STCFormer: Adaptive Spatio-Temporal Modeling with Dynamic Cluster Transformer for Station-based Weather Forecasting

Rongwen Li; Haixin Xie; Mingyang Wang; Hongwu Liu; Kun Fang; Changjian Chen; Zhuo Tang; Kenli Li

cs.LGSep 30, 2026

STCFormer: Adaptive Spatio-Temporal Modeling with Dynamic Cluster Transformer for Station-based Weather Forecasting

Authors: Rongwen Li, Haixin Xie, Mingyang Wang, Hongwu Liu, Kun Fang, Changjian Chen, Zhuo Tang, Kenli Li

Organizations: Hunan University · China Meteorological Administration · Hunan Provincial Meteorological Bureau

Abstract

Station-based weather forecasting supports daily life and economic activity, yet accurate forecasts require modeling complex spatial dependencies among stations. Recent clustering-based selective modeling offers a promising alternative to dense inter-station interactions. However, a grouping shared across an observation window may obscure local changes in station relationships, while intra-cluster interactions alone may miss important global context. The theoretical advantages of selective interactions over dense connectivity also remain insufficiently understood. We therefore propose STCFormer, an adaptive spatio-temporal Transformer that dynamically groups stations according to their local evolution within each temporal patch. Its Cluster-Guided Attention Block combines fine-grained local attention within clusters and global attention over regional state summaries, allowing each station to access information beyond its own cluster. We further show that a derived Lipschitz upper bound for cluster-conditioned local attention is no larger than its fully connected counterpart, explaining a potential robustness benefit and motivating the design of InfoLoss. Experiments on three real-world weather datasets spanning eight temperature and wind forecasting tasks show that STCFormer achieves the lowest 24-hour mean squared error on all eight tasks and ranks first or second in 47 of 48 comparisons across metrics and forecasting horizons. Ablations and case studies further confirm the benefits of locally adaptive grouping and complementary local-global interactions. Our code can be obtained at https://github.com/hnu-vis/STCFormer.

Figures & tables

Figure 1: Motivation for locally adaptive station grouping. (a) A single grouping is shared across an observation window. (b) A real 72-hour case from the French temperature dataset shows the strongest relationship shifting from A–B to B–C before all three stations become highly correlated. Insets report Pearson correlations within each 24-hour segment.

Figure 2: Overview of STCFormer. (a) The forecasting pipeline stacks CGAB encoders over patch embeddings and dual-view features. (b) Dual-view representation separates temporal state and local evolution. (c) Spatio-temporal patch embedding forms joint station–time tokens. (d) CGAB combines dynamic clustering, local attention within clusters, and global attention over regional summaries.

Spatio-Temporal Methods
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
DCRNN	6.428±0.062	6.111±0.159	8.091±0.133	4.921 ±2.835	1.947±0.007	2.815±0.039	8.401±0.138	3.675±0.005
Corrformer	7.911±0.161	4.700±0.068	6.411±0.001	5.594±0.723	2.044±0.006	2.640±0.030	7.709±0.009	3.889±0.004
EasyST	7.823±0.697	4.735±0.092	5.884±0.047	6.673±1.390	2.026±0.034	2.680±0.039	7.333±0.028	3.715±0.007
CDPNet	7.592±0.136	4.478±0.049	4.998±0.065	5.432±0.006	1.979±0.000	2.590±0.047	7.029 ±0.018	3.638±0.001

Table 1: 24-hour forecasting results (MSE,

\downarrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold and underlined means indicate the best and second-best reported values in each column; ties share the same marking.

Variant	French			Hunan			Global
Variant	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
Window-shared	6.516±0.093	4.181±0.041	4.996±0.081	4.891±0.078	1.913±0.024	2.428±0.032	6.954±0.027	3.758±0.012
Full Attention	6.334±0.059	4.197±0.118	5.044±0.183	4.930±0.118	1.932±0.004	2.518±0.012	6.976±0.019	3.787±0.004
Static Clustering	6.503±0.175	4.204±0.062	5.079±0.130	4.904±0.401	1.905±0.013	2.437±0.018	6.932±0.016	3.796±0.006
w/o InfoLoss	6.634±0.310	4.269±0.044	4.891±0.027	5.119±0.018	1.902±0.017	2.439±0.025	6.930±0.006	3.765±0.008
w/o Global Attn.	6.363±0.065	4.193±0.019	4.926±0.048	5.185±0.083	1.902±0.002	2.421±0.007	6.966±0.012	3.760±0.003

Table 2: 24-hour ablation results (MSE,

\downarrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold means indicate the best reported values in each column; ties are both bold.

