OneForecast: A Universal Framework for Global and Regional Weather Forecasting

Dear Reviewer yiSD,

We are truly grateful for the time you have taken to review our paper and your insightful review. Here we response your questions point by point.

Q1. The claim for solving over-smooth challenge needs more elaboration.

A1. Please refer to our reply A1&A2 for Reviewer z4XB.

Q2. Submit the results to WeatherBench.

A2. We will submit the results to WeatherBench after the paper is accepted.

Q3. Use real typhoon track data, such as best track, rather than relying on ERA5.

A3. Please refer to our reply A2 for Reviewer SzD8.

Q4. In Table 1, whether the model has been sufficiently trained. Instead of using a normalized comparison across all variables, evaluate each variable separately, and refer to comparsion manner offered by weatherbench2.

A4.

• The reason we retrain all models in the same framework. Although previous ML-based models have tremendous breakthroughs, they use different experiment settings. These models have differences in terms of the spatial resolution ($1.5^\circ$, $0.25^\circ$), temporal resolution (1h, 3h, 6h, 24h), and optimization strategy (1-step training or multi-step finetune). As studied in [1], these factors seriously influence the results. However, due to the huge computing resource consumption, few works retrain them in the same framework. To fairly compare different models, in Table 1, we initially report the results of different models retrained using the same settings and use simple 1-step training for 110 epochs. We acknowledge that other tricks are beneficial to the model's performance, but our comparison is fair for all models. To rule out the models not fully converged, we will report the results of fully training 200 epochs for all models. And following your suggestion, we will also add the results released by WeatherBench2.
• The reason we compute normalized metircs. To display more variables's results in the limited page, we calculate the mean of all variables. In the revision, we will show more variables individually.

Following your suggestion, we show 2 types comparison, the first type is the comparison between 1-step supervised models, which includes our retrained models (Pangu, Graphcast, Fuxi, and Ours), numicial method IFS-HRES, and the model provided by Fengwu's author. Note that the input of Fengwu is 2 consecutive state, other ML-based model is 1. And the resolution of Fengwu (128×256) is higher than others (120×240). The second type is the comparison between the results released by WeatherBench2 (with many finetune tricks), which includes IFS-HRES, 2 sota models (Pangu published on Nature and Graphcast published on Science), and our model finetuned only for 1 epoch with simple multi-step supervision due to the limination of time. Note that comparisons are fair only between results of the same type. It is worth mentioning that Fengwu and our 1-step models also achieve better results than IFS-HRES. And more results are available at https://anonymous.4open.science/r/rebuttal-8C5E/RMSE_ACC.jpg

#RMSE

For the ACC results, please refer to our reply A1 for Reviewer McMn.

[1] Exploring the design space of deep-learning-based weather forecasting systems.

Q5. Fig 3 does not include key variables. The evaluation manner should same as previous works.

A5. For more results, please refer to Appendix Fig 8-28. The evaluation manner please refer to our reply A4.

Q6. In Fig 4, q700 is over-smoothing, please add spectral analysis.

A6. Please refer to our reply A1 for Reviewer McMn.

Q7. Long-term forecast accuracy of OneForecast.

A7. Please refer to our reply A4 for Reviewer McMn.

Q8. Include statistical metrics to evaluate the model's performance in predicting more extreme events.

A8. For statistical metrics of typhoon and more extreme event analysis, please refer to our reply A2 for Reviewer SzD8.

Dear Reviewer McMn,

We are truly grateful for the time you have taken to review our paper and your insightful review. Here we response your questions point by point.

Q1. There might be an issue with the ACC-Q700 scale in Fig 4.

A1. Thank you again for your careful review of our paper, it exactly the issue with the decimal point precision retention when drawing. And we will update Fig 4 in the revision. Following the suggestion of Reviewer yiSD, we compare all our retrained models which trained for 200 epochs with the results released by weatherbench2 with the same initial conditions (the total numbers are 700). And following the suggestion of Reviewer yiSD, we add the spectral analysis of Q700 and Wind10M in this link: https://anonymous.4open.science/r/rebuttal-8C5E/spectral_analysis.jpg

Below are the ACC results. More results are available at: https://anonymous.4open.science/r/rebuttal-8C5E/RMSE_ACC.jpg

#ACC

Q2. The number of parameters and efficiency.

A2. Our OneForecast has a competitive performance for Parameters and MACs. For the MACs, the size of input tensor is set to (1, 69, 120, 240). Not that for the ML-based weather forecasts, the computational cost is less important compared with the forecasting accuracy because the ML-basd model is several orders of magnitude faster (maybe tens of thousands of times) than traditional numerical methods. For instance, in numerical forecasting, a single simulation for a 10-day forecasts can take hours of computation in a supercomputer that has hundreds of nodes. In contrast, ML-based weather forecasting models just need a few seconds or minutes to produce 10-day forecasts using only 1 GPU.

