1. A study of relations between activity centers of the climatic system and high-risk regions Vladimir Penenko & Elena Tsvetova

2. Goal Development of theoretical background and computational technology for: revealing and identification of activity centers of the climatic system; assessment of risk/vulnerability domains; study of relations between activity centers and risk domains; applications to ecology and climate.

3. Mathematical background Analysis of multi-dimensional vector spaces with the help of orthogonal decomposition; Variational principles for joint use of measured data and models; Sensitivity theory.

4. Multicomponent spatiotemporal bases and factor spaces in orthogonal decomposition: focuses and applications data compression ( principle components and factor bases); typification of situations for analysis and modeling ; revealing the key factors in data; variability studies; classifying the processes with respect to informativity of basic functions: climatic scale, interannual scale, weather noises

5. efficient reconstruction of meteo-fields on the base of observation; development of a few component models; construction of leading phase spaces for deterministic- stochastic models; formation of subspaces for long-term climatic and ecological scenarios; focus on “ activity centers”, ”hot spots”, and “risk/vulnerability” studies Multicomponent spatiotemporal bases and factor spaces in orthogonal decomposition: focuses and applications

6. Primary concept and data bases Sensitivity studies: forward modeling, inverse modeling, adjoint problems Computational technology and tools

7. Basic idea: Representation of multi- component and multi-dimensional data base as a set of orthogonal spaces Internal structure of decomposition State vector functions ( space, time): temperature, wind velocity components, geopotential, humidity, gas phase and aerosols substances, etc Principle variable for general (external) structure decomposition: year number

8. Basic algorithm of orthogonal decomposition of linear vector spaces Main stages of decomposition: extraction of principle components; construction of main factors;

9. Basic algorithm of orthogonal decomposition of linear vector spaces Realization: constructing inner scalar product; generating Gram matrix (GM) with respect to principle variable; creating GM elements for inner structure of decomposition by means of scalar product; solving eigenvalue and eigenvectors problem for GM; assembling large units of factor spaces

12. for the sensitivity functions Inner products for basic constructions for the state functions

13. Principle components and Factor analysis Data set

14. Multicomponent inner product

15. Gram Matrix Data preprocessing

16. with restrictions Successive minimization Principle components and EOF

17. Spectral problem

18. Principle components

19. Informative function Empirical orthogonal functions (EOF)

20. Caution ! Due to huge dimensions of vector spaces and individual vectors of this spaces it is recommended to conserve informative quality of calculations of GM elements It needs to provide exact orthogonality of principle components vectors and multi- blocks factor spaces (especially important).

21. The principle component ( eigenvector N1), November, 1960-1999 20,3%

22. 17% The principle component ( eigenvector N1), June, 1960-1999

23. The main basis vector (EOF N1) for 1950-2002, HGT500mb, January The main activity centers in the global atmosphere

24. The main basis vector (EOF N1, 16,06%) for 1950-2002 Horizontal velocities at 500 mb Informativity of orthogonal spaces

25. Revealing the areas of ecological risk Sensitivity function of the atmospheric quality functional of the zone-receptor is taken as a measure of ecological risk for the receptor to be polluted by the sources distributed on the Earth’s surface in the Northern Hemisphere. Here are four scenarios. In each scenario the same configuration of the zone-receptor was taken. But each receptor was placed in the different parts of the Northern Hemisphere: in the Far East, Central Asia, North America, and Western Europe ( in some activity centers). Quality functionals were estimated in the interval 14-24 of April, 1999. Inverse modeling was carried out within the interval 24.04- 23.03.1999 in back time

26. USA Central Asia Western Europe Far East The risk functions for the receptors

27. Comparative analysis of the sensitivity functions shows that there are the areas of high potential vulnerability with respect to the pollution from the sources which can be distributed over the Northern Hemisphere. It is seen, that Far East region and West Europe are examples of such areas of high vulnerability. In the contrary, the receptors located in North America has got relatively favorable conditions.

28. Conclusion The set of numerical algorithms for multicomponent 4D factor analysis and sensitivity studies is developed for climate and ecology applications The orthogonal bases ( principle components and EOFs) are constructed as a result of decomposition of Reanalysis data for 53 years The main activity centers in the global atmosphere are revealed. The structure of risk domains is demonstrated in dependence on the position of receptors with respect to activity centers.

29. Acknowledgements The work is supported by RFBR Grant 04-05-64562 Russian Ministry of Science and Education Contract № 37.011.11.0009 Russian Academy of Sciences Program 13 Program 14 Program 1.3.2 Siberian Division of Russian Academy of Sciences Interdisciplinary projects NN 130, 131, 137, 138