TianQuan-S2S: A Subseasonal-to-Seasonal Global Weather Model via Incorporate Climatology State
Authors: Guowen Li
Xintong Liu
Yang Liu
Mengxuan Chen
Shilei Cao
Xuehe Wang
Juepeng Zheng
Jinxiao Zhang
Haoyuan Liang
Lixian Zhang
Jiuke Wang
Meng Jin
Hong Cheng
Haohuan Fu
Venue: ICLR 2026 Poster (2026)
Keywords: Subseasonal Weather Forecasting
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: This paper introduces TianQuan-S2S, a novel machine learning model that provides accurate global daily mean forecasts up to 45 days by integrating climatology state information.

Abstract: Accurate Subseasonal-to-Seasonal (S2S) forecasting is vital for decision-making in agriculture, energy production, and emergency management. However, it remains a challenging and underexplored problem due to the chaotic nature of the weather system. Recent data-driven studies have shown promising results, but their performance is limited by the inadequate incorporation of climate states and a model tendency to degrade, progressively losing fine-scale details and yielding over-smoothed forecasts. To overcome these limitations, we propose TianQuan-S2S, a global S2S forecasting model that integrates initial weather states with climatological means via incorporating climatology into patch embedding and enhancing variability capture through an uncertainty-augmented Transformer. Extensive experiments on the Earth Reanalysis 5 (ERA5) reanalysis dataset demonstrate that our model yields a significant improvement in both deterministic and ensemble forecasting over the climatology mean, traditional numerical methods, and data-driven models. Ablation studies empirically show the effectiveness of our model designs. Remarkably, our model outperforms skillful numerical ECMWF-S2S and advanced data-driven Fuxi-S2S in key meteorological variables. The code implementation can be found in https://github.com/zhangminglang42/TianQuan.

Published as a conference paper at ICLR 2026
TIANQUAN-S2S: A SUBSEASONAL-TO-SSASSO GLOBAL WEATHER MODEL VIA INCORPORATE CLI- MATOLOGY STATE
Guowen Li Xintong Liu', Yang Liu²t, Mengxuan C Shilei Cao' Xuehe Wang', Juepeng Zhengt.41, Jinxiao Zhang', Haoyuan Liang', Lixian , Jiuke Wang',
Meng Jin Hong Cheng", Haohuan Fu
Sun Yat-Sen University, "The Chinese University of Hong Kong, Tsinghua University, Naaional Supercomputing Center in Shenzhen, 'Huawei Technologies Co., Ltd
ABSTRACT
Accurate Subseasonallto-SSaasnn (S2S) forecasting is vital for decision-making in agriculture, energy production, and emergency management. However, it mains a challenging and underexplored problem due to the chaotic nature of the weather system. Recent data-driven studies have shown promising results, but their performance is limited by the inadequate incorporation of climate states and a model tendency to degrade, progressively losing fine-scale details and yielding over- smoothed forecasts. To overcome these limitations, we propose TianQuan-S global S2S forecasting model that integrates initial weather states with climato- logical means via incorporating climatology into patch embedding and enhancing variability capture through an periments the Earth Reanalysis 5 (ERAS) reanalysis dataset demonstrate that our model yields a significant improvement in both deterministic and ensemble fore- casting over the climatology mean, traditional numerical methods, and data-driven models. Ablation studies empirically show the effectiveness of our model designs. Remarkably, our model outperforms skillful numerical ECMWF-S2S and advanced data-driven Fuxi-S2S in key meteorological variables. The code implementation can be found in https::////o /tttpp:://gtttuuu htt.bbb.tttttt//g////o///t..b... com/ Changminglanggg 42 anQuan.
a
-augmmete Transformer. Extensive ex-
INTRODUCTION
Subseasonal-to Satetssoonltt--Saaasseeee to-Seasonal forecasting (beyond 15 days) is crucial for various applications, including agriculture, energy production, and emergency management, where it plays a vital role in planning and decision-making processes (Pegion al., 2019). Accurate subseasonal forecasts reduce agricultural losses, balance energy supply, and improve disaster preparedness. Over the past 40 years, Numerical Weather Prediction (NWP) models have significantly advanced weather forecasting skills for the short to medium term (up to 15 days), contributing notably to Sustainable Development Goals (SDGs) (Bauer et al., 2015). Nevertheless, since the parameterization within NWP models introduces errors due to function approximations (Beljaars et al., 2018), the accumulated errors are significant on the S2S time scale. In addition, they require substantial computational resources and time (Saha et al., 2014). Even with supercomputers operating on hundreds of nodes, simulating single variable can take hours (Bauer et al., 2020). Recently, data-driven models (Bi et al., 2023; Lam et al., 2023; Chen et al., 2023b; Price et al., 2024) present promising future due to their comparable accuracy in medium-range raagee forecasting and much faster inference speeds. Once trained, these models can predict future weather conditions in seconds (Pathak et al., 2022).
However, data-driven subseasonal forecasting remains challenging and less explored (Chen et al., 2024; Liu et al., 2025a). The extended time horizon renders the initial weather conditions and key variables inadequate for making accurate predictions due to the chaotic nature of the weather system (Mariotti et al., 2018). Deterministic machine learning models are typically trained data
Corresponning authors

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Published as a conference paper at ICLR 2026
from recent historical data, which provides limited support for subseasonal forecasting (He et al., 2019). As the forecast horizon extends, the initial state becomes less informative, resulting in blurred and unrealistic predictions. This limitation hampers the effectiveness of machine learning models on subseasonal time scales, despite their importance for climate- applications (Lam et al., 2023).
Specifically, two critical issues have not been well explored in S2S forecasting: (1) Insufficient climate modeling. Climatol-
Forecasting
Model Collapse
kad thee
ogy, the persistent, slow-varying climate modes that influence atmospheric condi- tions on the S2S time scale. While both it and initial conditions are crucial for S2S forecasting, existing approaches have pre- dominantly focused on the former, neglect- ing its importance.
(2) Model collapse. The use of discrete numerical grids in mod- eling inherently smooths out small-scale weather features due to spatial and tempo- ral averaging at grid points. With extended lead times, the forecasting system progres- sively deteriorates, failing to preserve re- liable structures and ultimately producing unrealistic predictions. As shown in Figure with the increase in lead time, the prediction of the same target days becomes smoother and finally loses predictability.
Figure 1: Model collapse in Subseasonal-to-Sessse (S2S) Forecasts. As the lead time increases. the forecast results for the same target time gradually exhibit the loss of data contours across the three regions, which can be considered form of model collapse.
To address these issues, we propose TianQuan-S2S, where TianQuan (meaning Weather Hub in Chinese) reflects its role as a central system for subseasonal prediction. The framework consists of two key components to improve single-step forecasts. First, patch embedding layer integrates both the initial weather states and climatological mean features to compensate for the limited predictive information, enhancing forecast skill beyond 15 days. Second, inspired by the traditional perturbed forecasting, which incorporates noise to enhance model performance, we extend the Vision Transformer with uncertainty blocks that inject Gaussian noise into feature representations, preventing over-smoothing and better capturing realistic variability at longer lead times. Extensive experiments are conducted on the high-quality Earth Reanalysis 5 (ERA5) dataset, showing that the proposed methods outperform skillful numerical S2S systems and data-driven models. In summary, our main contributions are as follows.
We highlight the importance of incorporating climate information in data-driven S2S forecasting and the model collapse issue in long lead time.
We proposed Tian QuanQ,,S,,2 consisting of a patch embedding that incorporates climatological Transformer that captures weather variability, enhancing S2S forecasting and mitigating over-smoothing.
information and an
Extensive experiments on the ERA5 dataset show that TianQuan outperforms traditional and data-driven methods, including ECMWF-S2S and Fuxi-S2S. in both deterministic and ensemble forecasting. Ablation studies show that the proposed two simple designs, climatology and noise incorporation, significantly enhance the model performance.
2 PRELIMINARIES
Perturbed forecasting In weather forecasting, perturbed forecasting is used to generate ensemble predictions by adding small perturbations to the initial atmospheric state (Zhou et al., 2022). Because the atmosphere is a chaotic system, even minor uncertainties in the initial conditions can lead to large differences in forecast outcomes (Nakashita & Enomoto, 2025). Perturbed forecasting generates multiple forecasts from slightly modified initial states to capture possible atmospheric evolutions. In addition to perturbing initial conditions, ensemble systems also introduce perturbations within the model itself. For example, ECMWF and NCEP apply stochastic parameterization schemes such as the Stochastically Perturbed Parametrizations (SPP), which randomly modify model tendencies like convection or turbulence (Tsiringakis al., 2024). Moreover, data-driven methods such as Swin VRNN use learned distribution perturbations to generate diverse ensemble members, improving forecast reliability by explicitly modeling uncertainty (Hu et al., 2023).
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Transformer
Initial State
Attention-based Fusion
Patchify and Fourler Embedding
Embedding. Addition
Uncertainry
Hadamard product
00000000
CNN
VIT Dlack
Climatology X.m
Prediction X
HsW*K
Figure 2: The diagram TianQuan QuannuunnS2 framework. The input variables include initial state X and climatology X X After attention based fusion, the features enhanced and fused, then patchified and fed into the augmeeted model, where Gaussian noise is injected at each layer. Finally, predictions X for days 15 to 45 are generated.
