Learning Continuous Regional Temperature Fields with Lead-Time and Resolution Queries

Chunlei Shi; Jiong Wang; Yi-Lin Wei; Junming Hou; Jinjin Liu; Yecheng Zhang; Dan Niu

Fig. 1: Comparison between conventional fixed-output and proposed query-conditioned temperature forecasting paradigms. (a) Fixed multi-head models predict predefined lead times and output resolutions. (b) Autoregressive rollout extends forecasts step by step but can accumulate errors across forecast steps. (c) Post-hoc resizing changes the display grid without enforcing consistency across resolutions. (d) Our CSTF formulates regional T2M prediction as continuous field evaluation conditioned on spatial, lead-time, and resolution queries, enabling flexible forecast requests.

Fig. 2: Overall architecture of the proposed CSTF framework. The model encodes ERA5 multi-variable input history into a latent regional weather state within a unified query-conditioned forecasting pipeline. Conditioned on this latent state, a coordinate decoder predicts regional T2M fields from lead-time, spatial-coordinate, and output-resolution queries. Training combines deterministic, gradient, temporal-difference, and scale-consistency objectives, so the same trained model supports continuous lead-time queries, resolution-controllable outputs, and scale-consistency evaluation.

Model	t+6 h		t+5 h		t+4 h		t+3 h		t+2 h		t+1 h
Model	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE
Baseline	8.196	3.741	7.992	3.378	7.782	2.968	7.583	2.529	7.419	2.108	7.309	1.779
SMAAT-UNet [ 28 ]	1.989	1.425	1.785	1.270	1.581	1.141	1.347	1.000	1.106	0.840	1.000	0.765
EarthFormer [ 18 ]	2.784	1.254	2.668	1.154	2.600	1.064	2.590	0.990	2.600	0.939	2.615	0.902
ARROW [ 9 ]	1.625	1.131	1.444	1.015	1.246	0.892	1.051	0.768	0.870	0.655	0.739	0.567
Weather-RF [ 29 ]	1.609	1.112	1.446	1.008	1.284	0.908	1.126	0.812	0.970	0.720	0.853	0.647

TABLE I: Lead-wise quantitative comparison for short-range T2M forecasting over Southeast China. RMSE and MAE are reported in degrees Celsius at each supervised forecast lead, where lower values indicate better accuracy. The best result in each column is highlighted in green , and the second-best result is underlined.

Model	RMSE $\downarrow$	MAE $\downarrow$	Bias $\downarrow$	Corr. $\uparrow$
Baseline	7.720	2.751	1.247	0.576
SMAAT-UNet [ 28 ]	1.510	1.074	0.329	0.987
EarthFormer [ 18 ]	2.644	1.051	0.598	0.963
ARROW [ 9 ]	1.203	0.838	0.389	0.992
Weather-RF [ 29 ]	1.243	0.868	0.446	0.992
Ours	1.123	0.811	0.273	0.993

TABLE II: Overall quantitative comparison for integer-lead T2M forecasting over Southeast China. Lower is better for RMSE, MAE, and bias magnitude, while higher is better for correlation.

Fig. 3: Qualitative comparison of deterministic T2M forecasts over the Southeast China benchmark. Panels show the ERA5 input context, integer-lead CSTF predictions, ERA5-Land references, and absolute-error maps.

Fig. 4: Global-scope diagnostic visualization of T2M field prediction. Panels compare ERA5-Land references, CSTF predictions, and absolute-error maps under a Robinson projection with polar insets. Zoomed-in views are provided in Appendix.

