OneForecast: A Universal Framework for Global and Regional Weather Forecasting
Authors: Yuan Gao
Hao Wu
Ruiqi Shu
huanshuo dong
Fan Xu
Rui Ray Chen
Yibo Yan
Qingsong Wen
Xuming Hu
Kun Wang
Jiahao Wu
Li Qing
Hui Xiong
Xiaomeng Huang
Venue: ICML 2025 poster (2025)
Keywords: AI for Science
AI for Earth
Weather Forecasting
Earth System Science
Primary area: applications->chemistry_physics_and_earth_sciences

Abstract: Accurate weather forecasts are important for disaster prevention, agricultural planning, etc. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneForecast) based on graph neural networks. By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that OneForecast performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions. Codes link: \url{https://github.com/YuanGao-YG/OneForecast}.

OneForecast: A Universal Framework for Global and Regional
Weather Forecasting
Yuan Gao
Hao Wu 11 Ruiqi Shu 1 Huanshuo Dong Fan Xu² Rui Ray Chen 4 Yibo Yan 56 Xiaomeng Huang
Qingsong Wen? 7 Xuming Hu 56
Kun Wang* 8
Jiahao Wu 9 Qing Li Hui Xiong 56
Abstract
Initial Coodition
Grouhd-Truth
Prodiction
m/s
Accurate weather forecasts are important for dis- aster prevention, agricultural planning, etc. Tradi- tional numerical weather prediction (NWP) meth- ods offer physically interpretable high-accuracy predictions but are computationally expensive and fail fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and in- sufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneFore- cast) based on graph neural networks. By combin- ing dynamic system perspective with multi-gria theory, we construct a multi-scale graph struc- ture and densify the target region to capture lo- cal figuefrey features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event fore- casting. For high-resolution regional forecasts, we propose neural nested grid method to miti- gate boundary information loss. Experimental re- sults show that OneForecast performs excellently across global to regional scales and short-tern to long-term forecasts, especially in extreme event predictions. Codes link: https: //tpps:/g/ //t///gittt github. com/ Homm/YunnGao-Yoe YG/OneForecastt
MARA
20M
13Pe
20%
130re
Typhson Tracking
Figure 1. Forecast results of extreme typhoons. (a) OneForecast's predicted wind speed for Typhoon Molva (2020) at 850 hPa pres- sure level with 60-hour lead time. (h)-(c) the predicted cyclone tracks of Typhoon Yagi (2018) and Typhoon Molva (2020) using different models
1. Introduction
Accurate weather forecasting is crucial for disaster preven- tion, optimizing agriculture and energy planning, and ensur- ing water resource management (Chen et al., 2023a; Pathak et al., 2022: Ahmed et al., 2021). Traditional Numerical Weather Prediction (NWP) methods (Bauer et al., 2015) rely the numerical solution of atmospheric dynamic equa- tions (Achatz et al., 2023; Buzzicotti et al., 2023), ensuring consistency across spatiotemporal scales from a physical perspective. However, with the growing volume of obser- vational and historical data, and the increasing demand for high- righ-resolution and long-term forecasts, NWP methods of- ten struggle with computational costs and fail to fully lever- age the potential value of vast data.
Equal contribution 'Department of Earth System Science, Ministry of Education Key Laboratory for Earth System Mod- eling. Institute for Global Change Studies, Tsinghua University 'TEG, Tencent 'Department and Computer and Science, Univer- sity of Science and Technology of China IIntitute for Interdisci- plinary Information Sciences, Tssinghua University Department of Computer Science and Engineering, The HongKong University of Science and Technology AI Thrust, The Hong Kong University of Science and Technology (Guangzhou) "Squirrel Ai Learning "School of Computer Science and Engineering, Nanyang Techno- logical University 'Department of Computing. The Hong Kong Polytechnic University. Correspondence to: Xiaomeng Huang <hxm @ wsinghua.cdu.cn.
Recent developments in deep learning (DL) models offer new perspectives for weather forecasting. Early spatio- temporal prediction algorithms (Wu et al., 2024a), such as LSTVLSTM (Shi et al., 2015) and PredRNN (Wang et al., 2022), focus on regional precipitation. Recent large- scale scientific computing models, like Pangu-weather (Bi et al., 2023), GraphCast (Lam et al., 2023), and Now- castNet (Zhang et al., 2023), achieve significant results in medium- and short-term forecasts and show high potential in extreme event prediction (e.g.. precipitation and Typhoon track prediction) (Chen et al., 2024; Espeholt et al., 2022; Gong et al., 2024; Wu et al., 2024b). However, pure Al
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
methods still face several core challenges:
achieving high-aceuracy results for multi-scale and multi- time frame weather forecasts within the same framework. (2) Adaptive Information Propagation Mechanism. Through Dynamic Gating Units and graph attention modules, we deeply integrate node and edge features, more accurately capturing extreme events and other high-frequency distur- bance signals within the multi-scale graph structure. As shown in Figure 1, OneForecast delivers better performance in tracking extreme events like typhoons. (3) Nested Grid and Long- Term Forecasting. By using nested grid to merge global and regional information, we overcome the boundary loss issue in regional forecasting. This method effectively mitigates the loss of details caused by over-smoothing in long-term forecasts.
Global and regional high-resolution forecasts are hard to balance. Regional predictions often lack boundary in- formation, making it difficult to effectively nest global data. @ Extreme events and long-term forecasts suffer from over-smoothing. They fail to capture high-frequency dis- turbances, leading to reduced forecast accuracy. 2 Lack of dynamic system modeling capability. This is especially true for capturing complex interactions between nodes at multi- ple scales and learning high-frequency node-edge features.
To address these challenges, we propose OneForecast, a global-regional nested weather forecasting framework based on Graph Neural Networks (GNNs). Inspired by heuristic learning from numerical methods, we construct a multi-scale graph structure based on dynamical systems and multi-grid theory (He & Xu, 2019; He et al.), refining it for the target re- gion to capture local high-freyuency features with greater de- tail. Additionally, to solve issues like over-smoothing in ex- treme events and long-term forecasts, which hinder the cap- ture of high- frequency disturbances, we introduce an adap- tive information propagation mechanism. This mechanism deepens the integration of node and edge features through dynamic gating units. Finally, for regional nigh-resolution forecasting, we adopt nested grid strategy (Phillips & Shukla, 1973) that inherits large-scale background infor- mation from the global scale, significantly alleviating the boundary information loss. Through this integrated frame- work, we aim to effectively capture frequeryy features and extreme events across global regional scales, as well as from short-term long-term forecasts.
2. Method
Problem Definition In this study, we model weather fore- casting as an autoregressive problem (Lam et al., 2023). At each time step I, we use the meteorological state compris- ing surface variables X, and pressure level variables P. to forecast the state at the next time step. We concatenate the surface and pressure level variables along the channel dimen- sion form the combined input: Z,- = [X, P.] E RRxx where N Hf x W represents the number of grid loca- tions (nodes), and d = d₂ + dp is the total number of variables. Here, da and d, are the numbers of surface level and pressure level variables, respectively. In our setup, the initial input contains 69 variables: 4 surface level vari- ables and 65 pressure level variables. Our model aims to forecast the combined variables at the next time step Z++1 using the current input Z, capturing the spatiotempo- ral evolution of the atmosphere: Z,+1 = Model θ), where Q denotes the model parameters. The training objective is to minimize the relative mean squared error (MSE) between the forecasts and the true values across
The method most similar to ours is Graph-EFM (Oskarsson et al., 2024). It also uses hierarchical graph neural net- work for global and regional weather modeling. However, for high-resolution regional forecasts, it treats global low- resolution data as non-trainable forcing conditions, making it unable adaptively couple multi-scale information based on actual needs. And it doesn't 't treats the forecasts of the global model in the region as forcing, which unable to fully utilize the information of the global model. In contrast, our neural nested grid method applies trainable local refinement to the target region in the network structure. It also updates boundary and background information with global model future forcing dynamically through end-to-end training dur- ing global-regional coupling. This design better captures the interaction between large-scale global backgrounds and high-frequency regional details. Our experiments (Sec 3.3) show that our method achieves greater stability and accuracy in long-term rolling inference.
all time steps: ming 1 ETD |2c-1- -2411l During in- ference, we adopt a rollout strategy to forecast longer se- quences. Starting from the initial state Zo. the model recursively uses its previous forecasts the next input: Ze+1 MZdel θ), = 0, 1, 2, ... T 1. This strat- egy allows the model to generate extended weather forecasts using its own forecasts.
1|:,+:16
2.1. Earth-specific Region Refined Graph Encoder
In the encoder of OneForecast, inspired by (Fortunato et al., 2022) (Lam et al., 2023), we introduce an Farth-specific Re- gion Refined Multi-scale Graph to improve the interaction of node features in complex dynamical systems. Inspired by the idea of multigrid methods (He & Xu, 2019), we con- struct multi-level Graph Neural Network architecture that includes grids of multiple granularities. Each grid has the same number of nodes but different grid densities, thereby
The contribution of this paper can be summarized as fol- lows: (1) Regional Unified Forecasting Framework. We propose a Graph Neural Network method that supports both global scale and regional high-resolution forecasting,
2

