On Spatiotemporal Spectral Analysis

The wavenumber-frequency spectrum reveals dynamic features of spatiotemporal processes such as traveling oscillatory components, turbulent structures, and linear transfer functions. It can be used to estimate multidimensional covariance, or to directly perform parameter estimation with reduced computational cost. However, simple extensions of univariate spectral estimators can be shown to have poor statistical properties. In this talk I will extend the univariate multitaper spectrum estimator to the multidimensional case, using optimally bandlimited functions (Slepian functions) for spacelimited Cartesian domains. Multitaper spectrum analysis has the advantage of (a) restricting bias in frequency-wavenumber domain due to usage of Slepian functions (b) variance reduction due to averaging of multiple approximately independent spectral estimates. On a toy example in one spatial dimension and one time dimension, sea surface temperatures are shown to exhibit a strong traveling El Niño Southern Oscillation (ENSO) pattern, from which it is possible to derive velocity and signal strength. In a real data example, we investigate the fluid properties of Von Karmán vortex shedding off a square mounted cylinder in turbulent flow, by high dimensional spectral analysis applied to data from a simulation of fluid flow equations on a complex gridded geometry.