Modern Methods in Oceanography
Syllabus
Normal modes decomposition of geophysical fluid. The linearized motion of geophysical stratified fluid on a rotating Earth is decomposed to normal modes. By applying this method, the equations of motion are transformed in a sum of equations of motion, which are in form similar to the equations for the non-stratified fluid. Each normal mode (‘eigen motion’) propagates around a fluid with the baroclinic velocity, linked to the internal Rossby radius of deformation. The latter represents typical horizontal length scale of structures in a geophysical fluid. By this method of decomposition the low-frequency geophysical fluid motion is decomposed into non-dispersive long-waves, the phase speed of which equals the group speed.
EOF (Empirical Orthogonal Function) and PCA (Principal Component Analysis) method mean decomposition of space and time distributed quantities (e.g. sea-water temperature) fluid motion on principal (‘eigen’) space distribution of quantities, which are variable in time and which also contain largest space variance. This analysis also means a significant reduction in a mass of the data, assimilated in numerical forecast models while it still keeps major characteristics of their space-time distribution.
Kalman filteringr – this method is besides the optimal ionterpolation method one of key methods in the data assimilation in forecast numerical models. It represents significant improvement of the forecast by measured quantities.
Fourier analysis and HHT (Hilbert-Huang Transformation) of time series. In Fourier analysis, the energy (variance) shares in Fourier components are fixed and frequency dependent, the modern HHT method, which combines the EMD (Empirical Mode Decomposition) and HAS (Hilbert Spectral Analysis) enables an insight into the time evolution of frequencies. This is the adaptive analysis suitable for the observation and decomposition of non-linear dynamic systems to IMF (Intrinsic Mode Functions) which preserve the number of zero crossings, as well as the number of extremes and symmetric form around them. This adaptive method suits the needs for the observation of non-stationary processes in which shares of the energy on frequencies vary in time. It also enables clear separation of trends from periodic motions, which may vary in time by themselves.
Wavelet analysis – this is also one of the modern analyses of time series by their decomposition on orthogonal functions of wavelets, which are limited in their range of time and frequency. Wavelets enable clear separation of energy (variance) to frequencies within a time variability of processes.
Goals and competencies
Students acquire knowledge on modern methods applied in physical oceanography, which are in use in the forecast of circulation, data assimilation in it and in the analysis of mass of data.
Basic literature
- Emery W.J. in R.E. Thomson, 2014: Data Analysis Methods in Physical Oceanography (3rd Ed.). Pergamon Press, 716 pp.
- Computer implemented Empirical Mode Decomposition apparatus, method and article of manufacture. US Patent 5,983,162, Granted Nov. 9, 1999 (NASA).
- Empirical Mode Decomposition apparatus, method and article of manufacture for analyzing biological signals and performing curve fitting. US Patent 6, 738,734 B1, Granted May 18, 2004 (NASA).
- Ensemble Empirical Mode Decomposition: A Noise Assisted Data Analysis Method by Zhaohua Wu and Norden Huang. Application Pending 2007.
- Wu, Z., Huang, N. E, S. R. Long, in C.-K. Peng (2007), On the trend, detrending, and the variability of nonlinear and non-stationary time series, Proc. Natl. Acad. Sci. USA., 104, 14889-14894.
- Wu, Z. in N. E Huang (2008). Ensemble Empirical Mode Decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analysis. 1, 1-41.
- Huang, N. E. in Wu, Z. (2008). A review on Hilbert-Huang transform: method and its applications to geophysical studies. Reviews of Geophysics, 46, RG2006.
- Meyers, S. D., Kelly, in J. J. O'Brien (1993). An introduction to wavelet analysis in oceanography and meteorology: with application to the dispersion of Yanai waves. Monthly Weather Review, 121, 2858-2866.
- Torrence, C. in G. P. Compo (1998). A practical guide to wavelet analysis. BAMS (Bull. of the American Meteor. Soc.), 79, 61-78.
- Rozier D. in sod. (2007). A reduced-order kalman filter for data assimilation in physical oceanography. SIAM, 49, 449-465.