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
(a). architecture parts: input, encoding, message passing, decoding, forecast results.
Armosphere (I)
Earth-specifle Gruph Encoder
Multi-stream Messaging
Decoder
Atmosphere (T+1)
Skip connection
Embedding
SILU
15 Proseure Levele (,Q.T,
Pressure Levels (2
Signood
Tdge ML.P
Feedforward Network
Surface
(UhM, VIM, 12M, MSLP)
Begisnd Goid
Multi-ode Atemitinn
Node
(UTOM, VinM, T2M, MSL.P
(b). Global forecusts
(c). Neural nested grid method for regional resolacnon forecasts
(d). Long-term forecasts
Hell out a forecase
Inciill cundition
Icital conditons 2a
Freeze weight
Fieream eouul
Low-tescluton
Roll our
weight
Freeze weight
Ensenble forecarting
Surface
Surfice
High-renolazion
Regional ligh-sciohttion tapur Z
Poreaast MSLP 2
Typhoon
Figure Overview of Our OneForecast. decoder, and visualization of forecast variables; (b) The global forecasts module uses rollout technology to generate future forecasts; (c) The neural nested grid method specializes regional high-resolution weather forecasts tasks; and (d) The ensemble forecasting module generates long-term forccast results.
(a) The overall architecture includes input variables, an encoder, message passing module, a
capturing spatial features at different scales. Specifically, we define the multi-scale graph structure as:
is the bias term, and o()) is the activation function. To enhance the forecasting accuracy in specific regions, we introduce a region-refined grid on the finest global grid. For nodes within the target region, we add denser edge connections to capture local high-frequency features. In this way, the update of node features not only considers global multi-scale information but also incorporates region-specific fine-graines information.
g g (vo, --(vo, V. V,E(1, ((.)...., g(L), g(()) , g22 , MM2G)
(1) where G represents the set of lat-lon grid nodes, with total of N = H x W nodes; V represents the mesh nodes. g(l) denotes the edge set at the (-th scale, corresponding to grids of different granularities, where ...,..... L, and e(R) represents regional refined edges. &G2 and M2G are the unidirectional edges that connect lat-lon grid nodes and mesh nodes. All scales share the same set of nodes V.
2.2. Multi-stream Messaging
To address the issue of information transmission between nodes in complex dynamic systems, propose mod- ule called Multi-stream Messaging (MSM). This module consists of an adaptive messaging mechanism, including a dynamic multi-head gated edge update module and a multi- head node attention mechanism. And OneForecast includes 16 MSMs for messaging.
More details can be found in Appendix E.
In the encoder, we first map the input meteorological state
Z, E TR: Nxd to the initial node feature representation:
h (0) (Z..)) = 1,2, N,
where (6-) is the feature mapping function, and Zr is the input feature at node i. Next, we iteratively update the node features on the multi-scale graph structure. At itcration k; the feature update formula for node is:
Dynamic Multi-head Gated Edge Update Module. Un- like traditional message passing methods based MLPs, we introduce dynamic gating and multi-head mechanisms to control the information flow more precisely. For each edge, we concatenate its own features with those the source node and the target node:
I.
h (k)
Σ 1=1
Σ jEA!
wOnth (k-1) (0)
(3)
(4) where e; is the feature of edge i, ha()) and hag)) are the features of the source and target nodes of edge i, D, is the edge feature dimension, and Dj, is the node feature
C, Concat batt) ha()) R De+2DD
where (, is the set nodes adjacent to node i at the 1-th scale, Wil is the weight matrix the 1-th scale, b
3

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
dimension. Next, we generate gating vectors through two- layer MLP to regulate the information flow. Specifically, the gating vector is divided into three parts: edge feature update gate Je. source node feature gate Is, and destination node feature gate Dd- First, we perform the first layer linear transformation and activation:
where E(k) denotes the of all incoming edges node k, and o; (h) is the attention weight of the /t-th attention head for edge e,. Next, we perform weighted aggregation of the edge features. For each node k; based on the attention weights, we compute the weighted sum of the features of all edges incoming node ki generating the aggregated feature for each head:
= SiLU (Wic, + b,).
(5)
(h) m k
(h) E, E.EE())
new R
(11)
where W1 E (Rx((D.22ss) is the weight matrix of the first layer, and 11 R² is the bias term. Then, we perform the second layer linear transformation and Sigmoid activation:
Then, we flatten and concatenate the aggregated features from all heads:
g: = a (W2z: + b2) RR
(6)
(2) M Flatten [m] mm m
(m) ["] E D (12)
where, W₂ E R is the weight matrix of the linear transformation of the second layer, and D the feature dimension for each gate. For each head h, the gating val- ues g. (h,e) B, corresponding to the edge feature gate, source node feature gate, and destination node feature gate, respectively. Sub- sequently, we use Edge Sum MLP (ESMLP) (Pfaff al., 2020) to perform linear transformation and nonlinear acti- vation on the edge features to generate the updated edge features:
Finally, concatenate the aggregated edge features with the original node features and, through MLP, perform nonlinear transformation to generate the updated node features:
[h.s) and g. (h.d) are vectors of dimension D,
h hew MLP,, x (Concat (Mę, h&)) + hy- (13)
In summary, in each iteration, we use the multi-stream mes- saging module to update the node features. Specifically, the node feature update formula is:
h (K) = SEMSN (04-D,E00) - 1=1
ESMLP, e (ei, (()) hags) E R..,
(14)
where D' is the dimension of the updated edge features. Finally, we combine the gating vectors and the updated edge features generate the final updated edge features through weighted averaging and residual connections:
where MSM represents the aforementioned multi-stream messaging operation, g() is the set of edges at the (-th scale, and (-.) is the activation function. In the region- refined graph structure, for nodes within the target region, we additionally consider the set of edges within the region gregion to capture finer local information.
H
(h.e)
(h.a)
new
g:
e
gi
o ha(0)
3
1=1
(8) Theoretical Analysis. From a theoretical perspective, we explain why our method helps capture high-frequency in- formation. This enhances long-term prediction ability and improves the ability to detect extreme events.
(h ba(3)
+ g,
+ cii
where: @ denotes element-wise multiplication.
Theorem 2.1. High-pass Filtering Property of Multi- stream Messaging. Considering the improved multi-stream message passing mechanism, suppose the graph signal f E ENN has a spectrum f U under the graph Fourier basis U [ui,-.., uN), where L U UUU is the normal- ized graph Laplacian matrix and A diag( (bngg( .......) is its eigenvalue diagonal matrix (0 < X1 S... S AN S 2). Define the frequency response function of the message pass- ing operator as p x A R. If the dynamic gating weights satisfy:
Multi-head Node Attention Mechanism. Compared to traditional message passing mechanisms, multi-head atten- tion mechanisms can more precisely capture complex de- pendencies between nodes and dynamically adjust the way information is aggregated through attention weights. For each edge e; = (j + k),, we use MLP to calculate the attention score:
MLP, a (e E R.
(9)
Then, we normalize the attention scores:
9,
(h,e)
-9; -9.
(h,s)
(h.d)
1|+c (c 0)
(15)
exp (a!")) (h)
(h)
Yh = 1,2,...
=h=1,2,... ...,,, H, (10)
then there exist constants a > 0 and k. > 0 such that the frequency response the operator satisfies:
Σ EeyeE(K) exp (a)
4

---

OneForecast: A Universal Framework for Global and Regional Weather Forecasting
are then interpolated match the resolution of the high- resolution regional data, which are concatenate as Ze to acted as global forcing, We then combine the regional high- resolution data at time with the 2, to form the input of the regional model. The global forecasts provide the nec- essary boundary conditions for the regional forecasts. The regional model then produces the high high-resolution forecasts for the regional state time + 1:
p(A.) 2 al}; -1| and p(Ac) 2 KA;
(16)
that is, the operator is a strictly high-pass filter.
The proof of Theorem A.I can be found in Appendix A.
2.3. Decoding and Optimization
The decoder's goal is to decode the latent information back to meteorological variables on the latitude-longitude grid. We obtain the updated feature representation h, for each node. For each node the decoder applies the mapping function:
2
region 1+1
Modelegion
(Concat (Zetial Z
regionn)
2 region
(19)
Long- TergTTermoee and Esemble Weather Forecasting, The ini- tial condition of the atmospheric state is uncertain, so rea- sonable quantification of this uncertainty is conducive to improve to forecast performance. To account for the un- certainty in the atmospheric initial state for long-term en- semble forecasting, we generate N perturbed initial con- ditions Zn") by adding Perlin noise e(1) to Zo (Chen et al., 2023b). Each perturbed initial condition is input into the model, and through recursive rollout over time steps, we obtain individual forecasts 2 Finally, at each time step t + 1, we compute the ensemble mean predic- tion [+1 Zengemble = 1
2,+1,5 = (b:),,
(17)
where (-) is an MI.P that converts the latent node features into the predicted variables 2.+1. for the next time step.
We use relative L2 loss function for model training. The loss function is defined as:
W
== KHW ΣΣΣ
(18)
Pi.j.k
N Σ Z 2 by averaging the forecasts from all N ensemble members. In this work, we set N=50,
18t where f.j, and jijkk are the predicted and true values for variable (channel) k at spatial location (i and time t +-+ 1öt; K' is the number of variables (channels); H and W are the
3. Experiments
height and width of the spatial dimensions, respectively; öt is the time interval of single-step prediction (we use öt = 6 hours).
In this section, we extensively evaluate the performance of OneForecast, covering metric results, visual results, and extreme event analysis. We conduct all experiments on 128 NVIDIA A100 GPUs.
2.4. Downstream Tasks
We consider three principal downstream tasks:
3.1. Benchmarks and Baselines
Global Weather Forecasting. As detailed in Section 2 and illustrated in Figure 2(b), we employ a rollout approach during inference, using the trained model for multi-step extrapolation. Specifically, starting from the initial state Zg. the model recursively uses its previous predictions as inputs for subsequent time steps, generating sequence of future global weather forecasts.
We conduct the experiments on the WeatherBench2 (Rasp et al., 2024) benchmark, a subset of the fifth generation of ECMWF Reanalysis Data (ERA5) (Hersbach et al., 2020). The subset we use includes years from 1959 to 2020, which is 1959-2017 for training, 2018-2019 for validating, and 2020 for testing. We use 5 pressure level variables (each with 13 pressure levels), geopotential (2), specific humidity (Q), temperature (T), U and V components of wind speed (U and V), and 4 surface level variables 10-meter U and V components of wind (U10M and V1OM), 2-meter tempera- ture (T2M), and mean sea-level pressure (MSLP). For the global weather forecasting task, we choose the 1.5e (121 x 240 for the global data) version of WeatherBench2 as our dataset. For convenience, we just choose 120 x 240 data to train models. For the regional high-resolution weather forecasting task, we use the original 0.25" (721 x 240 for the global data) ERAS data. More details can be found in the Appendix C. We conduct 2 types comparison, the first type is the comparison between 1-step supervised models retrained using the same framework and settings, which in-
Regional Righ-Resolution Forecasting. To enhance the accuracy of high-resolution forecasts in specific regions, we propose a neural nested grid method, illustrated in Fig- ure 2(c). This method combines global low-resolution future forecasts with regional high-resolution data to produce de- tailed forecasts for the target region. We first input the global low-resolution data at time t into the pre-trained global model to obtain the global forecasts Z at time t + 1. We extract Zzpoball from Z which shares the same spa- tial range as the region, and Z which includes the boundary of the region (the boundary are defined as two grid points around the region). Both 2 241 and 2global2
5

