An approximate geostrophic streamfunction for use in density surfaces

An approximate expression is derived for the geostrophic streamfunction in approximately neutral surfaces, φn, namelyφn=12Δpδ˜˜-112TbΘρΔΘΔp2-∫0pδ˜˜dp′.This expression involves the specific volume anomaly δ˜˜ defined with respect to a reference point (S∼∼A,Θ∼∼,p˜˜) on the surface, Δp   and ΔΘ are the differences in pressure and Conservative Temperature with respect to p˜˜ and Θ∼∼, respectively, and TbΘ is the thermobaric coefficient. This geostrophic streamfunction is shown to be more accurate than previously available choices of geostrophic streamfunction such as the Montgomery streamfunction. Also, by writing expressions for the horizontal differences on a regular horizontal grid of a localized form of the above geostrophic streamfunction, an over-determined set of equations is developed and solved to numerically obtain a very accurate geostrophic streamfunction on an approximately neutral surface; the remaining error in this streamfunction is caused only by neutral helicity.