A PROPOSED DEFINITION FOR VECTOR CORRELATION IN GEOPHYSICS - THEORY AND APPLICATION

A universally accepted definition for vector correlation in oceanograp hy and meteorology does not presently exist. To address this need, a g eneralized correlation coefficient, originally proposed by Hooper and later expanded upon by Jupp and Mardia, is explored. A short history o f previous definitions is presented. Then the definition originally pr oposed by Hooper is presented together with supporting theory and asso ciated properties. The most significant properties of this vector corr elation coefficient are that it is a generalization of the square of t he simple one-dimensional correlation coefficient, and when the vector s are independent. its asymptotic distribution is known; hence, it can be used for hypothesis testing. Because the asymptotic results hold o nly for large samples, and in practical situations only small samples are often available, modified sampling distributions are derived using simulation techniques for samples as small as eight. It is symmetric with respect to its arguments and has a simple interpretation in terms of canonical correlation. It is invariant under transformations of th e coordinate axes, including rotations and changes of scale. Finally, to assist in interpreting this vector correlation coefficient, several cases that lead to perfect correlation and zero correlation are exami ned, and the technique is applied to surface marine winds at two locat ions in the northwest Atlantic.