10.1016/0967-0653(96)80188-8

Several major techniques (Stommel-Schott method, Wunsch method, and Bernoulli method) that have been developed to quantitatively estimate the geostrophic velocity at the reference level, have the same order of dynamical sophistication (geostrophy, hydrostatic, and density conservation.) From a technical point of view, the Stommel-Schott method is an overdetermined system (the number of equations is much larger than the number of variables), however, the Wunsch method is an underdetermined system (the number of equations is much smaller than the number of variables). Based on the same dynamical and thermodynamical framework, a simple, well-posed system (P-vector method) is proposed in this study. Consistent with geostrophy, the system is assumed non-dissipative. The conservation of mass and potential vorticity leads to the condition that the velocity vector is perpendicular to both density (ρ) and potential vorticity (q = f∂ρ/∂z) gradients, and that the velocity can be represented as V(x, y, z) = r(x, y, z)P (x, y, z), where P = (⊇ρ x ⊇q)/|⊇ρ x ⊇q|. The unit vector, P, is computed from the density field, and the parameter r(x, y, z) is determined by the thermal-wind relation. Furthermore, an error reduction scheme is also proposed in this study.