Ocean Engng, Vol. 19, No 6, pp. 511-526, 1992. 0029-8018/92 $5.00 + .00 Printed in Great Britain. Pergamon Press Ltd THE EIGENVALUE PROBLEM AS A FORM OF MINIMUM LEAST-SQUARED APPROXIMATION R. TATAVARTI* and Y. ANDRADEJ" Department of Oceanography, Dalhousie University, Halifax, B3H 4J1 Canada Abstract--Two important tools used in the interpretation of ocean engineering data are the Minimum Least-Squared approximation technique (MLS) and the spectral analysis technique. Often, the inherent assumptions in these analytical techniques are overlooked by users which may, at times, bias the picture of the physics that remains to be understood. The present study focuses on a modified version of the MLS technique and the Empirical Orthogonal Function (EOF) analysis which have many advantages compared to the more commonly used techniques. It is shown that the eigen-decomposition technique of EOF analysis and a variation of the Minimum Least-Squared Approximation, known as the MLS2 technique, are the same, as has been documented in the literature. Unlike the MLS approximation, the MLS2 approximation or the EOF analysis does not depend on which variable is called "independent" or which "dependent", as both the variables are treated symmetrically. Field data collected during the C2S z program from Pointe-Sapin beach, New Brunswick, Canada, were used in a simple example to demonstrate the advantages of employing complex EOF analysis. INTRODUCTION THE INCREASING number of satellite observations and the development of more and more sophisticated data acquisition systems are forcing ocean scientists and engineers to develop and apply methods of analysis which can extract maximum information from the observed data without jeopardizing the accuracy. In recent years ocean engineers are extensively using the least-squares approximation and spectral analysis techniques as analytical tools to describe data from the oceanic environment and discuss the relationships between different oceanic parameters. The method most commonly used when seeking a linear model between two variables is the standard Minimum Least-Squared approximation (MLS), also known as linear regression. This method has an underlying assumption that the variable chosen as independent is assumed to be noiseless. This assumption is frequently overlooked by users. While, in spectral analysis, the time series of one parameter is designated as a base series and the coherence and phase computed between this series and those of other parameters. The underlying assumption that the base series is free of noise obviously produces a bias in favour of the base series. If the coherence between various parameters and the base series is not large the bias can result in considerable distortion in the pattern of amplitudes of the parameters. Moreover, this does not exploit the information contained in the cross-spectra between parameters other than the base * Present address: Naval Physical and Oceanographic Laboratory, Thrikkakara, Kochi 682 021, India. t Present address: Instituto de Fomento Pesquero (IFOP), Oceanography Department, Blanco 1067, Valpa- raiso, Chile. 511