Dynamical Characterization of the Loop Current Attractor

Abstract

The Gulf of Mexico circulation is modulated by a mesoscale current, the Loop Current (LC), and large anticyclonic eddies that detach from it. The LC dynamics are recurrent, and its evolution is in and from a few preferential states. This observation points to the existence of a low‐dimensional dynamical attractor. Building upon advancements in dynamical system theory, this work characterizes the average and instantaneous dimensions of such an attractor. The instantaneous dimension and its evolution in time are compared among an altimeter‐based data set, an ocean reanalysis and an operational hindcast. The LC complexity, measured by its dimension, differs among them, especially when the dimension is high. During shedding events, differences between datasets emerge in the second principal component. The information provided by this analysis is relevant to operational ocean forecasts and points to where improvement should occur.

The Role of Freshwater Forcing on Surface Predictability in the Gulf of Mexico

“…In CROCO the large Rings tends to detach from the LC earlier than observed and move toward the west, while the LC remains in its extended configuration for longer in the HYCOM analysis. We note that the length of periods spent by the LC in an extended configuration in fall 2014 into spring 2015 was underestimated by all forecasts as well (National Academies of Sciences, Engineering and Medicine, 2018) and may be an intrinsic bias of ocean‐only models (Liu, Falasca, & Bracco, 2021; Sheremet et al., 2021). CROCO simulations capture also the observed standard deviation (STD) patterns of the surface fields (Figure 5 and S4 in Supporting Information ).…”

“…This points to the relevance of the external forcing-The atmospheric one and the flow at southern boundary which contains information about the Yucatan Strait forcing (see e.g., Ezer et al, 2003)-On the LC. Large differences between CROCO runs and HYCOM are usually associated with the detachment of the large Rings from LC, and the Ring propagation, which is more chaotic than the LC evolution as quantified by the number of degrees of freedom needed on average to represent them (Liu, Falasca, & Bracco, 2021).…”

Systematic Bias Correction in Ocean Mesoscale Forecasting Using Machine Learning

“…(2019) is based on a modeling system which has a systematic bias, as noted by Liu et al. (2021). Here we propose a ML approach that circumvents both issues and builds upon dynamical system theory.…”

“…In Liu et al. (2021) we adopted a dynamical system approach to describe the mesoscale motions in the Gulf of Mexico in the sea surface height (SSH) field and explored the local dimension of the low‐dimensional attractor (Lorenz, 1980), following previous works (Falasca & Bracco, 2022; Faranda et al., 2017; Lucarini et al., 2016). We compared this metric in the GCOOS (Gulf of Mexico Coastal Ocean Observing System) altimeter derived SSHa data and in the HYCOM analysis over 16 years, finding that most of the time less than 10 degrees of freedom are sufficient to describe the average dimension of the LC attractor.…”

“…This is shown in Figure 2, where the two-dimensional projection of the (higher dimensional) attractor is plotted over the period considered in this work. The discrepancy among the attractors, which could be due in part to the temporal processing and spatial interpolation of the satellite data, was quantified in terms of local dimension in Liu et al (2021) and points also to the common knowledge that forecast/hindcast models and ocean circulation models in general are systematically biased and tend to overestimate the rate at which LCEs form in the Gulf of Mexico (NASEM, 2018). In other words, the LC is more stable to eddy detachments than shown by HYCOM and more generally by ocean-only models.…”