STORM: Synergistic Cross-Scale Spatio-Temporal Modeling for Weather Forecasting
Authors: Qihe Huang
Zhengyang Zhou
Yangze Li
Jiaming Ma
Kuo Yang
Binwu Wang
Xu Wang
Yang Wang
Venue: ICLR 2026 Poster (2026)
Keywords: spatial-temporal forecasting
Primary area: learning on time series and dynamical systems

Abstract: Accurate weather forecasting is crucial for climate research, disaster mitigation, and societal planning. Despite recent progress with deep learning, global atmospheric data remain uniquely challenging since weather dynamics evolve across heterogeneous spatial and temporal scales ranging from planetary circulations to localized phenomena. Capturing such cross-scale interactions within a unified framework remains an open problem.  To address this gap, we propose \textbf{STORM},  a spatio-temporal model that disentangles atmospheric variations into multiple scales to uncover scale-specific dependencies. In addition, it enables coherent forecasting across multiple resolutions, maintaining consistent temporal evolution. Experiments on benchmark datasets demonstrate that STORM consistently delivers superior performance across both global and regional settings, as well as for short- and long-term forecasts.

Published as a conference paper at ICLR 2026
STORM: SYNERGISTIC CROSS-SCALE SPATIO- TEMPORAL MODELING FOR WEATHER FORECASTING
Qihe Huang's Zhengyang Zhou , Yangze Li', JJiaing Ma', Kuo Yang', Binwu Wang Xu Wang',, Yang Wang 12+ 'University of Science and Technology of China (USTC), Hefei, Anhui, China
Suzhou Institute for Advanced Research, USTC, Suzhou, Jiangsu, China heh@mail ustu. edu. on
ABSTRACT
Accurate weather forecasting is crucial for climate research, disaster mitigation, and societal planning. Despite recent progress with deep learning, global atmo- spheric data remain uniquely challenging since weather dynamics evolve across heterogeneous spatial and temporal scales ranging from planetary circulations localized phenomena. Capturing such cross-scale interactions within a unified framework remains an open problem. To address this gap, we propose STORM, a synergistic cross-scale spatio-temporal model that disentangles atmospheric vari- ations into multiple scales to uncover scale-specific dependencies. In addition, it enables coherent forecasting across multiple resolutions, maintaining consis- tent temporal evolution. Experiments on benchmark datasets demonstrate that STORM consistently delivers superior performance across both global and regional settings, as well as for short- and long-term forecasts. The code is available at https:// /g/ htgggttthhu.ggg///////ggg hwtpcc////009/9/////00
INTRODUCTION
Accurate weather forecasting plays a pivotal role in climate research, disaster mitigation, and support- ing decision-making in agriculture, energy, and public safety (Kuligowski & Barros, 1998; Baboo & Shereef, 2010; Lam et al., 2022; Gao et al., 2025). Traditional Numerical Weather Prediction (NWP) systems (Bauer al., 2015) are grounded in the numerical solution of atmospheric dynamics (Buzzicotti et al., 2023), ensuring physical consistency across scales (Achatz et al., 2024). However, with the rapid growth of observational data and the demand for high-resolution, long-horizon fore- casts, NWP approaches are increasingly constrained by high computational costs and difficulties in leveraging data-driven knowledge at scale (Rasp et al., 2023).
Deep learning (DL) has recently emerged as a promising paradigm for spatio-temporal forecasting (Yu et al., 2018; Wu al., 2019; Guo al., 2022; Wang et al., 2024a; Ma et al., 2025c;baa;d;fze; 2026a;b; Huang et al., 2025b;a;c; 2024a;c; Lin et al., 2023). Early efforts, such as ConvI.STM (Shi et al., 2015) and PredRNN (Wang ct al., 2017), demonstrated the potential of neural architectures for regional precipitation prediction. More recent large-scale weather models, such Pangu-Weathe Weather (Bi et al., 2023), GraphCast (Lam et al., 2022), and FourCastNet (Pathak et al., 2022), have achieved impressive advances in global forecasting and even in predicting extreme events (Chen et al., 2023b). Despite these successes, current Da-based approaches still face several critical limitations: Multi-scale heterogeneity. Global atmospheric circulation evolves coarse scales, while regional variability emerges at finer scales. Balancing these dynamics within a single model remains challenging (Zhou al., 2023). Diverse temporal evolution. Distinct scales exhibit different temporal dynamics. and existing models struggle to learn coherent cross-scale evolution, often leading to degraded performance in long-term forecasts (Wang et al., 2024b). Weak cross-scale interaction. Most methods process different spatial or temporal scales independently, overlooking their complementary roles and the synergistic effects across scales (Huang et al., 2024b). To address these challenges, we propose STORM, synergistic cross-scale spatio-temporal method for accurate weather forecasting. As shown in Figure 1, STORM explicitly disentangles atmospheric variations across fine-to-coarse
"Zhengyang Zhou and Yang Wang are corresponding authors.

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Published as a conference paper at ICLR 2026
Forcast
One Step Per Turn
Coarse Scale
Muep Forecast
Multi-scale
A
24c
34r
5Ac
6Ar
7AL
8AL
Correlation
Spotial
Lightweight Temporal Encoding
Temporal Evolution Capture
Spatial En& Decode
Multi-view Spatial Learn
Mid- and Long- -term Forecasting
S
Single-view of Earth
Initial Condition
Fine Scale
At
24r
34t
4
Global Regional Adaptability
(a) Weather Model
(b) Our STORM
Figure 1: Comparison of main stream weather forecasting model and our STORM.
resolutions and integrates them via a cross-scale collaboration mechanism with temporal evolution learning. This design enables the model to capture global circulation patterns while preserving local bigh-freyuency details, thereby enhancing both short- and long-term predictive skill. Through extensive experiments on benchmark meteorological datasets, demonstrate that STORM achieves state-of-the-art forecasting performance. Our main contributions are summarized as follows:
To address the challenge scale coupling in atmospheric data, we propose the first spatio- temporal modeling framework for weather forecasting. In particular, (i) it emphasizes cross-scale spatial learning to capture both unique local patterns and shared dependencies across different spatial resolutions, and (ii) focuses on multi-step temporal evolution, rather than merely learning single-step mapping from past to future states.
We introduce STORM, a unified spatio-temporal framework for weather forecasting. comprises (i) Hierarchical Earth Embedder build multi-resolution representations, (ii) a seale-Bridging spatial interactions across scales, and (iii) Level-Aligned Forecasting Decoder generate coherent multi-scale future predictions, enabling accurate decomposition, integration, and reconstruction of atmospheric dynamics.
Encoder to jointly model temporal evolution and
Extensive experiments ERA5 datasets multiple spatial resolutions (5.625", 1 and 0.25%) show that STORM consistently outperforms existing baselines across both global and regional domains. The framework demonstrates superior accuracy for short-term (hours) as well as long-term (several days) forecasts, effectively capturing fine-scale local patterns, medium-scale regional structures, and large-scale planetary circulations.
2 RELATED WORK
Global Weather Forecasting Global weather forecasting has seen rapid progress with the adoption of deep learning models Weyn et al. (2021); Nguyen et al. (2023). FourCastNet (Pathak al., 2022), built upon Fourier neural operators, achieves forecasts comparable to numerical methods like IFS while being orders of magnitude faster. Pangu-Was Weather (Bi et al., 2023), leveraging Swin Transformers with earth-specific location embeddings, surpasses NWP baselines and demonstrates strong scalability. GraphCast (Lam al., 2022) advances further by introducing message-passing networks to efficiently capture global dependencies and improve accuracy. FuXi (Chen et al., 2023b) extends the forecasting horizon, delivering 15-day predictions skill levels comparable to ECMWF operational systems. FengWu (Chen al., 2023a) integrates multi information flow, enabling improved representation of different atmospheric dynamics. Despite these advances, most existing models are primarily designed to learn mapping from the current state to the next-step state, which limits their ability to capture long rang-rnnge temporal evolution and synergistic cross scale interactions.
Modeling Recent advances in time-series forecasting have significantly im- proved modeling capacity across diverse settings, including loss-function design (Wang et al., 2026b; 2025c;bça; 2026c; Qiu et al., 2025b), architectural innovations spanning linear, MLP-, Transformer-, and graph- models (Wang et al., 2023b; 2026a; Yue et al., 2025; Qiu et al., 2025c; Wu et al., 2025b; Hu et al., 2025b), exogenous and irregular multivariate modeling (Li et al., 2026; Qiu et al., 2025d; Liu et al., 2026a;b), probabilistic and multimodal forecasting (Wu et al., 2025c; 2026), as well as comprehensive benchmarking efforts (Qiu et al., 2024; 2025a; Hu et al., 2025a). Building upon these developments, research has progressively extended from temporal modeling spatio-temporal
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forecasting, where spatial interactions, graph structures, and scoss-scale dynamics become central modeling challenges (Ma et al., 2025c; Hu et al., 2026). Deep learning approaches for spatio-tepporal modeling mainly focus on two data forms: graph -raph-structured and grid-structured data (Liang et al., 2025). While graph-based methods have also been explored for irregular domains (Zhang et al., 2022; Wang et al., 2023a; 2024a), grid-based modeling remains particularly suitable for global-scale atmo- spheric data due to its structured nature, Early approaches such as ConvLSTM (Shi et al., 2015) and PredRNN (Wang et al., 2017) explicitly model temporal dependencies through recurrent connections, achieving promising results on precipitation nowcasting. To improve efficiency, SimVP (Gao et al., 2022a) replaces recurrent structures with pure convolutional operators, demonstrating competitive performance on benchmark sequence modeling tasks. More recently, Transformer-basee architec- tures have been introduced, with models such as Earthformer (Gao et al., 2022b) leveraging attention mechanisms on gridded climate data to enhance long-range spatio-temporal dependencies. However, these models are primarily designed as general- spatio-temporal learners and lack specialized adaptations to the unique multi-scale dynamics of weather and climate systems.