Climatology Climatology is the scientific study of long-term weather patterns and atmospheric processes, typically based on decades of observational and model data. Unlike short-term forecasting, climatology emphasizes statistical averages, variability, and extremes to understand the baseline state of the climate system (White et al., 2023). It plays a central role assessing long-term climate change, shifts in temperature, precipitation, and circulation patterns evaluated against climatological norms. As a reference framework, climatology provides essential context for detecting anomalies, attributing trends natural variability anthropogenic forcing, and guiding adaptation and mitigation strategies in response to global climate change (Forster et al., 2024). In this work, the climatology computed based on the 38-year daily climatology from 1979 2016 (366 days).
Problem Definition We study the prediction of K weather parameters at the latitude-longitad grid G E R#x where and W are the height and width of the grid that depend on the resolution of latitude and longitude, and Gr, (An, Φw: 52 [-90", 90%] [-180", 180%] Let the state of global weather time be represented by 3-dimensional tensor X, E Hx xx where K = VA x C + Vs. with VA denoting the number of upper-air variables, Vs the number of surface variables, and the number of pressure levels. Similarly, the climatology represented by Xetim E IR x > Thus, our goal is to train a neural network to forecast weather variables with lead times between and 45 days, as shown in the following:
Eessttas fe Xelsm X ),
where O denotes the parameters neural networks. X &tnssaa is the predicted value from day 15 to day 45, In this work, we employ the 5-day historical data Xt as the input, which empirically found beneficial for model performance.
PROPOSED MODEL
Figure 2 illustrates the TianQuan-S25 framework, which consists of (1) patch embedding that fuses the input and climatology embeddings; (2) a vision transformer that is perturbed by random noises. We illustrate their details follows.
3.1 PATCH EMBEDDING
Previously, some researchers (Zhang Patel, 2018: Wang et al., 2021; Kumar Tiwari, 2023) have utilized edge priors to enhance details. Building this work, we introduce multi- layer convolutional layer to extract climate information Fatm E H Xetin- In this convolution, pixel pair differences calculated, and prior information is explicitly encoded into the CNN, enhancing the model's representation by learning valuable trend information.
Convolutions
x W from the climatology
For the initial input fields, propose novel convolutional design that enhances weather prediction by jointly modeling spatial and chamnel- wise relationships. Spatial Convolution captures regional variations in initial fields, while Channel Convolution models the relationships among variables,
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such temperature, pressure, and wind. Together, these two mechanisms generate feature maps F, E R and Fe E 2dxWxX defined as follows:
x
F, Jcon Scono (VPAr, Yfmr)),
= (YPa))
where fcono() represents neural network of convolutional layer, and [-] denotes channel-wise con- catenation. PAP A and YPMP represent features processed by partial average pooling across the channel or spatial dimension and global max pooling across the spatial dimension, respectively, Then we compute through element-wise addition to obtain the enhanced climate data as follows:
Fx = Fg + Fe Hxwxk
Note that the fusion feature information Fx can guide attention across channels, producing clearer and more refined results.
Attention-based fusion Research has shown that feature fusion can enhance these climate informa- tion features, aiding long-term predictions (Chen et al., 2024; Li al., 2024). Inspired by the above, we proposed an attention- based fusion module to guide the fusion process of the features Fati and Fx. This module fuses two input features by first computing spatial weights that determine their relative importance. We first flatten spatial dimensions with N = H x W and fuse each variable feature with (*) reshape(A (F
F RCXN, where C denotes the number of pressure levels (13 for upper-air variables and for surface variables). Define:
A (0) WQ.
K (v) A (0) WK.
V =
Work/v E NNN,
(4)
Compute the spatial weights W att unreshape(o q K(
V 10,1] Finally,
VN
convolutional layer maps the fused representation the output F E &HHWWK
F = fcoav Falim Wat + Fx Watt) + Fatim Fx):
(5)
where denotes a matrix with all elements equal to 1. In summary, the aitention-basee fusion adaptively integrates complementary features, ensuring more effective fusion for long-ten seng-termmae prediction.
Patchify and Fourier Embedding We divide the upper-air data of shape C' VA x H W into L H
x W P denotes the number of patches. These patches are then flattened and stacked into tensor FA R X which is embedded into latent space to generate an upper embedding E E Rx D. Similarly, surface variables, influenced by terrain and the land-sea mask, represented with C 1 as Es E RRLD
patches (F ) where F()) E VXXPPxP and L = P
To retain spatial (latitude and longitude) and temporal information, these variables are mapped into D-dimensional tensors using Fourier encoding, which embeds periodic positional signals preserve variations across space and time, implemented as follows:
2T
2x
2
2T
2TT Ap/2
2x
FourEnc(z)) [sin(
cos(
sin
) cOs
sin
cos(
(6)
A
X
A;
DD/2
represents the wavelength of the Fourier basis function, ensuring that the encoding captures various frequency components of the input variable. For time, since climate follows yearly cycle, the wavelength range for encoding is set with Xmin and Amax 365. For position, the wavelength range is set with Amin = 0.1 and Amax = 360, representing the spatial scale of longitude. After being processed by linear layer, the temporal and spatial information (W pos. W (C+1)xx are integrated into initial embedding E RR (C+1)xLXD follows:
where X; = Ammin (Amuuss
E = Es, EA] + W + Wi
pos
where [.] denotes C channel-wise concatenation and * denotes that broadcasting applied during the computation. Subsequently, this embedding E is fed into the Transformer for further processing.
3.2 TRANSFORMER
Transformer with noise generation The Vision Transformer (ViT) architecture has proven effec- tive for various prediction tasks, including climate modeling (Nguyen al., 2023). By processing
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imput data with stacked attention blocks, the transformer captures both local and global dependencies. In the context of weather forecasting, each block learns hierarchical representations.
El..)) = h1, (,,(El))) = softmax Q(..)) K(l..) V
(8)
VD
where Q(..)) El. W K(..)) = E W V(.n) E(..) W and / E DRD
are learned projection matrices, and represents the n-th layer of transformer. By stacking these transformed representations, we obtain the reconstructed embedding E(n) (B
In general, adding stochastic perturbations helps prevent the forecast from collapsing onto a single deterministic trajectory and better captures the growth of uncertainty at extended lead times. partic- ular, instead of perturbing only the initial conditions, which lose impact as lead time increases (Buizza et al., 2005), we inject learnable Gaussian perturbations each Transformer layer during the forward pass, stabilizing forecasts and mitigating over-smoothing at extended ranges.
Specifically, an uncertainty block introduces Gaussian noise each transformer block produce the next prediction E(++1), as described by the following formula:
El++1) E()) + hn (E(")) + (E(m) (O,
Here, n E (I,..., N) denotes network layer index, and (,)(.) represents parameters layer n-th of transformer. In addition, (.) is learnable parameter function introduced by the uncertainty block.
Unpatchify To convert the prediction embedding É E R(C+I)XXXD back into the prediction variables, we separate the embedding for surfce embedding Es E BRILXD and upper-air embedding decoded into P P patches via linear layer to reconstruct
EA E RC These embeddings the gridded data. By combining and stacking, we obtain the final output predictions, Xs and XA. for the target time range from day 15 to day 45.
3.3 LEARNING OBJECTIVES
TianQuan-S2S$ is trained to forecast the predictions X tasttas at lead time from day 15 to day 45. The objective function used the latinude-weighted mean squared error (Rasp et al., 2020). The loss is calculated between the prediction X CeLoitas and the ground truth Xessitus as follows:
V
#
W
L V ΣΣΣ
1(i
P.e.. Cisifan
(10)
in which L(i) Σ. (os( is the latitude weighting factor, and lat(i) represents the latitude
nos(lat(1))
of the jth row in the grid. The coefficient size varies because grid cells near the equator cover more area than those the poles, thus receiving higher weights.
4 EXPERIMENTS
Datasets We conducted experiments using the ERAS dataset (Hersbach et al., 2020), covering 40 years (1979-2018) with global hourly data across multiple pressure levels and the surface. To improve the accuracy of long-term predictions, we preprocess the hourly ERA5 data by averaging it daily six-hour intervals. Bilinear interpolation is used to downsample the data 5.625 (32 64 grid points) and 1.40625 (128 x 256 grid points), while selecting the 13 most critical pressure levels. For more details on data processing, refer to Appendix F.4. We obtained the dataset variables as shown in Table 10 in Appendix F. We divided the daily averaged ERAS dataset into training (1979-2013 validation (2016), and testing (2017-2018) sets based on years.
Metrics Following existing works (Bi et al., 2023; Rasp et al., 2024), we primarily quantify the performance improvement the model using latitude-weightt RMSE and Anomaly Correlation Coefficient (ACC), and then assess its long-term forecasting capability through Continuous Ranked Probability Score (CRPS), Spread Mean Error (SME), and Relative Quantile Error (RQE). All of these metrics be found in the Appendix G.
