Analysis of tidal flows through the Strait of Gibraltar using Dynamic Mode Decomposition

TL;DR

This study applies Dynamic Mode Decomposition (DMD) to 3D MITgcm simulations of tidal flows in the Strait of Gibraltar to extract interpretable Koopman modes representing waves, jets, and gyres. It introduces practical enhancements—augmenting observables with horizontal speed, TLSQ subspace corrections, column normalization, and leave-one-out robustness checks—to produce stable, physically meaningful modes. The analysis identifies persistent modes tied to the Western Alboran Gyre, semidiurnal and diurnal tidal dynamics, jet meanders, Kelvin- and coastal-trapped waves, and higher harmonics, and demonstrates low-rank ROMs that retain bulk dynamics while reducing dimensionality. Overall, the work demonstrates DMD as a valuable, data-driven tool for diagnosing and predicting complex oceanographic dynamics in topographically constrained regions.

Abstract

The Strait of Gibraltar is a region characterized by intricate oceanic sub-mesoscale features, influenced by topography, tidal forces, instabilities, and nonlinear hydraulic processes, all governed by the nonlinear equations of fluid motion. In this study, we aim to uncover the underlying physics of these phenomena within 3D MIT general circulation model simulations, including waves, eddies, and gyres. To achieve this, we employ Dynamic Mode Decomposition (DMD) to break down simulation snapshots into Koopman modes, with distinct exponential growth/decay rates and oscillation frequencies. Our objectives encompass evaluating DMD's efficacy in capturing known features, unveiling new elements, ranking modes, and exploring order reduction. We also introduce modifications to enhance DMD's robustness, numerical accuracy, and robustness of eigenvalues. DMD analysis yields a comprehensive understanding of flow patterns, internal wave formation, and the dynamics of the Strait of Gibraltar, its meandering behaviors, and the formation of a secondary gyre, notably the Western Alboran Gyre, as well as the propagation of Kelvin and coastal-trapped waves along the African coast. In doing so, it significantly advances our comprehension of intricate oceanographic phenomena and underscores the immense utility of DMD as an analytical tool for such complex datasets, suggesting that DMD could serve as a valuable addition to the toolkit of oceanographers.

Figures (20)

• Figure 1: a) Time average surface velocity. Colors indicate the flow speed ($S_{\overline{U}}$); arrows indicate the flow direction. b) Time average along-strait velocity in a vertical cross section following the Strait’s axis (red line in panel a). The location of the Camarinal Sill (CS) is labeled in both panels.
• Figure 2: Snapshots of along-strait velocity (colors) and salinity (contours) during a tidal cycle (a-f). Arrows in each panel indicate the strength and direction of the barotropic flux. The time series of barotropic flux is shown in the bottom panel (g), with dots corresponding to the frames a-f.
• Figure 3: Snapshot of vertical velocity at 100 m depth. The two wave patterns in the Alboran Sea correspond to two internal bores generated during consecutive semi-diurnal tidal cycles. A third trailing wave front in the strait narrows corresponds to a nascent internal bore progressing eastward. Inset: cross section of vertical velocity and salinity (contours), showing the vertical structure of the bore at 5.5ºW.
• Figure 4: Time-depth plot of zonal velocity anomaly (anomaly with respect to the time mean) at 5.4º W, 36.0º N (eastern side of the Strait of Gibraltar).
• Figure 5: Singular values of the data matrix do not show significant separations of scale beyond the initial modes. The vertical line indicates the truncation value employed in our analysis.