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Richard F. Marsden

Abstract

In cases of modest correlation, parameters calculated from a standard least squares linear regression can vary depending on the selection of dependent and independent variates. A neutral regression that addresses this problem is proposed. The eigenvector corresponding to the smallest eigenvalue of the cross-correlation matrix of the two variates is used as a set of regression coefficients. Error bars are calculated for the eigenvalues and eigenvectors by means of a perturbation expansion of the cross-correlation matrix and are then verified by Monte Carlo simulation. A procedure is suggested for extension of the technique to the multivariate case. Examples of a linear fit for low-correlation and a quadratic fit for high-correlation cases are given. Conclusions are presented regarding the strengths and weaknesses of both the least squares and the neutral regression.

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Barbara-Ann Juszko
,
Richard F. Marsden
, and
Sherman R. Waddell

Abstract

An open ocean, deep water air–sea interaction experiment was conducted in the Gulf of Alaska. Wave amplitude and slope data were measured using a WAVEC heave, pitch, and roll buoy that was let drift in the Alaska gyre. Wind stress estimates were obtained from a fast-sample anemometer using the dissipation technique and from synoptic measurements through a boundary-layer model. The fundamental correlation and predictive relationships between wind friction velocity and wave spectral properties were established. A comparison of the slope spectrum to simultaneous wind stresses allowed us to estimate the Phillips proposed universal constant β. Reintroducing this constant β into the Phillips slope spectrum and using measured slope spectral characteristics, an inferred wind stress was calculated that was shown to agree well with both the dissipation and model stresses thereby validating both Phillips theory and the boundary-layer model. Any discrepancies with the model stresses were attributed to second-order wave age effects. The roughness length z 0, nondimensionalized by the sea rms wave height, was shown to decrease with wave age in a manner consistent with Kitaigorodskii's functional form. A general expression for Cd as a function of wind speed or friction velocity and wave age was proposed and verified with independent data.

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