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
Table global weather forecasting task, we compare the performance of OncForecast with 3 baselines, which trained in the same framework. The average results for all 69 variables of RMSE (normalized) and ACC are recorded. A small RMSE (4) and a bigger ACC (1) indicate better performance. The best results are bold, and second best are with underline.
METRIC
MODEL
6-HOUR
1-DAY
4-DAY
7-DAY
10-DAY
RMSE
ACC
RMSE
ACC
RMSE
ACC
RMSE
ACC
|RMSE
ACC
PANGU-WEATHER (BI ET AL., 2023)
0.0826
0.9876
0.1571
0.9581
0,3380
0.8167
0,5092
0.5738
0.6215
0,3542
GRAPHCAST (LAM ET AL.,, 2023)
0.0626
0.9928
0.1304
0.9705
0.2861
0.8705
0.4597
0.6692
0.6009
0.4275
FUXI (CHEN ET AL., 2023B)
0.0987
0.9820
0.1708
0.9511
0.4128
0.7379
0.5972
0.4446
0.6981
0.2391
ONEFORECAST(OURS)
0.0549
0.9943
0.1231
0.9737
0.2732
0.8825
0.4468
0.6888
0.5918
0.4457
ONEFORECAST(PPROOOTONN 12.24%
0. %
5.54%
0.33%
4.50%
1.38%
2.81%
2.92%
1.51 % 4.25%
Inital Condition
Pangu
Fengwu
Grapheest
Fuxi
Our
Ground Truth
300
T2A
100000
MSLP
100000
28550
1000
98230
Figure 3. 10-day forecast results of different models.
cludes Pangu (Bi et al., 2023), Graphcast (Lam et al., 2023), Fuxi (Chen et al., 2023b), and Ours. The second type is the comparison between the results released by WeatherBench2 (with many finetune tricks), Fengwu (Chen et al., 2023a) (results released by the author), and our finetune model.
improvement is primarily attributed to integrating the pro- posed adaptive message passing module, which enhances OneForecast's ability to model the relationships between atmospheric states across different regions of the earth that allows for the simulation of atmospheric dynamics at vari- ous spatial and temporal scales adaptively. In summary, the forecasts exhibit more consistency with the actual physical field, effectively mitigate over weossmoot,,ng, and demonstrate superior predictive performance, particularly for extreme atmospheric values.
3.2. Comparison with state-of-the-art methods
We utilize four metrics, RMSE, ACC, CSI, and SEDI eval- uate the forecast performance. More details can be found in F.I. Since the magnitudes of different variables vary greatly, we first normalize the 69 variables and then calcu- late the indicators for the 1300 initial conditions. As shown Table 1, OneForecast achieves satisfactory performance compared with the ttate-of-the-ar models. As shown in closer with the ground truth. We also show the forecast results of several important variables in Figure 4, which are not normalized. Our FoeForaa performs better than other models. More results compared with WeatherBench2 can be found in Appendix G.4. This
3.3. Regional High Resolution Forecast
Although the training cost of low-resolution forecast models is relatively low, their prediction results lack sufficient de- tails. However, directly training high-resolution regional data often results in poor regional forecasts performance due to issues such as missing boundary conditions and lim- ited data samples. Although the regional forecasts method proposed by (Oskarsson et al., 2024) improves prediction
Figure 3, OneForecast
6

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
I04DE U1UME
HMAEE-1IM
HNSSE: USSQ
HNSEE: 2,00
JM4BE1500
300
3
13000
10400:
TOANI
I04GE
TO/SE
10/SIE
4000
1.0
2002
2.-
Forocast Dagsa
Plemsord Days
Perersal Days
Ponocaat Dags
Partcunt Days
Furopast Daps
ACC-ULOM
ACCVIOM
ACC-U850
ACC-0700
ACCN500
ACC
ACD
ACIC
ACC
64
0.
03
022
Poccous Days
Forooas: Days
Forocast Days
Forecast Days
Porecost Days
Focecost Days
IFS-HRES
Pangu
Geophcast
Fengwu odficial
Pangu
Grephcast wh
Ours,
Figure 4. We select the latihude-wiighedd RMSE (lower is better) and ACC (higher is better) of several variables.
accuracy, it remains constrained by the absence of global information in high-resolution regional models. In contrast, our proposed Neural Nesting Grid method (NNG) incor- porates boundary conditions and global future information, enabling more accurate high-resolution regional predictions. Furthermore, NNG makes full use of the forecast results of global models, which achieves high-resolution regional forecasts an exceptionally low training cost. Therefore, shown in Figure 6, we only demonstratively conduct high- resolution predictions for two regional variables without requiring training on all variables (c.g., the 69 variables used for training global models). It can be seen that the poor long-term inference results are poor when only using regional data for training. Graph-EFM takes into account boundary conditions and the effect is improved. And our proposed NNG not only takes into account regional bound- ary conditions, but also makes full use of the future forecast information of the global model, which achieves stable long- term forecast performance.
Table 2. Comparison results of RMSE between deterministic fore- casts and ensemble forecasts (ENS), the best results are in bold.
MODEL
FORECAST DAY
7-DAY
8-DAY
9-DAY
10-DAY
PANGU PANGU (ENS)
0.4875
0.5321
0,5742
0.6213
0.4435
0.4743
0.4979
0.5205
GRAPHCAST GRAPHCAST (ENS)
0,4440
0.4923
0,5346
0.5823
0.4412
0,4759
0.5072
0.5331
FUXI
0.5928
0.6314
0.6604
0.6968
FUXI (ENS)
0.4898
0.5175
0.5353
0.5498
ONEFORECAST ONEFORECAST (ENS)
0.4268
0.4834
0.5313
0.5809
0.4393
0.4699
0.4951
0.5167
shown in Figure 1, OneForecast achieves competitive perfor- mance in typhoon tracking during two extreme events, Yagi (2018) and Molva (2020). For Yagi, due to Best Track (Ying et al., 2014) (Lu et al., 2021) doesn't 't report intact track, we treat ERA5 as the ground truth. For Molva, we treat Best Track as the ground truth. The details of tracking algorithm can be found in Appendix F.3. Additionally, load the forecast results of baseline models (e.g.. Pangu, Fuxi and Graphcast) from WeatherBenchh, which is trained using high resolution (0.25") data, to better illustrate the performance of the baselines. Although OneForecast uses lower-resolution (1.5") data, which may limit its capacity to predict cyclones, it nevertheless shows strong forecast skills in tracking tropical cyclones comparing with the baselines.
down-
Pangu
Graphcast
53000
45000
Ours
Ground Truth
50000
3.5. Long-term and Ensemble Forecasts
43000
As shown in Figure 5, we evaluate long-term forecasts with the two best models on Z500 (500 hPa Geopotential). Pangu exhibits patch artifacts in 100-day forecasts, while Graph- Cast experiences error accumulation that degrades the fore- casted physical fields, rendering them physically implau- sible over time. In contrast, OneForecast achieves stable long-temn forecast performance, effectively capturing large- scale atmospheric states without the aforementioned issues.
Figure 5. Comparison results of 100-day forecasts between the two best models and our OneForecast.
3.4. Extreme Events Assessment
Extreme events, such as tropical cyclones, can significantly impact human society. In this section, we evaluate our model's 's ability in forecasting those extreme cyclones. As
7

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
lnki Coudition
Trul Inatil Coodition
Pred Jeiial Gondition
Pred Esital Condition
Pred Inital Condition
Goog-3PM
2022
MSLP
Sa
0.0
G0OLD
203
50
0700
190
300
100
300
0:20
57
100
150
200
156 200 20
163
150
50
100
150
230
Gruph-EFM
ShadniTT
Fonecasting Time (hours)
Figure 6. High-resolution regional results. In the left figure, we select two variables, MSLP and U10M, for visualization. We compare our model with Graph-EFF Eamp--EMMMM and the method that directly trains on high-resolution data. The right figure shows line charts of RMSE and ACC for different models over time. These figures demonstrate that our proposed neural nesting grid method achieves the best performance.
These results highlight OneForecast's superior capability in maintaining accurate and physically consistent predictions over extended forecasting horizons. Table 2, we show the results for 10 initial conditions (starting from 00:00 UTC January 2020, and the interval between consecutive initial conditions is 12 hour). The ensemble forecast (ENS) results are averaged from 50 members. Obviously, in most cases (especially for longer time), the forecasting performance is enhanced for each model when uncertainty is incorporated, and OneForecast still achieves the best performance.
Table 3. Ablation studies on 1.5" WcatherBench2 benchmark, the best results are in bold.
VARIANTS
RMSE ACC
ONEFORECAST w/O REGION REFINED GRAPH
0.3793 0.6075 0.2609 0.8099
ONEFORECAST W REGION REFINED GRAPH
ONEFORECAST R w/O NNG
0,5828 O. 0.2450
ONEFORECAST R BF ONEFORECAST R W NNG
0.4428 0.47 11
0.2180 0.8856
ONEFORECAST w/O MSM ONFFORECAST
0.3921 0.9305
0.2954 0.9577
3.6. Ablation Studies
To verify the effectiveness of the proposed method, as shown in Table 3, we conduct detailed ablation experiments. We introduce the following model variants: (1) OneForecast w/o Region Refined Graph, we remove the region refined mesh from the finest mesh and compute the regional metrics.
64
Frequenyy
c2-
(2) OneForecast w Region Refined Graph, we reserve the region refined mesh (3) OneForecast R w/o NNG. we remove the neural nested grid method (NNG) in the regional forecasts and only use the regional data to train the model. (4) OneForecast R BF, we remove the NNG in the regional forecasts and only use the boundary forcing method to train the model. (5) OneForecast R w NNG. regional forecast model with NNG. (6) OneForecast w/o MSM, we remove the multi-strean messaging module (MSM) and use tra- ditional MLP-based messaging module. (7) OneForecast, the full version of OneForecast for the global forecasts. For (1) and (2), we only evaluate the region-refinet data, For (3), (4), and (5), we only evaluate the specific regional data. For (6) and (7), we evaluate the global data. And these results are based on d-d forecasts for 100 ICs. Experi- mental results show that whether it is a global or regional forecast task, the lack of any component will degrade the performance of OneForecast, which proves the effective- ness of the proposed method. And as shown in Figure 7, the proposed MSM can better capture of high and low fre- quency information, which achieves satisfactory results in long-term forecasts and extreme event forecasts, such typhoons.
6.1
Time Strre
Time Steps
Nocnzlioed Spectral Eroor
Figure 7. Normalized spectral error of the proposed MSM and the traditional MLP- massaging.
4. Conclusion
In this paper, we propose OneForecast, a global-regional nested weather forecasting framework leveraging multi- scale graph neural networks. By integrating dynamical sys- tems principles with multi-grid structures, our approach re- fines target regions for improved capture of high-frequency features and extreme events. The adaptive information prop- agation mechanism, featuring dynamic gating units, miti- gates over-smoothing and enhances node-edge feature rep- resentation. Additionally, the proposed neural nested grid method preserves global information for regional forecasts, effectively relieves the loss of boundary information, which improves the regional forecast performance. Empirical re- sults show that the proposed OneForecast achieves higher prediction accuracy at global and regional scales, especially for long-term and extreme event predictions, marking a step towards more robust data-driven weather forecasting.
8