3 PROBLEM DEFINITION
In this study, we formulate weather forecasting as a multi-step spatiotemporal forecasting problem. At each time step f. the metcorological state consists of surface variables S, and atmospheric variables A across 13 pressure levels. We concatenate them along the channel dimension to form the combined input: X [S, A,] E # where H x W is the number of spatial grid locations, and + C. is the total number of variables, with C, and C. denoting the numbers of surface
C. C= and atmospheric variables, respectively. Our formulation based on a history of T steps to directly forecast the next I. steps. Specifically, given historical inputs X,-7+1: 1:t, the model predicts the future
X Model (X, θ) where O denotes the model parameters. To support ultra-long forecasting horizons (far beyond L), we adopt a recursive rollout strategy. After generating the first L predictions, the most recent T predicted states are fed back as inputs to produce the next block of L forecasts, and this process is repeated. This block-wise multi-step forecasting significantly alleviates the error accumulation typical of purely autoregressive one-step methods, enabling stable and accurate long-horizon predictions.
4 METHODS
As illustrated in Fig. 2, we introduce STORM, a unified framework for multi-scale spatio-temporal forecasting. The design of STORM is motivated by the intrinsic hierarchical nature of atmospheric dynamics, where large-scale circulations and small-scale local processes interact across different temporal horizons. To capture such complex dependencies, STORM consists of three key com- ponents: (i) Hierarchical Earth Embedder that progressively downsamples raw observations to construct multi-resolution representations, (ii) Scale-bridging Spatio-temporal Encoder that jointly models temporal evolution and spatial interactions while enabling information propagation from fine- coarse-grained levels, and (iii) Level-Aligned Forecasting Decoder that projects multi-scale representations into future prediction through depth-specific transposed convolutions. Together, these components allow STORM effectively decompose, bridge, and reconstruct atmospheric dynamics across scales for accurate weather forecasting.
4.1 HIERARCHICAL EARTH EMBEDDER
Earth observation data inherently exhibit multi-scale characteristics: coarse scales capture large-scall circulation patterns, while fine scales reflect local variations and detailed structures. To effectively leverage information across these scales, we propose the Hierarchical Farth Embedder for multi-scale embedding of global meteorological features. Given input data X [S, A] X xc, where T' denotes the historical length, C' represents the total number of surface and atmospheric variables, and H W defines fine-grained global grid, the data contains rich local details but makes it challenging to directly capture coarse-scale scale circulation and large-scale dependencies. To address this, adopt progressive, layer-wist downsampling strategy for multi-scale modeling and embedding.
First, a X 3 spatial convolution is applied to the original aineggrained input to obtain the initial embedding Ho E RRXxxxX>xx where D is the hidden embedding dimension. This step allows the
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Input [8,TCC,H.W]
Hlerarchical
Scale-Bridgiinn Spatio-
Level-Aligned Forecasting Decoder
Earth Embedder
Temporal Encoder
Spatial
Temporal
Encoder
Encoder
Decoder
Earth Embed
D.
Earth Mixing
Me
Prediction
13 Pressure Levels (RUZ
Encoder
Spatial
Temporal
Encoder
Decoder
Messagre
[.L.D.
Spatial
Temporal
Encuder
Encoder
Decoder
US3 M0
Surface
B.T.C.R.,,W.. W..l
C-
Layers
B...O.
Depth-wise Decoder
General Spatial Encoder
Temporal Envolving Encoder
correitiion icaming
Large-zsie
srtii learing
Tempreal
T-1
Bood
[M W.l
IM...
T-T
Figure 2: Illustration of the multi-scale collaborative metcorological forecasting model.
model to learn localized spatial representations while embedding the raw data. Subsequently, a series of strided convolutional layers with stride are applied progressively downsample the embeddings and capture increasingly coarser spatial structures:
Hm
(er.U CaaipooorrCCoo2l2 (Conv2d (m 11: kernel 3, stride = 2)))),
(1)
where Leaky LeakyReLU denotes the activation function and GroupNorm normalizes feature channels to improve training stability and convergence.
The resulting multi-scale embeddings H = (Ho, H2, HM), where Ho E T T x
retains fine-gra seee-rained local representations and Has E I x W xD encodes coarse scase global structures, capture multi-scal spatio-temport features. These embeddings are then fed into the Scale-bridging Spatio-Temporal Encoder.
4.2 SCALE-BRIDGIN SPATIO-TEMPORAL ENCODER
After obtaining the multi-scale Earth representations, we design scale-bridging spatio-temporal encoder jointly capture spatial dependencies, temporal dynamics, and inter-scale interactions. Unlike traditional meteorological models that often emphasize either temporal or spatial aspects in isolation, our encoder integrates both perspectives while enabling information flow across scales. which is critical for representing hierarchical atmospheric processes.
Spatial encoding. Given multi-scale features H. each level first processed by an independent spatial encoder inspired by the Vision Transformer (Dosovitskiy et al.) structure. Specifically, for the m-th scale and the n-th encoder layer, we perform 2D patch embedding, followed by multi-head self-attentic and feed-forward transformations:
H
(n) m
+ +MIA[LaaeeNoommmPPtaaaaa ((()))
(2)
(()) m
DePatch2D (LayerNorml (H)())) + IFN((ayyrNorm((H (m))))
where Patch2D partitions the grid of size
W into (P1, patches, producing 74 x7, tokens,
HxW
2
and DePatch2D restores the tokenized representation back its grid structure. This operation yields the spatial encoding (m)) E Tx #he x thm x which captures scale-specific meteorological spatial dependencies.
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Cross-scale message passing. To enhance coherence between adjacent scales, introduce cross-scale messaging mechanism. Information from the finer resolution is downsampled and injected into the coarser scale, facilitating hierarchical knowledge transfer:
Hcfa) = CrossSaleeMessagingg.... + H
(4)
Here, CrossScaleMMessagingg is implemented as stride-2 convolution, which aligns the resolution of H with H This design enables the encoder to integrate localized fine-grained patterns into broader global representations, crucial for multi-scale weather forecasting.
Temporal encoding. Finally, we model the temporal evolution of the cross-scale features H While self-attention could be applied across temporal tokens, the extremely high dimensionality of meteorological grids makes it computationally prohibitive. Motivated by recent findings in long-term time series forecasting, we adopt lightweight linear temporal encoder that achieves stable temporal modeling with minimal overhead:
(5) This lightweight network is used to extract temporal dependencies. Here, W1 E TTx2 and W2 E RTx22 enabling effective modeling of historical time steps across multiple scales with extremely small number of parameters (fewer than 100). It efficiently captures multi-scale temporal relationships in past observations.
H W2 x GELU(W, X H + Bi) + B2
4.3 LEVEL-ALIGNED FORECASTING DECODER
The outputs from the N-layer scale-bridging spatio-temporal encoder are subsequently fed into level-aligned forecasting decoder to generate multi-scale forecasts future atmospheric states. The decoder is designed to progressively reconstruct high-resolution spatio- tertooll fields from the encoded representations, while ensuring that temporal forecasting and spatial upsampling remain coherent across scales. For each resolution level m. we apply an independent temporal linear layer that maps the 7"step historical features into L-step future predictions. This design explicitly decouples temporal forecasting across scales, enabling each level to capture temporal dynamics consistent with its own resolution:
Zm Linear,
(M)) m
IRLX
(6)
To progressively upsample the spatial resolution, we adopt depth- adaativee transposed convolution block. Each block doubles the resolution along both spatial dimensions, and the depth of upsampling matched to the level index m. Thus, the m-th scale undergoes m successive upsampling layers, ensuring that coarse-scale features are refined consistently into finer spatial grids:
Um DeCony (Zm) BxXHxWxD
(7)
This hierarchical upsampling ensures that global context encoded coarse scales is gradually transformed into high-resolution local forecasts.
After spatial refinement, all scales share common variable-wise linear projection layer, which maps the hidden dimension into the full set of meteorological variables, including both surface and atmospheric fields. This shared mapping enforces consistency across scales and guarantees that all outputs lie in the same physical variable space:
Vm Linear (U,) L
(8)
Finally, the forecasts from all scales are integrated to form the unified prediction. Each level provides complementary information, with fine-scale forecasts capturing localized details and coarse- scale forecasts contributing global stability. In EarthMix, this integration is performed by directly summing the scale-specific representations:
= EarthMix ([Vm)M))) E RLXH*WXC
This simple aggregation efficiently combines multi-scale information to produce the final high- resolution, multi-variable prediction.
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Published as a conference paper at ICLR 2026
5 EXPERIMENTS
Dataset. We conduct experiments on the fifth generation of ECMWF Reanalysis data (ERAS) (Rasp al., 2023). The temporal range spans from 1993 2021, where 1993-2017 is used for training, 2018-2019 for validation, and 2020-2021 1 for testing. We consider both atmospheric and surface variables. The atmospheric variables include five pressure-level quantities, each with 13 pressure levels: geopotential (2), specific humidity (0), temperature (T), and the U and V components of wind speed. The surface variables include 10-meter wind components (U1 OM, V1 V10M), 2-meter temperature (T2M), total precipitation, and mean sea-level pressure (MSIP). To comprehensively evaluate our method, we construct three datasets at different spatial scales: Global-level: We use the preprocessed ERA5 dataset with a 5.625 spatial resolution and 6-hour temporal frequency. @ Continental-level: We extract ERA5 data over South America, covering the region from S to 1 and W 34 with a 1 spatial resolution. @ Regional-level: We extract subset with 0.25 resolution over East Asia (20"N-28'N E10'E-126'B) More data and pre-processsing details available in Appendix
Metrics. To evaluate forecasting performance, we report two widely adopted metrics in numerical weather prediction: latitude- -etitud--weighted Root Mean Squared Error (RMSE) and Anomaly Correlation Coefficient (ACC). All predictions are first de-normalized before metric computation. Given L forecasting steps. the prediction Sthw and ground truth yehw lead time and spatial grid (h, w). the metrics are defined as
Expo a(h) Yetow Eetw
RMSE-
a(h) (yehew - &eew)) (etm)),AAC. ACC =
HW
Ee (1h) Viro V Ee, a(h) &2
(10)
B 2h==1 cos(N(), and = y are anomalies relative to the empirical climatology C L.W Een. Vehw- More Details is in Appendix D.
where the laittude-deennent weight is ( = cos(())
Σ# H
Baselines. We benchmark our approach against diverse set of representative baselines span- ning operational weather forecasting models, spatio-temporal sequence learners, and image-based architectures. For single-step metcorological forecasting, we include Pangu- Weather (Bi et al., 2023), FuXi (Chen et al., 2023b), FourCastNet (FCN) (Pathak et al., 2022), and Triton (Wu et al., 2025a), which represent of-th- Transformer-based designs for data-driven numerical weather prediction. For multi-step spatio-temporal modeling, we evaluate against Sim (Gao et al., 2022a), leading video prediction framework adapted for geophysical data. Additionally, we incorporate canonical vision backbone, U-Net (Ronneberger et al., 2015), to assess the performance of convolu- tional architectures this setting. All baselines are re-trained on our datasets with identical variables and splits to ensure faimess of comparison. More Details can be found in Appendix E.
