FuXi-Ocean: A Global Ocean Forecasting System with Sub-Daily Resolution

Dear Reviewer sFCf,

Thank you for your comments and suggestions on our work. We appreciate your recognition of the novel contributions of our work and are grateful for the opportunity to address your concerns.

The effectiveness of the MoT module.

A: We appreciate your interest in understanding the effectiveness of the Mixture-of-Time (MoT) module in ocean sub-daily forecasting models. To evaluate its performance, we replace the MoT module with temporal attention mechanisms, which force the model to consider the influence of all historical temporal features for each variable. We test on HYCOM 2015 reanalysis data, and average the results across the depth dimension for each variable. While we cannot provide intuitive line graphs to illustrate the comparison, we present the normalized RMSE to highlight the impact of the MoT module on forecasting accuracy.

The normalized RMSE is calculated as:

$\frac{RMSE - RMSE_{FuXi-Ocean}}{RMSE_{FuXi-Ocean}} *100\%$

The results are shown in the table below:

It is evident from the table that while the model was provided with all temporal features, more feature information does not always lead to better performance, particularly in the case of ocean sub-daily forecasting tasks. The performance of the model significantly deteriorates at 24-hour forecasts, suggesting that the inclusion of more temporal features interferes with the learning of diurnal cycle characteristics. This is an important observation that highlights the challenge of balancing the complexity of temporal information in sub-daily ocean forecasting models.

The U and V components of ocean currents.

A: As we mentioned in our paper, while the MoT module has shown significant improvements for variables with diurnal cycles (e.g., temperature and salinity), its application to ocean currents presents a different set of challenges due to the slower timescales of these variables. We acknowledge that U and V currents are more complex and may require additional design considerations. However, the model’s limitations in this regard do not detract from the broader impact of our work.

Our objective was not to fully solve the challenge of predicting ocean currents but to introduce the first global ocean forecasting model with sub-daily resolution. This was the primary aim of our paper. The improvements we’ve achieved for surface variables with diurnal cycles demonstrate that FuXi-Ocean paves the way for future advancements in this field. We believe that specialized techniques for ocean currents can be developed as a natural extension of our work, and we plan to explore this in future research.

Dear Reviewer 7qdU,

Thank you for your insightful review and constructive feedback. We appreciate your recognition of our work's strong motivation and clear experimental setup. Your expertise in ocean dynamics is evident from your thoughtful questions about atmospheric forcing and temporal memory. We have conducted additional experiments and analyses to address all your concerns comprehensively.

Q1. Compare with baseline.

A: We have added persistence baseline comparisons as requested. Following WenHai's approach, we present results on observational data for sea surface variables to avoid introducing HYCOM data biases. The baseline uses HYCOM initial fields to calculate persistence RMSE.

Units: S0 (PSU), T0 (°C), U0/V0 (m/s) The results clearly demonstrate that FuXi-Ocean consistently outperforms persistence for all variables, with the advantage increasing over time.

Q2. Atmospheric forcings.

A: We strongly agree that atmospheric forcing is crucial for ocean forecasting. To quantify this, we conducted experiments incorporating five atmospheric variables from ERA5 (10-m zonal/meridional winds, mean sea level pressure, 2-m temperature, and 2-m dewpoint temperature) using an additional encoder network for atmosphere-ocean fusion.

The table shows relative RMSE improvement when adding atmospheric forcing: $\frac{\text{RMSE}_{with\_atm} - \text{RMSE}_{FuXi-Ocean}}{\text{RMSE}_{FuXi-Ocean}} \times 100\%$ (negative values indicate improvement):

Units: S (PSU), T (°C), U/V (m/s), SEL (m) Specifically, we conducted comprehensive testing on the 2015 HYCOM reanalysis data and average the results across the depth dimension. As expected, atmospheric forcing improves all variables, particularly temperature at longer lead times. However, our key contribution is demonstrating that effective sub-daily forecasting is achievable using ocean variables alone, with performance exceeding daily numerical models. This approach:

1. Reduces data dependencies and computational overhead
2. Leverages the ocean's inherent predictability from its large heat capacity and momentum
3. Provides a strong baseline that can be enhanced with atmospheric coupling

This represents a different paradigm from traditional ocean forecasting—utilizing the ocean's internal dynamics rather than treating it as purely atmospherically driven. Our upcoming work will present a fully coupled ocean-atmosphere system building on this foundation, but the current results establish the surprising effectiveness of ocean-only deep learning approaches for short-term forecasting.