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
Acknowledgements
Buzzicotti, M.. Storer, B. A., Khatri, H., Griffies, S. M., and Aluie, H. Spatio-temporal coarse-graining decom- position of the global ocean geostrophic kinetic energy. Journal of Advances in Modeling Earth Systems, 15(6): e2023MS003693, 2023.
This work was supported by the National Natural Science Foundation of China (42125503, 42430602).
Impact Statement
Chen, K., Han, T. Gong, J., Bai, L.., Ling, F., Luo, J.-J., Chen, X., Ma. L., Zhang, T., Su, R., al. Fengwu: Push- ing the skillful global medium-range weather forecast beyond 10 days lead. arXiv preprint urXiv:2304.09944 2023a.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal con- sequences of our work, none which we feel must be specifi- cally highlighted here. In addition, we propose OneForecast, global-regional weather forecasting model based on graph neural networks. In the future, we will further study the combination of graph neural networks and dynamic systems to improve the accuracy of forecasts, especially for extreme event forecasts.
Chen, L.,, Zhong, X., Zhang, F., Cheng, Y., Xu, Y., Qi, Y., and Li, H. Fuxi: A cascade machine learning forecasting system for 15-day global weather forecast. npj Climate and Atmospheric Science, 6(1):190, 2023b.
Chen, L.,, Zhong, X., Li, H., Wu, J., Lu, B., Chen, D., Xie, S.-P., Wu, I.., Chao, Q. Lin, C., et al. A machine learning model that outperforms conventional global subseasonal forecast models. Nature Communications, 15(1):6425, 2024.
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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
A. Proofs of Theorems
Theorem A.1 (High-pass Filtering Property of Multi-stream Messaging). Consider an improved multi-stream message passing mechanism. Let a graph signal f RN have spectrum U under the graph Fourier basis U
[uj, ......., u where L = UAU is the normalized graph Laplacian and A diag ()g Ag,.... AN S 2. Define the frequency response function of the message passing operator by p: X ++ R. the dynamic gating weights satisfy
with X S
9i Di
(b.c)
(h.s)
9i
(lidd)
1 + (E>0) 0),
(20)
then there exist constants a > 0 and K > O such that the frequency response p(>i) of the operator satisfies
p(>.) 2 a a1 and p(>;) 2 K x>;
(21)
which means the operator is strictly high-pass filter.
Proof. We consider a multi-stream message passing operator that we denote by G. This operator depends on both node features and dynamic gating on edges. We let E RR be an arbitrary graph signal, and we write its graph Fourier transform as f ff,, f, where L UAU is the normalized Laplacian and A diag(A1, ......... Ax) with 0 S À S ..... S AN S 2. Step 1: Integral analogy of gating on discrete graph. We first recall that on a continuous domain, a gating operator often admits a representation of the form
(ff) fK(x,))
where ((x E) is a kernel that encodes the gating weights. On a discrete graph, the integral turns into a finite sum. Hence for node i, we write
(Gf); Σ Kig
JEN,
where NG denotes the neighbors of node i, and K.y depends on the dynamic gating parameters (0!hhr), 9. , (.ad)) We assume these gating parameters scale proportionally to | 1 + which implies larger weights when À is around high or mid-frequency regions.
(1..))
Step 2: Spectral decomposition of the operator. We decompose f in the eigenbasis of L:
N Σ
f
ue,
fo Ee
E=1
The operator G acts on u, with some gain factor p()e), which call the frequency response. In other words, write
Gu
p(Xe) ue.
Thus the value of p(Ae) reveals how the operator scales the amplitude of the 8-th eigenmode.
(h.c) (h.s)) (h.d) Step 3: High-pass filtering behavior from gating design. We now analyze the effect of gating weights g; 9 91 that satisfy
(h.c) 91 9; 9;
(h..))
(h,d)
x 1> +
Because X [0, 2]. when A is close 2, represents high-frequency component on the graph. In that regime, the gating weights become larger, and the message passing operator G amplifies those components. Similarly, when X, is near the factor A 1| can still be significant enough to enhance mid-to-high frequencies. Conversely, for X; near 0 (low frequency), the gating is relatively small and thus tends to suppress those components.
Step 4: Combining inequalities to show strictly high-pass. We combine partial inequalities for different ranges of X
Since < X4 S 2, we use the gating assumption to show there are positive constants a and x such that
p(),) |>; 1| and p(A:) 2 A
Hence the operator G behaves like high-pass filter, because it provides higher gain to higher (or mid-high) frequency components and less gain to low-frequency components. Therefore, G is strictly high-pass operator in the graph spectral domain.
This completes the proof of Theorem A.
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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
B. Related Work
B.1. Deep Learning based Weather Forecasting
Global Weather Forecasting. Global weather forecasting has seen significant progress with deep learning models. FourCastNet, based on Fourier neural operators, provides global forecasts comparable to traditional numerical methods like IFS, but much higher speeds (Pathak et al., 2022). Pangu, utilizing the Swin Transformer, exceeds NWP methods, incorporating earth-specific location embeddings for better performance (Bi al., 2023). The Spherical Fourier Neural Operator (SFNO) extends Fourier methods using spherical harmonics, offering more stable long-term predictions (Bonev et al., 2023). FuXi focuses on long-term bangtterm forecasting, achieving a 15-day forecasts comparable to ECMWF (Chen et al., 2023b). GraphCast leverages message-passing networks to improve efficiency and forecasting accuracy (Lam et al., 2023), and GenCast builds on this to enhance ensemble forecasting (Price et al., 2023). Further, diffusion models like those in (Li et al., 2024) generate probabilistic ensembles by sampling, while NeuralGCM (Kochkov et al., 2024) focuses on atmospheric circulation with a dynamic core, offering climate simulation capabilities but at higher training and inference costs.
Regional Weather Forecasting. The goal of regional weather forecasting is to enhance local prediction accuracy with high-resolution models. CorrDiff (Mardani et al., 2023) combines U-Net and diffusion models to improve local forecasts. MetaWeather (Kim et al., 2024) adapts global forecasts to regional contexts using meta-learning. GNNs are also widely applied in regional forecasting, with Graphcast (Lam et al., 2023) enhancing accuracy by modeling complex spatial dependencies. MetNet-3 (Espeholt et al., 2022) offers high-accuracy forecasts for weather variables, such as precipitation, temperature, and wind speed, at 2-minute intervals and 1-4 km resolution, outperforming traditional models like HRRR. NowcastNet (Zhang al., 2023) and DGMR (Ravuri et al., 2021) excel in short-term extreme precipitation forecasts using deep generative models and radar data. In spatiotemporal prediction, NMO (Wu et al., 2024b) models the evolution of physical dynamics, providing new insights for local weather forecasting. Similarly, SimVP (Gao et al., 2022) and PastNet (Wu et al., 2024c) achieve good results in forecasting local precipitation evolution using spatiotemporal convolution methods.
B.2. Numerical analysis methods
Multigrid methods (McCormick, 1987; Wesseling, 1995; Hackbusch, 2013; Bramble, 2019; Hiptmair, 1998; Brandt et al., 1983; Borzi & Schulz, 2009) and nested grid strategies (Miyakoda & Rosati, 1977; Zhang et al., 2012; Sullivan et al., 1996) are widely used to solve PDEs and handle multi-scale problems (Debreu & Blayo, 2008; Xue et al., 2000). Multigrid methods use grids of different resolutions to transfer information and accelerate iterations. They efficiently solve large-scale problems and improve computational accuracy. By eliminating low-frequency errors on coarse grids and high-frequency errors on fine grids, multigrid methods effectively handle error convergence at different scales (He & Xu, 2019; He et al., 2023; Shao et al., 2022). Nested grid strategies embed higher-resolution fine grids into regions of interest based on a global coarse grid to capture local complex physical phenomena in detail. In weather forecasting, this method provides large-scale background fields on a global scale while refining the grid for target regions to accurately simulate the evolution of local weather systems and the occurrence of extreme events (Bacon et al., 2000).
C. Data Details
C.1. Dataset
In this section, we are going to introduce the dataset we used in this study detailedly. For the global forecasting, we conduct experiments on the WeatherBench2 (Rasp al., 2024) benchmark, subset of ERA5 reanalysis data (Hersbach et al., 2020).
The WeatherBench2 benchmark we used is the version of 1.5" resolution (121 x 240), which spans from 1959 to 2020. This subset contains 5 variables (Z, Q. T, U, V) with 13 pressure levels (50 hPa, 100 hPa, 150 hPa, 200 hPa, 250 hPa, 300 hPa, 400 hPa, 500 hPa, 600 hPa, 700 hPa, 850 hPa, 925 hPa and 1,000 hPa) and 4 variables (U10M, V1OM, T2M, MSLP) with surface level. For the regional forecasting, a higher resolution data (0.25 resolution) of ERAS is also used, which can be downloaded from https: / cds. el imate. coperni cunii..u... eu/, the official website of Climate Data Store (CDS). All the data we used are shown in Table 4. For both global and regional forecasts, we use the data from 1959 to 2017 for training. 2018 to 2019 for validating, and 2020 for testing.
13

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
Table 4. The data details this work.
VARIABLE
SPATIAL RESOLUTION
LAT-LON
TASK
LAYERS
DT
TIME
NAMB
RANGE
GEOPOTENTIAL (Z)
1.50
-00S-1800
1959~~2020
SPECIFIC HUMIDITY (Q)
13
1,50
6H
-90$-1100"~99'' 8
1959~~2020
TEMPERATURE (T)
13
1.5
6H -90S-180""~990'11000
1959~~2020
U COMPONENT WIND (U)
1.5
6н -00S-1180"~~90011050
1959~~020
GLOBAL
V COMPONENT OF WIND (V)
1.50
-00S-1800"~990'110077
1959~2020
I0 METRE U WIND COMPONENT (U10M)
1,5
6н -905-1100'~-90'
1959~~020
10 METRE V WIND COMPONENT (VI0M)
1,50
6H 9088-180"~99'''8800
1959~2020
2 METRE TEMPERATURE (T2M)
1,5
6H 90'S-180'"-990'18800
1959~2020
MEAN LEVEL PRESSURE (MSLP)
1.5
-00S-1800~-90018000
1959~2020
MEAN SEA LEVEL PRESSURE (MSLP)
0.25
6н B
1959~2020
REGIONAL.
10 METRE U WIND COMPONENT (U10M)
0.25
1959 2020
Table 5. The Params and MACs comparsion of different models.
MODEL
PARAMS (M)
MACs (G)
PANGU (BI AL.., 2023)
23.83
142.39
FENGWU (CHEN ET AL., 2023A)
153.49
132.83
GRAPHCAST (LAM ET AL., 2023)
28.95
1639.26
FUXI (CHEN AL., 2023B)
128.79
100.96
ONEFORECAST
24.76
509.27
C.2. Data preprocessing
Different atmosphere and ocean variables have large variations in their magnitude. To allow the model focusing on predictions rather than learning the differences between variables, we normalized the data before putting the data into the model. We calculated the mean and standard deviation of all variables using data from 1959 to 2017 (training set). Each variable has corresponding mean and standard deviation. Before feeding the data into the model, first subtract the respective mean and divided it by the standard deviation.
D. Algorithm
We summarize the overall framework of OneForecast in Algorithm 1.
E. Model Details for Global Forecasts
E.1. Earth-specifie Region Refined Multi-scale Graph
The graph used in OneForecast be defined G(VG, E,E, gM2G).
Grid Nodes. yo is the ensemble of grid nodes, which contains 120 x 240 28800 nodes for 1.5 global data in global forecast task. And each node consists of 69 atmospheric features (5 variables at 13 pressure levels and variables at surface level, 5 13 + = 69). Since we just consider step historical state, the input features of OneForecast are 69. For regional forecast, the region size can be arbitrary within the permission of GPU memory. For simplicity, we choose the region size of 120 x 240 from 0.25 data, the node still 120 x 240 28800.
the ensemble of mesh nodes, which contains multi-scale mesh nodes of different fineness and region refined mesh nodes that cover the global area. The mesh nodes distributed over refined icosahedron that has undergone five levels of subdivision, and the coarsest icosahedron consists of 12 vertices and 20 triangular faces. By dividing each triangular face into four smaller triangles, an additional node is generated at the midpoint of each edge. The new nodes are then projected back onto the unit sphere, gradually refining the grid. To enhance the forecasting performance in key regions, we further refine specific areas the finest mesh, achieving localized mesh densification. For the global forecast and 10 330 The features of each node include the
Mesh Nodes.
task, we refine the 2 areas: E05300300
14