Panel of Figure 3 — Figure 3: Hyperparameter sensitivity on three temperature tasks (24-hour MSE). Red markers indicate the lowest reported MSE within each dataset’s sweep.

Figure 4: Efficiency on Hunan temperature (48-to-24-hour forecasting, batch size 8).

Figure 5: Dynamic, fixed, and random grouping on all French-temperature test windows (

48\!\rightarrow\!24

). Parentheses report MSE.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Operator compared	Time complexity
DCRNN	Diffusion recurrence over $T$ steps	$\mathcal{O}(Tq(N+\|\mathcal{E}\|))$
Corrformer	Multi-correlation	$\mathcal{O}(NT\log T)$
PatchTST	Per-channel temporal attention	$\mathcal{O}(NP_{t}^{2})$
Crossformer	Temporal attention and routers	$\mathcal{O}(NP_{t}^{2}+NP_{t}r)$
CCM (DLinear)	Cluster assignment and prototype cross-attention	$\mathcal{O}(NK_{\mathrm{CCM}})$
DUET	Masked channel-attention fusion	$\mathcal{O}(N^{2})$

Appendix

Table 3: Computational complexity of representative dependency-modeling operators among the current baselines.

N,T

denote stations and history steps.

P_{t}

is each baseline’s actual temporal-token count (accounting for its patch length and stride),

r

is Crossformer’s router count,

K_{\mathrm{CCM}}

is CCM’s cluster count, and

q,|\mathcal{E}|

are DCRNN’s diffusion order and graph-edge count. For STCFormer,

n=\lceil N/L_{s}\rceil

m=\lceil T/L_{t}\rceil

, with spatial and temporal patch sizes

L_{s},L_{t}

. Widths are fixed; the stated scope excludes embeddings, output heads, and training losses.

Statistic	French	Hunan	Global
Stations	234	3,570	3,850
Time steps	8,784	4,368	17,544
Start	2016-01-01 00:00	2023-04-01 09:00	2019-01-01 00:00
End	2016-12-31 23:00	2023-09-30 08:00	2020-12-31 23:00
Interval	1 hour	1 hour	1 hour
Variables	Temp., U-wind, V-wind	Temp., U-wind, V-wind	Temp., wind speed

Appendix

Table 4: Statistics of the processed weather datasets. Each variable defines a forecasting task.

Spatio-Temporal Methods
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
DCRNN	1.894 ±0.017	1.791±0.040	2.157±0.025	1.558±0.456	0.654±0.005	0.783±0.009	1.941±0.023	1.282 ±0.000
Corrformer	2.121±0.018	1.540±0.016	1.794±0.005	1.662±0.126	0.675±0.001	0.756±0.002	1.888±0.004	1.304±0.011
EasyST	2.138±0.100	1.554±0.023	1.673±0.000	1.829±0.230	0.683±0.012	0.762±0.012	1.843±0.003	1.289±0.002
CDPNet	2.083±0.022	1.502±0.004	1.535±0.007	1.696±0.009	0.691±0.000	0.789±0.004	1.843±0.001	1.290±0.002

Appendix

Table 5: 24-hour forecasting results (MAE,

\downarrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold and underlined means indicate the best and second-best reported values in each column; ties share the same marking.

Spatio-Temporal Methods
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
DCRNN	0.556±0.061	0.676±0.006	0.607±0.053	0.583±0.091	0.561±0.030	0.613±0.052	0.920 ±0.003	0.648±0.008
Corrformer	0.503±0.012	0.645±0.019	0.616 ±0.015	0.649±0.058	0.532±0.001	0.627±0.001	0.887±0.008	0.595±0.002
EasyST	0.632±0.004	0.598±0.000	0.483±0.003	0.701±0.134	0.541±0.010	0.551±0.007	0.901±0.001	0.631±0.001
CDPNet	0.625±0.002	0.671±0.004	0.607±0.004	0.735±0.021	0.522±0.006	0.629 ±0.015	0.916±0.001	0.639±0.008

Appendix

Table 6: 24-hour forecasting results (SEDI,

\uparrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold and underlined means indicate the best and second-best reported values in each column; ties share the same marking.

