David E. Dietrich

A numerically effective calculation of sea water density

Abstract Accurate density calculation that includes pressure effects is achieved with negligible computational cost in the context of three-dimensional ocean modelling. Local linear (or quadratic) fits to the full UNESCO ( Anon, 1981 ) equation of state can be used in many model applications where the potential temperature and salinity at a model grid point vary slightly in each model time step. The local polynomial fit is achieved by computing a Taylor series expansion about a local reference state. The terms in the Taylor series are calculated analytically for optimal accuracy and minimal computational cost. All calculations can be done with single precision arithmetic, without compromising accuracy. In a three-dimensional nonhydrostatic ocean model applied to a deep convection problem, the local density calculation reduced the total computational cost of the model by 7% relative to that when the full UNESCO density calculation was used. The computational advantage is 15% for an application in which the nonhydrostatic part of the calculation is turned off. The computational advantage is, however, a function of the nature of both the model being used and the problem being solved. The principal algorithms are coded in Fortran 90, fortran 77, and as Matlab functions. The complete set of routines and test programs is coded in Fortran 90.