Estimation of vertical velocity is a key issue for understanding ocean physics and transport of biogeochemical tracers. We examine the accuracy of estimating vertical velocity in fronts with the omega equation. The diagnostic performance of the omega equation is evaluated by using vertical velocities obtained from simulation of frontal instabilities in a primitive equation model as a reference. We use two traditional quasigeostrophic methods in which the flow is either a geostrophic flow computed from density or a nondivergent flow derived from vorticity and also test two new formulations: a quasigeostrophic method using the total flow field and the semigeostrophic omega equation. Results show that all four formulations correctly diagnose the vertical velocity pattern. However, estimates provided by the traditional quasigeostrophic formulations have systematic bias. In contrast, the two new techniques, which are practically equivalent, produce unbiased vertical velocity diagnostic at fronts. These results point out the importance of including higher order dynamics than quasigeostrophy to take into account the ageostrophic advection in the front. Since adequate filtering of ADCP data is not yet available to obtain a suitable total flow, the semigeostrophic omega equation is proposed as the most valuable tool to compute vertical velocities from high resolution density measurements.
Pinot, Jean-Michel, Joaquin Tintoré, and Dong-Ping Wang. 1996. "A study of the omega equation for diagnosing vertical motions at ocean fronts." Journal of Marine Research 54, (2). https://elischolar.library.yale.edu/journal_of_marine_research/2179