Local Analysis of Ocean Wave Measurements
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This master thesis investigates the Short Time Fourier transform and the Continuous Wavelet transform in relation to a directional analysis of in situ ocean wave measurements. We have determined the statistical properties of the transform coefficients when applied to a weakly stationary Gaussian process, and we have tested the analyzing methods on both simulated and real ocean wave measurements. It is shown how the Wavelet Directional Method (WDM) can be extended to triplet measurements, and how the built-in averaging procedure in this method leaves it inadequate in situations where the directional distribution is multimodal. The Local Triplet Analysis (LTA) is more robust than the WDM, though the directional spread estimate is severely biased. However, this bias can be corrected by sacrificing the advantage of having a time-frequency representation of the spread. Our findings show that the local methods performs equally good as the traditional methods when the assumptions posed by the latter are met. In addition, the local methods give answers where the traditional methods do not work, e.g. in non-stationary situations, thus giving us information about the true structure of the ocean measurements previously unattainable.