INSTMCOTRHD Ocean Model

• The INSTMCOTRHD Ocean Model is a deep learning-based global ocean circulation model that employs a U-shaped encoder–decoder with skip connections to capture both linear and nonlinear ocean–atmosphere interactions.
• It integrates partial convolution with masked land–sea boundaries and adversarial training via a conditional GAN to ensure realistic simulation of features such as coastal complexity and eddy activity.
• The model robustly simulates key phenomena including Kelvin and Rossby wave propagation, Ekman dynamics, and climate teleconnections, yielding improved forecast skills up to 200 days.

The INSTMCOTRHD Ocean Model is a global ocean general circulation model constructed as a deep learning system to simulate, at high spatiotemporal resolution, the three-dimensional evolution of the ocean in response to atmospheric forcing. Its distinguishing features—an encoder–decoder “U-shaped” visual attention architecture, partial convolution for masked land–sea boundaries, and adversarial training in a conditional GAN paradigm—enable robust representation of both linear and nonlinear ocean-atmosphere coupling phenomena, with demonstrated skill on processes such as Kelvin and Rossby wave propagation, upwelling/downwelling in response to wind stress, and climate-relevant teleconnections.

1. Model Architecture and Computational Elements

At its core, the INSTMCOTRHD (“KIST-Ocean”) model employs a U-shaped encoder–decoder neural network that alternates downsampling and upsampling stages, connected by skip connections for preservation of spatial detail. The backbone generator integrates Visual Attention Network (VAN) components, realized via large kernel attention (LKA) modules. Mathematically, each attention block is defined as:

• Attention = Conv₁ₓ₁ (DW-Conv(DW-DilatedConv(V)))
• Output = Attention ⊙ V

Here, DW refers to depth-wise convolution, Conv₁ₓ₁ to pointwise convolution, and ⊙ to element-wise multiplication, enabling scalable enlargement of receptive fields while containing parameter growth.

Partial convolution (PConv) is applied to all weight-sharing layers except final pointwise convolutions to explicitly mask land regions. For input feature map V and land–ocean mask M:

• PConv(V, M) = (∑₍ᵢ∈Ω₎ wᵢ vᵢ mᵢ) / (∑₍ᵢ∈Ω₎ mᵢ + ε) where Ω is the neighborhood, w is the kernel, m the mask, and ε avoids division by zero. This method ensures that spatial convolution is physically meaningful along highly convoluted or discontinuous coastlines and over complex bathymetry.

The discriminator follows a PatchGAN design, evaluating overlapping regions rather than the global field, thus constraining the generator to maintain both global structure and local realism.

Transfer learning is central: initial training occurs on synthetic data (CESM2 Large Ensemble), and fine-tuning adapts the model to observational reanalysis. This dual-stage pipeline enables skillful learning given the sparsity and nonstationarity of observational ocean data.

2. Predictive Capabilities and Ocean Dynamics

KIST-Ocean achieves robust predictive skill on a range of oceanic processes:

• Kelvin waves: Accurately simulating eastward-propagating downwelling anomalies following westerly wind bursts (WWBs) in the equatorial Pacific, which are central to El Niño events.
• Rossby waves: Correct reproduction of the meridionally and longitudinally varying phase speeds consistent with linear theory for baroclinic long-waves, as

$$C_\text{phase} \approx -\beta \frac{c_0^2}{f^2},\quad c_0 = \sqrt{g' H},\quad f=2\Omega\cos\varphi, \quad \beta = \frac{\partial f}{\partial y}$$

• Ekman vertical motions: By diagnosing vertical velocity from the continuity equation,

$$w(z) = -\int_0^z \left(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}\right) dz'$$

The model infers upwelling (cyclonic forcing, divergence) and downwelling (anticyclonic, convergence) patterns with spatial structure that agrees with theory and observation.

Simulations document the model's capability to represent multi-month evolution of sea surface temperature, currents, and subsurface anomalies, thus supporting the paper of seasonal to interannual variability.

Quantitative benchmarks include anomaly correlation coefficients (ACC), root mean square error (RMSE), and comparative performance against persistence or operational baselines. Skillful forecasts persist at lead times up to 200 days, with consistent improvement over persistence and strong relative skill compared to state-of-the-art operational systems.