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
Algorithm 1 OneForecast Framework for Global Weather Forecasting
Require: Initial atmospheric condition Zr-
Ensure: Next step atmospheric state Zt+1.
1: Initialize OneForecast
2: repeat
3: Encoder
4: Embedding features of grid nodes Z, mesh nodes V, mesh edges E, grid mesh edges EG2M, and mesh to grid
edges MMG into latent space using respective MLP: (VJ. h, & g _ff EM12G) MLPs(Z,, V,E, g02M EM2G)
5: Project the atmospheric state from the lat-lon grid into the mesh nodes: Eg ESMLP(V9 h, E
h' = MLPPt (h. >EY EEGAM)
6: Update grid node feature: Dÿ' = MMP (V
7: Apply residual connection to update the feature of grid to mesh edge, mesh node, and grid node again: gg Eg2M' + E h' = h' + h. D9
= -/=v"""
vg
8:
Multi-stream Messaging
9:
Apply dynamic multi-head gated edge update module (DMG) to update edge feature: E'G DM he, hr) Apply multi-head node attention mechanism (MHA) to update mesh node feature: h = MH(h,, E
10:
11: Apply residual connection to update the feature of edge and mesh node: Eg = = + Eg., =1' +h
Decoder Project the feature from mesh back to lat-lon grid: Ex22' = ESMLP(VS,E,, E,,, Vg¹
12:
aLPa1 (VF 5 E DG = vg + DJ" Ze11 = MMLPa2(V9
13:
until converged
14: return Fneeareaast
cosine value of the latitude, as well as the sine and cosine values of the longitude. We only keep the finest mesh nodes, since the nodes on the coarse mesh are its subset. In total, the graph structure of OneForecast comprises 12337 mesh nodes, each characterized by three features.
Mesh Edges. & are the bidirectional edges that connect mesh nodes (sender and receiver nodes). Similar to mesh nodes, there are corresponding edges for each scale of mesh, and & is the ensemble of multi-scale edges. And the features of each edge include the length of edge, the 3D position difference between sender and receiver nodes. In total, OneForecast comprises 98296 mesh edges, each characterized by four features.
Grid2Mesh Edges. EG2M are the the unidirectional edges that used in the encoder, which connect grid and mesh nodes. To ensure that each grid node has a corresponding mesh node connected to it, we add gG2M grid nodes and mesh nodes if the distance between them is less than equal to 0.6 times the edge length of the finest E. Similar to mesh edge E, each grid2mesh edge comprises 4 features, and OncForecast has 49233 grid2mesh edges in total.
Mesh2Grid Edges. M2G are the unidirectional edges that used in the decoder, which connect grid and mesh nodes. For each grid node, we find the triangle face containing it on the finest mesh and connect mesh nodes to it. Similar to other edges, each mesh2grid edge has 4 features. In total, OneForecast has 86,400 mesh2grid edges.
E.2. Encoder
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 MIP(-), except ESMLLP()) 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. We first apply embedder MLP to map the data to the latent space, which can be defined as:
MLP LN (Linear (aemneaar(emmedeee)) [embedderr)).,
(22)
(VG, E,, E EFOM GGM.EM22G EX22 = MLPs(Z,, V,E, gG2M g gMMGG,
(23)
where, Tembedder is the input of embedder MLP. For the linear function, we set the latent dim to 512. SiLU(-) is the SiLU activation function, (.N is the layernorm function. 7,, V.E, E, gG2M, and M2G are embedded features of grid nodes, mesh
15

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
nodes, mesh edges, grid to mesh edges, and mesh to grid edges. We then project the atmospheric state from the lat-lon grid into the mesh nodes. Specifically, first update the edge features through an Edge Sum MLP (ESMLP):
&qaai We eee &
(24)
hg = Wahe:
(25)
1/4 = W Waha + ba:
(26)
haum = _7 + hig + h/g
(27)
EG2M` LN (W ESMLP (houm) + BESMLP). 8
(28)
where, We, w.. Wa are the linear transformation matrix of grid2mesh edge features, send node feature, and target node features. W WESMPP is the linear transformation matrix of output layer. ba is the bias of mesh node during linear
transformation. DESMLP is the bias vector of ESMLP. In summary, the grid2mesh edge update process can be define as:
EGIMM ESMLP (E h,g ha).
(29)
After updating the grid2node features, we update the mesh node features using another MLP:
(L, Σ Eg
(30)
where, Σ E are the edges that arrives at mesh node. Then, we update the grid node features using another MLP:
Di' = MLP (V9)
(31)
Finally, residual connections are applied to update the feature of grid to mesh edge, mesh node, and grid node again.
E.3. Multi-stream Messaging
The proposed multi-stream messaging is implemented by an adaptive messaging mechanism, which contains dynamic multi-head gated edge update module and a multi-head node attention module. This part has been introduced in detail in the main text, so we only added the hyperparameter settings here. For the dynamic multi-head gated edge update module, the dimensions of the gating vector are set to 64. In the multi-head node attention module, the LL used to calculate the attention score consists of a linear layer, a SiLU activation function, a linear layer, and a Sigmoid function. The hidden dimension of the linear layer 64.
E.4. Decoder
In the decoder, we map the feature from mesh back to lat-lon grids, similar to encoder, we first update the mesh2grid features:
EX12'' ESMLP (VG, (VG, EM2
(32)
Then, update the grid node features:
Dg' = MLPPa EMMO''
(33)
where, EM are the edges that arrives at grid node.
After that, a residual connection is applied to update the grid node features again:
Dg = DG Dg"
(34)
Finally, we apply a MLP predict the next step results:
Z+11 MT.P d2 (V9).
(35)
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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
F. Experiments Details
F.I. Evaluation Metric
We utilize four metrics, RMSE (Root Mean Square Error) and ACC (Anomalous Correlation Coefficient), CSI (Critical Success Index), and SEDI (Symmetric Extremal Dependence Index) to evaluate the forecasting performance, which can be defined
Nun
L(i) (Aise Ats.e) )²
RMSE(K,t)
(36)
Nist x Nion
Nig Nise
L(i) Wi A E3.e
==
AC =
(37)
Mu Mup
Ni Nus
L(1)
L(i) (A.)"
where AY,, represents the value of variable v at horizontal coordinate (i,j) and time t. Latitude-dependent weights are defined as L(t) = Ni x cos
Eiiin cos where o; is the latitude at index i. The anomaly of A, denoted as A', is computed as the deviation from its climatology, which corresponds to the long-term mean of the meteorological state estimated from 59 years of training data. To evaluate model performance, RMSE and ACC are averaged across all time steps and spatial coordinates, providing summary statistics for variable at a given lead time At.
TP
CST(K: () TP + FP + FN
(38)
log(P') log (I) log(1 (1 F) + log [1 Hi) log( + log (H) + log(1 F) + log(1 H)'
SEDI(K;
(39)
where, true positives (TP) indicate the number of cases in which the state is accurately simulated. False positives (FP) and FP
false negatives (FN) are defined in a similar manner. The false alarm rate is denoted as F FP4TF. while the hit rate is
represented H TF+EN
TP
F.2. Model Training
For the first type comparison, we train baseline models and OneForecast using the same training framework. We set the total model training epochs 200, the initial learning rate Ie-3, and use the cosine annealing scheduler adjust the learning rate until the model converged. The model codes of Pangu and Grapheast we used are released by NVIDIA modulus (https:/ / /gi thub. com/ For all models, we select the checkpoint that performed best on the validation set for comparative analysis.
www.cooo///........ NVIDIA, I.I.Dduu/o///////o////// us)) The model code of Fuxi is obtained by sending an email to the author.
F33 Typhoon Tracking
To track the eye of tropical cyclone, we follow (Bi et al., 2023; Magnusson et al., 2021) to find the local minimum of mean sea level pressure (MSLP). The time step of forecast lead time is set to be 6 hours. Specifically, once the initial position of the cyclone eye is provided, we iteratively search for a local minimum of MSLP that meets the following criteria:
There is a maximum 850hPa relative vorticity greater than 5 10-3 within 278km radius (in the Northern Hemisphere).
There is a maximum thickness between 850hPa and 200hPa within 278km radius when the cyclone is extratropical.
The maximum 10m wind speed exceeds 8m/s within a 278km radius when the cyclone is over land.
Once the cyclone eye is identified, the tracking algorithm continues to find the next position within a 445km vicinity.
This study focuses on two extreme cyclones: Tropical Storm Yagi and Severe Typhoon Molave. The Yagi formed near Iwo Jima, Japan on August 6, 2018, and landed over Wenling, China on August 12. The Molave formed on October 11, 2020, and landed over the Philippines on October 25, 2020. The initial conditions for these two cyclones are set
17

