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

This study demonstrates that a computationally efficient deep learning algorithm, when trained with annealed learning rates and utilizing synergistic surface inputs—particularly surface velocity—can effectively disentangle internal tides from balanced motions in satellite data, though residual errors persist at small scales due to information limitations and architectural constraints.

The Gist

The Big Picture: Untangling the Ocean's "Static" from its "Music"

Imagine the ocean is a giant, noisy room. Inside this room, there are two very different types of movement happening at the same time:

1. The "Balanced Motions" (The Room's Furniture): These are slow, long-lasting currents and giant swirling eddies. They are like the heavy furniture in the room—steady, predictable, and they take up most of the space.
2. The "Internal Tides" (The Music): These are waves that travel under the surface, generated when tides flow over underwater mountains. They are like music playing in the background. They move fast, change direction, and are much harder to see.

The Problem: Scientists want to study the "music" (internal tides) because it helps mix the ocean and move energy around. But the "furniture" (currents) is so big and loud that it drowns out the music. When we look at the ocean from space using satellites, we only see the surface. It's like trying to hear a violin solo in a room where a heavy bass drum is also playing.

The New Tool: A Smart AI Detective

For a long time, scientists tried to separate these two using math tricks called "harmonic analysis." But this is like trying to separate the violin from the bass drum by only listening to the sound for a few seconds every few weeks. It doesn't work well because the "music" changes its tune (phase) as it travels through the "furniture."

This paper introduces a new solution: Deep Learning (Artificial Intelligence).

Think of the AI as a super-smart detective who has studied thousands of hours of "perfect" ocean simulations. It knows exactly what the "music" looks like when it's mixed with the "furniture." Instead of trying to filter out the noise mathematically, the AI looks at a snapshot of the ocean surface and says, "I recognize this pattern; that's the internal tide."

The Secret Ingredient: What Does the AI Need to See?

The researchers tested the AI with different "clues" (input data) to see which ones helped it solve the mystery best. They treated the ocean surface like a puzzle with three types of pieces:

1. Sea Surface Height (SSH): How high or low the water is.
   • Analogy: Looking at the ripples on a pond.
   • Result: Good, but the ripples from the "furniture" (currents) are huge, making the tiny "music" ripples hard to spot.
2. Surface Temperature (SST): How warm or cold the water is.
   • Analogy: Feeling the temperature of the air.
   • Result: The "music" barely changes the temperature, but the "furniture" does. So, this clue helps the AI understand where the "furniture" is, but it can't hear the music on its own.
3. Surface Velocity (Currents): How fast and in what direction the water is moving at the surface.
   • Analogy: Watching the wind blow leaves across the ground.
   • Result: This was the winner. The "music" (internal tides) creates very specific, fast-moving patterns in the currents that are distinct from the slow "furniture." When the AI saw the currents, it could separate the music from the furniture almost perfectly.

The Best Strategy: The paper found that if you give the AI all three clues at once (Height, Temperature, and Currents), it works even better. It's like giving the detective a map, a thermometer, and a wind gauge all at the same time.

Key Discoveries in Simple Terms

• Currents are King: If you can only pick one clue, pick the surface currents. They tell the AI the most about where the internal tides are hiding.
• Context Matters: The AI needs to see a big picture, not just a tiny zoomed-in spot. The "furniture" (currents) affects the "music" over huge distances (hundreds of kilometers). If the AI is too "myopic" (can only see a small area), it gets confused. It needs a wide-angle lens to understand how the big currents are scattering the waves.
• The "Blur" Effect: Even the best AI makes a small mistake. It gets the big waves right, but it tends to "blur" the tiniest, fastest ripples. This is partly because the "perfect" data used to train the AI isn't actually perfect (it has some noise), and partly because the AI plays it safe, smoothing out the tiny details to avoid making wild guesses.

Why This Matters

This research is a big step forward for future satellites. A new satellite (SWOT) can take wide, high-resolution pictures of the ocean surface, but it only passes over the same spot every few weeks. Traditional math can't handle that gap in time.

