Measurements of Oceanic Fine Structure

Abstract

The spectrum of internal wave vertical displacements as a function of vertical wavenumber in the ocean has often been estimated from data derived at unequal depth intervals. The analysis has apparently been by approximate means to date and this thesis explores the importance of using fully rigorous techniques. Two methods (Brillinger, 1972, 1983) are used on real data sets after testing on simulated data with known spectral characteristics. The simulation trials permit the derivation of approximate confidence intervals for the Brillinger (1972) estimator in the situation where the sampling point process has spectral colour. The real data sets are derived from a Neil Brown CTD (conductivity, temperature, depth) probe which displays an irregular sampling process as a result of ship motion and winch speed variations. Two data sets are examined by the Brillinger methods and found to have spectra significantly different from each other and with a steeper background roll-off than the k^-2 (where k is the vertical wavenumber) power law currently accepted for such spectra. Analysis by approximate equispacing techniques (including the use of cubic spline interpolation to create equally spaced data sets) fails to resolve the true spectra, despite the apparent reasonableness of the approach. The equispacing techniques produce the same spectrum for both data sets: the k^-2 power law form. It is therefore argued that the use of fully appropriate irregular spacing techniques is important for ocean profile (and other) data sets, even if the degree of irregularity in the sampling appears small.