.N // Vychislitelnaja matematika i matematicheskaja fizika. 1961. T. 1. S. 412.
16. Fisher R.A. The design of experiments. London: Oliver and Boud Ltd. 1935.
17. Kiefer J // J. Roy. Stat. Soc. 1959. Bd. 21. № 2. P. 272−319.
18. Fedorov V.V. Teorija optimalnogo ehksperimenta. M.: Nauka. 1971. 312 s.
19. Menke W. Geophysical Data Analysis: Discrete Inverse Theory. NewYork: AcademicPress. 1984. 289 p.
20. Prunet P., Minster J., Ruiz-Pino D., Dadou I. Assimilation of surface data in a onedimensionalphysical-biogeochemical model of the surface ocean. 1. Methodandpreliminaryresults //GlobalBiogeochem. Cycles. 10. 1996. P. 111−138.
21. Prunet P., Thepaut J., Casse V. The information content of clear sky IASI radiances and their potential for numerical weather prediction // Q. J. R. Meteorol. Soc. 1998. 124. P. 211−241.
22. Rogers C.D. Information content and optimisation of high spectral resolution measurements // Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research II. SPIE. 1996. V. 2830. P. 136−147.
23. Huang H.L., Purser R.J. Objective measures of the information density of satellite data // Meteorology and Atmospheric Physics, Springer Wien. 1996. V. 60. № 3. P. 105−117
24. Kozlov V.P. CHislennoe vosstanovlenie vysotnogo profilja temperatury po spektru ukhodjashhejj radiacii i optimizacii metoda izmerenijj // Izvestija AN SSSR. FAO. 1966. T.II. № 12. S. 1230−1234.
25. Twomey S. Mathematical aspects of inverse problem // Monthly Weather Rev. 1966. V. 964. № 6. P. 363−366.
26. Kozlov V.P., Timofeev JU.M. Ob optimalnykh uslovijakh izmerenijj ukhodjashhego teplovogo izluchenija v polosakh pogloshhenija SO2 i tochnosti metoda termicheskogo zondirovanija atmosfery // Izvestija AN SSSR. FAO. 1979. T. 15. № 2. S. 1253−1261.
27. Kozlov V.P. Ob odnojj zadache optimalnogo planirovanija statisticheskogo ehksperimenta // Teorija verojatnosti i ee primenenija. 1974. T. 19. S. 226−230.