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OneForecast: A Universal Framework for Global and Regional Weather Forecasting
0:00 UTC, August 6, 2018 and 0:00 UTC, 11 October 2020, respectively. Since there is no Fuxi results in 2018 on WeatherBench2, we can not compare it with Yagi. The results of Best Track (Ying al., 2014) (Lu al., 2021) can be found in sttpps//ttcaat typhoon. org cn/en/.
G. Additional Results
G.1. Efficiency Analysis
As shown in Table 5, 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 several orders of magnitude faster (maybe tens of thousands of times) than traditional numerical methods. For instance, in numerical forecasting, single simulation for 10-day forecasts can take hours of computation in supercomputer that has hundreds of nodes. In contrast, ML-based weather forecasting models just need few seconds or minutes to produce 10-day forecasts using only GPU.
G.2. Spectral Analysis
As shown in Figure 8, we compute the surface kinetic energy spectrum and Q700 spectrum for baseline models using Weath- erBench2's 's official results (averaged across the first 700 ICs). Our OneForecast model achieves comparable performance in this standardized evaluation framework. Notably, as Q700 data for Fuxi were not available in the WeatherBench2, only its surface kinetic energy spectrum could be analyzed.
Energy Spectrum Q700
Energy Spectrum of 10m Wind Field
10-4
10-23
Energy Spectrum E(k) (m1/s))
10-3
Energy Spectrum
10
10'9
10-25
10-7
Ground Truth
Ground Truth
Oneforecast
Oneforecast
Pangu
Pangu GraphCast
10
Fuxi
GraphCast
10-4
FuXi
10
10
10
10-a
Wave number k (1/km)
Wave number k (1/km)
Figure 8. Spectral analysis of different models.
G.3. Quantitative analysis of Extreme Event
To assess the forecast performance of more extreme events, as shown in Table 6, we present extreme event assessment indicators (the higer the better) CSI and SEDI. And we also add a quantitative metric for typhoon prediction in Table 7, lower value represents better results. It can be seen that OneForecast also achieves satisfactory results in quantitative analysis.
G.4. Additional quantitative comparison with the results from WeatherBenche
As shown in Figure we compare all models released by WeatherBench2, except for ENS (ensemble forecasting, not the same task) and Spherical CNN (too few ICs, only 178 compared with our used 700). While the WeatherBench2 baseline leverages numerous training strategies, we only conducted 1-epoch of finetuning (Ours finetune) during the brief rebuttal period. Nevertheless, a 2-epoch finetune model (Ours finetune2) demonstrates improved results, indicating the potential for further gains with additional finetuning. If we finetuned for more epochs, OneForecast can achieve better result. However, our primary objective to introduce a novel paradigm for global and regional weather forecasting rather than solely optimizing metries, we just finetune for few epoch as an example.
18

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Table Quantitative analysis of extreme event for different models.
WINDIOM
WIND10M
T2M
T2M
MODEL
CSI
SEDI
CSI
SEDI
PANGU
0.11
0.29
0.16
0.34
GRAPHCAST
0.13
0.29
0.20
0.38
FUXI
0.11
0.20
0.19
0.27
OURS
0.14
0.31
0.21
0.40
Table 7. Quantitative analysis of typhoon for different models.
MODEL
TRACK POSITION ERROR(KM)
FS-HRES PANGU 1.5"
222
GRAPHCAST 1,5
212
PANGU
231
GRAPHCAST
197
OURS
157
19000
2.2
DOMISE
400.
10
12
10
10
1.3-
0.8
30E
34
05
Donecast
Forecost
ITS JIRES
Pangu meb
Graphcast wb
Ours, finetune
Ours, finetune2
NeuralGCM wb
Fuxi wb
Keisler wb
Figure 9, Additional quantitative comparison with the results from WcatherBench2 for several important variables.
G.S. Additional Visual Results
We present more additional results in Figure 10, 11, 12 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 20, including 18 variables that are importmant to weather forecasting, each with results ranging from 6 hours to 10 days. These additional results further demonstrate the effectiveness of OneForecast. Same as the Figure 3, the initial conditions is 00:00 UTC, January 2020.
19

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
Ro0000
100000
2500
50000
2830
Z1000
2000
DURT3
T500
TE30
1200
13500
11000
1500
1850
V1000
Figure 10. 6-hour forecast results different models.
20

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwn
Graphcast
Ou
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
G000
0000
DURT3
T500
TB30
1500
18550
U1000
1500
1850
V1000
Figure 0.5-day forecast results of different models.
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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwy
Graphcast
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
0000
DUETO
T500
TE30
1500
18550
11000
1500
1850
V1000
Figure 1-day forecast results of different models.
22

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwy
Graphcast
Qur
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
2000
0000
DUET3
T500
TE300
1500
18550
11000
1500
1850
V1000
Figure 1.5-day forecast results of different models.
23

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pungr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
100006
2500
2830
Z1000
2000
G000
DUET3
T500
TE300
1500
18550
01000
1500
1850
V1000
Figure 2-day forecast results of different models.
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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengww
Graphcast
Our
Ground Truth
U1OM
VIOM
T2M
Bo0000
100006
2500
2830
Z1000
2000
DUET3
T500
TE30
1500
18550
01000
1500
1850
V1000
Figure 2.5-day forecast results of different models.
25

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangy
Pengwa
Graphcast
Our
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
DUET3
T500
TE30
1500
18550
01000
1500
1850
V1000
Figure 3-day forecast results of different models.
26

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangu
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
DORT3
T500
TE30
1200
18550
01000
1500
1850
V1000
Figure 3.5-day forecast results of different models.
27

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
DURT3
T500
TE30
L500
18550
01000
1500
1850
V1000
Figure 4-day forecast results of different models.
28

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
Bo0000
100006
2500
2830
Z1000
2000
DUETO
oata
T500
TE30
1500
18550
01000
1500
1850
V1000
Figure 4.5-day forecast results of different models.
29

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwy
Graphcast
Ground Truth
U1OM
VIOM
T2M
Ro0000
100006
2500
2830
Z1000
2000
DURT3
T500
TE30
1200
13500
11000
1500
1850
V1000
Figure 5.0-day forecast results of different models.
30

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangru
Pengww
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
100000
2500
2830
Z1000
2000
G000
DUET3
T500
TE300
1200
18550
11000
1500
1850
V1000
Figure 5.5-day forecast results of different models.
31

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwy
Graphcast
Ground Truth
U1OM
VIOM
T2M
Bo0000
100006
2500
2830
Z1000
2000
DUET3
T500
TE30
1200
13500
11000
1500
1850
V1000
Figure 6.0-day forecast results of different models.
32

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwy
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
MELLP
100006
2500
2830
Z1000
DUETO
T500
T830
1200
18500
11000
1500
1850
V1000
Figure 6.5-day forecast results of different models.
33

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
1000e6
2500
2830
Z1000
2000
DURT3
T500
T830
1200
18550
10000
1500
1850
V1000
Figure 24. 7.0-day forecast results of different models.
34

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangy
Penmwn
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
MELLP
100006
2500
2830
Z1000
DURT3
T500
TE30
1500
18500
11000
1500
1850
V1000
Figure 7.5-day forecast results of different models.
35

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Penmwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
MELLP
100006
2500
2830
Z1000
DURT3
T500
TE30
1200
18550
10000
1500
1850
V1000
Figure 8.0-day forecast results of different models.
36

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Penman
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
100006
2500
2830
Z1000
2000
DUET3
T500
TE300
1500
18550
110000
1500
1850
V1000
Figure 8.5-day forecast results of different models.
37

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Penrww
Graphcast
Ground Truth
U1OM
VIOM
T2M
Io0000
MELTP
100006
2500
2830
Z1000
2000
DUETO
T500
TE30
1200
18550
11000
1500
1850
V1000
Figure 9.0-day forecast results of different models.
38

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pungr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
Bo0000
MELLP
100006
2500
2830
Z1000
DURTO
oata
T500
TE300
1500
18550
01000
1500
1850
V1000
Figure 9.5-day forecast results of different models.
39

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OneForccast: A Universal Framework for Global and Regional Weather Forecasting
Inital Condition
Pangr
Pengwa
Graphcast
Ground Truth
U1OM
VIOM
T2M
1o0000
100006
2500
2830
Z1000
DURTO
T500
TE30
1500
13550
01000
1500
1850
V1000
Figure 10.0-day forecast results of different models.
40