5.1 GLOBAL WEATHER FORECASTING
Table 1: Quantitative comparison of short-term (up to 24 hours) global weather forecasting perfor- mance. Metrics are reported as weighted RMSE and ACC, averaged over A/ {6, 12, 18, 24) hours.
Metrie
RMSEL
ACC1
Variable
STORM
Triton
Pangu
FCN
Fuxi
SP
UNet
STORM
Triton
Pangu FCN Fuxi SimVP UNel
T2M
0.675
0.873
1.106
1,579
1.356
1.343
2.445
0,999
0.998
0,997 0.994 0.995 0.996 0.986
U10
0.669
0.819
1.377
I.529
1.314
1.488
1,971
0,991
0.987
0.959 0.953 0.965 0.939
0.952
V10
0.713
0.868
1.483
1.658
1,381
1,556
1,867
0,984
0.976
0.924 0.910 0.940
0.923
0.915
Pree
5.4F-04
6.45-04
8.4F-04
9.8--04
8.
8.76-04
9.6F-04
1.0E-03
0.923
0.891
0.802 0.728 0.791 0.744
0.765
MSLP
71.8
93.7
215.8
217.1
170.1
185.8
257.3
0.998
0.996
0.978 0.979 0.988 0.986
0.976
U500
1.903
2,500
3.410
4.607
3,962
4.066
4.677
0.993
0.988
0.975 0.958 0.969 0.968
0.963
V500
2.055
2.597
3.709
5.021
4.160
4.380
4.999
0.983
0.974
0.942 0.899 0.934 0.926
0.914
T500
0.524
0.696
0.886
1.251
1.111
1.242
1.237
0.99%
0.997
0.995 0.991 0.993 0.991
0.99T
Z500
79.8
109.4
225.7
268.5
215.3
223.5
308.3
1,000
0000
0.998
0.998 0.999
0.999
0.997
Q500
3.91-05
5.0L-05
5.6L-05
7.3L-05
6.90-05
7.76-05
7.30-05
0.976
0.962
0,949
0,918
0.926
0,909
0.924

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Published as a conference paper at ICLR 2026
Short-term Forecasting, We first evaluate the proposed multi-scale spatiotemporal forecasting model, STORM, on short-term global weather prediction. Specifically, we conduct 24-hour forecasts and compare method against range of state-of-the oweooff-thattttee the approaches, including Pangu, Fuxi, Four- CastNet, Triton, SimVP, and U-Net. The evaluation covers both surface variables (2m temperature (T2M), 10m winds (U10, V10), precipitation (PREC), and mean level pressure (MSLP)) as well as mid tropssropoppeeiic fields (500 hPa U/V winds, temperature (T), geopotential height (Z), and specific humidity (Q)) For each method, we report weighted RMSE and ACC averaged over the prediction horizons At = {6, 12, 18, 24) hours. The results, summarized in Table 1, show that STORM consistently achieves the best performance across all variables. In terms of RMSE, our method surpasses even Triton, model particularly tailored for short-term forecasting, by significant margin, while also delivering superior ACC scores. These improvements highlight the advantage of incorporating multi-scale spatiotemporal representations, which enable the model to capture both local details and global circulation patterns effectively. Full results are available at Appendix
Figure 3: Visualization of 24-hour forecasts for multiple atmospheric variables.
To further illustrate the predictive capability of our model, Figure visualizes 24-hour forecasts across multiple variables. Compared with other baselines, the predictions of STORM are visually closer to the ground-truth reanalysis, preserving fine-grained regional structures while maintaining coherent large-scale dynamics. These results confirm that our approach not only improves numerical accuracy but also produces more realistic spatial patterns in short-term global weather forecasting. The visualizations for all variables are provided in Appendix I.
Table 2: Quantitative comparison of long-tem termttermmm (7-10 days) global weather forecasting performance. Metrics are reported as weighted RMSE and ACC, averaged over At = {168, 192, 216, 240} hours.
Metric
RMSEL
ACC1
Variable
STORM
Triton
Pangu
PCN
Fuxi
Sim VP
UNet
STORM
Triton
Pangu FCN
Fuxi SimVP UNet
T2M
2.596
3.386
3.633
4.181
3,500
3.168
4.477
0.984
0.965
0.955 0.971 0.969
0.976
0.937
U10
3.857
4.271
5.127
5.363
4.696
3.901
5.828
0,716
0.650
0.615 0.604 0.574
0.684
0.559
V10
4.106
4.504
5.095
5.569
4.795
4.180
6.045
0.464
0.370
0.325 0.297 0.282
0.383
0.262
Prec
1.4E-03
2.1E:03
1.8E-03
1.615-03
1.6E-03
1,55-033
2.35-03
0.432
0.305
0.288 0.223 0.243
0.214
MSLP
735.4
815.6
1125.4
10414
950.0
784.7
1149.3
0.782
0.725
0.741 0.718 0.641
0.741
0.679
U925
6.582
8.918
10.794
9.159
10.152
8.117
12.236
0.884
0,787
0.803 0.793 0.747
0.827
0.747
V925
6.588
7,910
9.707
9.618
8.794
7.148
10.858
0.519
0.369
0.299
0.284 0.212
0.336
01,205
T925
2.797
3.718
4.308
3.879
4.513
3.565
5,331
0.966
0.937
0.931 0.938 0.912
0.945
0.902
Q925
0,3
5.4E-07
4.5E-07
4.70-07
S 5.50-07
4.06-07
6.3E-07
0.749
0,556
0.556
0.572 0.535
0.630
0.519
7925
813.4
1049.4
1419.2
968.8
1304,1
10974
1537.9
0.981
0.959
0.955 0.963 0.958
0.971
0.936
Long-term Forecasting, Beyond short horizons, we further evaluate STORM on extended-ramn range forecasting, covering 7-day, 8-day, 9-day, and 10-day predictions. Table 2 reports the average weighted RMSE and ACC across these horizons. The results show that STORM consistently outperforms all competing methods, with clear margins over strong baselines such Pangu and
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FourCastNet. Even day 10, where the forecasting task becomes extremely challenging due accumulation and chaotic dynamics, our model maintains significantly lower RMSE and higher ACC, demonstrating its robustness and superior long-ter term predictive capability. Full results available at Appendix K. To provide further insight, Figure visualizes the evolution of RMSE and ACC from
INUSED V922
HNSII--U22
RMSS-- 1925
BMdii- 12M
RMAS
KMSS
Fusoual Days ACT-49924
Feccal Days
Fassar Daps
Feream: Days
FusueD Dap
Facmal
ACC-V995
ACC--255
ACK-Q924
ACX--195
ACT-12M
5/6
LH
Fusora Days
Feccal Days
Farcad SimMP
Ferozm
Dops
Fup
Feceal
Tuxi
Ours
Triton
Pangu
ICN
UNet
Figure 4: RMSE and ACC of U925, V925, 2925, Q925, T925, and T2M from day to day 10.
day to day 10 for several key variables, includingU925,, V925, 7925, Q925, T925, and T2M. We observe that different baseline methods tend to exhibit strengths over specific forecast horizons-for example, some achieve relatively competitive results at shorter lead times but deteriorate rapidly afterwards. In contrast, STORM consistently maintains the best accuracy across both short- and long-term horizons. This highlights the effectiveness of our multi-scale spatiotemporal design, which enables stable and reliable forecasts over a wide range temporal scales.
5.2 REGIONAL HIGII RESOLUTION FORECASTING
To further demonstrate the scalability and robustness of our approach, we conduct forecasting experiments on higher-resolution regional subsets. Specifically, we consider two representative cases: Continental-level: South America, spanning from S to N and 81 to W, at 1 resolution; Regional-level: East Asia, spanning 20 N0 N and E-16E-126' E, at 0.25" resolution.
Table 3 summarizes the RMSE and ACC across all variables for horizons of 6 hours, day, 4 days, days, and 10 days. We observe that STORM consistently achieves the lowest RMSE and the highest ACC at both continental and re- gional scales, highlighting its ability to maintain strong predictive skill under different spatial res- olutions. particular, the advantage STORM becomes more pronounced at longer horizons, demonstrating its superiority in long-range re- gional forecasting. Figure 5 provides qualita- tive visualization the 10-day forecasts for se- lected variables in both South America and East Asia. By zooming into local details, we see that STORM captures fine-gu fineinnained structures more faithfully and is visually closer to the ground truth compared to baselines. These results confirm the effectiveness of multi-scale design in enhancing both large-scale consistency and small-scale detail preservation.
Conticerra lovel Reskation
Figure 5: Visualization of 10-day forecasts over South America (19) and East Asia (0.25%).
