A comparison of Francesco’s and Francois’ routines to compute FSLE

The following figures show the onward-in-time finite-size Lyapunov exponents (FSLE) computed from the surface geostrophic flow using T/P Sea Surface Height (SSH) for Aug. 25, 2004. The initial distance is 0.03° and the final one is 0.6° . The upper panel is from Paulo using Francesco’s routine, the three other panels are from Francois’ routines. In the second panel starting from top, the method uses the maximum separations between a parcel on a grid and its neighbors to the north, east, west and east; in the third panel, the method uses the distances with the neighbors to the northeast, southeast, southwest and northwest of the parcel; in the bottom panel, the method uses the deformation of a circle into an ellipse.

Figure 1: Stable manifold of the T/P SSH surface geostrophic flow for Aug. 25, 2004 with initial distance of 0.03° and final distance of 0.6° calculated from various methods.

As you can see, the comparison is good overall, most of the time even to the smallest scales. However, there are regions where Francesco’s and Francois’ routines differ, quite a lot: for instances, near 161°W and 24°N, near 159°W and 20°N, the eddy around 158°W and 17°N, etc. Francesco’s routines seem to produce a much better-looking picture, while Francois’ routines seem to produce a fuzzy one. The three panels obtained with Francois’ routines, suggest, however, that the differences do not come from the details of the choice of the neighbors or of the method to compute the Lyapunov exponents. Differences may still arise from 1) the trajectories and 2) the way the distances between neighbors are computed –in Francois’ routines, distances are computed along great circles; what about in Francesco’s routines? I would put my money on the trajectories at this point.