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Notes on Klein et al. (2009, GRL)


In Klein et al. (2009), the authors demonstrate that by using high-resolution sea surface height (SSH) and the climatological stratification, they could recover the 3D submesoscale (20-400-km) and low-frequency (non-inertial) velocity field, including the vertical velocity, from below the mixed layer (ML) down to about 500 m. The method used is that of the Surface Quasi-Geostrophy (SQG) theory described by Lapeyre and Klein (2006).

Although SQG has been developped for low Rossby number and weak wind-driven motions (see Isern-Fontanet et al. (2008) for an application in low Rossby number to a realistic simulation of the North Atlantic), the paper shows that SQG could potentially be used in the case of large Rossby number and strong wind-driven motions. To demonstrate this, they use a high-resolution (2-km) numerical simulation that has 100 levels in the vertical over a domain of 1000 by 2000 km in the horizontal extending down to 4000 m in the vertical. The model is a beta-plane centered at 45N.


  • Why do they suggest that large Rossby number implies low-frequency motion? I understand you expect nonlinear interactions but with a spread of energy toward all, not necessarily only low, frequencies.
  • Why do they suggest a complex scenario, involving the advection, to explain that SSH does not capture inertial motions? Pure inertial motions involve horizontal motions only so that there should be no signal in w.


Isern-Fontanet et al. (2008): Three-dimensional reconstruction of oceanic mesoscale currents from surface information, J. Geophys. Res., 113, doi:10.1029/2007JC004692.

Klein et al. (2009): Diagnosis of vertical velocities in the upper ocean from high resolution sea surface height, Geophys. Res. Lett., 36, doi:10.1029/2009GL038359.

Lapeyre and Klein (2006): Dynamics of the upper ocean layers in terms of surface quasigeostrophy theory, J. Phys. Ocean., 36, 165–176.