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 and unusually energetic ocean-atmosphere corridor, making it a useful region for testing whether climate products that agree in conventional statistics also organize their variability in comparable ways. We compare ERA5, CESM2, and ICON-ESM-LR over their strictly common historical period, 1979-2014 (432 months), using multivariate singular spectrum analysis (M-SSA) applied to 2-m air temperature, mean sea-level pressure, and zonal surface wind stress. Each series is standardized, smoothed with a 17-month moving average, and embedded using a 24-month M-SSA window. We then estimate correlation dimension, maximum Lyapunov exponent, permutation entropy, Jensen-Shannon complexity, and the dispersion of the leading M-SSA subspace. Global correlation-dimension estimates are similar among the three products (4.43-4.72), although ICON-ESM-LR combines the highest ordinal entropy with the smallest three-dimensional subspace dispersion while showing the strongest linear agreement with ERA5 temperature. Moving-window estimates vary considerably more than the global values, and several windows produce correlation-dimension slopes exceeding the embedding dimension, indicating that they cannot be interpreted as intrinsic dimensions. The results therefore do not establish the existence of a particular strange attractor. Instead, they show that reduced-state geometrical diagnostics can reveal differences between reanalysis and climate-model variability that RMSE and correlation alone do not capture, provided that scaling range, temporal dependence, and finite-sample limitations are explicitly considered.