Q3. The temperature variable has seasonal changes, I am curious whether it will be better to subtract the climate mean from the temperature before putting it into the network.

A3. This question is rarely considered in previous works. And we conduct experiments to research this point. Unfortunately, we find this even leads to poorer performance of temperature forecasts. Honestly speaking, we do not know the reason, maybe the interaction between different features, just as the question proposed by Review z4XB, please refer to our reply A12 to Review z4XB. Below are the results of two training strategies for some important level temperature variables, specifically, 'Our_t' represents the training strategy that subtracts the climate mean.

#RMSE

#ACC

Q4. OneForecast achieves multi-time spans (from short-term warning to long-term forecasting) weather modeling within a unified framework.

A4. Thanks for your agreement with our work. We want to add some details about long-term forecasts. For adequate evaluation, we conduct quantitative analysis for long-term forecast and compute the RMSE and ACC for 100-day forecast in this link: https://anonymous.4open.science/r/rebuttal-8C5E/100days_forecast.jpg Our model has better RMSE and ACC. Note that atmospheric prediction is limited by the chaotic nature of dynamical systems, making 100-day forecasts theoretically unattainable. This experiment mainly validates our model’s ability to preserve atmospheric physics consistency, rather than focus on numerical accuracy. Existing methods often fail in extended forecasting, with high-frequency artifacts and physical collapse. In contrast, our model maintains plausible physical fields. In general, addressing the physical collapse is the first step, the next step is to improve the accuracy.

Dear Reviewer z4XB,

We are truly grateful for the time you have taken to review our paper and your insightful review. Here we response your questions point by point.

Q1&Q2. Explicitly define dynamic system modeling capability.

A1&A2: Dynamic systems modeling represents multi-scale interactions, like energy transfer between low-frequency atmospheric circulation and high-frequency vortices. Meteorological dynamics follow $\frac{dx}{dt} = f(x)$ and decompose into a spectrum $x(t)=\sum\hat{x}_ne^{i\omega_n t}$. High-frequency components ($\omega_n\gg\omega_c$) correspond to local discontinuities (e.g., vortices). Models like Pangu (Transformer-based) and GraphCast (MLP-based) act as low-pass filters[1][2][3], limiting their ability to capture high frequencies and causing errors in long-term and extreme event predictions. OneForecast’s Multi-Stream Messaging (MSM) module introduces dynamic gating to enhance high-frequency information. Gating weights $g^{(h,e)}_i,g^{(h,s)}_i,g^{(h,d)}_i\propto|\lambda_i-1|+\epsilon$ depend on spectral features, where $\lambda_i$ (graph Laplacian eigenvalues) indicates frequency. Using the frequency response function $\rho(\lambda_i)$, MSM boosts signals as $\lambda_i$ approaches 2, ensuring $\rho(\lambda_i)\geq\alpha|\lambda_i-1|$ and $\rho(\lambda_i)\geq\kappa\lambda_i$. This design improves high-frequency capture while reducing low-frequency noise, as shown in Fig 7.

[1]How do vision transformers work?

[2]Fourier features let networks learn high frequency functions in low dimensional domains.

[3]On the spectral bias of neural networks.

Q3. Explanation of Theorem 2.1.

A3. Based on graph signal spectral analysis[4], the MSM module performs adaptive high-pass filtering using dynamic gating weights ($g^{(h)}\propto|\lambda_i-1|+\epsilon$). When the graph Laplacian eigenvalue $\lambda_i\to2$, the weight amplifies high-frequency components. Conversely, when $\lambda_i\to0$, the weight suppresses low-frequency effects. The frequency response $\rho(\lambda_i)$ satisfies $\rho\geq\alpha|\lambda_i-1|$ and $\rho\geq\kappa\lambda_i$, ensuring enhanced high-frequency signals, unlike traditional GCNs[5]. This design is inspired by[6].

[4]The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains.

[5]Semi-supervised classification with graph convolutional networks.

[6]Convolutional neural networks on graphs with fast localized spectral filtering.

Q4. Quantitative analysis for long-term forecast.

A4. Please refer to our reply A4 for Reviewer McMn.

Q5. Comparison with GenCast.

A5. Ensemble forecasting is part of our downstream tasks. We aim to show that it can enhance accuracy. Our OneForecast isn't specifically for ensemble forecast, and we'll conduct in-depth research on it later.

Q6. For typhoon track, add 1.5° results and quantitative metric.

A6. For typhoon track, high-resolution modeling enhances accuracy but increases resource demands. Oneforecast delivers superior results at lower resource costs. As suggested, we present 1.5° resolution results with quantitative analysis, detailed in our reply A2 to Reviewer SzD8.