Variant	t+6 h		t+5 h		t+4 h		t+3 h		t+2 h		t+1 h		Mean
Variant	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE	RMSE	MAE
w/o aux. losses	1.555	1.085	1.403	0.984	1.248	0.890	1.096	0.800	0.960	0.720	0.871	0.668	1.213	0.858
w/o $\mathcal{L}_{\mathrm{scale}}$	1.575	1.096	1.422	0.996	1.263	0.898	1.100	0.802	0.949	0.712	0.852	0.654	1.220	0.860
w/o $\mathcal{L}_{\mathrm{grad}}$	1.581	1.106	1.420	1.003	1.264	0.907	1.116	0.817	0.974	0.730	0.875	0.669	1.230	0.872
w/o $\mathcal{L}_{\mathrm{temp}}$	1.476	1.043	1.337	0.948	1.203	0.861	1.059	0.773	0.921	0.689	0.831	0.636	1.160	0.825
Ours	1.414	1.014	1.284	0.925	1.162	0.845	1.036	0.765	0.909	0.685	0.823	0.631	1.123	0.811

TABLE III: Extended lead-wise ablation of CSTF objective terms on the Southeast China test split. RMSE and MAE are reported in degrees Celsius at each supervised hourly lead; lower is better. This table extends the main-text lead-wise ablation by separately removing the spatial-gradient and temporal-difference regularizers. The best score in each column is highlighted in green , and the second-best score is underlined.

Fig. 5: Continuous lead-time query. The same trained model is queried at

0.5

,

2

,

4.5

, and

6

hours. The

0.5

h and

4.5

h panels are non-integer forecast-only queries, while the

2

h and

6

h panels align with supervised hourly targets.

Fig. 6: Global continuous lead-time query on a Robinson projection with polar insets. The same checkpoint is queried at

0.5

,

2

,

4.5

, and

6

hours, using the same lead-time set as the regional query visualization.

Fig. 7: Resolution-controllable prediction. Fixed input and lead-time query are decoded at

96\times 96

,

128\times 128

,

160\times 160

, and

192\times 192

grids. Panels show direct resolution-conditioned decoding rather than post-hoc resizing.

Fig. 8: Global resolution-controllable prediction. Orthographic visualizations are generated for different output grid sizes from the same input state and lead-time query.

Variant	$96\rightarrow 128$	$160\rightarrow 128$	$192\rightarrow 128$	Mean
w/o aux. losses	1.396	1.165	1.233	1.265
w/o $\mathcal{L}_{\mathrm{scale}}$	1.449	1.171	1.266	1.295
w/o $\mathcal{L}_{\mathrm{grad}}$	1.111	1.082	0.997	1.060
w/o $\mathcal{L}_{\mathrm{temp}}$	1.099	1.131	0.988	1.072
Ours	1.098	1.077	0.982	1.052

TABLE IV: Scale-consistency ablation for resolution-controllable prediction. Values are normalized cross-resolution RMSE after resampling to

128\times 128

; lower is better. Best results are highlighted in green , and second-best results are underlined.

Variant	RMSE $\downarrow$	MAE $\downarrow$	Bias $\downarrow$	Grad. err. $\downarrow$	Scale err. $\downarrow$
w/o aux. losses	1.213	0.858	0.339	0.468	1.265
w/o $\mathcal{L}_{\mathrm{scale}}$	1.220	0.860	0.350	0.382	1.295
w/o $\mathcal{L}_{\mathrm{grad}}$	1.230	0.872	0.356	0.455	1.060
w/o $\mathcal{L}_{\mathrm{temp}}$	1.160	0.825	0.281	0.376	1.038
Ours	1.123	0.811	0.273	0.361	1.052

TABLE V: Objective-term ablation on the Southeast China test split. All variants use the same nine ERA5 input variables and architecture. Scale error is the mean normalized cross-resolution RMSE after resampling non-base queries to

128\times 128

. Best results are highlighted in green , and second-best results are underlined.

Fig. 9: Additional deterministic forecast diagnostic for the global domain (

180.0^{\circ}

W–

180.0^{\circ}

E,

90.0^{\circ}

S–

90.0^{\circ}

N). The case shows input context, ERA5-Land references, CSTF predictions, and absolute-error maps under the main-text global visualization protocol. It supplements the idx0 main-text case and assesses whether the qualitative global diagnostic remains consistent across forecast initializations.

