Diagnosing Lateral Mixing in the Upper Ocean with Virtual Tracers: Spatial and Temporal Resolution Dependence

Abstract

Several recent studies diagnose lateral stirring and mixing in the upper ocean using altimetry-derived velocity fields to advect “virtual” particles and fields offline. However, the limited spatiotemporal resolution of altimetric maps leads to errors in the inferred diagnostics, because unresolved scales are necessarily imperfectly modeled. The authors examine a range of tracer diagnostics in two models of baroclinic turbulence: the standard Phillips model, in which dispersion is controlled by large-scale eddies, and the Eady model, where dispersion is determined by local scales of motion. These models serve as a useful best- and worst-case comparison and a valuable test of the resolution sensitivity of tracer diagnostics. The effect of unresolved scales is studied by advecting tracers using model velocity fields subsampled in space and time and comparing the derived tracer diagnostics with their “true” value obtained from the fully resolved flow. The authors find that eddy diffusivity and absolute dispersion, which are governed by large-scale dynamics, are insensitive to spatial sampling error in either flow. Measures that depend strongly on small scales, such as relative dispersion and finite-time Lyapunov exponents, are highly sensitive to spatial sampling in the Eady model. Temporal sampling error is found to have a more complicated behavior because of the onset of particle overshoot leading to scrambling of Lagrangian diagnostics. This leads to a potential restriction on the utility of raw altimetry maps for studying mixing in the upper ocean. The authors conclude that offline diagnostics of mixing in ocean flows with an energized submesoscale should be viewed with some caution.