Q3. The maximum temporal history of the model.

A: Thank you for pointing out the ambiguity in our terminology. We will revise "temporal windows" to "historical time points" for clarity.

Regarding the temporal extent accessible to FuXi-Ocean: While the architecture could theoretically accommodate longer histories, our design choices are guided by the specific requirements of sub-daily ocean forecasting:

1. Physical considerations: The 6-hour interval with 4 historical time points (24 hours total) captures the complete diurnal cycle—the dominant mode of variability for sub-daily forecasting.

2. Practical constraints: Extending the temporal history significantly increases:

   • Memory requirements (linear with time points)
   • Computational cost during training and inference
   • Data loading overhead in operational settings

3. Task-specific design: FuXi-Ocean targets medium-range (1-10 day) forecasting where 24-hour history provides optimal information content. For seasonal/subseasonal prediction, different architectural choices would be appropriate, as you correctly note.

We acknowledge that processes like deep ocean memory spanning decades exist, but these operate on timescales beyond our forecast horizon and would require fundamentally different modeling approaches.

Q4. Sensitivity of K in the MoT module.

A: We conducted extensive experiments with K = 2, 3, 4, and also tested a soft aggregation approach. The table below shows the relative RMSE change compared to K=1, calculated as $\frac{\text{RMSE} - \text{RMSE}_{K=1}}{\text{RMSE}_{K=1}} \times 100\%$. For each variable, we averaged the results across the depth dimension. The "attn" group performs soft aggregation on the four temporal features using attention mechanisms.

Units: S (PSU), T (°C), U/V (m/s), SEL (m)

Our experiments reveal that K=1 consistently yields optimal performance. The degradation at 24-hour lead time is particularly revealing—it coincides with the diurnal cycle period, supporting our hypothesis that single-context selection prevents interference between incompatible temporal signals. The attention-based soft aggregation, despite its theoretical appeal, underperforms because it forces the model to reconcile conflicting temporal patterns. Ocean currents show somewhat different behavior, suggesting variable-specific temporal dependencies, though K=1 remains optimal overall.

Q5. Fairness of Figure 4.

A: In Fig 4, the initial fields (0 days) of all methods are analysis data, with no reanalysis data included. All methods at subsequent lead times are forecast results rather than analysis or reanalysis results, ensuring fairness of comparison.

Permutation Feature Importance and Sensitivity Analysis.

To address the reviewer's question about whether the model has learned the correct sensitivities to each input variable, we performed a Permutation Feature Importance (PFI) analysis. In this approach, we perturb each input variable independently by replacing it with randomly selected values from other time steps, and then calculate the RMSE after each perturbation. The RMSE is then normalized to show the relative impact of each perturbation compared to the original, unperturbed predictions. This method helps assess how well the model relies on the most important variables and whether it has overfitted to spurious correlations. The results are presented in a 5×5 matrix, where each row corresponds to a perturbed variable, and each column shows the degraded performance defined as relative change in RMSE. The relative RMSE, $\text{relative RMSE} = \frac{RMSE_{\text{perturbed}} - RMSE_{\text{original}}}{RMSE_{\text{original}}} \times 100\%$ reflects how sensitive the model's predictions are to changes in each variable.

Leadtime=120h

When perturbing temperature and salinity separately, these two variables are more sensitive to each other relative to other variables. Ocean current components (U and V) exhibit minimal cross-sensitivity to each other, consistent with their orthogonal relationship as zonal and meridional velocity components. This low interdependence validates that the model has correctly learned the independent nature of these directional flow components. However, due to time constraints, we only randomly sampled half a month's worth of samples for averaging, requiring further analysis in subsequent work.

Other non-technical issues.

A: We acknowledge your suggestions for improving clarity:

1. We will refine our terminology regarding ocean depth ranges and temporal scales to avoid ambiguity
2. Figure 2 will be updated with clear unit labels for all variables
3. The discussion of IV-TT data quality issues will be incorporated concisely into the main text

Dear Reviewer 8ZnV,

Thank you for your thoughtful review and constructive feedback. We appreciate the opportunity to clarify several aspects of our work and provide additional context to address your concerns. Below, we have provided a more detailed and structured response.

Q1. The "First" Claim - Important Clarification.

