Geometrical Assessment of Climate Models in the Drake Passage Using Multivariate Singular Spectrum Analysis

Alec Oshua Sahagún Rodríguez, Fabrice Lambert

The Drake Passage is a narrow oceanic bottleneck that also acts as a geographic constriction. Here, both2
the Antarctic Circumpolar Current and the Southern Westerly Winds are forced through a topographic gap3
between the Andes and the Antarctic Peninsula, reducing the system’s effective degrees of freedom. This4
study applies Multivariate Singular Spectrum Analysis (M-SSA) to three surface variables, temperature,5
sea-level pressure, and zonal wind stress, from ERA5 reanalysis and two CMIP6 models, CESM2 and6
ICON-ESM-LR, over 540 months. To isolate the underlying dynamics from the dominant seasonal7
forcing, a 17-month uniform moving average filter is applied prior to phase-space reconstruction. The8
phase-space attractor is reconstructed and topological invariants are computed: correlation dimension9
D2, maximal Lyapunov exponent λ, permutation entropy H, statistical complexity C, and attractor10
volume V . The ERA5 reanalysis shows a moderately low-dimensional attractor (D2 = 3.91). CESM211
(D2 = 3.72) and ICON-ESM-LR (D2 = 3.70) appear globally stable, but block-wise temporal analysis12
reveals severe structural anomalies. Topological invariants can detect numerical instabilities in climate13
models that linear statistics miss.