The inverse method developed by Wunsch (1978) is widely used to determine circulation in the oceans (Fu , 1980; Wunsch , Hu and Grant, 1983 ; Joyce and Wunsch , 1986; Rintoul, 1988). However, for inversion manipulation, measurements down to the bottom are required, and so is a certain solid boundary. In the present paper an equation of potential condition satisfied by the velocity field at the reference level is added to Wunsch’s underdetermined matrix equation in order to make the method adequate for the case where measurements do not touch bottom and when a solid boundary does not exist. The western boundary current in the Pacific is calculated and examined in terms of the velocity field and transport with CTD data gathered by the R/V Science I in October 1988 .
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