3. Adversarial Training and Distributional Robustness

The learning procedure is framed as conditional adversarial training. The generator loss functional is

$L_G = -\alpha \log D(G(X)) + \beta L_1$

where $D(G(X))$ is the discriminator output for generated field $G(X)$, $L_1$ is per-pixel L1 reconstruction loss, and $(\alpha,\beta)$ control emphasis on realism versus strict fidelity to ground truth. The discriminator is trained to distinguish between real reanalysis samples and model outputs, using the cross-entropy:

$L_D = - [ \log D(Y) + \log(1 - D(G(X))) ]$

Adversarial loss regularizes long-term autoregressive prediction, reducing the risk of mode collapse and distribution drift that commonly limit unregularized generator-based forecasting. By leveraging PatchGAN’s localized discrimination, fine-scale eddy activity and sharp fronts are preserved without sacrificing large-scale coherence.

4. Handling Coastal Complexity and Transfer Learning

Instabilities near the land–ocean interface pose challenges for convolutional neural architectures. Partial convolution, as implemented here, applies binary ocean–land masks to each convolution window, ensuring that only valid (ocean) nodes contribute to updates, dynamically correcting for variable coastline geometry and bathymetric discontinuities.

Transfer learning is operationalized by pretraining on a climatologically rich, long simulation (CESM2) and transferring learned parameters to observational reanalysis. This approach reduces overfitting and ensures physically plausible generalization to different regimes, including climate nonstationarities and unexplored event classes.

This architecture contains 6.6 million parameters and can be trained and deployed efficiently on modern GPU hardware (e.g., one NVIDIA A100), with pretraining and fine-tuning requiring several tens of hours.

5. Ocean–Atmosphere Coupling Dynamics and Climate Phenomena

KIST-Ocean (INSTMCOTRHD) is formulated as the oceanic component of a coupled system, designed for experimentation with prescribed or idealized atmospheric forcing. Experiments with prescribed westerly wind bursts and spatially structured wind stress anomalies reveal:

• Propagation and reflection of baroclinic Kelvin and Rossby waves, modulated as a function of latitude and basic-state stratification.
• Realistic Ekman divergence/convergence and thermocline displacement, foundational for representing Bjerknes and other ocean–atmosphere feedbacks.
• Modulation of deep ocean heat content, critical to recharge–discharge dynamics implicated in ENSO occurrence and phase transition.

By accurately modeling these coupled processes, the system can investigate the response of the ocean to a wide range of atmospheric perturbations, supporting assessment of teleconnections, feedbacks, and the probability of extreme events (e.g., strong El Niño episodes).

6. Implications for Climate Prediction and Earth System Modeling

The demonstrated accuracy and efficiency of the INSTMCOTRHD Ocean Model in representing key ocean–atmosphere coupling mechanisms has broader implications for future climate modeling. Its:

• High computational efficiency (multiyear predictions in seconds on a single GPU).
• Transfer-learning capacity, enabling rapid adaptation to new reanalyses or coupled model data.
• Strong physical consistency in both wave dynamics and forced oceanic responses.

These attributes make it a promising candidate to serve as a building block in deep learning–based Earth system modeling, facilitating rapid ensemble forecasting, improved predictability of climate extremes, and real-time applications in operational climate monitoring. The design allows for seamless integration into fully coupled ocean–atmosphere frameworks, encouraging the replacement or augmentation of traditional ocean general circulation models with scalable data-driven analogs.

7. Mathematical Formulations and Key Operations

A summary of the fundamental mathematical operations utilized includes:

• Large Kernel Attention (LKA):

$$\text{Attention} = \text{Conv}_{1 \times 1}(\text{DW-Conv}(\text{DW-DilatedConv}(V)))$$

• Partial Convolution:

$$\text{PConv}(V, M) = \frac{\sum_{i \in \Omega} w_i v_i m_i}{\sum_{i \in \Omega} m_i + \epsilon}$$

• Adversarial and reconstruction losses:

$L_G = -\alpha \log D(G(X)) + \beta L_1$

$L_D = - [ \log D(Y) + \log(1 - D(G(X))) ]$

• Vertical velocity estimation via continuity:

$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0, \quad w(z) = -\int_0^z \left( \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} \right) dz'$$

These formulations underlie both the physical interpretability and algorithmic tractability of the INSTMCOTRHD approach, providing a rigorous computational foundation for future ocean–atmosphere modeling.

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In summary, the INSTMCOTRHD Ocean Model (KIST-Ocean) is a state-of-the-art, adversarially trained, U-shaped attention network that enables computationally efficient and physically consistent global ocean forecasting, robustly captures ocean-atmosphere interaction processes, and is structured for seamless integration into next-generation deep learning–based Earth system prediction frameworks (Kim et al., 31 Jul 2025).