Q7. The code lacks clear instructions.

A7. We will add details after the paper is accepted.

Q8. Regional forecasts should be framed as a downstream task.

A8. We have removed Appendix Section D. And in Section 2.4, we’ve defined regional model as a downstream task, that’s essentially the same as your suggestion. Extensive experiments for our regional model are shown in Fig 6, Table 3, Section 3.3, and Section 3.6. To address your concerns, we’ve incorporated your valuable feedback and revised the manuscript accordingly.

Q9. A deeper discussion of rationale design for each module.

A9. Please refer to A1 for our motivation.

Q10. Explain line 094-096.

A10. Our NNG method enhances Graph-EFM through global model integration. Let $A_t$ denote temporal region data, $B_t$ its boundary, $A_{t+1}$ the regional forecast, and $A^\prime_{t+1}$ the coarser global forecast (matching the spatial range of $A_{t+1}$). While Graph-EFM predicts $A_{t+1}$ using $A_t$ and $B_t$, NNG incorporates $A^\prime_{t+1}$ as dynamical forcing. Although $A^\prime_{t+1}$ lacks fine-scale details, its synoptic information improves regional forecast accuracy-unexploited in Graph-EFM. Details appear in Section 2.4 and Fig 2c (expanded in revision).

Q11. What is boundary loss?

A11. This is the issue caused by overlook of boundary information, and our NNG alleviates this issue, please refer to Fig 2c, Section 2.4, and Section 3.3.

Q12. Conduct ablation study to assess the contributions of each feature.

A12. GNN requires both edge/node features. We perform ablation study on feature's impacts on U10M/V10M in 4-day forecasts. Due to time constraints, we employ 5-year data (20 epochs) with averaged results from 50 ICs shown at: https://anonymous.4open.science/r/rebuttal-8C5E/ablation_study.jpg

Dear Reviewer SzD8,

We are truly grateful for the time you have taken to review our paper and your insightful review. Here we response your questions point by point.

Q1. The paper is missing comparisons with traditional numerical methods.

A1. We add the comparison with the traditional numerical method (IFS-HRES), which is considered the best deterministic numerical method. We choose some key variables for comparison and compute the average results of RMSE and ACC for 700 initial conditions (ICs). The first IC is 0:00 UTC Jan. 2020, and the next IC is 12 hours later. Model 'Ours' represents our 1-step supervised model, and 'Ours_finetune' represents our multi-step supervised model finetuned only for 1 epoch due to the computing resources and time constraints. We acknowledge that more advanced tricks used in previous works are beneficial to the performance, but this simple finetune strategy has proven the potential of our proposed model. Below are the RMSE and ACC results:

#RMSE (the smaller the better)

#ACC (the higher the better)

Q2. Ground truth cyclone path is missing from Fig. 1.

A2. In Fig. 1, we initially treat ERA5 as the ground truth cyclone. In the revision, we will replace the EAR5 with the ground truth produced by best track [1][2], although the result is similar. The results can be found in this link: https://anonymous.4open.science/r/rebuttal-8C5E/typhoon.jpg

[1] An overview of the China Meteorological Administration tropical cyclone database.

[2] Western North Pacific tropical cyclone database created by the China Meteorological Administration.

And we also add a quantitative metric, a lower value represents better results:

To assess the forecast performance of more extreme events, we also show 2 extreme event assessment indicators (the higer the better) CSI and SEDI. Below are the average results for 700 ICs:

Q3. A reference to Edge Sum MLP will be helpful to the reader.

A3. We will add the reference of Edge Sum MLP [3] in the revision. And in Appendix E.2 Eq 24-29, we present detailed information about Edge Sum MLP.

[3] Pfaff T, Fortunato M, Sanchez-Gonzalez A, et al. Learning mesh-based simulation with graph networks.

Q4. Equation 14: please be specific on what MSM means.

A4. As shown in Section 2.2, MSM means Multi-stream Messaging, which includes a dynamic multi-head gated edge update module and a multi-head node attention mechanism. And MSM is used for massaging. The corresponding equations can be found in Eq 4-14. If you have any question about MSM, please do not hesitate to let us know, we will re-write the expression of MSM according to your suggestion.

Q5. Provide details about MLP.

A5. As shown in Appendix E.2 Eq 22-29, this paper uses 2 types MLP. We denote the first type as MLP(·), the number of layer is 1, the latent dim is 512, and followed by the SiLU activation function and Layernorm function. And we denote the second type as ESMLP(·), the other hyperparameters are the same as MLP(·), except ESMLP(·) transforms three features (edge features, node features of the corresponding source and destination node) individually through separate linear transformations and then sums them for each edge accordingly.