Spectral description of low frequency oceanic variability
Citable URI
http://hdl.handle.net/1912/4307DOI
10.1575/1912/4307Keyword
Frequency spectra; Ocean wavesAbstract
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 streamfunction
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 largescale lowfrequency 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 broadband 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 1040%
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. Nonequatorial 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.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2000
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