5.3 ABLATION STUDY
To better understand the contribution of each component in STORM, we conduct an ab- lation study by removing or modifying key modules. Specifically, we consider the fol- lowing variants, w/o T: which removes the temporal evolution encoder from the en- coder; w/o M: which changes the Hierarchical Earth Embedder, the Bridging Spatio- Temporal Encoder, and the Level-Aligned Forecasting Decoder to replace multi-scale model- ing with single-scale modeling: w/o S: which removes the spatial encoder from the encoder.
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Table 3: Regional high-resolution forecasting results. We report averaged results for hours, day, days, 7 days, and 10 days over South America (1 resolution) and East Asia (0.25 resolution).
6Hour
IDay
4Day
7Day
10Day
Data
Methods
RMSEL
A ACC1
RMSEL
ACC1
RMSEL
ACC1
RMSEJ
ACC1
STORM
0.874
0.945
1.560
0.847
2.866
0.601
3.322
0.519
3.510
0.499
Triton
0.927
0.941
1.808
0.817
3.689
0.480
4.687
0.347
5.433
0.251
FCN
1.411
0.933
2.466
0.816
4.186
0.498
5.176
6.018
Cont-SA (19)
Pangu
0.989
0.876
1.794
0.702
3,557
0.440
4.235
0.375
4.613
0.368
Fuxi
0.941
1.677
0.830
3,253
0.547
3.632
0.500
3.797
0.466
SimVP
0.947
0.939
1.619
0.843
3.110
0.554
3.603
0.476
3.891
0.426
UNet
1.528
0.873
2.696
0.661
6,994
0.291
11.50
0.248
15.62
0.252
STORM
14.53
0.980
41.71
0.920
154.6
0.627
187.8
0.548
200.9
0.524
Triton
14.55
0.976
51.65
0.919
183.7
0.579
218.7
0.499
234.3
0.482
FCN
33,00
0.954
98.15
0.832
256.4
0.559
297.4
0.495
315.6
0,471
Reg-EA (0.25%)
Pangu
17.35
0.963
47.31
0.895
157.5
0.625
206.2
227.5
0.511
Fuxi
17.69
0.969
54.67
0.903
178.1
0.592
211.2
0.522
227.7
SimVP
32.17
0.935
53.44
0.887
158.5
0.615
189.0
0.546
202.5
0.523
UNet
22.77
0.956
63.05
0.875
195.1
0.566
241.6
0.480
261.8
0.450
Figure 6 reports the RMSE for ten key variables: T2M, 010, V10,PREC, MSLP, U500, V500, T500, Q500,
and Z500. The results demonstrate several important findings: (1) Every module contributes significantly the overall forecasting performance; (2)
RMSE
T2M
U10
V10
Prec
MSLP
US00
V500
T500
0500
Z500
The spatial encoder (S) plays a partic- ularly critical role in improving pre- diction accuracy; (3) The combination of multi-scale mixing and spatial encoding achieves the largest performance gains, indicating that capturing both spatial dependencies and multi-scale interactions is crucial for accurate global weather forecasting. These observations confirm the effectiveness of our design in modeling complex spatiotemporal dependencies inherent in meteorological data.
Figure 6: Ablation study results of STORM.
5.4 STORM ANALYSIS
We perform a multi-scale analysis of STORM understand the contribution of different spatial scales to forecasting accuracy. Figure 7(a) visualizes predictions at different scales. The finest scale (sca 0) captures rich local details, while the coarsest scale (sca 1 e2) better represents global circulation patterns. Individually, each scale exhibits distinct prediction errors, but combining multi- scale predictions results the most accurate forecasts, demonstrating the effectiveness of multi-scale integration. Figure 7(b) further analyzes the effect of the number of scales hyperparameter. As the number of scales increases, the predictive performance improves, but the gains diminish beyond three scales. Based on this analysis, set the number of scales in STORM to three, achieving balance between local detail preservation and global structure representation.
Scaleo
Scale
Prediction (T2M)
Prediction (MSLP)
Scale 1
Scale 1
2
Scale
Scale Nunher
(a) Visualization of Predictions at Different Scales
(b) Analysis of Seale Number Impact
Figure Visualization of multi-scale predictions and the analysis of scale number.

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Published as a conference paper at ICLR 2026
CONCLUSION
Despite rapid advances in deep learning for weather prediction, modeling atmospheric dynamics remains challenging due their heterogeneous spatio-temporal scales. We introduced STORM, unified framework with a Hierarchical Earth Embedder, Scale-Bridging and Level-Aligned Forecasting Decoder explicitly capture cross-scale dependencies. Extensive experiments on ERA datasets with resolutions of 5.625", 1 and 0.25% show that STORM consistently achieves state-of-the the-art performance across global and regional settings, well as short- and long- term horizons. Our results highlight the necessity of synergistic multi-scale modeling for reliable weather forecasting. Looking ahead, we envision STORM as a step toward new generation of spatio-temporal models that integrate fine-gres tinegnained detail with global coherence, offering foundation for more accurate, efficient, and robust climate and Earth system prediction.
Encoder,
ETHICS STATEMENT
All authors confirm compliance with the ICLR Code of Ethics. This study does utilize human participants, private information, or sensitive content. Our work relies entirely on publicly available datasets and established benchmarks, with no anticipated negative social environmental conse- quences. There are no conflicts of interest or external funding sources that might influence the findings.
REPRODUCIBILITY STATEMENT
We have taken care ensure that experiments can be replicated. The architecture and training details of our model are fully described Sections 4 and Appendix E. All datasets are publicly accessible, and the preprocessing steps documented in Appendix C. Furthermore, we provide anonymized code and usage instructions as supplementary material to support reproducibility of our results.
ACKNOWLEDGMENT
This paper is partially supported by the National Natural Science Foundation of China N8.62502488, No. No.12227..1 Natural Science Foundation of Jiangsu Province (BK20240460), the grant from State Key Laboratory of Resources and Environmental Information System. The Al-driven experiments, simulations and model training were performed on the robotic Al-Scientist platform Chinese Academy of Sciences.
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Appendix
Table of Contents
LLM Usage
B Theoretical analysis: why multi-scale modeling helps
B.1 Setup and assumptions
B.2 Generalization bound imporvement
17
B.3 Improved optimization speed regarding convergency
18
B.4
Putting pieces together: overall error and sample complexity
18
C More Data Details
19
D More Metric Details
20
E More Implementation Details
20
F Efficiency Analysis
20
G Full Sensitive Analysis
21
More Details of Ablation Analysis
Forecast Visualization
22
Mean Sea Level Pressure (MSLP)
22
1.2
Specific Humidity 500 hPa (...............................
23
L.3
Precipitation
24
1.4
2-meter Temperature (T2M)
25
1.5
Temperature at 500 hPa (T500)
................................
26
16
10-meter Zonal Wind (U10)
27 "o..............................
Zonal Wind at 500 hPa (US00)
"...............................
28
10-meter Meridional Wind (V10)..
................................
29
1,9
Meridional Wind 500 hPa
................................
30
L.10
Geopotential Height 500 hPa (Z500)
31
J Full short-term forecasting results.
32
K Full long-term forecasting results.
33
16

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A LLM USAGE
Following the conference guidelines regarding large language models (LLMs), we disclose that
LLMs were utilized solely to improve sentence clarity and grammatical correctness, All aspects of conceptual development, experimental methodology, data analysis, and core manuscript content were independently produced by the authors without LLM assistance
B THEORETICAL ANALYSIS: WHY MULTI-SCALE MODELING HELPS
In this section we present theoretical results that explain why synergistic cross-scale spatio-temporal architecture can outperform single-scale counterpart in (i) statistical generalization (smaller expected prediction eтror) and (ii) optimization speed (faster convergence). We adopt bias- Dias-variance decom- position perspective for generalization, and a cnnttioonnummerrr PL-ttye argument for optimization. Proofs are sketched; full technical details follow the argument outlines below.
B. SETUP AND ASSUMPTIONS
Let BTXCXHxW denote one time-slice grid and consider target spatio-temporal mapping I" ":RTXXXXM xxx that maps T historical frames to L future frames (all variables vectorized as needed). Denote by the data distribution and by (X Y;) DD the training set. We consider two model classes: O Single-scale model Fsingle of effective cesameter-dimenssie d (e.g., monolithic spatio-tempora network operating at full resolution). Multi-scale model Fis which decomposes the prediction into M scale-specife modules with parameter-dimensee d1, d dM (so ΣM dm S d depending on parameter sharing). We make standard regularity assumptions: Assumption B.1 (Decomposability), The target admits scale decomposition
T'=Esm fm.
f E 9m.
m=
where each Jm captures variations at spatial scale m, and 9m is the function space for scale m signals fine, medium, or coarse patterns).
Assumption B.2 (Model capacity allocation). Each scale-model class Fm has Rademacher complexity (m I Pm / dm for constants Pm 0, while the single-scal class satisfies
RR, (F S PPV
Assumption B.3 condition for optimization). The empirical loss i.(0) is T-smooth and satisfies the Polyak-tojasiewic: (PL) inequality in neighborhoods of interest: there exists > s.t.
\vi(00) 2 ((((()- -.r)-
B.2 GENERALIZATION BOUND IMPORVEMENT
We first bound the excess risk (population loss minus Bayes risk) via a bias-variance decomposition and Rademacher complexity.
Theorem B.1 (Generalization bound imporvement). Assume squared loss and hypotheses above. m= fm be ERM solutions in Fsingle and F respectively. Then with Lei fenggl and f'se Σ MM probability at least 8.
d
log(1/0) 12
E(faingt)) S
inf feFuia
1f 1+ p n
+0
approx.
and
M E(fms) <
M Σ m=l
dm +
o
log(1/0)
log (//))
inf [gg fill +B g m=1
Pm
multi-scale approx.
17

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Published as a conference paper at ICLR 2026
where B > 0 is a universal constant and & denotes population squared error.
