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10.14.10: Understanding the decomposition into surface and interior modes

I look here at several aspects of the decomposition into surface and normal modes. The region chosen is the Gulf Stream from 63°W to 53°W and from 30°N to 40°N. 18 vertical modes are used. The depth range used is from 10 m to 5400 m. The surface mode amplitude (γ in Lapeyre 2009) is calculated for the upper 400 m. The Rudnick correction is applied. I have not found (yet) no radical qualitative change in the results shown below by varying these parameters, individually or in concert.

The ratio of the mean buoyancy to the local Coriolis parameter is less than 80 as in the model used by Lapeyre (2009; his Fig. 1a). The vertical profiles of the surface mode for the same three horizontal wavelengths as in Fig. 1b of Lapeyre (2009)’s paper are plotted in Fig. 2. The modes obtained here seem similar to those obtained by Lapyere (2009).

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Figure 1: Ratio of the buoyancy frequency to the local Coriolis parameter.

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Figure 2: Vertical profile of the surface mode E(K,z) for three horizontal wavelengths.

I, then, plot the vertical profiles of the potential density and streamfunction at one location in the domain. The total, surface and interior component for the 30-km zonal wavelength are shown in Fig. 2. In this case, the pattern appears reasonable: the surface mode (red) does not have any influence at depth –as expected given the small horizontal wavelength– and cancels the interior mode (blue) near the surface as described by Lapeyre and Klein (2006).

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Figure 3: total, surface and interior components of (a) the potential density and (b) the streamfunction. In (b) is also given the initial streamfunction before it is being modified by the Rudnick’s method (Lapeyre 2009).

Fig. 4 shows the same quantities than in Fig. 3 except for horizontal wavelengths between 20 and 400 km. Again, the profiles appear consistent with what has described in previous studies. Notice, in particular, the consistent cancellation between the surface and interior mode in both the potential density and the streamfunction. The horizontal pattern for each component at three different depths are given in Fig. 5 for the potential density and Fig. 6 for the streamfunction. An inconsistency with plots sent to me by Guillaume is that the surface component of the potential density field first increases with depth before decreasing (Figs. 4a and 5).

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Figure 4: As Fig. 3 but for horizontal wavelengths between 20 and 400 km.

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Figure 5: Total (left), surface (middle) and interior (right) components of the potential density at 13 m (upper), 241 m (middle) and 460 m (lower) when considering horizontal wavelengths between 20 and 400 km.

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Figure 6: Same as Fig. 5 except for the streamfunction. The total component is the component modified after applying Rudnick’s method.

Figs. 7 to 9 are the same as Figs. 4 to 6 except that all horizontal wavelengths are included. Notice how the cancellation between the surface and interior mode becomes the dominant characteristic (Fig. 7).

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Figure 7: As Fig. 3 but for all horizontal wavelengths.

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Figure 8: Same as Fig. 5 except all horizontal wavelengths are considered.

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Figure 9: Same as Fig. 6 except all horizontal wavelengths are considered.


Computed with main_script_1.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/Decomp_Surface_Normal_Modes/analysis/OFES_qscat_0_1_global_3day.