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TuanQuan
1850
Z,000
T2m
Wind10
(8)
RMSSE
1.50
3.8
1.20
310
3775
1660
0.00
ACC
0.75
0.89
0.38
6:70
0.55
0.6
(h)
3.50
ROMSE
135
18
2.75
16
0.00
8:66
ACC
0.75
0.70
0.55
0.19
0.65
15
20
25
30
25
20
15
28
25
39
35
15
28
25
38
Forecast time (days)
Figure 3: TianQuan-S2S outperforms FuXi-S2S, ClimaX and ECMWF-S25 deterministic forecasts 1.40625'(a) and 5.625%(b) daily ERA5 datasets. The comparison involves four variables in terms of weightd RMSE (lower is better) and ACC (higher is better). The time range for the metric calculations is from 2017 2018.
Baselines
We compare our proposed model with the following baseline models:
ECMWF-S25 (Vitart et al., 2017) is a WWRP/THOR PEX-WCRP joint research project estab- lished to improve forecast skill and understanding on the sub-seasonal to seasonal time scale.
ClimaX (Nguyen et al., 2023) is a deep learning foundational model for weather and climate science, capable of training ERA5 datasets with varying variables and spatio-temporal coverage. The model itself makes deterministic forecasts, and ensemble forecasts can also be obtained by adding disturbances to the initial field, mentioned above.
FuXi-S2S (Chen et al., 2024) is state-of-the-an global subseasonal ensemble forecasting model that leverages machine learning to improve prediction accuracy, providing forecasts up to 42 days, with 40 days used here for comparison. In the comparison of deterministic forecasts, use the FuXi-S2S (00 member) without perturbations as a contrast.
Climatology utilizes the long-term average of historical data for each time step as the reference prediction, providing simple yet effective benchmark for comparison. In this work, we refer to the Climatology Baseline standard comparison process in WeatherBench2 (Rasp et al., 2024).
We run our approach once to generate single time value for deterministic forecasting, In addition, as an Al-based method, our model can perform large-member ensemble forecasts with small computa- tional costs. For ClimaX, we implemented ensemble forecasting by introducing random perturbations to the initial weather states. In the case of TianQuan-S2 S22S we incorporated learnable noise at each block level to generate multiple forecasts. Specifically, we ereated 50 random perturbations, which were then added to the original unperturbed state. This approach results 51-member ensemble, and the ensemble mean forecast computed by averaging the individual forecast outputs.
Implementation Details We used the AdamW optimizer (Kingma, 2014; Loshchilov & Hutter, 2017) with parameters λ₁ = 0.9 and X2 = 0.99. weight decay of le was applied all parameters except the positional embeddings. The learning rate set to -5 with linear warmup schedule

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Table I: Comparison of ensemble forecast performance across variables and models.
CRPS
SME
(L)
RQE
(L)
Model
15
20
25
30
35
40
15
20
25
30
35
40
15
20
25
30
35
40
ClimaX 2.278
2.343 2.378
2,409
2,475
2.481
2.190
2.271
2.314
2.352
2.433
2.453
2.187
2.312
2.384
2.437 2.562
2.592
FuXi-S2S
2.238
2.293 2.328 2.359
2.426
2.437
2.140
2.223
2.264
2.302
2.383
2.414
2.136
2.263
2.338
2.382 2.513
2.544
Ours
2.256 2.276 2,304 2.297
2.318
2.341
2.048
2,141
2,316
2.235
2.328
2.338
2.158
2.244
2.348
2.331
2.417 2.469
Z500 Wind10 T850
ClimaX
2.831 2.827 2.842 2.833 2.847
2.866
12.364
2.354
2.389
2.379
2.404
2.414
2.748 2.815
2.842 2.883 2,952 2.967
TuXi-S2S
2.824 2.818 2.844 2.832 2.848 2.867
2.331
2.355
2.362
2.343
2.395
2.405
2.729
2.716 2.783 2.769 2.771 2.808
Ours
2.805 2.812 2.836 2.819 2.836
2.852
22.34
2.326
2.358
2.335 2.401
2.39
2.711
2.725 2.743
2.784 2.753 2.787
ClimaX 1.801
2,004 1,954 1.907 1861
1.831
1.050
L.033
1.094
1.175 1,088
1.158
1.747
1.781 1.805
1.814
1.848 1.869
FuXi-S2S
1.798
1.902 1,963
1.856 1.852
1.835
1.038
1.053
1.065
1.152 1.075
1.099
1.736
1.763
1.813
1.791 1.803 1.851
Ours
1.799
1,901
1.894
1.852
1.834
1.826
1,020
1.034
1.075
1.128
1.052
1
1.729
1.754
1.825
1.779
1.804
1.834
ClimaX
650
653
655
655
658
663
655
659
673
682
679
688
653
684
703
736
777
779
FuXi-S2S
645
648
655
653
654
661
634
659
663
670
669
634
665
693
705
718
723
Ours
644
647
652
650
653
658
640
648
663
654
656
660
620
658
684
716
705
714
Table 2: RMSE comparison of ensemble mean results. Our method generally achieves better performance, outperforming the climatology baseline across multiple variable metrics.
Model
15
20
25
30
35
40
45
Model
15
20
25
30
35
40
45
FuXi-S2S
2.450
2.454
2.484
2.520
2,542
2,563
7550 1ind10
FuXi-S2S
3,407
3.574
3.668
3.678
3.771
3.752
Ours
2.424
2.457
2.459
2.502
2,471
2.532
2.601
Ours
3.345
3.502
3.595
3.711
3.753
3.723
3.742
Climatology
2.610
2.610
2.610
2.610
2.610
2.610
2.610
Climatoloyy
2.430
2.430
2.430
2.430
2.430
2.430
2.430
1350
FuXi-S2S
3,323
3.192
3.141
3.286
3,386
3,317
FuXi-S25
795
787
773
807
814
775
Ours
3.255
3.187
3,193
3,109
3,321
3,298
3.402
Ours
791
779
766
798
805
766
796
Climatology
3.410
3.410
3,410
3.410
3,400
3.410
3.400
Climatology
820
820
820
820
820
820
820
over 5000 steps (5 epochs), followed by a cosine annealing schedule over 95000 steps (95 epochs). Our model training was implemented using PyTTrrc (Paszke et al., 2019). In the training process, we train multiple models with different lead time settings, where the lead time ranges from 15 to 45 days with an interval of days. The output from each model, corresponding to a single step prediction, is combined to form a 45-day subseasonal forecast target. The model was trained eight GPUs with 80GB of memory, achieving 77.6 TFLOPS of computing power.
4.1
MAIN RESULTS
Compared with deterministic forecast We compare the ACC and RMSE of TianQuan for lead times of 15-45 days with the baselines in 4 target variables: temperature in 850hPa (T850), geopotential at 500hPa (Z500), 2m temperature (T2m) and 10 metre wind speed (Wind10) in Figure 3. Based on these results, we have the following findings:
Regardless of whether the resolution is 1.40625 or 5.625%, TianQuan S2S consistently outperforms all baselines in all variables. Specifically, the average RMSE improves by 0.14 on T850 (K), 59 on Z500 (m²² /n²//²), and 0.353 on Wind10 (m/s) compared to the best baseline, all representing significant improvements.
Compared with the transformer-base direct prediction model ClimaX, FuXi-S2S (00 member) performs worse on T850, Z500, and 10 before 25 days due to iterative error accumulation at each step. However, beyond 25 days, FuXi-S2S stabilizes and avoids the model collapse and severe metric degradation observed in ClimaX. Unlike ClimaX, TianQuan-S adds attention-basse climatology fusion and Iearnable Gaussian noise in the Transformer blocks to anchor forecasts, reduce drift, and stabilize long-lead predictions.
We can find that wind forecasting is more challenging for all baselines. However, TianQuan-S25 generally achieves higher accuracy across all lead times. For example, day 45 Wind ACC of ClimaX is 0.172, and ACC of ECMWF-SS S2S is 0.1 while ACC of TianQuan-S22 is 0.297. Under such cases, TianQuan-ST still performs the best, further verifying its effectiveness.
Compared with ensemble forecast To better investigate the long-term prediction performance of TianQuan-S2. S2S, compare it with the ensemble forecast models in Table 1, where lighter colors our model results. We further compare the RMSE of the ensemble mean forecast with the Climatology baseline in Table 2. From the results, we can find that:
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ClimaX
FuXi-S2S
Tian
ERAS (ground truth)
T2m
T850
Wind10
Figure 4: Visualization of forecast results on 1,40625 daily ERA5 data. The 30-day forecast of one upper-air variable (T850) and two surface variables (T2m and Wind10). For each case, the input time is 00:00 UTC on 15 February 2018
ClimaX
FuXI-S28 6-857
TianQuan
ECMWF-S28
R² 1.300
12
Prediction
Bias 8,994-9
4.950
MAR 2.790 Bias 8.283
Bius 0.893
4.221
Ground truth
Ground truth
Ground truth
Ground truth
Figure 5: Scatter chart of prediction and the ground truth. The input time 00:00 UTC on 15 February 2017 with the lead time of 25 days.
Our method remarkably outperforms FuXi- SSS and ClimaX almost all cases, demonstrating an improvement in the effectiveness of long-ten mergteemmyyy predictions. In addition, the RMSE of our ensemble mean forecast remains above the Climatology baseline at T2m, T850, and 7500. However, since the average value has a greater impact wind speed, FuXi-S2S and approach are worse
We can observe that ClimaX achieves worse forecast results in ensemble forecast metrics. Also, as a direct forecast model, our method achieves significant improvements in results, particularly the RQE of day 35 Z500 (m²/ /s²), which improves by 72. Such results show that models with noise generative are more stable than direct data-driven models.