A: We acknowledge the concern regarding the claim that FuXi-Ocean is the "first" data-driven 1/12° resolution global ocean forecasting model, especially in light of the XiHe model. To clarify, FuXi-Ocean is indeed the first to achieve sub-daily (6-hourly) predictions at 1/12° spatial resolution across a depth range of 0-1500m, making it a unique contribution to the field. While XiHe also operates at 1/12° resolution, it focuses on daily forecasting, which poses fundamentally different challenges. To better emphasize these differences, we have updated the comparison table to highlight additional technical specifications:

Technical Challenges of Sub-Daily Prediction:

• Diurnal Cycle Modeling: Predicting ocean variables at sub-daily intervals requires capturing rapid changes in surface temperature, salinity, and currents driven by daily atmospheric and oceanic processes. Sub-daily prediction models must handle diurnal cycles and inertial oscillations, which are not as significant in daily models. FuXi-Ocean incorporates this by modeling diurnal dynamics with higher temporal resolution.

• Higher Frequency Ocean Dynamics: At 6-hour intervals, the model can track faster oceanic processes, such as mesoscale eddies and surface current fluctuations, which are not resolvable in daily predictions. This leads to more accurate short-term forecasts for applications such as maritime operations and coastal hazard monitoring.

Note that ocean variable forecasting tasks are significantly different from video generation. The time interval gap from daily to sub-daily is substantial, and many variables such as temperature have significant diurnal cycle characteristics. Direct migration of daily models by simply increasing parameter size would cause serious prediction errors, and this is a discovery made for the first time.

Q2. Compare with other models.

A: We appreciate the reviewer’s interest in comparing our model with others in the field. While we acknowledge that comparing sub-daily resolution models with daily resolution models is not entirely fair—due to the inherent difficulty of sub-daily forecasting—we have nevertheless conducted a direct comparison. Specifically, we calculated the RMSE using observed ground truth from the IVTT dataset for Sea Surface Temperature (SST) in 2022 and compared the results with those from WenHai, a state-of-the-art daily model. SST is a critical ocean variable and is typically the most accurately measured in the IVTT dataset, which is why we focused our comparison primarily on SST (issues with other variables are discussed in the supplementary materials).

The unit is ℃, the lower is the better.

To more intuitively demonstrate the slope of interest, we further convert the table results into daily error increments, shown as follows:

The unit is ℃, the lower is the better.

It is important to highlight that daily models, such as WenHai, forecast daily mean values, whereas sub-daily models like FuXi-Ocean predict instantaneous values at specific time steps. For a fair comparison, we averaged the sub-daily predictions within a day, which inevitably introduces some loss of accuracy and potential error. Despite this, the table shows that FuXi-Ocean demonstrates either similar or even lower error growth slopes compared to WenHai. A common challenge in autoregressive models is that the error tends to grow with each iteration. FuXi-Ocean, with its 40 autoregressive iterations over a 10-day forecast period, naturally experiences more error accumulation compared to daily models like WenHai, which only require 10 iterations. Nevertheless, the results indicate that FuXi-Ocean remains competitive and even superior in terms of error growth, especially over shorter forecast periods.

Dear Reviewer,

Thank you for your valuable feedback. The authors have addressed your comments in their rebuttal. We kindly ask that you engage in discussion with the authors before submitting your Mandatory Acknowledgement.

If your concerns have been adequately addressed in the rebuttal, please let the authors know.

If your concerns remain unresolved, please communicate that clearly as well.

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Thank you for contributing to a fair and constructive review process at NeurIPS.

Dear Reviewer TuNU,

Thank you for your thorough review and positive evaluation. We particularly appreciate your recognition of FuXi-Ocean as the first sub-daily deep learning model for global ocean forecasting, and your acknowledgment of the practical value of the 6-hour predictions and the MoT module innovation. We have carefully addressed all your questions in the responses below.

Q1. How sensitive is FuXi-Ocean to the choice of K = 1 in MoT? Would adaptive K or soft aggregation outperform hard Top-K?

A: Following the reviewer’s suggestion, we conducted additional experiments with K = 2, 3, 4, and also tested a soft aggregation approach. The table below shows the relative change in RMSE compared to K=1, calculated as $\frac{\text{RMSE} - \text{RMSE}_{K=1}}{\text{RMSE}_{K=1}} \times 100\%$. Positive values indicate that K=1 yields better performance. For each variable, results are averaged across the depth dimension. The "attn" group refers to the soft aggregation on the four temporal features using attention mechanisms.

