cLCS differ from typical Lagrangian Coherent Structures (LCS) in that the Cauchy-Green tensor is averaged over different initial times, and that the time-dependant velocity is a climatological velocity. Regarding the climatological averaging, it is shown in the first section of the results in \citet{Duran_2018}, that the Eulerian climatological velocity preserves the main Lagrangian circulation in an ensemble-mean sense, where ensemble averaging of the instantaneous trajectories is over different initial times. However, the averaging of the Cauchy-Green tensor formally destroys the transport-barrier property of LCS \citep{Haller_2015}. Thus, the interpretation of cLCS requires careful comparison with additional Eulerian and Lagrangian information, as for example described in \citet{Gouveia_2021} where it is shown that cLCS may deform as chevrons. When cLCS deform as chevrons, they do not represent transport barriers, but instead, they identify a jet-like structure, as is the case in this paper where cLCS identify a coastal jet-like current. However, depending on the local circulation, cLCS may also indicate persistent and efficient transport barriers (\citealt{Duran_2018}, \citealt{Gough_2019}) or recurrent attractive pathways (\citealt{Duran_2018}, \citealt{Maslo_2020}). The different interpretations for cLCS follow the fact that cLCS can be thought of as a superposition of 7-day LCS from the climatological velocity, with the integration initiating at different times (see e.g. Appendix C of \citealt{Duran_2018}). In the Supporting Information (Appendix A) of \citet{Duran_2018}, it is shown that the deformation due to along-path horizontal divergence is negligible and therefore the patterns identified by cLCS are due to large-scale two-dimensional flow (see also supporting information in \citealt{Gouveia_2021}).
Results
In-situ and remote observations:
The Yucatan shelf is a shallow environment defined by a very smooth slope, 1 m/3000 m off Campeche and 1m/1000m off Yucatan, where the mobility of the vessels is limited by draft restrictions. In this work, the sampling stations of the surveys fell on depths ranging between 2 to 20-m depth, capturing the thermohaline variations of the first ~30 Km of the coast. Figure \ref{554331} depicts the T/S diagram of the campaign, where two water types were found: (1) Caribbean Tropical Surface Water (CTSW), also called Yucatan Seawater (off Yucatan state, \citealp{Enriquez_2013}) or Gulf Common Water (off the GoM west coast, \citealp{Vidal_1994}), and (2) Caribbean Subtropical Under Water (CSUW). The former occupied most of the study region, presenting a modification of the CTSW having saltier values than the reported for the region (\citealt*{mclellan1967}, \citealp{Vidal_1994}, \citealp{Merino_1997}, \citealp{Aldeco_Ram_rez_2009}, \citealp{Enriquez_2013}). Waters located in the first 5 m showed very warm temperatures (29.6\(\pm\)1 °C) with large salinity and density ranges, influenced mainly by evaporation processes between the lower atmosphere and the surface ocean, and to a lesser extent by nearshore freshwater inputs from the Champoton river, coastal lagoons, and submarine groundwater discharges located near the coast, particularly in the northern part of the study area between Lerma and Isla Arena (20-21°N, 91°W).
On the other hand, water temperatures below 26 °C were seen between 7 to 16-m depth, located on the farthest sampling stations to the shore. At these depths, saltier Caribbean Subtropical Under Water-type signature was found. This water is commonly found in the Yucatan Channel at 250-m depth, and its presence over the Yucatan shelf is attributed to upwelling processes between the Yucatan current and bottom friction on the northeastern side of the Yucatan Peninsula (\citealp{Merino_1997}, \citealt{Jouanno_2018}), approximately 600 Km to the east from the study region. This result illustrated a two-layer distribution of coastal waters on the deepest parts of the study region, represented by the CTSW above the CSUW, with local processes (evaporation/freshwater inputs) modifying their characteristics. It was found that evaporation processes greatly exceeded precipitation (or freshwater inputs) as both water types showed saltier values, even though the survey was carried in July which is at the middle of the rainy season defined from May to November.