Spatio-temporal analysis

Monthly mean correlations for the combined stream function were computed for all boxes with the objective of identing the areas best suited for the reconstruction of ocean dynamics us-ing SST. Results shown Figure 5.6 clearly reveals that the reconstruction is better in regions near the major extratropical current systems such as the Gulf Stream, the Kuroshio, and the Antarctic Circumpolar Current (ACC), where intense mesoscale activity can be observed. On the other hand, lower correlations (ranging between 0.2 and 0.4) are obtained at low latitudes (15^◦N − S). Although, in some cases, they can increase up to 0.6 in winter months, January to March in the northern hemisphere, and June to August in the Southern hemisphere. However, some dierences are found depending on the area. For instance, in the Northern hemisphere, the Kuroshio region presents consistently lower correlations than does the Gulf Stream region, even in boreal winter season when the combined reconstruction is enhanced. This example can be juxtaposed with an area in the southern hemisphere, in the ACC region, where the combined stream function retrieval seems perform reasonably well throughout the entire year with slightly higher correlation in austral winter months.This seasonal variability is conrmed by the estima-tion of the Lomb periodogram. Most of the boxes presented the maximum peak of the Lomb Periodogram in the range of 300 to 400 days (Figure 5.4), with a few exceptions in which the peak is present within this period but it is not the maximum peak.

The average correlation for winter months, from January to March in the northern hemi-sphere and from June to August in the Southern hemihemi-sphere, was computed for the stream function, both components of the velocity eld and vorticity (ζ = ∇²ψ). Only signicant corre-lations were taking into account when averaging. In most of the boxes the number of correcorre-lations averaged range between 130 and 271, with the exception of 7 boxes in which less than 100 cor-relations were averaged (white contour in gure 5.7). We focused on the winter season since it is the period of the year for which reconstruction is best , as shown in gure 5.6. Results show that all parameters present similar geographical patterns (gure 5.7). Furthermore, they also show that higher correlations correspond to the stream function, while the lowest correspond to the vorticity. Indeed, the capability of reconstructing vorticity is moderate. The highest mean correlation for vorticity is 0.79 and corresponds to the box selected in section 5.3 located in the ACC. For the box located in the GS region, this correlation is 0.67. For most of the boxes located in the southern hemisphere (111 of the 176 boxes), higher mean correlations are obtained for the zonal component of the velocity, when compared with the meridional component; whereas in the southern hemisphere, half of the boxes have higher mean correlations for the zonal component of velocity (49 of the 97 boxes).

In order to evaluate if the combined method reproduces the temporal variability of the currents retrieved by the altimeters, we computed the Eddie Kinetic Energy (EKE), dened as

E_EKE= 1

2[σ_u²+ σ²_v], (5.4)

where σu² and σ²v are the temporal variance of the the zonal and meridional components of the velocity eld, respectively. We then computed the spatial correlation between the EKE

5.5. Spatio-temporal analysis

Figure 5.6: Global monthly mean correlation between stream functions retrieved by SSH measurements and Combined method. Wide line delimits selected boxes in Figure 5.2.

Figure 5.7: Winter mean correlations between the combined method and al-timetry. From left to right and from top to bottom: stream function (ψ), vorticity (ζ), zonal velocity (u) and meridional velocity (v). For Northern hemisphere January, February and March were considered. For Southern hemisphere: June, July and August. Wide black line delimits selected boxes in Figure 5.2. Wide white line delimits boxes that have less than 100 signicant correlations.

for the ow reconstructed from SST (equation 5.3) and the EKE for the ow reconstructed from SSH (Figure 5.8). Results show that in high energetic regions, the correlations between combined EKE and altimetry EKE exceed 0.95 (Figure 5.8). Moreover, it can be observed that EKE correlations have similar geographical patterns to the correlations shown in Figures 5.6 and 5.7. In general, high EKE correlations boxes also have high stream function correlations and correspond to high energetic regions. This is not the case, however, for three of the boxes located in Kuroshio region, which have high EKE (0.10 m²/s²), and high combined winter correlations (between 0.71 and 0.75) but low EKE correlations (between 0.2 and 0.34). Nevertheless, for most of the boxes, the combined method reproduces the temporal variability of the currents retrieved from altimetric measurements quite well, even in the tropics, where correlations higher than 0.5 are obtained for most of the boxes.

To get insight on the link between EKE and the performance of the reconstruction from SST observations, we compared mean correlations for the combined stream function with the EKE (gure 5.9). Here again, results reveal that the combined method reproduces the temporal variability of the currents retrieved from altimetric measurements very well, even for those boxes that performance poorly (e.g. boxes with correlations lower than 0.5 (gure 5.7) have EKE correlations higher than 0.6 (gure 5.8)).

5.5. Spatio-temporal analysis

Figure 5.8: Eddy Kinetic Energy. From right to left: Eddy Kinetic Energy from October 2002 to May 2005. Correlations between Eddy Kinetic Energy of reconstructed velocities from altimetry measurements and from Combined method spanning from October 2002 to May 2005. Wide line delimits selected boxes in Figure 5.2.

Figure 5.9: Scatter plot of the mean correlation for the combined stream func-tion and the Eddy Kinetic Energy. Blue points correspond to boxes located in low latitudes (between ±20^◦), red points correspond for boxes located at higher latitudes. Black is used to represent the two selected boxes in the local study: triangle (4) for ACC box, and square () for the GS box.

Figure 5.10: Enviromental conditions. From top to bottom: standard deviation of the thermal gradient, mean wind and RMS of the MLD. All elds were estimated for the period under study with the exception of the MLD, which was estimated from a climatology.