We note that for Wind10 S2S lead times, both FuXi-S2S and our model are worse than climatol- ogy, mainly because ML-based ensemble means over-smooth this highly variable field and thus increase RMSE. In contrast, the dayy sliding-window window climatology used in WeatherBench2 (Rasp et al., 2024) yields much smoother and more stable Wind10 baseline, especially at long leads.
Visualization To provide global view of model predictions, we visualize the day 30 prediction distribution in Figure 4. As shown in the figure, all models show global trend of change, but the results of ClimaX have a serious loss of details. FuXi-S2S shows high value changes on both T2m and T850, but its distribution on Wind10 is significantly different from the ground truth. In contrast, our model aligns more closely with the realistic observations provided by ERA5, easing the model collapse problem. In addition, to analyze the correlation between predictions and the ground truth, we draw day 25 scatter plot in Figure 5. It demonstrates that our method closer to the true values, and outperforms numerical model ECMWF-S2S and data-driven models, including FuXi-S2S and ClimaX, across correlation (R²), mean average error (MAE), and Bias metrics. After comparing these details, we further validated our framework of incorporating climatology state by attention-based fusion. More visualizations, such as different variable predictions, can be found in the Appendix G.
4.2 ABLATION STUDY
Effectiveness of the Model Design To validate the effect of each model design the overall model performance, we compare four experimental models based on whether they use attention- based fusion well noise injection, summarized in Table 3. The main observations are:
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Table 3: Ablation studies where Clim. is short for climatology.
RMSE ())
ACC (1)
Model
15
20
25
35
40
45
15
20
25
35
40
45
w/o noise and Clim.
888
891
909
921
936
991
1048
0.574
0.568
0.552
0.535
0.524
0.487
0,441
7500
w/o noise
859
875
896
904
914
918
940
0.591
0.584
0.563
0.557
0.542
0.537
0.521
w/o Clim.
857
879
9013
914
923
953
972
0.594
0.575
0.559
0,543
0.534
0.513
0,503
Default
843
869
882
887
901
904
921
0.603
0.589
0.571
0.569
0.561
0.558
0.535
w/o noise and Clim.
3.072
3.145
3.271
3.591
3.613
3.716
3.802
0.790
0.779
0.750
0.702
0.684
0.657
0.648
122
noise
2.926
2.934
3.025
3.124
3.174
3.214
3.221
0.810
0.807
0.798
0.782
0.776
0.764
0.756
w/o Clim.
3.010
3.072
3.184
3.224
3.352
3.471
3.567
0,804
0.794
0.775
0.754
0.735
0.718
0.708
Delault
2.641
2.734
2.828
2.922
2.942
2,998
3.052
0.816
0.814
0.812 0.810
0.807
0.805 0.796
Table 4: Comparison of Fusion and Perturbation Methods in Ensemble Mean RMSE. Our proposed method (Default) achieves the best performance compared other fusion strategies, perturbation methods, and varying the number of noise injection layers.
Methods
20
30
35
40
45
Methods
20
30
35
45
Concat
2.525
2.556
2.565
2.583
2.627
2.655
2.707
Concat
830
814
808
837
845
819
832
Gate
2.476
2.528
2.530
2.541
2.563
2.589
2.670
Gate
811
802
797
818
828
802
818
IC Perturb
2.446
2.506
2.527
2.538
2.556
2.624
2.674
IC Perturb
814
812 809
821
823
808
818
FL.N
2.497
2.556
2.560
2.583
2.601
2.616
2.617
FINN
825
814
818
827
825
816
823
Layer Only
2.599
2.626
2.653
2.714
2.777
2.802
2.841
Layer 1 Only
817
811
806
818
823
807
821
Layer 1-2
2,530
2.562
2.606
2.623
2.693
2.699
2.712
Layer 1-2
810
809
798
816
818
792
811
Layer 1-4
2,535
2.548
2.593
2.603
2.593
2.652
2.729
Layer 1-4
814
808
802
810
816
785
817
Layer 1-6
2.511
2.578
2.602
2.567
2.623
2.657
2.707
Layer 1-6
807
797
772
811
812
779
815
Layer 1-7
2.456
2.496
2.518
2.532
2.554
2.604
2.624
Layer 1-7
799
782
776
804
813
808
Default
2.424
2.457
2.459
2.502
2.471
2.532
2.601
Default
791
779
766
798
805
766
796
.
Comparing the models with and without the Climatology, it is evident that incorporating climate information significantly improves the metries for forecasts beyond 25 days. For example, 7500 RMSE of the model on w/o noise and Clim. increased by 160, and its T2m RMSE increased by 0.73 from day 15 to day 45, while Z500 RMSE of the model on w/o noise only increased by 81, and its T2m RMSE increased by 0.295. This shows that climate information can serve as auxiliary information to make the model perform better in long-term predictions.
Employing noise generation in transformer blocks improves model performance, and further gains are achieved when combined with attention based fusion. The results in the table show that the model on w/o Clim. lowers the average RMSE of 7.50/T2mm by 26/0. 19. In contrast, the reductions of the model on Default increase to 54/0.57. Such results not only suggest the effectiveness of our model designs but also validate the effectiveness of utilizing the transformer block with noise generation to extract the spatial periodic signal from climatology.
Analysis of Fusion and Perturbation Methods We investigate our method's superiority in three areas: (1) Fusion strategies, comparing Concatenation (i.e., Concat, merging climatology on channels) and a Learnable Gate (i.e., adaptive climatology selection per pixel); (2) Perturbation methods, comparing Initial-Condition Perturbation (i.e., IC Perturb, perturbing only initial conditions) and Fixed-Layerss Noise (i.e., FLN, removing learnable functions); where "Layers 1-2" refers to injecting noise into the 1st and 2nd blocks. Results in Table 4 show that:
(3) Impact of noise injection layers,
Comparing the two variants of fusion strategies and ensemble forecast perturbations on T2m and Z500 at all lead times, our method (Default) achieves the best performance, confirming that attention is a more effective and interpretable way to exploit climatological priors, and indicating that the proposed learnable noise injection is superior alternative to Initial-Condition Perturbations and better emulates the climate evolution process than Fixed- Noise.
Investigattng the impact of uncertainty blocks, we further conduct an ablation study on per-layer perturbation. As the number of perturbed layers increases, the overall performance consistently improves: the ensemble-mean RMSE of T2m and 7500 is reduced by up to 0.223 and 28.85, respectively, demonstrating that noise injection enhances forecast accuracy.
Impact of Noise Scale To further understand the impact of the standard deviation of Gaussian noise, we compared different noise standard deviations a and obtained the results shown in Figure From the results,
find that when o is around 1, the perturbation model generates better results, indicating that this noise scale strikes an optimal balance between regularization and model accuracy.

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T2m
T850
Wind10
Z,000
Gausian Nuise Scale
RMSE Min-Maa
2-2
25
35 (flays)
25
35 (1hays)
28
35
34
35
45
16
30
25
30
35
(Dlyy
(Days)
Figure 6: RMSE comparison between different Gaussian noise scales at all lead times, A lighter color indicates better results: overall, the effect is better when = 1.
5 RELATIVE WORK
Data-driven weather forecasts Weather forecasting mainly involves gridded prediction tasks, akin to image-to-image translation. Recent advancements (Zheng et al., 2025) have been made in short- to cediumm-tem weather and climate forecasting. Notable examples include FourCastNet (Pathak et al., 2022), which was the first to attempt multi-variable forecasting in the short term with results comparable to NWP models. Pangu-Weatte Weather (Bi et al., 2023) and GraphCast (Lam et al., 2022) surpass traditional numerical methods in achieving multi multi-variable forecasting in the medium term. Based on the framework of transformer, FuXi (Chen al., 2023b) and Weng (Chen et al., 2023a) developed model method adapted to the Earth system. NeuralGCM (Kochkov et al., 2024) is designed based on the GCM architecture to capture spatial dependencies in weather prediction. Exploring higher resolution forecasting, Feng FengWu-Gr Wu- GHR (Han et al., 2024) aims to improve predic- tion accuracy. Aurora (Bodnar al., 2025) and Prithvi-WxC (Schmude et al., 2024) both focus on Weather forecasting based on foundation models. Aardvark Weather (Allen et al., 2025) and FuXi Weather (Sun et al., 2025) both employ end-to-end deep learning models, directly processing raw observational data and assimilating satellite information for weather forecasting. While these advancements extend forecasting capabilities, the absence effective climate information leads to a significant decline in performance. This highlights the need for approaches specifically designed for subseasonal forecasting.
