Boundary value problems, meteorological fields in terms of orthogonal functions, normal modes, Fourier-Legendre transforms, FFT; Asymptotic expansions, method of multiple scales applied to atmospheric motions, Calculus of variations and Rayleigh-Ritz method; Probability, covariance and correlation, multivariate distributions and analysis, principal component analysis, singular value decomposition (SVD), Uncertainty analysis, Data assimilation techniques, error statistics, statistical softwares for satellite data analysis.
Empirical orthogonal functions, Fourier transforms, wavelet transforms, Neural networks, genetic algorithms, functions, matrices, fundamentals of signal theory, 1-D and n-D, discrete signals, 1-2 and 3-D computing/MATLAB/programming; Probability theory, least-square optimization, regression, non-linear; optimization. Highlighting information in the data: Interpolation; concept of frequency / wave number; Fourier transform and FFT 1-D and 2-D; spectra and power; spectral density (PSD); Filtering, 1-D and 2-D; applications of filtering, empirical orthogonal functions, Advanced techniques; random transforms, wavelets. Comparing different datasets: Auto and cross-correlation; relationship between correlation and PSD; cross spectra; applications; canonical correlation analysis.
Text/Reference Books:
1. Hans von Storch and Francis W. Zwier. Statistical analysis in climate research, Cambridge University Press
2. W. J. Emery, Richard E. Thomson. Data Analysis Methods in Physical Oceanography, Elsevier Science
3. Trauth, E. Sillmann, R. Gebbers, N. Marwan. MATLAB® Recipes for Earth Sciences, Springer
4. D S Wilks, Statistical Methods in the Atmospheric Sciences, Volume 100, Third Edition (International Geophysics), Academic Press |