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Vladimir Penenko & Elena Tsvetova

Studies of the climatic system variability by means of factor spaces. Vladimir Penenko & Elena Tsvetova. Multicomponent spatiotemporal bases and factor spaces. Objectives :. data compression ( principle components and factor bases);

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Vladimir Penenko & Elena Tsvetova

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  1. Studies of the climatic system variability by means of factor spaces Vladimir Penenko& Elena Tsvetova

  2. Multicomponent spatiotemporal bases and factor spaces Objectives: • data compression ( principle components and factor bases); • typification of situations for analysis and modeling ; • revealing the key factors in data; • variability studies; • 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 ”hot spots” and “risk/vulnerability” studies

  3. Inner products for basis construction for the state functions for the sensitivity functions

  4. Factor analysis Data set

  5. Multicomponent inner product

  6. Data preprocessing Gram Matrix

  7. Principle components and EOF Successive minimization with restrictions

  8. Spectral problem

  9. Principle components

  10. Empirical orthogonal functions (EOF) Informative function

  11. Global scale

  12. Байкал The main activity centers in the global atmosphere calculated from HGT500 The first EOFs extracted from Reanalysis data for 1960-1999

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

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

  15. The main activity centers in the global atmosphere The main basis vector (EOF N1) for 1950-2002 , T500mb, July

  16. Factor subspaces for deterministic- stochastic scenarios • Factor space is a linear subset of the vector space is arbitrary element from invariant !! Algebraic operations in X leave is a leading phase space, are generated perturbations

  17. Construction of the vector set Formation of vectors 1. Deterministic case: calculation by means of the process models 2. deterministic-stochastic case: generation of the stochastic processes of the fractal type described by gaussian process with variance H is a parameter of the fractal size, are the eigenvalues of the Gram matrix

  18. Conclusion • The set of numerical algorithms for multicomponent 4D factor analysis is developed • for climate and ecology research • The orthogonal bases are constructed ( principle components and EOFs) using Reanalysis data for 53 years • The main activity centers in the global atmosphere are revealed • The methods are applied for construction of the long-term scenarios for risk assessment with respect to anthropogenic impact

  19. 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 • Integrating projects 130, 131, 137, 138

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