This paper proves that Machine Learning can fill that gap. By combining different types of measurements (especially surface currents) and using a smart AI, we can finally "hear" the internal tides clearly, even when the ocean is noisy and the data is sparse. This helps us understand how energy moves through the ocean, which is crucial for understanding our climate.

In short: The ocean is a messy mix of slow currents and fast waves. By teaching an AI to look at water height, temperature, and—most importantly—surface currents, we can finally separate the two and understand the hidden music of the deep ocean.

Technical Summary

1. Problem Statement

The separation of Balanced Motions (BMs) (e.g., eddies, geostrophic currents) from Internal Waves (IWs), specifically Internal Tides (ITs), is a fundamental challenge in ocean dynamics.

• The Challenge: BMs and ITs often overlap in space and time scales. Traditional harmonic analysis fails when applied to global satellite observations (like SWOT) because the long repeat cycles (e.g., ~21 days) result in poor temporal sampling, making it impossible to resolve the incoherent phase shifts of ITs caused by turbulent BMs.
• The Gap: While new wide-swath satellites provide high-resolution 2D spatial snapshots, extracting IT signatures from these single snapshots without temporal evolution data remains difficult. Existing deep learning approaches have primarily focused on Sea Surface Height (SSH) alone or used complex architectures (like cGANs) that are computationally expensive. There is a lack of systematic comparison regarding how different surface fields (SSH, Surface Velocity, Surface Temperature) synergize to improve this separation.

2. Methodology

The authors employ a Deep Learning (DL) approach, reformulating the extraction of IT imprints as an image-to-image translation problem.

• Data Source: The study utilizes outputs from a well-established 3D Boussinesq simulation (Ponte & Klein, 2015; Dunphy et al., 2017). The simulation features a mode-1 IT propagating through a turbulent zonal jet (representing BMs) with varying levels of turbulence (T1–T5).
  • Training/Testing: The model is trained on turbulence levels T1–T4 and tested on the most complex case, T5 (high turbulence, strong incoherence), to test generalization.
  • Reference Labels: "Ground truth" IT fields ($h_{cos}, h_{sin}$) are derived via harmonic fitting over a short 1-day window (finely sampled in the simulation), representing the locally coherent component.
• Algorithm:
  • Architecture: A U-Net (convolutional encoder-decoder with skip connections) is used. The authors demonstrate that a U-Net, when trained with a periodically annealed learning rate, achieves performance comparable to the more complex Conditional Generative Adversarial Network (cGAN) used in previous work (W22), but with significantly lower computational cost.
  • Inputs: The study systematically tests all combinations of three surface fields:
    1. SSH ($H$): Total sea surface height.
    2. Surface Velocity ($U$): Zonal and meridional velocities.
    3. Surface Temperature ($T$): Sea Surface Temperature (SST).
  • Outputs: The two components of the IT imprint on SSH ($h_{cos}, h_{sin}$).
• Experimental Design:
  • Configurations: Tested inputs include $\{H\}$, $\{U\}$, $\{T\}$, $\{H, T\}$, $\{H, U\}$, $\{U, T\}$, and $\{H, U, T\}$.
  • Degradation Tests: Experiments were conducted with spatially smoothed inputs (simulating coarser satellite resolution) and temporally misaligned inputs (simulating non-simultaneous measurements).
  • Non-locality Test: A "shallow" U-Net with reduced receptive fields was compared against the main U-Net to quantify the importance of mesoscale context.

3. Key Contributions

1. Algorithmic Efficiency: Demonstrated that a standard U-Net with learning rate annealing can match the skill of complex cGANs for IT extraction, making the approach more accessible and computationally efficient.
2. Synergy of Surface Fields: Provided the first systematic benchmark quantifying the relative value of SSH, Surface Velocity, and SST for IT extraction.
3. Physical Interpretation Framework: Introduced a conceptual framework distinguishing "Wave Signature" (direct kinematic imprint of the wave) from "Scattering Medium" (information about the background BMs that modulate the wave).
4. Receptive Field Analysis: Quantified the necessity of non-local information (mesoscale context) for successful extraction, showing that local-only networks fail to capture the scattering physics.

