Disentangling Internal Tides from Balanced Motions with Deep Learning and Surface Field Synergy

TL;DR

The study tackles the problem of separating balanced motions from internal waves in ocean surface data by recasting IT extraction as image-to-image translation. It demonstrates that a simpler U-Net, when paired with a learning-rate annealing schedule, can match the performance of a prior cGAN while enabling broader exploration of input-field configurations. The results show a clear hierarchy: surface velocity $oldsymbol{U}$ provides the strongest IT signal, while sea-surface height $H$ and surface temperature $T$ contribute complementary wave-signature and scattering-medium information, yielding the best results when used together (H, $oldsymbol{U}$, T) with $R_2 o 0.95$ and $ -0.97$ correlation to the reference fields. These findings motivate multi-platform observational campaigns and underscore the value of direct surface-current measurements for accurate BM–IT disentanglement, with practical implications for SWOT-like missions and data-driven ocean state estimation.

Abstract

A fundamental challenge in ocean dynamics is the disentanglement of balanced motions and internal waves. Extracting internal tidal (IT) imprints on surface data is a central part of this challenge. For IT extraction, traditional harmonic analysis fails in the presence of strong incoherence and poor temporal sampling, as is common in global satellite observations. The advent of new wide-swath satellites, which provide two-dimensional spatial coverage, allows IT extraction to be reformulated as an image translation problem. Building on recent work where we developed a deep learning approach to extract IT signatures from sea surface height (SSH) in an idealized turbulent simulation, we show here that a simpler and computationally cheaper algorithm can perform equally well if the learning rate is annealed during training. Using this new, convenient algorithm, we experiment with different combinations of input surface fields -- SSH, surface temperature, and surface velocity. All fields contribute synergistically to disentanglement, with surface velocity by far the most informative. These findings underscore the value of coordinated multi-platform observational campaigns and highlight the critical importance of surface velocity observations for separating balanced motions and internal waves. Additional insights into the behavior of deep learning algorithm emerge: both wave signature and scattering medium aids IT extraction, and to exploit large-scale information in the scattering medium, the algorithm must be highly non-local. Residual errors of our algorithm concentrate at small spatial scales near mode-2 tidal wavelengths, likely arising from artifacts introduced during data preparation (e.g., Doppler shifts) as well as imperfections in the deep learning architecture.

Figures (10)

• Figure 1: Snapshot of raw SSH $H$ (panel (a)), IT signal $h^{\text{sim}}_{\cos}$ (panel (b)), and surface temperature $T$ (panel (c)) from the T5 simulation at day 200. Dashed boxes mark the up-jet, mid-jet, and down-jet regions define for analysis. The Sponge region and the central latitude of the wave-maker are marked in panel (b).
• Figure 2: Schematic of the U-Net architecture employed in this work. The network takes combinations of surface fields in ($H$, $\boldsymbol{U}$, $T$) as input and predicts two output channels corresponding to the IT imprints on SSH, $h^{\text{sim}}_{\cos}$ and $h^{\text{sim}}_{\sin}$. Labels below each block denote (a) the number of feature maps, i.e., channels (e.g., $16, 16$) and (b) the dimension along one direction of each feature map (e.g., $I, I/2$). Example input and output snapshots are taken from the same snapshot as in Fig. \ref{['fig:Bouss_setup']}. Plotting code is adapted from haris_iqbal_2018_2526396.
• Figure 3: Surface zonal and meridional velocities $(U,V)$ (panels (a,b)), derived surface vorticity $\zeta$, and divergence $D$ (panels (c,d)), taken at the same snapshot as in Figure \ref{['fig:Bouss_setup']}. The fields $\zeta$ and $D$ are computed by finite differencing the velocity field, and are non-dimensionalized by the Coriolis frequency evaluated at the central latitude of the domain (45 $^{\circ}$ N).
• Figure 4: Summary of relative performances across input configurations. Each circle corresponds to one input field in $(H,\boldsymbol{U},T)$; overlaps denote configurations that combine input fields. Numbers within circles show mean correlation ($100 \Upsilon$) averaged over the mid-jet region.
• Figure 5: Comparison of reference IT signal $h^{\text{sim}}_{\cos}$ (panel (a)) with U-Net reconstructions $h^{\text{gen}}_{\cos}$ from different input configurations (panels (b-h)). Numbers below each panel in (b-h) report $\Upsilon$ and $R_2$ computed between the respective panels and panel (a). Only the mid-jet region is plotted, taken at the same snapshot as in Figure \ref{['fig:Bouss_setup']}.