Space and time scales of low frequency variability in the ocean
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We have contrived a regional model Φ(K, ω, η, φ, λ) for the distribution of low frequency variability energy in horizontal wavenumber, frequency, vertical mode and geography. We assume horizontal isotropy, Φ(K, ω, η, φ, λ) = 2πKψ(k, l, ω, η, φ, λ), with K designating the amplitude of total horizontal wavenumber. The parameters of Φ(K, ω, η, φ, λ) can be derived from observations: (i) satellite altimetry measurements yield the surface eddy kinetic energy wavenumber and frequency spectra and the geographic distribution of surface eddy kinetic energy magnitude, (ii) XBT measurements yield the temperature wavenumber spectra, (iii) current meter and thermistor measurements yield the frequency spectra of kinetic energy and temperature, (iv) tomographic measurements yield the frequency spectra of range— and depth—averaged temperature, and (v) the combination of satellite altimetry and current meter measurements yields the vertical partitioning of kinetic energy among dynamical modes. We assume the form of the geography—independent part of our model Φ(K, ω, η) ∝Kpωq. The observed kinetic energy and temperature wavenumber spectra suggest p = 3/2 at K < K0 and p = —2 at K > K0 for the barotropic mode, and p = —1/2 at K < K0 and p = —3 at K > K0 for the baroclinic mods, where K0 is the transitional wavenumber of the wavenumber spectra. The observed frequency spectra of temperature and kinetic energy suggest that q = —1/2 for ω < ω0 and q = —2 for ω > ω0, where ω0 is the transitional frequency of the frequency spectra. The combination of satellite altimetry and current meter measurements suggests the vertical structure of the low frequency variability is governed by the first few modes. The geography—dependent part of our model is the energy magnitude. Although we have shown analytically that the tomographic measurements behave as a low—pass filter, it is impossible to identify this filtering effect in the real data due to the strong geographic variability of the energy magnitude and the vertical gradient of the mean temperature. The model wavenumber spectrum is appropriate only where the statistical properties are relatively homogeneous in space.
Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution January 18, 1988
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