Jubseassonalto-SSaasoo forecasts Subseasonal forecasting, which provides predictions 2 to weeks ahead, fills the erucial gap between short-term weather forecasts (typically up to 15 days) and long-term climate predictions that extend to seasonal and longer timescales. Although machine learning models have achieved significant progress medium-range and climate prediction, their effectiveness in subseasonal forecasting has been less pronounced (Wang et al., 2024; He et al., 2021). However, sub-seasonal to seasonal time scales, the predictive results of machine learning methods often lack the details of forecasting (Vitart et al., 2022: Nathaniel et al., 2024). This limitation leads to iterative errors in long-term forecasts, ultimately rendering the results unusable (Lam et al., 2023). Recent methods focus building more effective subseasonal forecasting models to enhance predictive skill (Chen et al., 2024; Liu et al., 2025a;b). To strengthen subscasonal forecasting capability, we proposed a patch embedding that incorporates climatological information and an incerrainty-augmente Transformer that captures weather variability. In particular, although both Fuxi-S2S and TianQuan- S2S add perturbations in the model, Variational Autoencoder- baseed FuXi- S2S adds perturbations only within the latent space, while TianQuan-S injects learnable Gaussian noise directly into the feature representations every layer of Transformer blocks, continuously reinforces variability, and more effectively mitigates model collapse in long-lead forecasts. In addition, Fuxi-S2S does not explicitly incorporate climate information.
CONCLUSION AND FUTURE WORK
In this work, we present TianQuan-S2S, novel framework that addresses the challenges in seneessonal-toseassoee (S2S) forecasting, particularly the limitations of model collapse and the insufficient use of climate information. Our extensive experiments on the ERA5 dataset demonstrate that TianQuan-SV outperforms both traditional numerical S2S systems and data-driven models, providing significant improvements in both deterministic and ensemble forecasting, Ablation studies have further substantiated the effectiveness model designs, and additional empirical analysis illustrates the superior performance across all lead times. In the future, we plan to optimize model framework to enable risouutocoolution forecasts and incorporate additional information such as land, ocean, and sea ice data to improve the learning capabilities of the model.
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7 ACKNOWLEDGMENTS
This work was supported in part by the National Natural Science Foundation of China under Grant T2125006; in part by GuangDong Basic and Applied Basic Research Foundation under Grant 2025A15155100 10016; in part by Shenzhen Science and Technology Program under Grant KCX7Z202400003355004 and Grant KJZD202309231 106001, 1506011 in part by the Open Research Fund of Pengcheng Laboratory under No. 202522 B0040. Yang Liu is supported in part by the Postdoctoral Fellowship Scheme of The Chinese University Hong Kong.
8 REPRODUCIBILITY STATEMENT
We are commited to ensuring the reproducibility of our research. Source code and README.dd file with detailed instructions for data preparation and script execution are available at https: / ///ittthe tuub..u.... com/ zhangminglangg / /ar44///ianuuaaaa Tianquan and also provided in the Appendix. The appendix offers comprehensive details to support our claims. Appendix C describes the details and hyperparameters of our proposed TianQuan-S25 In Appendix D, we further explored the differences in the prediction methods of each model and conducted extensive experiments on the prediction methods of our model. Furthermore, Appendix E and F list in detail the sources and processing methods of the experimental data, and the calculation formulas of the indicators are also included.
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TianQuan-S2S: A SubssasonaaltooSSeasnnal Global Weather Model via Incorporate Climatology State
(APPENDIX)
TABLE OF CONTENTS IN APPENDIX
The Use of Large Language Models (LLMs)
16
B Notations
16
Model Details
17
C.1 Improved details
17
C.2 Hyperparameters
17
Inference Details
17
D.I Forecast Strategy Research
18
Discussion
18
E.1 Consistency Analysis of Multi-Model Outputs
18
E.2 Challenge in Wind Forecasting
19
F
Employed Data
20
F.1
ERA5
20
F2
ECMWF-S25
20
F3
FuXi-S2S
20
F44
Data Processing
20
G Quantitative evaluation
Additional Results
23
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APPENDIX
A THE USE OF LARGE LANGUAGE MODELS (LLMS)
In this study, Large Language Models (LLMs) used assistive tool to enhance the overall quality and clarity of the text. The primary research, analysis, and intellectual contributions remain solely the work of the authors. The key applications LLMs in this study are as follows:
Text Refinement: LLMs were employed enhance the grammatical accuracy, structure, and consistency of the manuscript. This involved refining sentence flow and ensuring consistent phrasing and tone across the entire paper.
Coherence and Structure: LLMs were used to organize and strengthen the logical flow of ideas. Suggestions were incorporated to improve transitions between sections and paragraphs, making the narrative more cohesive.
Idea Articulation: At various stages, LLMs acted as a sounding board, helping to articulate complex ideas more clearly and explore alternative expressions for the concepts already proposed by the authors.
All recommendations made by the LLM were critically reviewed, revised, and approved by the authors to ensure accuracy and alignment with the research intent. The final responsibility for the content lies solely with the authors.
B NOTATIONS
Table 5 summarizes the notations appearing in this paper.
Table 5: Summary of key notations.
Symbol
Description
G
Latinde-longitude grid with dimensions H X W x 2
X Xelim
the state of global weather at time t and climatology #xxxk Total number of weather variables, calculated VA C V/s
K
C
Number of pressure levels
VA Vs
Number of upper-air variables, surface variables
& Knsstas
Predicted weather variables from day 15 to day 45
Fatim
Convolutional feature map extracted from climatology Xatim
F,, F.
Spatial and channel feature maps from convolution operations
Fx
Enhanced climate feature map after fusion of F, and F. Reshaped feature tensor after flattening spatial dimensions Query, key, and value matrices for attention mechanism Learnable projection matrices for query, key, and value Attention weights for spatial fusion
(v)
Q0),, K(t), (
WQykjv
Watt
E, EA, Es
Combined and upper-air and surface embedding tensors after patchify
Bl..)
Transformer output after applying attention mechanism
gn(.)
Learnable noise function in the uncertainty block
weighte mean squared error loss function, and latitude of the i-th grid row 4, lat(()
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C
MODEL DETAILS
This section presents the improved details of TianQuan-SS
C.1
IMPROVED DETAILS
After comparing our proposed TianQuan-S2S with FuXi-S2S and ClimaX in the experiments, identified the following details as critical for subseasonal forecasts performance:
Multi-scale Temporal Modeling: Capturing features at different time scales is crucial for sub- seasonal forecasts. Using multi-scale convolutions or multi-layer recurrent neural networks can effectively handle both short-term and long-term dependencies.
Incorporation of Attention Mechanisms: Self-attention mechanisms can dynamically assign importance to different time steps, allowing the model to focus more the time steps that have greater impact on future predictions, thereby improving accuracy.
Climate change trend information: For time series with significant seasonality and long-tenn -eemmtermmm climate trends, enhancing and fusing climate features separately can significantly improve prediction performance.
C.2 HYPERPARAMETERS
The hyperparameters of the model are shown in Table 6.
Table Hyperparameters and their meanings for the model.
Hyperparam
Meaning
Value
[
Number of default variables
67
D
Embedding dimension
384
Depth
Number of UD-ViT blocks
8
heads
Number of attention heads
12
Drop path
For stochastic depth
0.1
Dropout
Dropout rate
0.12
D INFERENCE DETAILS
PM20
PM25
PM30
PM35
PM40
PM45
Inputs
20
25
30
35
40
45
Outputs: 15-45 days predicted data
Figure 7: Multi-model forecasting strategy. PMK denotes forecast models with K--day lead times. With at least 5 days of input data, predictions can be made for the following 15-45 days.
Our approach differs from hierarchical temporal aggregation methods used in Pangu-Was Weather (Bi et al., 2023). We divide the 15-45 day prediction horizon into 5-day segments and train separate model PMc for each. Formally, this design can be written as:
X,-4t K. t-
PMK (X,-4....)) .) 1.E
(11)
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where K. {20, 25,... 45} represents the lead time of the prediction model. Each model generates its prediction solely from the initial fields spanning time steps - to t, without relying on outputs from earlier models, thereby preventing the accumulation of errors across models. Mcanwhile, proposed the Content Fusion Module to integrate auxiliary signals (e.g., I+n climatology) and utilize the robust backhone (UD-ViT) for improved long-range modeling. It can improve the accuracy of each segment.
D.1 FORECAST STRATEGY RESEARCH
At present, the methods of weather forecasting are mainly divided into autoregressive forecasting and multi-model single-step combination forecasting.
To help distinguish the predictions of currently common weather forecast models, we compare the models of Pangu-Weather Weather (Bi al., 2023), FuXi (Chen et al., 2023b), and ClimaX (Nguyen et al., 2023).
Table 7: Comparison of representative forecasting models.
Model
Pretrain
Single-Model AR
Horizon Gran.
Horizon
Pangu-Wcather Weather
X
X
1h, 3h, 6h, 24h
Up to 7d
FuXi
(ERA5)
(Cascade)
Each model 5d
Up to 15d
ClimaX
(CMIP6)
(ClimaX-iter)
1,3,5, 7, 10, 14, 30d
Up to 30d
TianQuan-S24 S2S
X
15, 20. .... 45d (step=5)
15-450
We have also implemented a single autoregressive model fine-tuned by scheduled sampling based on framework. The RMSE comparison results shown in the following table:
Table 8: Comparison of mulli-modee and single autoregressive model.
