Spectral description of low frequency oceanic variability

Abstract

A simple dynamic model is used with various observations to provide an approximate spectral description of low frequency oceanic variability. Such a spectrum has wide application in oceanography, including the optimal design of observational strategy for the deployment of floats, the study of Lagrangian statistics and the estimate of uncertainty for heat content and mass flux. Analytic formulas for the frequency and wavenumber spectra of any physical variable, and for the cross spectra between any two different variables for each vertical mode of the simple dynamic model are derived. No heat transport exists in the model. No momentum flux exists either if the energy distribution is isotropic. It is found that all model spectra are related to each other through the frequency and wavenumber spectrum of the stream-function for each mode, Φ(k, I, w, n, φ, λ), where (k, I) represent horizontal wavenumbers, W stands for frequency, n is vertical mode number, and (φ,λ) are latitude and longitude, respectively. Given Φ(k, I, w, n, φ, λ), any model spectrum can be estimated. In this study, an inverse problem is faced: Φ(k, I, w, n, φ, λ) is unknown; however, some observational spectra are available. I want to estimate Φ(k, I, w, n, φ, λ) if it exists. Estimated spectra of the low frequency variability are derived from various measurements: (i) The vertical structure of and kinetic energy and potential energy is inferred from current meter and temperature mooring measurements, respectively. (ii) Satellite altimetry measurements produce the geographic distributions of surface kinetic energy magnitude and the frequency and wavenumber spectra of sea surface height. (iii) XBT measurements yield the temperature wavenumber spectra and their depth dependence. (v) Current meter and temperature mooring measurements provide the frequency spectra of horizontal velocities and temperature. It is found that a simple form for Φ(k, I, w, n, φ, λ) does exist and an analytical formula for a geographically varying Φ(k, I, w, n, φ, λ) is constructed. Only the energy magnitude depends on location. The wavenumber spectral shape, frequency spectral shape and vertical mode structure are universal. This study shows that motion within the large-scale low-frequency spectral band is primarily governed by quasigeostrophic dynamics and all observations can be simplified as a certain function of Φ(k, I, w, n, φ, λ). The low frequency variability is a broad-band process and Rossby waves are particular parts of it. Although they are an incomplete description of oceanic variability in the North Pacific, real oceanic motions with energy levels varying from about 10-40% of the total in each frequency band are indistinguishable from the simplest theoretical Rossby wave description. At higher latitudes, as the linear waves slow, they disappear altogether. Non-equatorial latitudes display some energy with frequencies too high for consistency with linear theory; this energy produces a positive bias if a lumped average westward phase speed is computed for all the motions present.