ON COMPUTING THE HORIZONTAL PRESSURE-GRADIENT FORCE IN SIGMA-COORDINATES

Corby et al. present a finite-difference expression for the horizontal pressure gradient force in sigma coordinates that, in a barotropic at mosphere where the temperature varies linearly with logarithm of press ure, has the same net truncation error as the centered finite-differen ce approximation for the isobaric geopotential gradient. The requireme nt that the temperature vary linearly with logarithm of pressure is im posed on analyzed isobaric heights and temperatures using a variationa l procedure. This reduces the errors in geostrophic winds computed usi ng sigma coordinates. Initial surface pressures and temperatures are c alculated in a mesoscale model, assuming the temperature varies linear ly with logarithm of pressure and linearly with height. The first meth od (linear variation with logarithm of pressure) results in smaller er rors in computed initial surface geostrophic winds. The structure of a sigma coordinate model is described in which temperature varies linea rly with logarithms of pressure. Analytical expressions are derived fo r the truncation error in the case of temperature varying linearly wit h height. It is concluded that if a linear variation of temperature wi th logarithm of pressure is imposed and Corby et al.'s finite differen ce is employed, then truncation error in the horizontal pressure gradi ent force will be reduced.