Computing the Seawater Expansion Coefficients Directly from the 1980 Equation of State

Abstract

The polynomial structure of the 1980 equation of state for seawater lends itself to analytic differentiation with respect to pressure, temperature, and salinity. This enables one to compute the compressibility, thermal expansion, and haline contraction coefficients, respectively, without introducing any finite difference approximations whatsoever. Extensive use of Honer's rule (nested multiplications versus exponentiations) and careful bookkeeping of intermediate quantities from the computation of density allow the derivatives to be computed with about the same numerical effort as required to evaluate density itself twice. Thus, the algorithms presented yield all three expansion coefficients as efficiently, in terms of floating point operations, as a first difference estimate of a single coefficient. Since the expansion coefficients are computed by direct differentiation of the equation of state, they do not suffer from computational errors associated with taking first difference. However, the equation of state itself has less-squares fitting errors on the order of 10−3 kg m−3. It is estimated that this uncertainty in density yields an uncertainty in the expansion coefficients on the order of 1 percent.