Reviews:
[{"review_id": "taRbkMvWub", "reviewer": "Reviewer_SzD8", "summary": "This paper propsoes a novel method for deep learnig based weather forecasting. The proposed method is based on graph neural networks and introduces new approaches for message passing, and for integrating high resolution and low resolution data. The proposed method outperformed exisitng method in orth short and long-term forecasts across different scales.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer SzD8,\n\nWe 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.\n\n> Q1. The paper is missing comparisons with traditional numerical methods.\n\nA1. 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:\n\n#RMSE (the smaller the better)\n|Model|1-day|4-day|7-day|10-day|\n|---|:-:|:-:|:-:|:-:|\n|**U10M**|\n|IFS-HRES|1.31|2.29|3.63|4.57|\n|Ours|0.76|1.98|3.41|4.39|\n|Ours_finetune|0.78|1.84|2.95|3.60|\n|**V10M**|\n|IFS-HRES|1.43|2.40|3.79|4.81|\n|Ours|0.79|2.06|3.58|4.64|\n|Ours_finetune|0.82|1.91|3.09|3.78|\n|**U850**|\n|IFS-HRES|1.83|3.25|5.17|6.56|\n|Ours|1.17|2.86|4.90|6.36|\n|Ours_finetune|1.19|2.67|4.25|5.21|\n|**Z200**|\n|IFS-HRES|111.92|256.70|615.40|990.04|\n|Ours|59.20|257.09|621.66|1003.04|\n|Ours_finetune|67.14|249.26|556.53|838.94|\n|**V500**|\n|IFS-HRES|2.16|4.34|7.34|9.62|\n|Ours|1.53|3.96|7.04|9.42|\n|Ours_finetune|1.52|3.70|6.12|7.64|\n|**V850**|\n|IFS-HRES|1.86|3.28|5.22|6.61|\n|Ours|1.19|2.89|4.96|6.39|\n|Ours_finetune|1.21|2.70|4.28|5.18|\n\n\n#ACC (the higher the better)\n|Model|1-day|4-day|7-day|10-day|\n|---|:-:|:-:|:-:|:-:|\n|**U10M**|\n|IFS-HRES|0.94|0.83|0.56|0.31|\n|Ours|0.98|0.86|0.59|0.33|\n|Ours_finetune|0.98|0.88|0.65|0.42|\n|**V10M**|\n|IFS-HRES|0.94|0.82|0.54|0.27|\n|Ours|0.98|0.86|0.57|0.29|\n|Ours_finetune|0.98|0.87|0.63|0.38|\n|**U850**|\n|IFS-HRES|0.95|0.84|0.59|0.34|\n|Ours|0.98|0.87|0.62|0.36|\n|Ours_finetune|0.98|0.88|0.67|0.45|\n|**Q700**|\n|IFS-HRES|0.86|0.68|0.47|0.28|\n|Ours|0.94|0.75|0.51|0.30|\n|Ours_finetune|0.94|0.78|0.57|0.38|\n|**V500**|\n|IFS-HRES|0.97|0.86|0.60|0.31|\n|Ours|0.98|0.88|0.62|0.33|\n|Ours_finetune|0.98|0.89|0.67|0.42|\n|**V850**|\n|IFS-HRES|0.94|0.82|0.54|0.27|\n|Ours|0.98|0.86|0.57|0.29|\n|Ours_finetune|0.98|0.87|0.63|0.38|\n\n> Q2. Ground truth cyclone path is missing from Fig. 1.\n\nA2. 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\n\n[1] An overview of the China Meteorological Administration tropical cyclone database.\n\n[2] Western North Pacific tropical cyclone database created by the China Meteorological Administration.\n\nAnd we also add a quantitative metric, a lower value represents better results:\n\n|Model|Track Position Error(km)|\n|---|:-:|\n|IFS-HRES|332|\n|Pangu 1.5°|222|\n|Graphcast 1.5°|212|\n|Pangu|231|\n|Graphcast|197|\n|Ours|157|\n\nTo 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:\n\n|Model|Wind10M|Wind10M|T2M|T2M|\n|---|:-:|:-:|:-:|:-:|\n||CSI|SEDI|CSI|SEDI|\n|Pangu|0.11|0.29|0.16|0.34|\n|Graphcast|0.13|0.29|0.20|0.38|\n|Fuxi|0.11|0.20|0.19|0.27|\n|Ours|0.14|0.31|0.21|0.40|\n\n> Q3. A reference to Edge Sum MLP will be helpful to the reader.\n\nA3. 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.\n\n[3] Pfaff T, Fortunato M, Sanchez-Gonzalez A, et al. Learning mesh-based simulation with graph networks.\n\n> Q4. Equation 14: please be specific on what MSM means. \n\nA4. 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. \n\n> Q5. Provide details about MLP.\n\nA5. 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.", "claims_and_evidence": "Yes but the paper is missing comparisons with traditional numerical methods.", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "No", "experimental_designs_or_analyses": "Yes. Overall the comparisons shown in Tables and figures are convincing. Ground truth cyclone path is missing from Fig. 1", "relation_to_broader_scientific_literature": "This paper adds new contributions to the literature in weather forecasting. The use of multi-scale integrated analysis and multi-stream messaging are novel contributions that merit further investigation and may be broadly applicable to other domains.", "essential_references_not_discussed": "A reference to Edge Sum MLP will be helpful to the reader", "other_strengths_and_weaknesses": "Paper is well written and organized. The contributions are clear and in general the results support the claims made by the authors.\n\nSuggested edits to improve clarity:\n* Fig1: add the ground truth cyclone path\n* Equation 14: please be specific on what MSM means. Describe it using an algorithm or equations\n* add a reference to edge sum mlp\n* The term MLP appears frequently in the paper. provide more details on these networks (number of layes, activation function..)", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sBaP6ECCJT", "reviewer": "Reviewer_z4XB", "summary": "The paper introduces OneForecast, a universal weather forecasting framework based on GNNs. It aims to improve global-regional weather forecasting by leveraging multi-scale graph structures, adaptive information propagation mechanisms, and a neural nested grid method. The proposed framework improves forecast accuracy at both global and regional levels, particularly for extreme events. Extensive experiments show that OneForecast outperforms existing state-of-the-art models such as Pangu-Weather, GraphCast, Fengwu, and Fuxi.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer z4XB,\n\nWe 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.\n\n> Q1&Q2. Explicitly define dynamic system modeling capability.\n\nA1&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.\n\n[1]How do vision transformers work?\n\n[2]Fourier features let networks learn high frequency functions in low dimensional domains.\n\n[3]On the spectral bias of neural networks.\n\n> Q3. Explanation of Theorem 2.1.\n\nA3. 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].\n\n[4]The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains.\n\n[5]Semi-supervised classification with graph convolutional networks.\n\n[6]Convolutional neural networks on graphs with fast localized spectral filtering.\n\n> Q4. Quantitative analysis for long-term forecast.\n\nA4. Please refer to our reply A4 for Reviewer McMn.\n\n> Q5. Comparison with GenCast.\n\nA5. 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. \n\n> Q6. For typhoon track, add 1.5° results and quantitative metric.\n\nA6. 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.\n\n> Q7. The code lacks clear instructions. \n\nA7. We will add details after the paper is accepted.\n\n> Q8. Regional forecasts should be framed as a downstream task.\n\nA8. 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.\n\n> Q9. A deeper discussion of rationale design for each module.\n\nA9. Please refer to A1 for our motivation.\n\n> Q10. Explain line 094-096.\n\nA10. 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).\n\n> Q11. What is boundary loss?\n\nA11. 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.\n\n> Q12. Conduct ablation study to assess the contributions of each feature.\n\nA12. 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", "claims_and_evidence": "The challenge \"Lack of dynamic system modeling capability. This is especially true for capturing complex interactions between nodes at multiple scales and learning high-frequency node-edge features.\" is unclear. I think Pangu and GraphCast already capture dynamic systems effectively, as evidenced by their strong performance. The paper does not explicitly define what is \"dynamic system modeling capability\" or why other SOTA models fail in this regard. \n\nSimilarly, the concept of \"high-frequency features\" is frequently mentioned but never formally defined. The paper does not discuss why these features are essential for long-term forecasting or extreme event prediction.", "methods_and_evaluation_criteria": "The proposed methodology is simple, straightforward, and effective. However, the evaluation is insufficient (see “Experimental Designs or Analyses”).", "theoretical_claims": "I am unable to fully understand the proof of Theorem 2.1", "experimental_designs_or_analyses": "The long-term forecasting evaluation is too weak. The authors provide only one visualization map. A more detailed quantitative analysis is required, similar to Figure 4, including ACC and RMSE for forecasts at 10, 20, 30, ..., and 100 days. Can the model really achieve reliable and accurate 100-day forecasting?\n\nSince the paper studies the ensemble forecasts performance, can this model also be compared with GenCast?\n\nFor Figure 1, the authors state that OneForecast is trained on 1.5$\\degree$ data while other models use 0.25$\\degree$ data, making the comparison potentially unfair. Can the authors provide results for other models also trained on 1.5$\\degree$ data? Additionally, the typhoon tracking evaluation relies only on visualization. Is there a quantitative metric to compare different models in typhoon tracking?", "relation_to_broader_scientific_literature": "The paper tries to solve an important problem in ML-based weather forecasting and contributes to general AI for numerical simulation tasks.", "essential_references_not_discussed": "No missing references were identified.", "other_strengths_and_weaknesses": "NA", "other_comments_or_suggestions": "The regional forecasting method appears to function more as an auxiliary module rather than a core component of the framework. It lacks detailed methodological explanations, significant technical innovation, and robust experimental validation. The authors seem to even forget to write the Appendix section D Model Details for Regional Forecast to further introduce this. Given these limitations, the paper should not position OneForecast as a truly \"universal\" framework for both global and regional forecasting. Instead, regional forecasting should be framed as a downstream task rather than a fundamental part of the model's core design.\n\nThe paper primarily justifies its proposed modules through empirical results, but it would greatly benefit from a deeper discussion on the underlying rationale behind each module’s design.", "questions_for_authors": "Can you further explain \"And it doesn’t treats the forecasts of the global model in the region as forcing, which unable to fully utilize the information of the global model\"?\n\nWhat is \"boundary loss\" in the last paragraph of the Introduction?\n\nThe proposed approach extensively uses concatenation operations to merge different types of features. Would it be possible to conduct an ablation study to assess the individual contributions of each feature?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "srJk2JT8KI", "reviewer": "Reviewer_McMn", "summary": "Accurate weather forecasting is critical for disaster preparedness and resource management, yet traditional numerical methods are computationally intensive, and deep learning approaches often struggle with multi-scale predictions and extreme events. This paper introduces **OneForecast**, a graph neural network (GNN)-based framework designed to unify global and regional weather forecasting while addressing key challenges like over-smoothing and boundary information loss.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer McMn,\n\nWe 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.\n\n> Q1. There might be an issue with the ACC-Q700 scale in Fig 4.\n\nA1. 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\n\nBelow are the ACC results. More results are available at: https://anonymous.4open.science/r/rebuttal-8C5E/RMSE_ACC.jpg\n\n#ACC\n|Model|1-day|10-day|1-day|10-day|1-day|10-day|1-day|10-day|1-day|10-day|1-day|10-day|\n|---|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n||U10M|U10M|V10M|V10M|U850|U850|Q700|Q700|V500|V500|V850|V850|\n|IFS-HRES|0.94|0.31|0.94|0.27|0.95|0.34|0.86|0.28|0.97|0.31|0.94|0.27|\n|Pangu|0.94|0.25|0.94|0.21|0.96|0.28|0.91|0.22|0.97|0.24|0.96|0.21|\n|Graphcast|0.98|0.31|0.98|0.27|0.98|0.34|0.93|0.28|0.98|0.31|0.97|0.28|\n|Fuxi|0.96|0.14|0.96|0.10|0.96|0.17|0.89|0.19|0.96|0.12|0.95|0.11|\n|Fengwu_official|0.97|0.34|0.96|0.30|0.97|0.36|0.92|0.34|0.98|0.34|0.96|0.30|\n|Pangu_wb|0.96|0.35|0.96|0.31|0.97|0.38|0.92|0.35|0.97|0.36|0.96|0.32|\n|Graphcast_wb|0.97|0.39|0.96|0.35|0.97|0.42|0.93|0.41|0.98|0.39|0.96|0.35|\n|Ours|0.98|0.33|0.98|0.29|0.98|0.36|0.94|0.30|0.98|0.33|0.98|0.29|\n|Ours_finetune|0.98|0.42|0.98|0.38|0.98|0.45|0.94|0.38|0.98|0.42|0.98|0.38|\n\n> Q2. The number of parameters and efficiency.\n\nA2. 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.\n\n|Model|Params (M)|MACs (G)|\n|---|:-:|:-:|\n|Pangu|23.83|142.39  |\n|Fengwu|153.49|132.83|\n|Graphcast|28.95|1639.26|\n|Fuxi|128.79|100.96|\n|Ours|24.76|509.27|\n\n> 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.\n\nA3. 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.\n\n#RMSE\n|Model|1-day|4-day|7-day|10-day|\n|---|:-:|:-:|:-:|:-:|\n|**T500**|\n|Ours_t|0.63|1.70|2.94|3.77|\n|Ours|0.45|1.25|2.40|3.38|\n|**T850**|\n|Ours_t|0.85|1.94|3.17|4.05|\n|Ours|0.65|1.46|2.63|3.67|\n|**T2M**|\n|Ours_t|0.79|1.58|2.44|3.06|\n|Ours|0.72|1.34|2.15|2.88|\n\n#ACC\n|Model|1-day|4-day|7-day|10-day|\n|---|:-:|:-:|:-:|:-:|\n|**T500**|\n|Ours_t|0.98|0.86|0.57|0.32|\n|Ours|0.99|0.92|0.71|0.44|\n|**T850**|\n|Ours_t|0.97|0.83|0.55|0.29|\n|Ours|0.98|0.91|0.71|0.43|\n|**T2M**|\n|Ours_t|0.96|0.81|0.55|0.32|\n|Ours|0.96|0.87|0.68|0.44|\n\n> Q4. OneForecast achieves multi-time spans (from short-term warning to long-term forecasting) weather modeling within a unified framework.\n\nA4. 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\nOur 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.", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "I think this method is highly significant for the field of weather forecasting. I appreciate that the authors used a lot of computational resources to replicate all the experiments.", "theoretical_claims": "The paper provides a theoretical proof, showing that the author's designed module helps enhance the model's ability to capture high-frequency information.", "experimental_designs_or_analyses": "There might be an issue with the ACC-Q700 scale in Figure 4, but I'm not sure. Is it a problem of scale line offset or decimal point precision retention when drawing?", "relation_to_broader_scientific_literature": "Sure!", "essential_references_not_discussed": "I think the discussion is quite comprehensive.", "other_strengths_and_weaknesses": "## Strengths：\n\n1. The authors propose a global-regional nested graph neural network architecture, which is the first to implement multi-scale (from global low resolution to regional high resolution) and multi-time spans (from short-term warning to long-term forecasting) weather modeling within a unified framework.\n2. The paper is well-written, with thorough experiments and theory, and the figures and tables are beautifully designed.\n3. The authors have done a comprehensive replication, which is beneficial for contributing to the open-source community.\n\n## Weaknesses\n\n1. I'm curious about the number of parameters and efficiency. The authors should provide a comparison.\n2. 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. Has the author done similar experiments? Most related works did not consider this point, so there should be no problem in training without subtracting the climate mean of temperature. I am just curious whether subtracting it will improve the performance. If there is no time to make a comparison, it can be used as a future work for further exploration.", "other_comments_or_suggestions": "See weakness", "questions_for_authors": "See weakness", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "5q44wLReMw", "reviewer": "Reviewer_yiSD", "summary": "This paper introduces OneForecast which leverages multiscale graph neural networks. By integrating principles from dynamical systems with multi-grid structures, OneForecast refines target regions to better capture high-frequency features and extreme events. The adaptive information propagation mechanism, equipped with dynamic gating units, mitigates over-smoothing and enhances node-edge feature representation. Furthermore, the proposed neural nested grid method preserves global information for regional forecasts, effectively addressing the loss of boundary information and significantly improving regional forecast performance.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Dear Reviewer yiSD,\n\nWe 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.\n> Q1. The claim for solving over-smooth challenge needs more elaboration.\n\nA1. Please refer to our reply A1&A2 for Reviewer z4XB.\n\n> Q2. Submit the results to WeatherBench.\n\nA2. We will submit the results to WeatherBench after the paper is accepted.\n\n> Q3. Use real typhoon track data, such as best track, rather than relying on ERA5.\n\nA3. Please refer to our reply A2 for Reviewer SzD8.\n\n> 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.\n\nA4.\n- **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.\n- **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. \n\nFollowing 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\n\n#RMSE\n|Model|1-day|10-day|1-day|10-day|1-day|10-day|1-day|10-day|1-day|10-day|1-day|10-day|\n|---|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n||U10M|U10M|V10M|V10M|U850|U850|Z200|Z200|V500|V500|V850|V850|\n|IFS-HRES|1.31|4.57|1.43|4.81|1.83|6.56|111.92|990.04|2.16|9.62|1.86|6.61|\n|Pangu|1.28|4.46|1.34|4.69|1.57|6.52|92.90|1136.54|1.98|9.67|1.60|6.49|\n|Graphcast|0.81|4.43|0.84|2.15|1.25|6.42|63.48|1028.25|1.63|9.52|1.27|6.44|\n|Fuxi|1.09|4.98|1.16|5.24|1.68|7.27|114.63|1288.08|2.28|10.92|1.73|7.20|\n|Fengwu_official|0.97|4.37|1.09|4.62|1.45|6.32|101.08|985.49|1.82|9.36|1.48|6.37|\n|Pangu_wb|1.02|4.32|1.15|4.56|1.49|6.24|103.73|948.24|1.88|9.19|1.53|6.26|\n|Graphcast_wb|0.97|4.03|1.10|4.25|1.41|5.80|102.55|888.04|1.75|8.53|1.45|5.82|\n|Ours|0.76|4.39|0.79|4.64|1.17|6.36|59.20|1003.04|1.53|9.42|1.19|6.39|\n|Ours_finetune|0.78|3.60|0.82|3.78|1.19|5.21|67.14|838.94|1.52|7.64|1.21|5.18|\n\nFor the ACC results, please refer to our reply A1 for Reviewer McMn.\n\n[1] Exploring the design space of deep-learning-based weather forecasting systems.\n\n> Q5. Fig 3 does not include key variables. The evaluation manner should same as previous works.\n\nA5. For more results, please refer to Appendix Fig 8-28. The evaluation manner please refer to our reply A4.\n\n> Q6. In Fig 4, q700 is over-smoothing, please add spectral analysis.\n\nA6. Please refer to our reply A1 for Reviewer McMn.\n\n> Q7. Long-term forecast accuracy of OneForecast.\n\nA7. Please refer to our reply A4 for Reviewer McMn.\n\n> Q8. Include statistical metrics to evaluate the model's performance in predicting more extreme events.\n\nA8. For statistical metrics of typhoon and more extreme event analysis, please refer to our reply A2 for Reviewer SzD8.", "claims_and_evidence": "I partially agree with the claims made in the paper, as some of them are supported by the experiments provided. However, several claims do not seem very correct. Details will be discussed further in Questions.", "methods_and_evaluation_criteria": "This work presents a relatively rich set of comparative experiments to verify the performance of OneForecast and conducts a comprehensive analysis of the experimental details. However, the evaluation criteria do not seem very correct. Details will be discussed further in Questions.", "theoretical_claims": "From the equations and explanations provided in the paper, Oneforecast seems to be a reasonable approach.", "experimental_designs_or_analyses": "Yes, I have checked the work's elaboration on the setup of the experiment, the implementation method of the comparative experiment, and the analysis of other details of the experiment. Specific issues regarding the experimental section can be found in the Question.", "relation_to_broader_scientific_literature": "Some of the ideas of this paper are inspired by previous work, and it achieves better results.", "essential_references_not_discussed": "No, the paper makes a relatively comprehensive citation of the literature.", "other_strengths_and_weaknesses": "**Strengths**\n1.  This paper is well-written.\n2.\tThe motivation of this paper is clear.\n3.\tThe experiments are sufficient.\n\n**Weaknesses**\n1. The evaluations should be carefully improved to make them correct enough.\n2. The claim for solving over-smooth challenge needs more elaboration.", "other_comments_or_suggestions": "It is recommended to submit the results to WeatherBench for a standardized evaluation.", "questions_for_authors": "1.\tThe current model exhibits significant limitations in evaluating typhoon tracks. It is advisable to use real typhoon track data, such as best track, rather than relying on ERA5. The low resolution of ERA5 introduces substantial biases in simulating typhoons.\n2.\tFor most evaluations in Table 1, it is difficult to directly compare each model because the results do not represent the best models available in the literature. Instead of using a normalized comparison across all variables, it would be more appropriate to evaluate each variable separately, similar to the approach used in WeatherBench. I recommend adopting the evaluation methodology employed by Pangu-Weather and GraphCast for a more meaningful comparison.\n3.\tThe evaluation in Figure 3 has two notable issues. First, it does not include key variables of current interest. Second, the (ACC) values appear to be significantly overestimated, particularly for u10 at 10 days, which exceeds 0.7—a result that is highly impressive and potentially unrealistic. Additionally, other metrics show substantial discrepancies compared to open-source models like Pangu-Weather, raising concerns about the validity of the results.\n4.\tFigure 4 does not convincingly demonstrate the resolution of over-smoothing, as the results, particularly for q700, still appear excessively smooth. To address the smoothing issue more rigorously, it would be beneficial to include spectral analysis. Additionally, many of the images exhibit noticeable misalignments and artifacts, raising questions about whether the model has been sufficiently trained.\n5.\tFigure 6 does not sufficiently demonstrate the capability for long-term forecasts. While many models can perform long-term stable predictions, their results often converge toward a climatology. It appears that OneForecast may exhibit similar behavior, which raises questions about its ability to maintain accuracy over extended periods.\n6.\tFor the regional prediction of extreme events in Figure 5, focusing solely on the delta of a single event is insufficient to demonstrate accurate forecasting of extreme events. Instead, it would be more informative to include statistical metrics to provide a comprehensive evaluation of the model's performance in predicting extreme events.\n7.\tIt appears that the climatological baseline used in the ACC metrics differs from those used in other studies. This discrepancy may explain the unusual evaluation results and raises questions about the consistency and comparability of the reported metrics.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper introduces a new AI weather forecasting model based on graph networks. It's main contribution is unified global and regional weather forecasting through a single model, adaptive information propagation (through specific graph modules) to capture high frequency information (this is important for things like extreme weather forecasting and long horizon forecasting)