Spatio-Temporal Methods
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
DCRNN	3.302±0.016	1.987±0.126	2.103±0.127	2.388±0.034	0.733±0.003	0.891±0.026	2.924±0.340	1.492±0.003
Corrformer	2.711±0.030	2.100±0.034	1.996±0.008	2.813±0.245	0.721±0.002	0.893±0.005	2.784±0.005	1.465±0.002
EasyST	2.878±0.063	1.992±0.016	1.957±0.049	4.431±0.660	0.710±0.002	0.855±0.010	2.502 ±0.018	1.498±0.000
CDPNet	2.862±0.007	1.973±0.005	1.966±0.010	2.418±0.028	0.723±0.003	0.869±0.001	2.511±0.001	1.499±0.002

Appendix

Table 7: 72-hour forecasting results (MAE,

\downarrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold and underlined means indicate the best and second-best reported values in each column; ties share the same marking.

Spatio-Temporal Methods
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
DCRNN	19.294±0.154	7.819±0.883	9.671±1.655	11.447±0.063	2.369±0.052	3.567±0.109	17.582±4.554	4.852±0.018
Corrformer	12.053±0.319	9.043±0.302	8.401±0.023	14.779±0.658	2.223±0.027	3.735±0.001	13.125±0.010	4.826±0.006
EasyST	13.579±0.614	7.361±0.078	7.437±0.387	31.283±7.987	2.216 ±0.021	3.263 ±0.074	12.895±0.239	4.892±0.017
CDPNet	13.508±0.064	7.838±0.022	8.214±0.105	11.485±0.351	2.371±0.026	3.494±0.001	12.985±0.077	5.011±0.008

Appendix

Table 8: 72-hour forecasting results (MSE,

\downarrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold and underlined means indicate the best and second-best reported values in each column; ties share the same marking.

Spatio-Temporal Methods
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
DCRNN	0.394±0.173	0.456±0.004	0.406±0.010	0.548±0.025	0.416±0.006	0.441±0.025	0.867±0.010	0.521±0.003
Corrformer	0.342±0.015	0.472±0.010	0.370±0.014	0.328±0.046	0.481±0.007	0.473±0.016	0.849±0.004	0.450±0.003
EasyST	0.499±0.003	0.463±0.003	0.371±0.010	0.447±0.034	0.424±0.009	0.463±0.005	0.874±0.001	0.494±0.002
CDPNet	0.498±0.002	0.513±0.003	0.395±0.000	0.550 ±0.006	0.456±0.004	0.460±0.000	0.880±0.005	0.520±0.002

Appendix

Table 9: 72-hour forecasting results (SEDI,

\uparrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold and underlined means indicate the best and second-best reported values in each column; ties share the same marking.

Variant	French			Hunan			Global
Variant	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
Window-shared	1.885±0.015	1.411±0.008	1.497±0.016	1.522±0.020	0.652±0.008	0.721±0.006	1.766±0.003	1.325±0.010
Full Attention	1.869±0.010	1.412±0.019	1.490±0.032	1.518±0.023	0.649±0.000	0.722±0.001	1.766±0.001	1.298±0.001
Static Clustering	1.886±0.023	1.414±0.013	1.492±0.009	1.508±0.043	0.649±0.002	0.725±0.002	1.764±0.003	1.298±0.001
w/o InfoLoss	1.906±0.046	1.412±0.009	1.479±0.005	1.549±0.009	0.659±0.002	0.719±0.001	1.767±0.000	1.295±0.001
w/o Global Attn.	1.877±0.009	1.410±0.003	1.477±0.011	1.572±0.009	0.653±0.000	0.728±0.002	1.773±0.001	1.294±0.001

Appendix

Table 10: 24-hour ablation results (MAE,

\downarrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold means indicate the best reported values in each column; ties are both bold.

Variant	French			Hunan			Global
Variant	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
Window-shared	0.665±0.001	0.664±0.000	0.600±0.018	0.718±0.013	0.544±0.005	0.611±0.006	0.910±0.001	0.638±0.001
Full Attention	0.670±0.004	0.667±0.003	0.611±0.000	0.723±0.015	0.546±0.003	0.628±0.006	0.909±0.000	0.633±0.000
Static Clustering	0.668±0.013	0.656±0.004	0.609±0.031	0.724±0.036	0.546±0.001	0.625±0.009	0.914±0.002	0.649±0.001
w/o InfoLoss	0.670±0.003	0.655±0.002	0.596±0.007	0.713±0.010	0.553±0.007	0.632±0.004	0.911±0.000	0.645±0.000
w/o Global Attn.	0.665±0.000	0.658±0.006	0.607±0.017	0.712±0.017	0.553±0.001	0.627±0.013	0.912±0.001	0.646±0.001

Appendix

Table 11: 24-hour ablation results (SEDI,

\uparrow

) with a 48-hour look-back window. Values are mean

\pm

standard deviation over three runs. Bold means indicate the best reported values in each column; ties are both bold.