Proof sketch. Standard decomposition: population risk = approximation error estimation error. Estimation error is controlled by Rademacher complexity; using Assumption 2 we get the stated dV (single) and sum of pm / ddm./n (multi-scale). The remainder term follows from concentration (Talagrand/ McDiarmid), yielding the Vlog(1/0)/n term.
Interpretation. If (i) the decomposition is faithful so that each fm is well-approximated by Fm (small multi-scale approximation enror), and (ii) the per-scale capacities dm concentrate (c.g. dm < d), then
Σ dmn Vd.
hence the multi-scale estimation term Σm Pmr v dm n can be substantially smaller than PV d/n, yielding better generalization. Concretely, dm d/M and pm p, then
M
dm - M = Mdd < Vd MM<1,
so naive equal partition does not help; however, real atmospheric signals are compressible: coarse scales require tiny dm and only few fine-scale components need larger dm making Σm vdn < vd in practice. Thus the bound formalizes a bias-variance tradeoff where multi-scale modeling reduces variance without materially increasing approximation bias.
B.3 IMPROVED OPTIMIZATION SPEED REGARDING CONVERGENCY
We now sketch how hierarchical (coarse-to-fine) architectures improve optimization by reducing effective condition numbers and enabling faster gradient-bai convergence.
Theorem B.2 (Improved optimization speed regarding convergency). Under Assumption (PL. inequality and T-smoothness) consider gradient descent with step size 1) S 1/T. Let Ksingle T./p denote the condition number for the single-scale parameterization, and let Kms be the effective condition number for multi-scale architecture that first fits coarse parameters and then refines fine parameters (blockwise parameterization) If the pross-scale coupling operator has spectral gap ry (0, 1), then
Pens S (1 (1-7) 7) Esingles
and gradient descent on Fins converges linearly
i(0.)) - s (1- -
(()()) i²).
Proof sketch. Block- parcktaatiiion the parameter vector = (0coarse, O.ne]. The Hessian of the empiri- cal loss can be written in block form; coarse-to-fine structure makes the off-diagonal blocks small
relative to diagonal blocks due to localization (this is the spectral gap 7). Using matrix perturbation
bounds (Weyl-type inequalities) one shows the largest-to-smallest eigenvalue ratio of H is reduced by factor (1 7). Under PL, GD attains linear rate with factor MPPll. where Pef 101 7). O
The spectral-gap condition formalizes the intuition that coarse-scale variables capture low-frequency, high-energy components and are weakly coupled to many fine-scale modes; explicit coarse-to- fine parametrization reduces ill-conditioning caused by high-frequency components and thus accelerates optimization.
Remarks.
B.4 PUTTING PIECES TOGETHER: OVERALL ERROR AND SAMPLE COMPLEXITY
Combining generalization and optimization insights yields unified statement.
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Corollary B.3 complexxo advantage). Suppose the decomposition is faithful and the optimizer attains an e-accurate empirical minimizer in Te) iterations (GD linear convergence as above). Then achieve population error & E, the multi-scall scale model requires
M
nms = 0 g2
Σ m==1
Pm P dm
samples, while the single-scale model requires
0 1 (
Usingle =
If Em dmm & dd, then Tams & msingle
C MORE DATA DETAILS
To provide a more comprehensive description of the experimental setup, we summarize the datasets used in this work in Table 4. As introduced in the main text, all datasets derived from the ERAS reanalysis, covering the period from 1993 to 2021. Specifically, we split the data into 1993-2017 for training, 2018 2-10 for validation, and 2020-2001 2021 for testing. For atmospherie variables, include five pressure-level quantities, geopotential (Z), specific humidity (Q), temperature (T), and the U and V components of wind, each defined 13 standard pressure levels. For surface variables, we consider 10-meter wind components (U10M, V10M), 2-meter temperature (T2M), mean sea-level pressure (MSLP), and accumulated precipitation. Note that in Global- and Continental-leve settings, precipitation is additionally included compared to the original 69 ERA5 variables, while in the Regional-level dataset only near-surface variables (T2M, U10M, VIOM) are used. Regarding spatial coverage, we construct three datasets with different geographical ranges and resolutions: (i) Global- level: 5.625 resolution with 6-hour temporal frequency; (ii) Continental-level: 1 resolution over South America (56 N, W11W-34 W)) and (iii Regional-level: 0.25" resolution over East Asia (20'N-28 N, 110 E-126 E). For preprocessing, we standardize each variable using statistics (mean and standard deviation) computed from the training set only. During inference, model predictions rescaled back (de-normalized) to the original physical units to ensure consistency with evaluation metrics. This normalization scheme improves model stability and comparability across heterogeneous variables.
Table 4: The data details.
VARIABLE NAME
SPATIAL RESOLUTION
TEMPORAL FREQUENCY
LAT-LON RANGE
TASK
LAYERS
GEOPOTENTIAL (Z)
13
5.625
61l
--0000000 N. 180 W-180'E
SPECIFIC TEMPERATURE (T)
(Q)
5.625
68
-90S5-00 N, 180 E
13
5,625
61l
900 N, 180 W-180"E
U COMPONENT OF WIND (U)
5.625 13
66
-00S--00,, 180 180
V COMPONENT
(V)
13
3.625
-90 180" W E
GLOBAL
10M U WIND (U10)
5.625
68
900S 90 180 W 180"E
10M WIND (V10)
5,625
S0'S-90'N 180 E
2M TEMPER (T2M)
5.625
90'S 9, 180 180
MEAN SEA LEVEL PRESSURE (MSLP)
5.625
90 S-90 180" E
TOTAL PRECIPITATION (PREC)
5.625
6tl
5-90 N. 180 W-180'E
GEOPOTENTIAL (Z)
6
56"S-11"N, S1"W-30
SPECITIC HUMIDITY (Q)
13
1.0
61l
SAME AS ABOVE
TEMPERATURE (T)
13
1.0F
6H
SAME AS ABOVE
CUMPUNENT V COMPONENT OF WIND (V)
(U)
13
1.0"
13
1.0"
6H
SAME AS ABOVE
CONTINENTAL
10M WIND (U10)
1.0º
6н
SAME AS ABOVE
10M WIND (V10)
1.0
61l
2M TEMPERATURE (T2M)
1.0º
SAME AS ABOVE
MEAN LEVEL PRESSURE (MSLP)
6tt
SAME AS ABOVE
TOTAL PRECIPITATION (PREC)
1.0"
6н
AS
2M TEMPERATURE (T2M)
I
0.25"
6н
20 28 110" E 126"E
REGIONAL
10M WIND (U10)
0.25"
6H
SAME AS ABOVE
10M WIND (V10)
0.25"
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D MORE METRIC DETAILS
To evaluate forecasting skill, we follow standard practices numerical weather prediction and report latihude-weighted Root Mean Squared Error (RMSE) and Anomaly Correlation Coefficient (ACC). Before computing the metrics, model outputs are de-normalized back to physical units for consistency with observations.
RMSE
(h) (yerue ketww
(11)
HW
Ee,t, a(li Deton Terw
ACC
(12)
Ee,h, a(h) Virw Ee al
where (<h)) = cos(h) / ΣØ cos(I/)) compensates for unequal grid areas across latitudes. The anomaly terms are defined as Urnw = Yeko C' and herw = ierw C, with C = LHW Deth. Vthan representing the climatological mean.
RMSE reflects the average magnitude of prediction errors while accounting for the Earth's 's geometry. ACC instead measures the similarity between predicted and observed anomalies, emphasizing the model's ability to capture dynamical patterns rather than absolute values. Together, these two metries provide a balanced view of both error magnitude and anomaly-tracking skill.
E MORE IMPLEMENTATION DETAILS
All experiments are conducted on server equipped with 8 NVIDIA A100 GPUs. Our implementation of STORM is based on PyTTorch 2.1.0 (Paszke et al., 2019). For optimization, we adopt the Adam optimizer (Kingma, 2014) with a learning rate of 1 x 10-3 and mean squared error (L2) as the training objective. Each model is trained for 100 epochs with early stopping based on the validation loss. The multi-scale hierarchy is constructed with M 3 levels, and the hidden dimension is fixed to = 256 across all experiments. The Scale-Bridgee
Encoder is composed of N 3 stacked layers. To ensure faimess, all baselines are re-trained under the same data preprocessing, optimization, and training protocols. The model is trained using the mean squared error (MSE) loss between predicted and observed atmospheric states, which aligns with the RMSE evaluation metric and encourages accurate recovery of both large-scale patterns and fine-grained variations.
Spatio-Tempon
F EFFICIENCY ANALYSIS
As shown in Table 5, STORM delivers substantially better afficiency-accurray trade-off compared with existing data-driven weather models. Despite having only 15.8M parameters, STORM achieves the lowest inference latency (0.87s per 100 samples) and competitive FLOPs, while also attaining the highest prediction accuracy (ACC= 0.984). In contrast, large-scale models such Pangu and Fuxi incur significantly higher computational and memory costs but still fall short in accuracy. These results highlight that STORM's lightweight architecture effectively preserves predictive skill while enabling fast and resource-efficieee forecasting.
Table 5: Efficiency comparison across representative data-driven weather models.
Metric
STORM
Pangu
FCN
Fuxi
Inference Time (Seconds/ / 100 Samples)
0.87
5.11
6.99
19.37
Peak GPU Memory | (MB, Batch Size I)
729.22
408.75
265.95
2533.25
Parameters (M)
15.77
97.48
64.65
661.01
FLOPs J (GFLOPS)
84.59
91.26
58.50
302.46
ACC 1
0.984
0.952
0.933
0.950
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G FULL SENSITIVE ANALYSIS
Table summarizes the scaling behavior of STORM under varying branch numbers and model widths. Increasing either the branch depth or dmodel consistently improves accuracy, with ACC rising from 0.941 (1 branch, 64 hidden units) to 0.988 (5 branches, 256-512 units), while RMSE steadily decreases. Notably, these gains come with only moderate growth in FLOPs and inference time, indicating that STORM's 's multi-branch temporal encoder scales efficiently. The results highlight a clear efficiency-aceuracy trend: larger branches yield stronger predictive skill without incurring prohibitive computational cost.