Strengths identified:
* Important contribution - there are no unified regional-global AI weather models that are performant today. Their surrogate attempts to addresses existing challenges in weather emulation through AI models relating to high frequency information capture and long rollouts
* Significant compute was used to compare with SOTA baselines (graphcast, pangu, fengwu etc) to show their model's competitive performance
* Reviewers agreed that the paper was written well and experiments comprehensive.

Weaknesses:
* SOTA weather models are trained at 0.25 deg res - resolution is downsampled in this paper. Further, the authors do not use weatherbench2 directly for comparison for this reason. This is acceptable given their low resolution training and reviewers agreed that their framework is a notable contribution.
* Regional forecasting is also emulated with ERA5 - this is probably unrealistic. Typical datasets to be used for regional weather emulation include datasets like HRRR (see StormCast https://www.arxiv.org/abs/2408.10958 which also used boundary conditions from global models). One reviewer suggests recalibrating the regional model contribution as it lacks extensive experimental validation - the authors responded with framing it as a downstream task which is acceptable for this paper.
* Other comparisons include gencast type models (diffusion) that do not exhibit smoothing etc. However, it is acceptable that these comparisons may be too much given that cost associated with re-training diffusion models.

Several clarifications were raised in the author-reviewer discussion period. Overall, the authors rebuttal convinced reviewers to lean towards acceptance of this paper. The authors need to open-source their whole workflow which they have agreed to do.
Decision: Accept (poster)