Strategy
Vars
T2m
1.83
2,82
2.64
2.73
2.82
2.922
2.942
2.998
3.052
T850
2.95
3.249
3,283
3.307
3.346
3.442
3,481
3,563
mudti-model
Wind10
2.37
2,4185
2,4203
2.4219
2.4368
2.5043
2.5321
2.5984
7500
3.40
7,80
843.6
869.2
882.6
887.4
900.8
904.5
921.6
T2m
1.52
2.67
2.79
2.89
2.95
3.25
3.41
3.61
3.80
single auto-
T850
1.82
3.12
3.32
3,412
3,5142
3.6142
3.7814
3.941
4.023
Wind10
1.94
2.26
2.465
2,501
2.583
2.623
2.771
2.817
3.062
regressive model
Z500
3.10
7.74
875.1
888.9
899.3
935.4
948.2
967.1
985.6
As shown in the table 8, the autoregressive strategy outperforms the multi-model strategy in most metrics for lead times under 10 days. However, for longer-range forecasts (beyond 10 days), the multi-model strategy consistently achieves better performance across key metrics, highlighting its superiority in the subseasonal- forecasting domain.
E DISCUSSION
E.1 CONSISTENCY ANALYSIS OF MULTI-MODEE OUTPUTS
To address the concern regarding temporal discontinuities between adjacent lead times, our model primarily analyzes the continuity of the output at the two key points:
Residual connections for consistent representations: Residual connections in the Transformer preserve information across layers, helping the model maintain coherent representations from short long leads and reducing abrupt shifts in the forecasts.
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Smooth transitions and stability: Beyond climatology fusion, add lead-time and absolute-ting time embeddings (days since Jan 1970) so the model explicitly aware of the target time, which improves temporal continuity and stability between adjacent lead-time forecasts.
Additionally, we further assess temporal continuity by computing the first-order differences between adjacent model outputs and analyzing mean/std/max in the Table 9.
Table 9: Mean, standard deviation, and maximum of first-order differences for different variables and lead-time ranges.
Metrics
Vars
15-20
20-25
25-30
30-35
35-40
40-45
T2m
0.132
0.152
0.187
0.210
0.286
0.316
T850
0.199
0.206
0.227
0.239
0.302
0.329
mean
Wind10
0.0138
0.0189
0.0196
0.0255
0.0353
0.0531
Z500
13.01
13.96
16.47
16.60
18.15
27.90
T2m
1,973
1,986
2.432
2.596
2.603
2.716
T850
2.558
2.657
2.921
3.228
3.257
3.527
std
Wind10
0.971
1,128
1.180
1.377
1.414
1.497
Z500
176.2
173.7
203.5
182.3
204.5
226.2
T2m
11.88
13.01
15.36
16.45
17.57
18.79
T850
17.43
22.09
27.16
28.22
28.75
28.82
max
Wind10
6.852
7,331
8.595
9.913
12.33
12.36
Z500
1031
1078
1252
1361
1322
1482
Note: K-(K+5) denotes the continuity metric between the K-day and (K+5)-day model predictions.
Overall, the mean, standard deviation, and maximum of the first-order differences increase with lead time across all variables. consistent with the gradual degradation of forecast skill longer ranges. At the same time, the growth of these statistics across adjacent lead-time windows is smooth rather than abrupt, indicating that the fields evolve in a temporally continuous manner instead exhibiting erratic, frame-to-frane jumps.
E.2 CHALLENGE IN WIND FORECASTING
The challenge in accurately forecasting near-surface variables, such as Wind10, primarily stems from the extreme complexity of the underlying surface conditions and strong thermodynamic processes. Factors like heterogeneous terrain, land-sea contrast, and surface heating induce intense turbulence and high variability, making near-surface wind inherently less predictable than large-scale atmospheric variables.
We acknowledge that current rently limited by the absence of high-resolution surface data and explicit solar radiation inputs, which are essential for capturing these fine-scale processes. This limitation explains why simple climatology, which smooths out subseasonal variability, can sometimes appear more stable in evaluation metrics for 10nd10.
models, including FuXi-S2S and TianQuan-S25 are cur-
We fully agree on the importance of these inputs. The current model is evaluated primarily on lower-resolution data and does not yet incorporate other crucial Earth system components (e.g., land surface, ocean, and sea ice data), which significantly influence subseasonal climate variability.
We plan extend the model support higher-resole resooutinooot inputs and integrate multi-source Earth observation data (including detailed surface and radiation information) to enhance its physical consistency and forecasting skill.
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Table 10: Dataset Variable List for Different Types and Levels.
Type
Variable
Abbrev.
Levels
Static
Land-sea mask
LSM
Static
Orography
Surface
metre temperature
T2m
Surface
10m Wind speed
Wind
Upper
Geopotential
Z
50, 100, 150
Upper
Wind speed
Wind
200, 250, 300
Upper
Temperature
T
400, 500, 600
Upper
Specific humidity
Q
700, 850
Upper
Relative humidity
925, 1000
F EMPLOYED DATA
In this paper, two pre-generated datasets, ERA5 and ECMWF-S2S, are primarily utilized. The following sections will introduce their sources and respective roles.
F.I ERAS
We used the ERA5 (Rasp al., 2020) dataset to complete the model training process. ERAS was created
standard benchmark dataset and evaluation framework for compar- ing data-driven weather forecasting models. WeatherBench regridded the original ERA5 from 0.25 to three lower resolutions: 5.625 and 1.40625.. The corresponding data can be downloaded from
/dataset/
F.2 ECMWF-S25
The Sub-seasonal Seasonal Prediction Project (S2S) (Vitart et al., 2017), initiated in November 2013 by the World Weather Research Programme (WWRP) and the World Climate Research Pro- gramme (WCRP), aims enhance forecast skill and deepen understanding of the dynamics and climate drivers on the sub-seasonal to seasonal timescale (ranging from two weeks to a season). This project seeks bridge the gap between medium-range and seasonal forecasting by leveraging the combined expertise of the weather and climate research communities, thereby addressing critical issues relevant the Global Framework for Climate Services (GFCS). We can download its data from https: / apps. e ecmwf. int /wtaaaatassssseee aata/daaaas/sss/s
F.3 FUXI-S2S
The forecast results of FuXi-S2S were downloaded from Hugging Face to facilitate a direct compari- son with our model. The data, available https: //huggi ng face. co co/Fo///// FFuii 5225, were used to evaluate the performance of our approach in forecasting subseasonal--o-seaaomm (S2S) predictions. This comparison allowed us to assess the forecast accuracy and skill across various variables, such as temperature and precipitation, in order to better understand the relative strengths and weaknesses of our model.
F.4 DATA PROCESSING
Since our task is performed on ERA5 daily average data, we simply introduce this data processing here. We preprocess the hourly ERAS data by sampling every six hours (00, 06, 12, 18 UTC+00) and then computing daily averages over these four time points. For example, the 00-day average represents the of the average values from 23 to 00 the previous day. The calculation is
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expressed as follows:
to
Vart. = T 1
Σ
Var. T = 24
(12)
where Var represents other variables except wind speed. For wind speed, the daily mean is calculated as:
fo
Wind = T t----++1
Σ
Vut+
= 24
(13)
where uy and by are the zonal and meridional wind components at each sampled time.
G QUANTITATIVE EVALUATION
In this section, we detail the evaluation metrics applied in our experiments. The predictions and ground truth are formatted as N x H x W, where N indicates the quantity of predictions test samples, and H x W defines the spatial resolution. To address the varying sizes of grid cells, L(t) is introduced latitude-based weighting factor.
Root mean square error (RMSE) Root mean square error (RMSE) measures the average magni- tude of the prediction errors in dataset. quantifies how closely predicted values match the actual values, with lower RMSE indicating more accurate predictions.
N
H
W
RMSE =
1 N k=1
Σ
L(i( - -K,,,))
(14)
HxW
j=
Anomaly correlation coefficient (ACC) Anomaly Correlation Coefficient (ACC) assesses the accuracy of forecast by measuring the correlation between predicted and observed anomalies. commonly used in climate and weather forecasting to evaluate how well the model captures deviations from the climatological average. Higher ACC values indicate better predictive skill.
Enso LO0
ACC =
(15)
VEnN 1(0) KAd En.s L(DY R.L.
hi1 Vkii Cküis Vk.k. = Uk Ck
(16)
where Climatology C represents the average of the ground truth data across the entire test set over time.
R-squared (R2), Mean Absolute Error (MAE) and Bias R-squared (R3), Mean Absolute Error (MAE) and Bias are commonly used to assess the performance predictive models. The metrics are shown in 5.
(y. 0:)2
R2
(17)
Σ
7) Dim1
(yr
MAE
184 0el
(18)
N
i=1
N
Bias
(0i yi)
(19)
N
Continuous Ranked Probability Score (CRPS) CRPS measures the difference between the forecast CDF and the step function at the observed value, thus evaluating both the sharpness and reliability of a probabilistic forecast. A lower CRPS indicates more accurate forecast. Calculation Formula:
CRPS(F / (E())) (F(x)-1{=) - 1fx 1arz20 v1)² dr,
dr.
(20)
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where Fx)) is the forecast cumulative distribution function (CDF) and 1(x 2 y) is the indicator function for the observed value y.
Spread Mean Error (SME) SME quantifies the difference between the ensemble spread and the absolute error of the ensemble mean. This metric is useful to determine whether the ensemble is under-dispersive (negative SME) over-dispersive (positive SME), and thus helps in assessing the reliability of the ensemble prediction system. Calculation Formula:
SME Σ
1y - mil),
(21)
where for each case i, oj is the ensemble spread (e.g., the standard deviation), is the ensemble mean, and yi is the observed value.