Table 6: Scaling and efficiency analysis of STORM across different branch configurations.
Branch d d_model Total Params Temp. Enc. Params FLOPs
Max Mem.
ACC
RMSE
64
0.32
2.96E-04
3.17
0.28
13.75
0.941
16.415
128
1.20
2.96E-04
11.04
0.30
17.44
0.951
16.323
256
4.59
2.96E-04
40.88
0.30
30.01
0.954
16.267
512
17.96
2.96F-04
156.92
0.30
82.59
0.958
16.177
2
5,92E-04
0.963
16.136
2
128
2.45
5.92E-04
16.00
0.56
24.43
0.966
16.115
2
256
9.59
5.92F:04
60.32
0.56
51.66
0.971
16.093
2
512
37.92
5,920-04
233.92
0.59
164,49
0.974
15,983
3
64
1.03
8.88E-04
6.05
0.86
19.48
0.977
15.913
3
128
8.88E-04
22.16
30.35
0.981
15.854
3
256
15.77
8.88E-04
84.59
0.87
75.48
0.984
15.809
3
512
62.60
8.88F-04
330.25
0.87
257.33
0.985
15.798
4
64
1.46
1.18E-03
7.44
1.15
20.31
0.979
15.841
4
128
5.70
LI8E-03
27.61
1.16
37.27
0.983
15.813
4
22.54
L.18E-03
106.12
1.17
101.06
0.987
15.769
4
1.18::03
415.84
1,20
360.60
0.986
15.784
5
64
1.96
1,48E-03
8.23
1,49
335.52
0.983
15.808
5
128
7.69
1,48E-03
30.62
1.52
361.66
0.984
15.796
5
256
30.49
L48E-03
117.84
1.51
448.31
0.988
15.757
5
512
121.40
1. 1.88-003
462.11
1.53
908.50
0.988
15.716
H MORE DETAILS OF ABLATION ANALYSIS
Tables and highlight the contribution of message passing and scale heterogeneity in STORM's multi-branch architecture. First, enabling message passing consistently boosts performance across all branch counts, with ACC improvements 0.6-1.0% and reduced RMSE, indicating more effective cross-scale information flow. Second, branches configured with different temporal scales significantly outperform those using identical scales, showing clear gains that grow with larger branch numbers. These results confirm that both cross-scale communication and scale diversity are essential for extracting complementary temporal patterns and achieving stronger predictive skill.
Table Ablation on message passing across multi-scale branches.
Branch (Scale Numbers) ACC (with MP) RMSE (with MP) ACC (without MP) RMSE (without MP)
16,093
0.963
16.
0.984
15,809
0.976
15,948
0.987
15.769
0.981
15.886
0.988
15.757
0.980
16.879
Table 8: Effect of different vs same multi-brance designs.
Scale Number ACC (Diff Scale)
RMSE (Ditf) ACC (Same Scale) RMSE (Same)
2
0.971
16,093
0.939
16.547
3
0.984
15.809
0.948
16.382
0.987
15.769
0.954
16.285
0.988
15.757
0.957
16.179
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1 FORECAST VISUALIZATION
1.1 MEAN SEA LEVEL PRESSURE (MSLP)
time Lead time hours
hours
Lead
109959.6
Coound Trri
102010.5
ars ers
96162.9
103876.9
67N 3070
Okzx
90092.
961644
80%
Fange
1006011
2916401
Pusii
191666
FourCarNee
982152
902152
204440 A
07N
1021094
10244.11
SGoVP
100354.7
96466-4
965760
4PN
100340.5
96508.
DFF
1251
Figure 8: 24-hour forecast results different models for mean sea level pressure (MSLP).
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1.2
SPECIFIC HUMIDITY AT 500 HPA (Q500)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
emn 30n
00
am
Okn
00
Pingh
0.0
0.0
Panz
000
PoorCastNet
307
000
80%
Thilen
00
000
00
UNNe
00
Figure 9: 24-hour forecast results of different models for 500 hPa specific humidity (Q500).
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1.3 PRECIPITATION
Lead time hours
Lead time hours
Lead time 18 hours
Lead time hours
Groend Trath
00
305s
eir
0.0
Ouz
0.0
0PN
Phagu
30%
0.0
Pinti
00
FourCaatee
0.0
0.0
8PN
ScaVp
0.0
00
10/W
12019/
Figure 10: 24-hour precipitation forecast results different models.
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1.4 2 2-METER TEMPERATURE (T2M)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
67%
3010
2740
2529
4mh
294.
Okn
273.3
295.0
Pingz
231.5
31688
Panz
252.7
211.5
PoorCastNet
67h
270.2
240.4
295.2
Thiten
273.9
262.6
3167
294.
SanV
3064
2664
UNNe
206.4
Figure 11: 24-hour forecast results of different models for 2-meter temperature (T2M).
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Published as a conference paper at ICLR 2026
1.5
TEMPERATURE AT 500 HPA (T500)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
677
3010
2077
218.6
4m
237.0
Ozn
228.0
236.7
Pingh
209.4
245.7
Pant
210.6
PoorCastNet
67h
3070
229.2
2004
80%
Thile
225.4
219.7
246.3
237.9
SanV
266.1
237.5
UNNe
2003
211.7
Figure 12: 24-hour forecast results of different models for 500 hPa temperature (T500).
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1.6
10-METER ZONAL WIND (U10)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
6mn 30n
16
40
4mN
Oknn
0.7
94
Pingz
-2.1
18.8
Panz
-0.3
16.3
PoorCastNet
67N
307
59
8PN
Thile
4.6
10.0
SanV
14.6
80
UNNe
-1.9
Figure 13: 24-h forecast results of different models for 10-meter zonal wind (U10).
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1.7 ZONAL WIND AT 500 HPA (U500)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
677
3010
2699
36
47%
49.7
Okn
27.2
49.3
Pingz
18.3
78.8
Pant
-1.00
PoorCastNet
30%
67N
28.9
76
Thile
264
52.5
SanV
77.6
55.3
UNNe
10.0
-1.
Figure 14: 24-hour forecast results of different models for 500 hPa zonal wind (U500).
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1.8
10-METER MERIDIONAL WIND (V10)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
6mn 3010
19
10.7
6mh
75
Okn
1.3
7.8
Pingh
16.4
174
Panz
31.1
PoorCastNet
07N
30
9.0
80%
Thile
-.9
-1.0
10.2
16.5
82
UNNe
1655
Figure 15: 24-hour forecast results of different models for 10-meter meridional wind (V10).
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1.9 MERIDIONAL WIND AT 500 HPA (V500)
Lead time hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
6mn 3010
245
47N
33.6
Okn
53
57.1
30.3
Pingh
50.0
54.
Panz
41.5
PoorCastNet
67N
30
0.0
23.4
87%
Thien
26.9
25.1
20.0
99.0
30.4
UINE
55.5
Figure 16: 24-hour forecast results of different models for 500 hPa meridional wind (V500).
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1.10 GEOPOTENTIAL HEIGHT 500 HPA (Z500)
Lead time 6 hours
Lead time 12 hours
Lead time 18 hours
Lead time 24 hours
Chound Truth
6m% 30%V
87981.1
84036.0
am
91899.
Okn
87935.4
Pingg
Panz
PoorCastNet
87
Thilen
SanV
91927.5
UNNe
#4039.0
10094.7
13PW APW
12/2
12379/
DFF
Figure 17: 24-hour forecast results of different models for 500 hPa geopotential height (Z500).
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J. FULL SHORT-TERM FORECASTING RESULTS.
Table 9: Quantitative comparison of short-term (up to 24 hours) global weather forecasting perfor-
mance.
Metric
RMSE
ACC
Variable Hours
Ours
Triton
Pangu
FCN
Fuxi
SimVP
UNet
Ours
Triton Pangu
FCN
Fuxi
Sim
UNet
0.564
0.718
0.787
1,430
1.191
1.335
1.337
0.9999
0.999 0.998 0.995 0.996
0,996
0.995
12h
0.653
0.836
1.075
1.545
1,308
1.332
2.208
0.999
0.998
0.997 0.994 0.996
0,996
0.987
T2M
18h
0.705
0.929
1.219
1.632
1.415
1.341
2.789
0.999
0.998
0.996
0,993 0.995 0.996
0,982
24h
0.777
1,010
1.342
1,708
1.513
1,363
3.447
0.998
0.997
0.995
0,993 0.994 0.995
0,981
6h
0.495
0.598
0.775
1.169
0.994
1.279
0.955
0.995
0.993
0.988
0.973 0,981 0,968
0.981
0.608
0.749
1.2019
1.376
1.200
1.359
1.437
0.989
0.972
0.963 0,972 0.964
U10
18h
0.719
0.894
1,590
1.646
1.423
1.497
2.032
0.990
0.985
0.951
0.947 0.961 0.956
0.942
24h
0.853
1.034
1.933
1,926
1.637
1.659
3.462
0.986
0.979
0.927
0.927 0,948 0,946
0.924
6h
0.520
0.629
0.834
1.274
1.064
1.378
1.012
0.992
0.988
0.979
0,950 0,965 0.941
0.967
12h
0.647
0.796
1.304
1.492
1.268
1.467
1.491
0.987
0.981
0.947
0,930 0.950
0,933
0,933
V10
18h
0.768
0,950
1.713
1.782
1.490
1.608
1.994
0.982
0.973
0.908
0.899 0,932 0.919
0.898
24h
0.917
1.098
2,082
2,084
1.703
1.772
2.971
0.974
0.963
0.862
0.861 0.911
0,900
0.863
6h
4.2E--04
4.8E-04
6.
