Table Of Contents

This Page

FSLE and upwelling events along float trajectory

NOTA: Here, I was not using the correct SSH product.

The backward-in-time finite-size Lyapunov exponents (FSLE), representing the unstable manifolds, have been computed from the geostrophic flow deduced from T/P sea surface height anomaly and along the float trajectory of Johnson et al. (2009). The FSLE have been computed over a 3° range in longitude and latitude centered on the float position (Fig. 1). The timing of upwelling events observed by the float are shown with vertical dashed white lines. The FSLE within 0.03° in latitude and longitude from the float position are shown in Fig. 2.

../../../../../../_images/fsle_back_range_float.png

Figure 1: Unstable manifold over a range of longitudes (left) and latitudes (right) centered on the float trajectory. The timing of float cycles are shown by the ticks at the top of each panel and the timing of upwelling events are shown by the vertical dashed white lines. The last upwelling event shown is the one from 02/09/2009. The FSLE were computed from the geostrophic flow deduced from T/P sea surface height anomaly, with initial distance of 0.03° and final distance of 0.6° , after interpolating the flow every 3 days.

../../../../../../_images/fsle_back_float.png

Figure 2: As in Fig. 1, except the FSLE are averaged within 0.09° in (a) longitude and (b) latitude from the float position. The timing of float cycles are shown by the ticks at the top of each panel and the timing of upwelling events are shown by the vertical dashed blue lines. The last upwelling event shown is the one from 02/09/2009.

Of the 14 events that we could use, 10 are associated not only with relatively high FSLE values but also with the peak of FSLE in time. Unfortunately, the strongest upweeling event (last one, 414 days after 12/23/2007) is one of the event that does not appear to be associated with high FSLE values. Meanwhile, about a third (5-10) of high FSLE events could not be associated with upwelling events.

Fig. 3 shows the field of FSLE on 04/25/2008 (120 days after 12/23/2007) and on 09/02/2009 (414 days after 12/23/2007). The left panel shows (a) that the area can be very crowded with unstable manifold and (b) the float position on 09/02/2009 is within 0.15° from a strong FSLE events. Questions: (1) What is the chance that the upwelling events randomly corresponds to a peak in FSLE? and (2) what is the maximal distance that an upwelling event could be triggered by an unstable manifold? To answer question (1), I propose a Monte-Carlo calculation, where we would compute the percentage of upwelling events that can be associated to a peak in FSLE within a couple of days by pure chance.

../../../../../../_images/fsle_back_around_float_04252009_02092009.png

Figure 3: FSLE on 04/25/2008 (120 days after 12/23/2007) and on 09/02/2009 (414 days after 12/23/2007). The dashed lines show the float position at these two dates. The FSLE have been computed as described in the caption of Fig. 1.


For Figs. 1 and 2, the matlab file is unstable_manifold_along_float_traj.mat computed from compute_unstable_manifold_along_float_traj.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/FSLE/analysis/Johnson_etal_09.

For Fig. 3, the matlab file is unstable_manifold_cycles_around_float_traj computed from fsle_hr_back_cycles_around_float_traj.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/FSLE/analysis/Johnson_etal_09.