I believe the code to calculate the Gulf Stream separation and North Atlantic latitude has two errors:
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It assumes that the horizontal grid is a geographical grid (i.e., lon and lat are 1D), while it is a curvilinear grid - see https://github.com/JMMP-Group/MARINE_VAL/blob/main/SCRIPT/cal_GS_sep_NAC_lat.py#L28 -> I don't think this is creating a massive error (especially for the GS), although strictly speaking is not correct.
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is using deptht (see https://github.com/JMMP-Group/MARINE_VAL/blob/main/SCRIPT/cal_GS_sep_NAC_lat.py#L17), which is fine for standard z-levels with partial steps but is not correct with generalised vertical coordinates (e.g., MEs).