6.10-04
9.2E-04
7.4E-04
9.2E-04
6.7E-04
0.955
0.941
0,906
0,763 0.856
0.768
0.885
12h
4.9E-004
5.8B-08
04
7.9
04
9.5E
04
8.28-04
04
9.31
04
8.9E 04
0.938
0.913
0.833
0,748 0.819
0.758
0.792
Prec
18h
5.9E-04
7.0E-04
9.3E-04
1.0E-03
9.2E-04
9.7E-04
1.1E-03
0,911
0.872
0.765
0,717 0.768
0.737
0,719
24h
6.6F:-14
7.8F-04
1.0F-03
1.11-03
1.0F-03
1.0F-03
1,48:-03
0.886
0.839
0.705
0.682 0.722
0.713
0.663
46.808
60.49%
101.67
678
147.757
112.764
154.169
113.815
0.999
0.996
0.991 0,995
0.990
0,994
12h
61.834
82,905
179.577
186.644
148.871
168.679
198.949
0.998
0.997
0.987
0.986 0.991
0.989
0.984
MSLP
18h
78.448
104.797
410
337.317
188.986
194.126
389
0.998
0.996
0.973
0.977 0.986
0.985
0.971
24h
99.948
126.514
326.712
295.758
229.717
226.092
427. 427.862
0.996
0.994
0.956
0,964 0.979
0.979
0.956
6h
1.384
1,835
1,879
3.540
2.953
3.553
2.503
0.996
0.994
0.993
0,976 0.983
0.976
0.987
1.713
2.287
2.972
4.148
3.612
3.789
3.880
0.990
0.983
0.967 0,975 0.973
0.971
U500
18h
2.041
2.725
3.945
4,940
4.303
4.204
5.158
0.992
0.986
0.970
0.953 0,965 0.966
0.955
24h
2.472
3,151
4.845
5.802
4.980
4.719
7.166
0.988
0.981
0.955
0,935 0.953 0.957
0.939
6h
1.449
1.873
2,036
3.765
3.155
3.823
2.868
0.992
0.987
0.985
0.947 0,963
0.945
0.969
12h
1.835
2.367
3.228
4,486
3.817
4.093
4.259
0.987
0.979
0.961
0,924
0,946
0,936
0,933
V500
18h
2,221
2.843
4.290
5.418
4.500
4.530
5.508
0.982
0.970
0.930
0.887 0,925 0,922
0.897
2.714
3.305
5,284
6.414
5.169
5.073
7.363
0.972
0.960
0.893
0.841 0.902 0.901
0.859
6h
0.376
0.518
0.513
1.087
0.903
1.189
0.679
0.999
0.998
0.998
0,993 0.995 0.992
0.997
12h
0.478
0.646
0.802
1.177
1.036
1.210
1.087
0.999
0.998
0.996
0.992 0.994
0.991
0.993
T500
18h
0.566
0.760
1.024
1.300
1.182
1.255
1.410
0.998
0.997
0.994
0,990 0.992
0.991
0,988
24h
0.675
0.861
1.207
1.441
1.321
1.313
1.773
0.997
0.996
0.991
0,988 0.990
0.990
0.985
51.5
68.4
102.6
189.0
186.4
131.0
1.000
1.000
1.000
0.999 0,999 0.999
0.999
12h
66.3
93.4
184.6
223.6
185.5
200.9
233.4
1.000
1.000
0.999
0.999 0,999 0.999
0.998
Z500
18h
86.5
122.5
267.1 1
289.9
238.5
231.9
348.0
1.000
1.000
0.998
0.997 0.998
0.998
0.996
24h
114.9
153.3
348.5
371.5
294.8
274.6
$20.8
1.000
0.999
0.996
0.996 0.997
0.998
0.995
6h
2.8E-05
3.7E-05
3.4E-05
6.5E-05
5,8E-05
7.5E-05
4.3E-05
0,988
0.979
0.983
0,936 0.949
0,914
0,972
12h
3.71:005
4.6F-05
5.2F-05
7.00-005
6.58-05
7.5H-05
6.5
0,980
0.968
0.960
0.926 0,935
0.913
0.937
Q500
4.3E-00
5.4E-05
6.4E-05
7.5E-05
7.3E-05
7.7E-05
1.15-05
0.972
0.956
0.937
0.912 0.918
0.908
0.906
24h
4.9E-00
6.0E-05
7.4E-05
1.
8.0E-05
7.9E-05
1.0E-04
0.963
0.945
0.916
0.897
0.900
0.902
0.881
32

---

Published as a conference paper at ICLR 2026
K
FULL LONG-TERM FORECASTING RESULTS.
Table 10: Quantitative comparison of long-tern (7-10 days) global weather forecasting performance.
Metric
RMSE
ACC
Variable Days
Ours
Triton
Pangu
FCN
Fuxi
Sim
UNet
Ours
Triton Pangu
FCN
Fuxi VP UNet
7d
2.293
2.934
3,423
3.902
3,294
2.938
4,051
0.987
0.974
0.963
0.975 0.973
0.979
0.948
8d
2.516
3.263
3,574
4.104
3.442
3.100
4.358
0.985
0.968
0.958
0.971 0.970
0.977
0.940
T2M
9d
2.708
3.549
3.712
4.288
3,574
3.248
4,630
0.982
0.961
0.952
0.969 0.968
0.974
0.933
10d
2.865
3.799
3,821
4,430
3.689
3,384
4.867
0.981
0.956
0.948
0.967 0.966
0.972
0.928
7d
3.485
3.945
4,959
5.102
4.528
3,766
5,507
0.769
0,700
0.663
0.645 0.608
0.707
0.606
8d
3,773
4.192
5,088
5.301
4.660
3.872
5.753
0.730
0.662
0.627
0.614 0.582
0.689
0.567
U10
9d
3,954
4,397
5.192
5.464
4.762
3,997
5.953
0.697
0.631
0.597 0.588 0.561
0.675
0.541
10d
4.013
4.548
5,268
5,583
4.834
4.174
6.099
0.670
0.606
0,572 0.568 0,544
0.664
0.524
7d
3.787
4.205
4.961
5,364
4.652
3,982
5.757
0.559
0,451
0.392
0.358 0.326
0.427
0.306
8d
4,089
4,445
5.069
5,514
4.764
4.098
5.986
0.486
0,388
0,342 0.310 0.291
0.391
0.271
V10
9d
4.154
4.620
5.150
5.649
4.853
4.335
6,158
0.426
0.339
0.299
0.274 0.264
0.366
0.244
10d
4.201
4.747
5.201
5.749
4,911
4.500
6.277
0.383
0.302
0,266
0.247 0.245
0.349
0.225
7d
L,3E-03
1,9F-03
1.7F.03
1.5F.03
1.6F-03
L.4F-03
2.2F5-03
0.492
0.354
0.329
0.259 0.271
0.396
0.242
8d
1.4F-03
2F
1.8F-03
1.6F-003
1.6F-03
1.5F-00
2.3F-03
0.446
0,316
0.297
0.231 0.249
0.384
0.211
Prec
1.4E-03
2.26:-0
18E--0
1.6E-03
L.7E-03
1.51:-3
2.31-03
0.410
0.272
0.210
0.190
1.4E:03
2.3E-03
18EE00
1.6E-03
1.7E-03
L66--03
2.4E-03
0.381
0.252
0.193
0.370
0.173
731.4
1075.0
969.2
901.1
741.8
1067.9
0.835
0.785
0.764
0.733
8d
713.0
795.5
1114.5
1024.9
940.6
275.8
1128.5
0.796
0.738
0.754
0.730 0.650
0.748
0.695
MSL.P
9d
771.7
847.9
1145.0
1069.5
969.0
801.4
1181.0
0.762
0.706
0.725
0.701 0.627
0.730
0.660
10d
816.2
887.7
1166.9
1101.8
989.2
820.0
1220,0
0.734
0.678
0.700
0.678 0.608
0.716
0.630
7d
5.661
7.696
10.090
8.300
9. 9,408
7.572
11,118
0.915
0.839
0.842
0.833 0.782
0.848
0.796
8d
6.320
8.590
10.607
8.936
9.972
7,972
12.066
0.894
0.802
0.816 0.808 0.756
0.832
0.763
U925
9d
6.911
9.354
11.050
9.477
10.426
8,313
12.659
0.874
0,769
0.789
0.779 0.734
0.819
0.730
10d
7.436
10.031
11,430
9.921
10,803
8,611
13.103
0.854
0,739
0.765
0.752 0,716
0.807
0.699
7d
5.674
7.095
9.228
8.929
8,310
6.765
10.013
0.643
0.485
0.395
0.376 0.289
0.416
0.300
8d
6.344
7.733
9.602
9.466
8.704
7,061
10.684
0.556
0.397
0.323
0.307 0.226
0.355
0.223
9d
6.923
8.210
9.892
9,880
8.981 1
7,294
11.174
0.474
0.327
0,263
0.250 0.183
0.305
0,166
10d
7.412
8.603
10.105
10.198
9.182
7,478
11,560
0.402
0.268
0,214
0.204 0.151
0.266
0,131
7d
2.420
3,251
4.015
3.496
4.163
3,333
4,872
0.975
0.952
0.944
0.949 0.925
0.952
0.920
8d
2.690
3.585
4,232
3.777
4,421
3.504
5,204
0.969
0.942
0,935
0.942 0.916
0.947
0.908
T925
9d
2,932
3.882
4,420
4.022
4.642
3.649
5.523
0.963
0,932
0.926
0.934 0.908
0.943
0.896
10d
3.145
4.152
4,566
4.223
4.827
3.774
5.724
0.957
0.922
0.917
0.926 0.901
0.939
0.884
3.0E:00
4.7E-07
4.2E:07
4.3E:00
5.2E-07
3.88:07
5.8E-07
0.782
0.607
0.620
0.653
0.565
3.2E:-07
5.2E-07
4.4E:07
4.6E:07
5.5E-07
3.9
6.3E-07
0.760
0.637
0.524
Z925
3.3E:07
5.6E.07
4.6E.07
4.
