The Gulf of Mexico (GoM) is of primary societal and economic importance for the countries that surround it. The ocean circulation and dynamics in the GoM are characterized by an intense mesoscale activity that is mostly associated with the Loop Current (LC) and the eddies that separate from it.Some studies have highlighted the variability of this current system that is driven by the atmospheric variability (i.e. the forced part). Other studies focus on the intrinsic part of the variability, which spontaneously emerges from ocean flows and that has a chaotic behavior. The contributions of atmospheric and oceanic sources of the ocean variability in the GoM are not well known, although this question is central for understanding and forecasting the ocean flows in that region. Our objective is to study the interplay between the ocean intrinsic variability and the atmospheric forcing in the GoM, using a regional 20-year, 1/4° 50-member ensemble ocean simulation.We show that at most time scales, the simulated variability approximately matches altimeter observations in magnitude and spatial distribution. Our analyses also suggest that observed time series of Sea Level Anomaly (SLA) are not long enough presently to yield a robust description of the dynamics of the LC, in particular the timing of eddy sheddings. The daily SLA variability is then analyzed probabilistically from ensemble PDFs, and entropy-based metrics that we introduce. We identify regions (Gulf Stream, LC, central GoM, Caribbean Sea) where the subannual SLA variability is mostly intrinsic, with a persistently small sensitivity to the atmospheric forcing. This conclusion holds at annual and interannual periods as well in the first 3 regions listed above.The constraint exerted by the atmosphere on the intrinsic variability fluctuates more in other regions: hurricane and winter storms drive sharp entropy drops along their paths, in particular near the coasts along which subsequent storm surges propagate; interannual forcing anomalies can also exert large constraints on the ensemble members, yielding large-scale entropy anomalies that slowly propagate westward across the Caribbean Sea.The multi-scale oceanic variability in the whole region is thus the complex result of intrinsic/chaotic ocean dynamics modulated by the atmosphere, and can be fruitfully studied using ensemble modelling strategies.