Lynne Talley, Fall, 2019
DPO Chapter 6 (6.1, 6.2, 6.3.1, 6.4, 6.5 (not 6.5.3, 6.5.4), 6.6.2, 6.7.1, 6.7.2)
Time series analysis
Also known as spectral analysis, Fourier analysis, harmonic analysis
Can be done in either the time (frequency) domain or spatial (wavenumber)
domain.
Determines dominant frequencies of variability (especially useful when
the forcing has a well-defined frequency)
Shape of spectra can reveal underlying physics (red vs. white spectrum)
Fundamental frequency and Nyquist frequency
Multi-dimensional data analysis
Objective analysis
Maps spatially non-uniform data to a grid
incorporates correlation length scale and noise of observations
estimate is a weighted sum of nearby observations
Empirical Orthogonal Functions (EOFs)
Also known as Principle Component Analysis, Factor Analysis
Compact description of principal spatial and temporal variability
Called "empirical" because spatial structures are defined by the data
as opposed to a set of mathematical basis functions (e.g. sine waves, Bessel functions, Legendre polynomials)