Assessment of Traditional and New Eigenfunction Bases Applied to Extrapolation of Surface Geostrophic Current Time Series to Below the Surface in an Idealized Primitive Equation Simulation

Abstract

Abstract Three strategies were compared for extrapolating surface geostrophic velocities to below the surface: S1, using only the barotropic or first baroclinic mode; S2, using a fixed or “phase locked” linear combination of the first baroclinic mode and the barotropic mode; and S3, a strategy similar to S2 but using a new set of basis functions. For S2 and S3, the phase locking allows one to impose zero velocity at the seafloor. The new basis functions start from zero at the surface, are not degenerate with respect to the free-surface boundary condition, and represent the adjustment of the pressure at a given depth from density surfaces responding to sea surface height undulations. In idealized primitive equation simulations, strategy S3 had the least error and allowed extrapolation to deeper levels, suggesting the new basis functions performed significantly better than the traditional baroclinic modes. In contrast, strategies S1 and S2 made poor predictions by 400-m depth. Large temporal fluctuations in the fraction of energy in the barotropic and first baroclinic modes could explain the poor predictions by strategies S1 and S2. This brings into question the interpretation of the sea surface height gradients measured by satellite altimetry in terms of first baroclinic mode motions.