Fig. 10: Lead-wise absolute-error maps for the Southeast China case study (

100.0^{\circ}

E–

120.0^{\circ}

E,

20.0^{\circ}

N–

40.0^{\circ}

N). Errors are shown over the six supervised integer lead times, providing a spatial diagnostic of where forecast discrepancies grow with lead time. The overlaid number on each panel reports the per-frame spatial RMSE ( ∘ C) against the ERA5-Land T2M reference over valid land pixels.

Fig. 11: Continuous lead-time query examples over Southeast China (

100.0^{\circ}

E–

120.0^{\circ}

E,

20.0^{\circ}

N–

40.0^{\circ}

N). The three rows are independent test initializations at 2025-09-05 05:00 UTC, 2025-09-13 17:00 UTC, and 2025-09-22 05:00 UTC. Within each row, the same atmospheric input is queried at multiple lead times, including supervised hourly leads and non-integer lead times. The figure is therefore used to inspect whether the learned field evaluator produces temporally smooth and spatially coherent T2M fields when the requested forecast time is varied continuously. Non-integer lead panels are forecast-only diagnostics because the current ERA5-Land target sequence is available at hourly intervals.

Fig. 12: Resolution-conditioned query examples over Southeast China (

100.0^{\circ}

E–

120.0^{\circ}

E,

20.0^{\circ}

N–

40.0^{\circ}

N). The three rows are independent test initializations at 2025-09-05 05:00 UTC, 2025-09-13 17:00 UTC, and 2025-09-22 05:00 UTC. Within each row, CSTF directly evaluates the same forecast state at different requested output grids rather than resizing a single fixed-grid prediction. The visual comparison checks whether regional thermal structures remain consistent as the output resolution changes, complementing the cross-resolution RMSE values reported in the main text.

Fig. 13: Continuous lead-time query diagnostics over the global domain (

180.0^{\circ}

W–

180.0^{\circ}

E,

90.0^{\circ}

S–

90.0^{\circ}

N). The three rows are independent test initializations at 2025-09-05 05:00 UTC, 2025-09-13 17:00 UTC, and 2025-09-22 05:00 UTC, rendered with the same globe-style projection as the main-text global diagnostic. Within each row, the queried lead time is varied while the input state is fixed, allowing visual inspection of large-scale thermal evolution under the continuous-time interface. Non-integer leads are forecast-only diagnostics because the current target split provides hourly references.

Fig. 14: Resolution-conditioned query diagnostics over the global domain (

180.0^{\circ}

W–

180.0^{\circ}

E,

90.0^{\circ}

S–

90.0^{\circ}

N). The three rows are independent test initializations at 2025-09-05 05:00 UTC, 2025-09-13 17:00 UTC, and 2025-09-22 05:00 UTC. Within each row, the model is queried at multiple output grid sizes for the same forecast case, so changes across columns reflect direct resolution-conditioned field evaluation. These visualizations are used as qualitative checks of large-scale coherence under resolution queries, whereas quantitative cross-resolution consistency is reported separately in the main tables.

Fig. 15: Additional training, benchmark, and ablation diagnostics supporting the main quantitative results. From left to right and top to bottom, the panels show optimization curves, aggregate deterministic skill, lead-wise RMSE, cross-resolution scale consistency, objective-term ablation metrics, and lead-wise ablation behavior. The first panel checks whether model training is stable, the next two panels summarize forecast accuracy on the supervised hourly benchmark, the scale-consistency panel evaluates the resolution-query interface, and the ablation panels isolate the effects of the auxiliary objective terms. These plots are diagnostic summaries; the standardized test metrics and primary comparisons are reported in the main-text tables.

Learning Continuous Regional Temperature Fields with Lead-Time and Resolution Queries

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