Diagnosis of vertical velocities with the QG omega equation: an examination of the errors due to sampling strategy

Vertical motion at the mesoscale plays a key role in ocean circulation, ocean-atmosphere interaction, and hence climate. It is not yet possible to make direct Eulerian measurements of vertical velocities less than 1000 m day^?1. However, by assuming quasi-geostrophic (QG) balance, vertical velocities O (10 m day^?1) can be diagnosed from the geostrophic velocity field and suitable boundary conditions. Significant errors in the accuracy of this diagnosis arise from the necessary compromise between spatial resolution and synopticity of a hydrographic survey. This problem has been addressed by sampling the output of a numerical ocean model to simulate typical oceanographic surveys of mesoscale fronts. The balance between the number of observations and the synopticity of observations affects the apparent flow and in particular the diagnosed vertical motion. A combination of effects can typically lead to errors of 85% in the estimation of net vertical heat flux. An analytical two-layer model is used to understand components of this error and indicate the key parameters for the design of mesoscale sampling.