4. Key Results

A. Performance Hierarchy of Inputs

The study establishes a clear hierarchy of input utility (measured by correlation $\Upsilon$ and $R^2$ in the challenging mid-jet region):

1. Surface Velocity ($U$) is the most critical input. Configuration $\{U\}$ alone outperforms $\{H\}$ and $\{T\}$ significantly.
   • Reasoning: $U$ contains strong wave signatures (via linear polarization relations) and rich scattering medium information (BM velocities). It offers a cleaner conceptual pathway to separate waves (divergent component) from BMs (rotational component).
2. SSH ($H$) is moderately effective. It contains the target signal but is dominated by the much larger BM signal (entangled), making separation difficult.
3. Surface Temperature ($T$) is weak alone but highly synergistic. $T$ has almost no direct IT wave signature but provides excellent information on the scattering medium (BM structure).
4. Optimal Combination: The full set $\{H, U, T\}$ yields the best performance ($R^2 \approx 0.95$, $\Upsilon \approx 0.97$). $T$ helps disambiguate the BM imprints in $H$ and $U$.

B. Error Analysis and Spectral Behavior

• Residual Errors: The remaining errors (approx. 5% variance) concentrate at small spatial scales (near and below mode-2 IT wavelengths).
• Sources of Error:
  1. Reference Contamination: The "ground truth" derived from Eulerian frequency filtering may include spurious small-scale signals due to Doppler shifting by BMs.
  2. Deterministic Limitation: The U-Net produces a single point estimate. When the input allows for a broad distribution of plausible outputs (high uncertainty), the network defaults to a "conservative" smoothed prediction, damping small-scale features.
  3. Input Constraints: Small-scale ITs may be weakly constrained by instantaneous snapshots.

C. Robustness to Degradation

• Spatial Smoothing: Smoothing $U$ to coarse resolutions (e.g., 124 km) degrades small-scale performance but preserves performance at dominant IT scales. This suggests $U$ provides valuable large-scale contextual information even when fine details are lost.
• Temporal Misalignment: Inputs shifted by 48 hours (4 IT periods) still outperform SSH-only, provided the time gap is fixed during training. This highlights the persistence of BM-related contextual information.

D. Importance of Non-locality

• Networks with large receptive fields (spanning ~800 km, comparable to the jet width) perform significantly better than shallow, local-only networks.
• This confirms that extracting ITs requires understanding the mesoscale scattering environment, not just local wave patterns.

5. Significance and Implications

• Future Satellite Missions: The results strongly advocate for the development and deployment of satellite missions capable of measuring surface vector velocities (e.g., SEASTAR, HARMONY, ODYSEA). Surface velocity is identified as the single most informative observable for disentangling waves from balanced motions.
• Multi-Platform Synergy: The study supports coordinated observational campaigns that combine SSH (SWOT), SST, and surface currents (HF radar, drifters, or future satellites) to maximize IT extraction accuracy.
• Methodological Shift: The work suggests that future benchmarks for wave-BM separation should move beyond domain-averaged scalar metrics (like mean $R^2$) and include spectral diagnostics to assess scale-dependent performance, particularly at small scales.
• Path Forward: The authors suggest that future work should move toward probabilistic formulations (predicting distributions rather than single points) to better handle uncertainty and small-scale features, and to utilize Lagrangian filtering to create cleaner reference datasets free from Doppler-shift contamination.

In summary, this paper demonstrates that deep learning, when fed with the right combination of surface fields (particularly surface velocity) and designed with sufficient non-local context, can effectively disentangle incoherent internal tides from balanced motions, offering a promising pathway to interpret next-generation satellite ocean data.