5.7E. 07
4.1E:07
6.6E
0.738
0.537
0.554
0.622
0.504
3.5E:07
6.0F-07
4.8F.07
5.0F.007
5.8
4.21--07
6.8F-07
0.717
0.509
0.609
0.482
7d 673.038
871.088
1311.785
836.431
1172.687
989.917
1394.336
0.987
0.973
0.966
0.973 0.966
0.975
0.947
8d
773.302
999.146
1391.247
928.037
1270.395
1067.484
1499,221
0.983
0.964
0.958
0.965 0.960
0.972
0.938
Q925
9d
863.541
1113.102
1459.822
1017.677
1351.076
1135.576
1591.308
0.979
0.955
0.951
0.958
0.956
0.969
0.931
10a
943.733
1214.456
1513.909
1093.027
1422.259
1196.480
1666.658
0.975
0.946
0.946
0.954
0.951
0.966
0.926
33


Reviews:
[{"review_id": "SG9DuJ0BU5", "reviewer": "Reviewer_uXuB", "summary": "This paper proposes STORM, a spatio-temporal deep learning framework for weather forecasting that explicitly models cross-scale interactions between coarse global circulations and fine regional dynamics. The model introduces a hierarchical encoder–decoder design with cross-scale message passing to enable information flow across multiple spatial resolutions. Experiments on ERA5 demonstrate consistent improvements over recent strong baselines (GraphCast, FuXi, Pangu-Weather, Triton) in both short-term (24 h) and long-term (10 day) forecasts. The results are strong and empirically well-presented.", "questions": "1. Have you conducted any sensitivity analysis regarding the number of branches, stride size, or parameter count in the multi-scale architecture? If the model consistently maintains strong performance under such variations, I would significantly increase my score, as it would demonstrate real robustness rather than capacity-driven gains.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "1. Clear motivation and structure – The paper is well-motivated, addressing the nontrivial challenge of multi-scale atmospheric dynamics with a coherent architectural design.\n\n2. Strong experimental performance – STORM achieves notable RMSE/ACC gains over multiple competitive baselines across diverse forecasting horizons and regions.\n\n3. Comprehensive evaluation – Global, continental, and regional experiments are conducted with detailed visual and quantitative analysis.", "weaknesses": "1. Unsubstantiated “parameter-efficient” claim\nThe paper repeatedly emphasizes that STORM is parameter-efficient, yet it provides no quantitative evidence such as parameter counts, FLOPs, or inference latency. Given that the architecture involves multiple scale-specific branches and cross-scale message passing, the model design resembles a multi-branch or MoE-style structure that would typically increase parameters rather than reduce them.\nWithout compute-matched comparisons (e.g., same parameter budgets as GraphCast or FuXi), it is impossible to determine whether the reported gains stem from genuine architectural advantages or simply larger capacity.\n\n2. Lack of quantitative analysis on multi-scale effects\nWhile the paper stresses the importance of multi-scale synergy, it never analyzes how performance scales with the number of branches or levels. There is no experiment showing whether adding more scales continues to improve performance, when it saturates, or whether a simple increase in parallel branches (without explicit scale coupling) yields similar gains. Thus, the claimed “cross-scale synergy” remains empirically unverified.\n\n3. Missing ablation for the proposed message-passing mechanism\nAlthough the cross-scale message-passing block is presented as the core innovation, there is no isolated ablation showing how much it contributes to overall accuracy. This makes it difficult to assess whether the improvement originates from the proposed mechanism or from increased model complexity.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "hBHbNAlR0V", "reviewer": "Reviewer_7ifQ", "summary": "This paper introduces STORM, a synergistic cross-scale spatio-temporal framework for data-driven weather forecasting. The model explicitly disentangles atmospheric variations into multiple spatial and temporal scales through three key components: (i) a Hierarchical Earth Embedder that constructs multi-resolution representations, (ii) a Scale-Bridging Spatio-Temporal Encoder that integrates temporal evolution and cross-scale interactions, and (iii) a Level-Aligned Forecasting Decoder that generates coherent multi-scale predictions. Experiments on the ERA5 dataset show that STORM achieves state-of-the-art performance for both short-term (hours) and long-term (days) forecasts, outperforming strong baselines such as Pangu-Weather, FourCastNet, and GraphCast. Ablation and multi-scale analyses further demonstrate the contribution of each module and confirm the importance of explicit cross-scale modeling.", "questions": "1. How does the computational efficiency (training time, FLOPs, memory) compare with Pangu-Weather and FourCastNet at similar resolutions?\n\n2. Could the hierarchical design be combined with physics-informed constraints or hybrid NWP–DL methods for better interpretability?\n\n3. How sensitive is the model to the number of scales and the stride settings in the hierarchical embedder?\n\n4. Does STORM maintain robustness when applied to unseen years, extreme events, or real-time operational data?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper presents a coherent multi-scale framework that systematically integrates spatial hierarchies and temporal evolution, providing a unified structure for global-to-local forecasting.\n\n2. The evaluation is extensive, spanning multiple spatial resolutions and forecast horizons, and shows consistent superiority over strong baselines.\n\n3. The paper is clearly written and well organized, with careful theoretical justification and reproducibility statements.", "weaknesses": "1. The core ideas, such as hierarchical representation, multi-resolution encoding, and cross-scale feature fusion, are largely extensions of prior models such as Pangu-Weather (3D hierarchical Transformer) and FourCastNet (multi-frequency operator). The contribution is primarily architectural refinement rather than a new modeling principle.\n\n2. The paper does not quantify computational cost, efficiency, or scalability compared with existing models.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "AXfexPlSOW", "reviewer": "Reviewer_pYqi", "summary": "The paper proposes STORM, a cross-scale spatio-temporal framework for weather forecasting that disentangles atmospheric dynamics into multiple spatial scales and learns coherent temporal evolution. It includes a Hierarchical Earth Embedder, a Scale-Bridging Spatio-Temporal Encoder with fine-to-coarse messaging and lightweight temporal modeling, and a Level-Aligned Forecasting Decoder for multi-scale coherent outputs. Extensive ERA5 experiments show consistent SOTA performance across short- and long-range horizons with solid ablations and theoretical motivation.", "questions": "1 Can you report inference efficiency (FLOPs, latency, memory) versus baselines across resolutions/horizons?\n\n2 Do you observe error hotspots by latitude/terrain, and does cross-scale modeling alleviate them?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1 Strong problem fit: explicitly addresses multi-scale heterogeneity and cross-scale interactions, a central challenge in weather prediction.\n\n2 Clean, modular design: efficient hierarchical embeddings; ViT-style spatial encoder; simple but effective cross-scale messaging; lightweight temporal encoder; coherent multi-scale decoding.\n\n3 Comprehensive results: consistent gains over strong baselines (Triton, Pangu, FCN, FuXi, SimVP, U-Net) across variables and horizons; long-range robustness is notable.\n\n4 Clear ablations and scale analysis support design choices; theory gives intuitive generalization/optimization benefits.", "weaknesses": "1 Cross-scale interaction is one-way (fine→coarse) in the encoder; no analysis of bidirectional/gated messaging.\n\n2 Temporal module is extremely lightweight; scalability to very long histories/periodic signals (MJO/ENSO) not deeply evaluated.\n\n3 Efficiency reporting (FLOPs/throughput/memory vs. resolution/horizon) is limited in the main text.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "kNGaKvjLR1", "reviewer": "Reviewer_R3ZV", "summary": "- The authors propose the STORM architecture for weather forecasting, designed to capture cross-scale interactions in multi-scale weather data. They identify three key limitations in the forecasting performance of deep learning–based approaches: multi-scale heterogeneity, diverse temporal evolution, and weak cross-scale interaction. Accordingly, they propose STORM to address these challenges.", "questions": "- Please refer to the weaknesses section for detailed comments. Most importantly, the ablation study in Section 5.3 appears weak as the reported results with and without the main modules seem questionable when compared to the baseline methods.\n- Please correct the typos throughout the paper, even the title contains one.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The authors effectively highlight the need for the proposed architecture, with a well-written introduction that builds up to it clearly. The related work section is up to date and provides a solid understanding of the current state of the art. The intuition behind all three main modules is also well explained.\n- Section 5 presents comparisons with state-of-the-art baseline models from the literature on the ERA5 dataset across different scales. The authors provide both short-term and long-term forecasting results. Combined with the visualizations of predictions in the Appendix, the results appear convincing and satisfactory.\n- Section 5.4 clearly demonstrates the importance of using multi-scale information for forecasting, presenting both numerical results and visualizations at different scales. The motivation for setting the number of scales to three is also clearly justified.\n- Appendix B includes some theoretical analysis supporting the need for multi-scale modeling. However, it does not provide theory directly related to the proposed STORM architecture. Nonetheless, this section can still be considered a minor strength, as most recent baseline methods lack any theoretical component.", "weaknesses": "- The ablation study in Section 5.3 seems unsatisfying and weak. The STORM architecture has three key modules, and the authors report results by removing each one on the short-term global forecasting task (comparable to Table 1). Results are shown only in a small bar plot (Figure 6), not in a table. For variables such as T2M, U10, and V10, even the “w/o S&M” configuration appears to outperform baseline methods in Table 1 (losing only to Triton). This implies the T module alone would beat most baselines on some variables, which is unconvincing and undermines the need for all three modules separately. Why not provide tabular results for the ablation? And why restrict it to short-term global forecasting only?\n- Furthermore, the results show the necessity of each module for T, M, and S, but they do not justify the specific architectural choices within each module. For example, we are given no evidence of how effective the Hierarchical Earth Embedder is at leveraging cross-scale information, we are simply asked to understand its value from the RMSE differences with and without it in Section 5.3. Appendix E at least reports some hyperparameters (M=3, D=256, N=3), but the specific design choices inside each module remain questionable: there is no ablation to support them, nor results under alternative hyperparameters. From Appendix E, it appears the default parameters were set intuitively and used across experiments, with only the training epochs adjusted via early stopping on validation data. Furthermore, the manuscript provides no analysis of the STORM architecture’s sensitivity to hyperparameter tuning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)