# 10.19.10: Understanding the decomposition into surface and interior modes - Part 2¶

I show here pictures that are similar to those sent to me by G. Lapeyre in a recent email. As in the previous note, 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. In the pictures below, only wavelengths less than 400 km are used. The only difference is that I have corrected the way the amplitude of the surface mode is computed.

Fig. 1 shows the various components of the potential density anomaly and the streamfunction at a specific location in the domain. This figure needs to be compared to Fig. 4 of this note. We can see that the cancellation between the surface and interior components is much less systematic due to a better calibration of the surface mode.

Figure 1: Total, surface and interior components of (a) the potential density and (b) the streamfunction at one location in the domain. In (b) is also given the initial streamfunction before it is being modified by the Rudnick’s method (Lapeyre 2009).

Fig. 2 shows the root-mean-squared (RMS) of each component of the potential density anomaly and the streamfunction. The RMS is multiplied by the sign of the correlation between the component and the “true” quantity. The profiles are similar to those sent by G. Lapeyre except: 1) the interior component of the potential density anomaly is at every level correlated positively with the total component and 2) the surface component of the potential density anomaly is larger than the surface value of the total solution. I do not think exception #1 is a problem. Exception #2 is the reason why the surface component at 12 m in Fig. 3 (upper middle panel) has a larger amplitude than the “true” surface value (upper left panel). I do not know if exception #2 should be a worry or not.

Fig. 2 should be compared to Fig. 5 of this note. As for Fig. 1, the cancellation between the surface and interior component is much less systematic.

Fig. 4 shows the correlation. The profiles are similar to the ones sent by G. Lapeyre.

Figure 2: Root-mean-squared (RMS) of the various components of (a) the potential density anomaly and (b) the streamfunction. The RMS is multiplied at every level by the sign of the spatial correlation between that component and the “true” one.

Figure 3: Total (left), surface (middle) and interior (right) components of the potential density at 13 m (upper), 241 m (middle) and 460 m (lower).

Figure 4: Spatial correlations between the various components of (a) the potential density anomaly and the “true” one and between (b) the various components of the streamfunction and the “true” one.

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