Computation of oceanic vertical stability (Brunt-Väisäläfrequency) with an improved density equation

Vertical stability of a water column can be computed from the formula: $N^2=g^2\frac{d\rho }{dP}?\frac{1}{c^2}]$ where ρ is density, P is pressure, g is gravity, and c is sound speed.Because Ekman's density equation is not consistent with Wilson's sound speed equation, large errors are introduced by combining these two equations to calculate the vertical stability. However, this difficulty can be overcome with the Wang and Millero density equation derived consistently from Wilson's sound speed equation. In addition to its simplicity, the computation of vertical stability from the above formula using Wilson's sound speed equation and Wand and Millero's density equation can be shown to generally give the most accurate results.