Units: S (PSU), T (°C), U/V (m/s), SEL (m)

These results confirm that K=1 is the optimal choice. All alternatives, including K>1 and soft aggregation, lead to degraded performance, particularly at the 24-hour forecast horizon. This supports our hypothesis that selecting a single most reliable temporal context is crucial for capturing diurnal cycles. Mixing multiple temporal features, whether through higher K or soft aggregation, introduces interference that hinders the model's ability to learn periodic patterns.

For ocean currents (U, V), while soft aggregation shows some improvement over K>1, it still cannot match the performance of K=1. This suggests that even for variables with different temporal characteristics, adaptively selecting a single optimal temporal window remains the most effective strategy.

Q2. Quantitative demonstration of forecast uncertainty.

A: This is an important question about uncertainty quantification. While we were unable to complete ensemble model training within the rebuttal period due to computational constraints, we followed WenHai's approach and computed the continuous ranked probability score (CRPS) between our deterministic forecasts and observational data for sea surface variables.

The CRPS is defined as: $CRPS_{t,l}^i = \int_{-\infty}^{+\infty} \left[F(x) - H\left(x \geq V_{t+l}^i\right)\right]^2 dx$

where $F(x)$ is the cumulative distribution function of the pseudo ensemble forecast, $H$ is the Heaviside function, and $V_{t+l}^i$ is the observed value at time $t+l$. The pseudo ensemble is constructed from FuXi-Ocean predictions within a 1° × 1° box centered on the grid point nearest to $V_{t+l}^i$.

Given known biases in observational data, we used HYCOM full analysis fields for validation, as they provide the most accurate available estimates of ocean state. The results are shown below:

These results demonstrate that FuXi-Ocean maintains stable probabilistic performance over forecast horizons, with gradual and predictable error growth. The relatively low CRPS values, particularly for ocean currents, indicate that our deterministic forecasts provide reliable central estimates.

Regarding computational cost, a single-member forecast requires 72 seconds on one H100 GPU. Thus, a 10-member ensemble would take approximately 12 minutes on a single GPU, or significantly less if parallelized across multiple GPUs.

Q3. The extent to which covariate shift affects performance.

A: Thank you for raising this important question about potential covariate shift. To assess its impact, we retrained a model ($M_{new}$) using data from 2006.01 to 2013.06, validated it on 2013.07-2013.12, and tested it on 2014 reanalysis data. We then compared its performance with our original model ($M_{best}$) which was trained through 2014.06 and tested on 2015. The table below shows the relative RMSE difference, computed as $\frac{\text{RMSE}_{M_{new}} - \text{RMSE}_{M_{best}}}{\text{RMSE}_{M_{best}}} \times 100\%$.

The performance differences are minimal across all lead times. Interestingly, $M_{best}$ (trained with 2014 data) performed slightly better on the 2015 test dataset, despite the occurrence of a strong El Niño event. This suggests that:

1. FuXi-Ocean generalizes well to climate anomalies not seen during training
2. The impact of missing one year of El Niño training data (2014) is actually larger than the covariate shift from testing on a strong El Niño year (2015)

Q4. The mean bias error metrics (MBE).

A: We computed the mean bias error (MBE) for FuXi-Ocean and compared it with operational systems using IV-TT observations. As MBE does not show consistent trend with lead time, we present the average over all 11 forecast steps (from initialization to day 10) for clarity. FOAM does not provide surface salinity data, resulting in missing values at 0 m depth.

Salinity MBE (PSU):

Temperature MBE (°C):

Key observations:

1. All models show systematic biases of similar magnitude, reflecting uncertainties inherent in ocean observations and reanalyses
2. FuXi-Ocean's biases are comparable to or smaller than those of operational systems across most depths
3. The larger temperature bias at 300-500m in FuXi-Ocean is localized near the thermocline, where sharp gradients increase prediction difficulty

These biases represent systematic offsets rather than forecast errors. When considered alongside FuXi-Ocean’s superior RMSE performance, the results demonstrate the model's forecast accuracy and the effectiveness of our approach.

Q5. Inference time comparison.

A: We benchmarked the inference time for a full 10-day forecast (40 autoregressive steps):

Others.

We will incorporate all suggested revisions in the updated manuscript, including enhanced figure readability and corrected typos. Upon acceptance, we will release the code and model checkpoints to ensure reproducibility.