Relative Quantile Error (RQE) RQE measures the relative error between the forecast quantiles and the observation across different probability levels. It helps to assess how well the forecast distribution captures observed outcome. lower RQE indicates that the forecast quantiles are in closer agreement with the observations, implying more skillful probabilistic forecast. Calculation Formula:
Assuming K quantile levels ag, RQE is defined as:
Gas
RQE
Wk
(22)
y/
where Ya, denotes the forecast quantile probability level ars y the observed value, and wy weights (with 2i=1 Wk 1).
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H ADDITIONAL RESULTS
TianQuan-Se -2S T850
TianQuan-SBh Saaann-S2TTT T2m
TuanQuan-S2S Wind 10m
Russ m di
Blas +0 0.005
Plass -0034
11.9%
3.8%
22.3
20.0
13.0
24
12.0
21
Timee
20141 2014
2114
ane DOST 2014
Time
ClimaX T850
ClimaX T2m
ClimaX Wind 10m
21.3
Iltes 0.500
Biass -0.145
HEE = 10 cn%
RE 4.0%
13.0%
22.5
17.5
33.0
24
12.5
10.0
3074 20T4 WETTO 201T JAN
20800 LOR 2009
207787 2010 201R
20140 201- 201IC 20340 2004 2010 201-000 JIES4L
Figure 8: Fixed-point time series diagrams for TianQuan-S2S and ClimaX across three variables (T850, T2m, and 1o The time series covers the period from 2017 to 2018, with latitude and longitude fixed at 23 and 113".
Figure 8 primarily illustrates the differences between pointwise time series predictions and actual values on 5.625 data. The results show that both TianQuan- and ClimaX,, as machine learning methods, effectively capture the temperature trends associated with seasonal changes, demonstrat- ing the advantages of machine learning in climate forecasting. Although there is still some deviation in more complex variables like 10m wind speed, both methods achieve relatively stable forecasting. Notably, TianQuan-S2 S2S outperforms ClimaX in long-tern sequence metrics such as RE and SI on the variable of temperature, but ClimaX better on the variable of wind.
Z500
Q500
Wind500
TianQuan-S2
ClimaX
MC
102
47
pkg
Figure 9: Comparison of TianQuan-S25 and ClimaX in predicting deviations for three atmo- spheric variables: Z500, Q500, and Wind500. The top row shows deviations from TianQuan-Se and the bottom row from ClimaX.
The Figure illustrates the deviation of predictions from actual values for Z500, Q500, and W500 variables using TiamQuan-SS S2S and ClimaX. Overall, TianQuan-S2 exhibits more accurate pre- dictions with smaller and more evenly distributed deviations across all three variables, indicating
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TianQuan-S25
ClimaX
ECMWF-SB
Density
R²= 00945
R²= 0,891
R² = 0.799
MAE 2.915
MAE - 3.874
MAE 5.353
Bias 0.663
Bias 0.751
Bias -0.318
T850
Prediction
Prediction
Prediction
-42
-4
-254
224
R² 0.482
R² 0.440
R² -0.03
MAE 1.863
MAE 2.019
MAE- 2,713
Wind
Prediction
490
Bias 40.66
Bias -0.039
Prediction
200
Biaš = =0.04
200
280
270
272
412
470
270
460
270
-104
Deneity
R² 0.942
R² 0.936
R² 0.823
608.716
nn
645.214
MAE 1069
Bius 15.835
Bias 13,653
Bins 156.801
Prediction
Prediction
Prediction
Z500
48
5.5
Ground Truth
Ground Truth
Ground Truth
-10
Figure 10: The seatter plots in the figure compare the performance of TianQuan-S25,, ClimaX, and ECMWF-S25 across three variables: T850, Wind10, and Z500. Each model's predictions plotted against the ground truth, with density colors indicating the concentration data points. The performance metrics, including R², MAE, and Bias, are provided for each model.
better alignment with the actual atmospheric patterns. In contrast, ClimaX shows larger deviations, particularly in areas with more complex dynamics, suggesting it struggles to capture finer details and variations. The results demonstrate TianQuan-S22 S2S's superior capability in minimizing prediction errors across different atmospheric conditions.
The results shown in Figure 10 indicate the following: For the 10 and Z500 variables, all models show a reduction in predictive accuracy compared to T850, with lower RR values across the board. Despite this, TianQuan-S22 S2S consistently outperforms the other models. It achieves the highest R² values for both Wind10 (0.482) and 7500 (0.942), along with the lowest MAE values (1.863 and 608.716, respectively), indicating superior precision. While ClimaX performs reasonably well, its accuracy is slightly diminished, reflected in its higher MAE and marginally lower Ra values. ECMWF-S2S, however, struggles significantly with both variables, displaying minimal correlation with the ground truth, especially in Wind10, where it shows almost no predictive capability. The results confirm TianQuan-S23 -2S'ss robustness across varying atmospheric conditions, while ClimaX and ECMWF-ST S2S show limitations in handling more complex variables like Wind10 and Z500.
In addition, we have referred to the prior works and included a new comparison with traditional ML models, including XGBoost and Lasso, for forecasting T2m within the 15-45 day range.
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Table 1I: Comparison of Tian XGBoost, and Lasso across different forecast horizons.
Models
15
20
25
30
35
40
45
TianQuan-S2S
2.64
2.73
2.82
2.92
2.94
2.99
3.05
XGBoost
2.82
2.99
3.14
3.29
3.42
3.52
3.61
Lasso
3.05
3.22
3.38
3.53
3.65
3.74
3.79
As shown in the Table while these models perform reasonably well, our proposed TianQuan-S2. consistently achieves lower RMSE, particularly at longer lead times. This demonstrates the superiority of our architecture in S2S forecasting.
Table 12: T2m RMSE of ablation studies for North America and East Asia.
Regional
Model
35
40
w/o noise and Clim.
3.108
3.226
3.345
3.632
3.711
3.843
3.853
w/o noise
3.095
3.144
3.262
3.342
3,406
3.604
3.611
North American
wfo Clim.
2.980
3.027
3.103
3.203
3.250
3.332
3.312
Default
2.715
2.764
2,913
3.007
3.048
3,113
3.123
w/o noise and Clim.
3.037
3.151
3.275
3.554
3.577
3.751
3.797
w/o noise
2.951
2.943
3.039
3.102
3.153
3,188
3.253
East Asia
wfo Clim.
2.966
3.099
3.160
3.201
3.332
3,440
3.545
Default
2.591
2.686
2.834
2.919
2,886
2.965
3.011
Additionally, we have supplemented our analysis with ablation experiments across two different regions to further investigate the performance of our model in different places. Based on Table 12, we provide comprehensive discussion:
Due more complex orography and land-sea contrast, T2m RMSE over North America is overall higher than over East Asia; moreover, in North America, the "w/o Clim." case (only noise) is better than "w'o noise" (only climatology), indicating that noise perturbations bring larger gains than climatology in more complex terrain.
From 15 to 45 days, the advantage of the Default over all ablations persists and generally enlarges, confirming that our components are especially helpful for mitigating long-lead skill degradation while still improving short leads.
Table 13: T2m RMSE of ablation studies for North America and East Asia.
Variables
Model
15
25
35
w/o noise and Clim.
3.867
3.923
3.883
3.990
4.006
4.062
4.116
w/o noise
3.599
3.614
3.691
3.846
3.875
3.982
3.931
T850
w/o Clim.
3.412
3.495
3.573
3.666
3.666
3.698
3.860
Default
3.249
3.283
3.307
3.346
3,442
3.481
3.563
w/o noise and Clim.
2.844
2.861
2.894
2.815
2.919
2.922
3.110
w/o noise
2.694
2.719
2.756
2.793
2,804
2.903
2.923
Wind10
w/o Clim.
2.658
2.598
2.558
2.670
2.748
2.694
2.795
Default
2.418
2.420
2.422
2.437
2.504
2.532
2.598
From Table 13, for different variables (T850 and Wind10), the Default model (with noise clima- tology) consistently achieves the lowest RMSE across all leads, confirming that our design benefits variables with diverse physical scales.
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To investigate performance during challenging conditions, analyzed the model's results during the severe 2018 North American (NAM) and 2018 East Asian (EA) heatwaves, starting from June 28, 2018, and July 9, 2018, respectively in Table 14.
Table 14: T2m RMSE of ablation studies for North America and East Asia.
Lead Time
Model
NAM
EA
ClimaX
2.948
3.046
25-day
FuXi-S2S
2.634
2.851
TianQuan-S25
2.522
2.721
ClimaX
3.081
3.120
40-day
FuXi-S2S
2.724
2.942
TianQuan-S2S
2.685
2.843
We can find that TianQuan- achieves better results compared to existing models (ClimaX, FuXi- S2S) even under these extreme cases, demonstrating practical usefulness. While these results are encouraging, we acknowledge that improvements on extreme- extreme-weather metrics are more modest than for bulk statistics, suggesting that rare, high-impact events complex terrain remain more challenging and warrant further targeted investigation.
Table 15: T2m RMSE Comparison of Ensemble Mean Results for Different Noise Scale.
