Detecting Propagating Signals with Complex Empirical Orthogonal Functions: A Cautionary Note

Abstract

A limitation on the performance of complex empirical orthogonal function (CEOF) analyses in the time domain is illustrated with synthetic, noise-free, nondispersive, propagating signals. Numerical examples using a band-limited white spectrum and a simulation of costal-trapped waves sampled with an array of tide gauges, demonstrate that CEOF analysis is degraded with increasing ΔκΔχ (Δκ is the wavenumber bandwidth and Δχ is the instrument array length). A relatively wide wavenumber bandwidth [ΔκΔχ < 0(2π)] results in a significant loss of variance recovery towards the ends of the array. The CEOF method don yield an average frequency and wavenumber for the first mode, independent of ΔκΔχ, that accurately estimate the phase speed of the nondispersive propagating signal. These simple simulators indicate that modal spatial patterns from a time domain CEOF analysis of wide-banded signals should be interpreted cautiously.