# Partition between barotropic and baroclinic modes inferred from altimetric surface velocities and Argo float mid-depth displacements (2012)

**C. Cabanes, T. Huck, A. Colin de Verdière and M.Ollitrault (1)**

*** Corresponding author : ****Cécile Cabanes**

(1) : Laboratoire de Physique des Océans (UMR CNRS IFREMER IRD UBO), Brest France

At large scale, the large part of the oceanic eddy kinetic energy (EKE) is dominated by the barotropic and first baroclinic modes. Many studies suggest that a strong correlation exists at middle and high latitudes between mid-depth velocity anomalies and surface geostrophic velocity anomalies. Moreover, coherent vertical structures of the velocity field are also reported in mesoscale eddies (see Swart et al, 2008 for the Southern Ocean). The question is thus to identify the nature of such correlation, by checking if this correlation is consistent with a vertical structure mainly described by the bartropic mode and the first baroclinic mode.

In this study, the energy partition between the barotropic and first baroclinic mode is investigated for the period 1997-2007, through the correlation analysis between the mid-depth velocity anomalies at 1000 meters estimated from Argo floats, and the geostrophic velocity anomalies estimated from altimetry. Results show that in region of high eddy kinetic energy, the correlation is due to large eddies with wavelength 300-400 km. In areas of lower eddy kinetic energy, the correlation is largely due to smaller structures with 200-300 km wavelength and period longer than 8 months. The first baroclinic mode dominates in the subtropics while the barotropic mode is more important poleward, becoming dominant south of 40°S.

**Data and Method**

From the Yomaha’07 dataset (Lebedev et al., 2007), Argo data from floats with parking depths at 1000 m and 1500 m, cycling between August 1997 and May 2007, are used to evaluate a mid-depth velocity anomalies field. Only data with no flag denoting a time inversion or duplication in the sequences of fixes for surface positioning, and no vertical shear error exceeding the mid-depth velocity values, were kept. The mean flow at 1000m is estimated (**figure 1a**) by computing the mid-depth 1997-2007 mean for each component u and v, through an averaging of all the data within 500 km of the position of a velocity estimate, taking into account the anisotropy of velocities (Haung et al., 2007). The eddy kinetic energy (EKE) is also calculated at 1000m from the Argo floats mean displacements (**figure 1b**), confirming that large EKE at 1000m depth are associated with major currents.

*Figure 1. (left) : mean zonal velocity (cm/s) at 1000m ; (right) : EKE (in cm**2**.s**-2**) at 1000m.*

Surface fields are then constructed from altimetry-derived sea surface height (SSH) distributed by AVISO on the 1/3° Mercator grid from two satellites (Topex/Poseidon or Jason-1 and ERS1,2 or ENVISAT). The surface velocity anomalies were computed relative to the 1997-2007 mean, and were interpolated at positions and times of the mid-depth velocity estimates for the comparison.

The two velocity anomalies fields at the surface and at parking depth (85% at 1000m, 15% at 1500m) are compared in order to investigate in which range of wavelengths or periods they correlate the best. A correlation coefficient between the surface and the mid-depth velocity anomalies is computed at each observation location from all the points at the same depth within 500 km distance.

**Results**

The correlation map (figure 2), deduced from the surface and the 1000 m depth meridional velocity anomalies, exhibits high values at high and middle latitudes, and low values at latitudes below 15-20°. Taking all the meridional (zonal) velocity observations poleward of 20°, the global correlation coefficient is 0.56 (0.54). At 1500m, velocity anomalies are still well correlated (0.55 and 0.54 for meridional and zonal components respectively). Three areas are identified where the correlation between the surface and 1000m depth velocities is high : the North West Atlantic (NWA), The NorthWest Pacific (NWP) and the SouthEast Pacific (SEP).

*Figure 2. Correlation coefficient between the surface and the 1000m depth meridional velocity anomalies. *

In these areas, a spatial (temporal) filter is applied to the altimetry-derived velocity anomalies before the recalculation of its correlation with the mid-depth velocity anomalies field. It is found that in regions of high kinetic energy (NWP and NWA), the correlation is mainly due to large eddies with 300-400 km wavelength. In regions of lower eddy kinetic energy (SEP for example), the correlation is rather due to smaller structures with 200-300 km wavelength and period longer than 8 months.

In order to quantify the energy partition between the barotropic and first baroclinic modes, the fraction of u and v components in the first baroclinic mode versus the barotropic one are determined for the surface velocity anomalies. This was done in three steps :

- first, the variation of the velocity with depth is estimated by the computation of the linear regression coeﬃcients between the surface and the mid-depth velocity anomalies at 1000m,
- then, the structure of the first baroclinic mode magnitude at 1000 m is compared to the one at the surface from the WOA05 climatology (Locarnini et al., 2006)
- The comparison of those two ratios seems to show an apparent linear relation, with a global correlation of 0.6. The vertical velocity structure is thus checked from them at each latitude for the surface velocity anomalies values.

First results show that the partition obtained, valid for the part of the surface variability correlated to the one at mid-depth, is latitude dependent : the first baroclinic mode dominates equatorward of 30°, while equipartition is observed poleward of 40°N. The barotropic mode becomes more important poleward of 40°S. This partition supports the notion of a more efficient energy cascade to barotropy in high energy regions with broad thermoclines. Finally, we can expect that the increase of Argo dataset and further corrections on mid-depth velocities estimates will improve the determination of the partition between the barotropic and the first baroclinic modes.

**References**

- Cabanes, C., T. Huck, A. C. de Verdière, and M. Ollitrault : Partition between barotropic and first baroclinic mode from Altimetric Velocities and Argo Float Mid-depth, internal report 2008
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