Regional
Model
15
20
25
30
35
40
45
0.1
2.509
2.554
2.568
2.569
2.624
2.630
2.718
0.5
2.477
2.535
2.539
2,543
2.569
2,592
2.679
Input Perturbations
2.446
2.506
2.527
2.538
2.556
2.624
2.674
1.5
2.551
2.580
2.594
2.614
2.664
2.692
2.734
2.611
2.637
2.642
2.652
2.696
2.710
2.774
0.1
2.507
2.538
2.548
2.553
2.607
2.614
2.696
0.5
2.505
2.556
2.565
2,583
2.617
2.635
2.707
Fixed Noise
2.497
2.556
2.560
2.583
2.601
2.616
2.719
1.5
2.615
2.638
2.648
2.663
2.695
2.717
2.786
= 2
2.681
2.708
2.721
2.728
2.762
2.798
2.886
Notably, the results shown in Table 15, the performance of Input Perturbation and Fixed Noise rapidly drops when the noise scale increases to 1.5.
26


Reviews:
[{"review_id": "X782aLyVoq", "reviewer": "Reviewer_k6Rk", "summary": "This paper tackles the challenge of model collapse in Subseasonal-to-Seasonal (S2S) forecasting by introducing a simple yet effective framework, TianQuan-S2S.\nThe method (1) integrates climatology information into patch embeddings to complement the limited predictive power of initial states, and (2) injects Gaussian noise into Transformer blocks to preserve variability and reduce over-smoothing.\nExtensive experiments on the ERA5 dataset show clear improvements over ECMWF-S2S, FuXi-S2S, and ClimaX in both deterministic and ensemble settings.", "questions": "The paper introduces a learnable Gaussian noise injection within every Transformer layer, claiming that it helps sustain variability and prevent long-lead model collapse. However, it remains unclear how this mechanism fundamentally differs from existing stochastic regularization techniques such as dropout, layer noise, or even standard input perturbation used in ensemble forecasting.\n\nSpecifically, how is the proposed per-layer Gaussian perturbation different from simply perturbing the input fields or initial conditions, as done in conventional ensemble methods like FuXi-S2S or stochastic parameterization in NWP systems? Input perturbations are known to encourage diversity and uncertainty propagation—so what unique advantage does injecting noise throughout the Transformer depth provide?\n\nMoreover, the paper would benefit from a direct experimental comparison between:\n\n- input-only perturbation (ensemble IC perturbations),\n\n- fixed or dropout-style layer noise, and\n\n- the proposed learnable state-dependent Gaussian noise.\n\nSuch a comparison could clarify whether the improvement stems from deeper uncertainty modeling or simply from added stochasticity. Additionally, the authors should discuss sensitivity to noise scale and spatial correlation, since uncontrolled noise magnitude might act as a crude regularizer rather than a physically meaningful uncertainty representation.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- Well-defined problem motivation: Clearly identifies information loss and model collapse as key S2S challenges.\n\n- Simple but effective design: Climatology integration and noise augmentation yield robust long-lead forecasts.\n\n- Comprehensive experiments: Covers multiple variables, metrics, and spatial resolutions on 40 years of ERA5 data.\n\n- High writing quality and reproducibility: The paper is clearly structured and provides implementation details and code.", "weaknesses": "The main limitation of this work lies in its modest technical novelty. The proposed approach largely builds upon existing concepts such as climatology conditioning and stochastic perturbation within Transformer architectures, rather than introducing a fundamentally new modeling paradigm or theoretical insight.\n\nThe method can be viewed as a clever and carefully engineered recombination of previously explored ideas, rather than a conceptual breakthrough. While the integration of climatological priors and noise injection is executed elegantly, the individual components are well-known in both numerical and data-driven forecasting literature.\n\nMoreover, the design choices—such as attention-based climatology fusion and Gaussian noise injection at each Transformer layer—feel somewhat heuristic (“tricky”), lacking a deeper theoretical justification for why this specific combination should outperform alternatives like simple concatenation or dropout-based regularization.\n\nNevertheless, the paper demonstrates clear empirical benefits and provides a well-structured and reproducible evaluation. The proposed model achieves strong, consistent improvements across multiple meteorological variables and lead times, effectively mitigating the long-horizon degradation problem that limits many prior S2S models.\n\nGiven that research in subseasonal-to-seasonal forecasting remains relatively sparse, and that the paper delivers a tangible step forward in practical performance and stability, this work deserves publication. It represents a solid and valuable contribution that advances the field through thoughtful system design and comprehensive experimental validation, even if the underlying techniques are not entirely novel.", "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": "ndJ7xupXMf", "reviewer": "Reviewer_FKnz", "summary": "This paper proposes TianQuan-S2S, a global S2S forecasting model that pushes lead times out to 45 days. This paper highlights the importance of incorporating climatological information into patch embedding and an uncertainty-augmented blocks in terms of S2S forecasting. Experimental results on ERA5 reanalysis dataset and ablation studies demonstrate the validity of the proposed model.", "questions": "\tIn line 361-362, the paper mentions that wind forecasting is more challenging for all baselines. What is the specific reason that wind forecasting is a challenging problem?\n\n\tTable 1 indicates that performance decreases for both ClimaX and TianQuan-S2S as lead time grows. Is this due to the intrinsic difficulty of longer horizons, or does it reflect model collapse?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "\tImportant task – S2S forecasting\n\n\tThe experimental analysis is relatively thorough, and the paper reports performance gains in the long-lead (15–45 day) range across a variety of metrics.\n\n\tThe method directly targets over-smoothing with a concise design (climatology fusion + uncertainty blocks), thereby enhancing performance.", "weaknesses": "Major weaknesses are as below:\n\n\tThe impact of adding uncertainty blocks with Gaussian noise is under-explained. The paper claims gains in generalization and uncertainty, but the analysis is thin. In Table 3, the w/o climatology + noise variant outperforms w/o climatology, yet it remains unclear why the injected perturbations help. More clarification of this behavior would be helpful. \n\n\tThe paper frames long-lead degradation as over-smoothing and model collapse, yet shorter leads improvement is also reported. However, it remains ambiguous why the method helps even at shorter leads. As the authors mention in line 357-360, transformer-based direct prediction model ClimaX performs worse than Fuxi-S2S, but the paper does not clarify why this observation does not carry over to TianQuan-S2S.\n\n\tTable 2 shows that Fuxi-S2S performs worse than climatology for Wind10, but the paper does not discuss the reason. A clear explanation of the reason would help.\n\n\tIn Appendix D, the authors state that each lead-specific model inputs a 5-day input window and produces a 5-day forecast. In practice, adjacent days (e.g., D+19 vs D+20) come from different models (e.g., PM20 vs PM25). The paper provides no analysis of whether this block boundary introduces temporal discontinuities or not. This leaves the temporal coherence of the lead-specific single-step models in doubt.\n\nMinor comments are as below:\n\n\tLine 140: \\hat{X}_{t_{20}:t_{45}} -> \\hat{X}_{t_{15}:t_{45}}\n\n\tLine 211: Including the reference for climate models using ViT architectures would be helpful.\n\n\tFigure 3 lacks essential information. Please clarify what each column represents.\n\nIf the weaknesses are addressed well, I will reconsider the score.", "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": "rLQJ1Hy8Rr", "reviewer": "Reviewer_ekwb", "summary": "This paper proposes TianQuan-S2S, a novel deep learning model for subseasonal-to-seasonal (S2S) global weather forecasting. To address current data-driven approaches' limitations—namely, the inadequate modeling of climate states and the tendency for over-smoothed, less-detailed forecasts at long lead times—the authors introduce an architecture that fuses initial weather states and climatological means at the patch embedding stage. Furthermore, Gaussian noise (uncertainty blocks) is injected into every Transformer layer, enabling improved representation of variability and suppressing excessive smoothing. Extensive experiments on the ERA5 dataset show that TianQuan-S2S substantially outperforms both state-of-the-art numerical (ECMWF-S2S) and data-driven (FuXi-S2S, ClimaX) models, for both deterministic and ensemble forecasting. Ablation studies demonstrate that adding climatology and noise notably boosts performance. The paper also provides detailed comparisons of model structures and training/inference strategies.", "questions": "Please provide more granular ablation studies covering all combinations of climatology, attention, and noise, broken down by variable, region, and lead time.\n\nPlease clarify the underlying mechanism by which Gaussian noise improves uncertainty modeling; compare with other uncertainty methods both theoretically and empirically, and provide some interpretability analysis.\n\nCan you supplement analysis of performance under extreme events?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The work systematically incorporates climatological mean information with initial state in feature representation for S2S forecasting and leverages uncertainty modeling, effectively addressing over-smoothing and detail loss in long-term prediction—achieving clear improvements over existing baselines with practical significance.", "weaknesses": "Although some ablation tests are presented, the paper only compares “without climatology” or “without noise” scenarios. It does not explore all combinations of climate, attention fusion, and noise modules (e.g., climatology + no noise, no climatology + with noise), nor does it analyze their effects on different variables, regions, or lead times.\n\nThe paper claims layer-wise Gaussian noise helps capture climate variability and improve uncertainty estimation, but gives neither a detailed theoretical justification nor a direct comparison to other uncertainty methods (such as MC Dropout, latent space perturbation). The effect of different injection scales and strategies and interpretability are also not discussed.\n\nMost results focus on global average RMSE/ACC improvements. There is little discussion on model weaknesses or failures in complex terrain, extreme events, or other challenging conditions. This leaves the risk that claims are overgeneralized; more specific breakdowns are needed.", "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)