Empirical Orthogonal Function Analysis

Dippner, J. W., Pohl, C., 2004. Trends in heavy metal concentrations in the western and central Baltic Sea waters, detected by using empirical orthogonal functions analysis (EOF s). Journal of Marine Systems, 46, 69-83. 

Gebhart, K. A., Lattimer, D. A., and Sisler, J. F. (1990) Empirical orthogonal function analysis of the particulate sulfate concentrations measured during WHITEX, in Visibility and Fine Particles, C. V. Mathai, ed., AWMATR-17, Air Waste Management Association, Pittsburgh, PA, pp. 860-871. 

Finnigan and Shaw [188] conducted an Empirical Orthogonal Function (EOF) analysis of an extensive wind tunnel data set obtained in a model wheat canopy. The same authors have recently performed an equivalent analysis based upon the output from the large-eddy simulation described above. 

Principal Components Analysis (PCA) is a multivariable statistical technique that can extract the strong correlations of a data set through a set of empirical orthogonal functions. Its historic origins may be traced back to the works of Beltrami in Italy (1873) and Jordan in Prance (1874) who independently formulated the singular value decomposition (SVD) of a square matrix. However, the first practical application of PCA may be attributed to Pearson s work in biology [226] following which it became a standard multivariate statistical technique [3, 121, 126, 128]. 

Standing of source-receptor relationships for nonreactive species in an airshed. The.se methods include the chemical mass balance (CMB) used for. source apportionment, the principal component analysis (PCA) used for source identification, and the empirical orthogonal function (EOF) method used for identification of the location and strengths of emission sources. A detailed review of all the variations of these basic methods is outside the scope of this book. For more information the reader is referred to treatments by Watson (1984), Henry et al. (1984), Cooper and Watson (1980), Watson et al. (1981), Macias and Hopke <1981), Dattner and Hopke (1982), Pace (1986), Watson et al. (1989), Gordon (1980, 1988), Stevens and Pace (1984), Hopke (1985, 1991), and Javitz et al. (1988). 

Population analysis in semiempirical methods fall into two categories. Methods including overlap in the Fock equations use the Mulliken population analysis. The majority of semiempirical methods uses the ZDO approximation, and the net charges are interpreted on the basis of symmetrically orthog-onalized AOs. It is pointed out that this interpretation is not exactly valid, because of truncation and empirical adjustment. But the corresponding nonsymmetrical orthogonalization is not uniquely defined. Charge models based on semiempirical wave functions play an important role in the calculation of molecular electrostatic potentials for reactivity. 

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