Time Series Foundation Models
Method	French			Hunan			Global
Method	Temp.	U-Wind	V-Wind	Temp.	U-Wind	V-Wind	Temp.	Wind
Timer	7.304±0.014	4.831±0.008	5.694±0.033	5.041±0.012	1.987±0.008	2.769±0.020	8.002±0.008	4.873±0.015
Chronos-Bolt-Tiny	6.706±0.012	4.538±0.002	5.437±0.002	4.990±0.003	1.924±0.003	2.537±0.000	7.894±0.004	4.691±0.005
Time-MoE	6.427±0.014	4.231±0.017	5.026±0.009	5.138±0.008	1.947±0.011	2.429±0.014	7.267±0.007	3.798±0.006
Grid-Based Predictive Models

Appendix

Table 12: Additional 24-hour forecasting comparisons (MSE,

\downarrow

) with a 48-hour input window. Values are mean

\pm

standard deviation over three runs. Bold means indicate the best reported values in each column; ties are both bold.

Figure 6: Look-back sensitivity on French temperature with a fixed 72-hour forecasting horizon. The horizontal axis is the input-window length in hours.

Panel of Figure 7 — Figure 7: Joint sensitivity to temporal and spatial patch sizes (24-hour MSE). Each bar represents one $(L_{t},L_{s})$ configuration; colors distinguish spatial patch lengths.

Figure 8: Efficiency on French temperature (48-to-24-hour forecasting, batch size 8). Bubble area indicates peak training GPU memory; labels report time per epoch and memory. The time axis uses a logarithmic scale.

French temperature
Method	Time	Memory	MSE
Full Attention	12.478	0.315	6.334
CGAB	15.314	0.378	6.291
Global temperature
Full Attention	63.194	10.023	6.976
CGAB	70.427	8.913	6.917

Appendix

Table 13: CGAB versus full attention. Time: s/epoch; memory: GiB. All values are three-run means; lower is better. Best values per dataset are bold.

Construction	French	Hunan
Random	$6.381\!\pm\!0.043$	$4.982\!\pm\!0.284$
Hilbert curve	$\mathbf{6.152}\!\pm\!0.018$	$4.808\!\pm\!0.044$
Capacity-constrained geographic clustering	$6.259\!\pm\!0.140$	$4.782\!\pm\!0.155$
Serpentine (default)	$6.291\!\pm\!0.090$	$\mathbf{4.743}\!\pm\!0.149$

Appendix

Table 14: Spatial patch construction (temperature MSE). Values are mean

\pm

standard deviation over three runs; best means are bold.

Metric	Preferred	Full-1L	NoInfo-1L	$\Delta$
Mutual information $I$	$\uparrow$	2.2878	2.0283	$+0.2594$
Largest-cluster ratio $m(H)/n$	$\downarrow$	0.1248	0.2454	$-0.1206$
Cluster-size CV	$\downarrow$	0.1513	0.6951	$-0.5438$
Empty-cluster rate	$\downarrow$	0.0000	0.0225	$-0.0225$
Bound ratio $B(m(H))/B(n)$	$\downarrow$	0.4076	0.5337	$-0.1261$

Appendix

Table 15: French Temperature one-layer assignment and bound diagnostics, averaged over 13,480 test-window/patch records per model.

\Delta

is Full-1L minus NoInfo-1L.

Panel of Figure 9 — Figure 9: Numerical diagnostics on French temperature. (a) Normalized bound versus largest-cluster ratio; open markers denote test-record medians. (b) Maximum sampled fixed-partition amplification versus median $B(q)$ across five partition families.

Figure 10: Prediction visualization on French temperature with a 48-hour input and a 72-hour forecast horizon. All methods are shown for the same station and window. Gray: observed history; black: ground truth; red dashed: prediction. The shaded region denotes the forecast horizon.

Figure 11: Prediction visualization on Hunan temperature with a 48-hour input and a 72-hour forecast horizon. The plotting conventions follow Figure 10 . Values are shown in dataset units.

Figure 12: Prediction visualization on Global wind speed with a 48-hour input and a 72-hour forecast horizon. The plotting conventions follow Figure 10 . Stored values are divided by 10 for display, consistently for observations and predictions.

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