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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

arXiv:2608.25823v1cs.LGcs.MM

TL;DR

Regional T2M forecasters commonly return fixed future frames on prescribed grids, limiting query-dependent lead-time and resolution evaluation. CSTF instead encodes ERA5 histories into a shared latent state and decodes T2M as a query-conditioned continuous field. On the Southeast China 0–6 h benchmark, it improves fixed-lead deterministic skill while supporting non-integer lead-time and resolution-controllable queries.

  • Problem

    Regional T2M forecasters commonly expose fixed products, preventing native evaluation at intermediate lead times and alternative grids.

    Source: §I · p. 1, A. Problem definition · p. 3

  • Method

    CSTF encodes multivariable ERA5 histories into a shared latent state and decodes T2M fields from spatial, lead-time, and resolution queries.

    Source: §I · p. 1, C. Query-conditioned field model · p. 4

  • Results

    CSTF improves fixed-lead deterministic skill on the SE China benchmark while enabling non-integer lead-time and resolution-controllable queries.

    Source: §IV · p. 8

  • Takeaways & Limitations

    Lead time and output resolution become query variables, allowing one learned field evaluator to support flexible forecast requests.

    Source: §I · p. 2, C. Query-conditioned field model · p. 4

Abstract

from arXiv · show

Accurate regional near-surface temperature forecasting is fundamental to short-range weather services and downstream risk assessment. Existing deep learning-based regional forecasters commonly produce a fixed set of future frames on a prescribed grid, limiting their use when forecast products must be evaluated at query-dependent lead times or display resolutions. To overcome these fixed-output constraints, we formulate regional T2M forecasting as query-conditioned continuous spatiotemporal temperature field evaluation and propose the Continuous Spatiotemporal Temperature Forecaster (CSTF), a neural field that turns forecast lead time and output resolution into explicit queries when evaluating 2-m temperature (T2M). Specifically, CSTF first encodes multivariable ERA5 histories into latent meteorological states and then decodes T2M as a coordinate-based field. Accordingly, spatial location, forecast lead time, and output resolution are introduced as queries, enabling standard hourly forecasts, intermediate lead-time diagnostics, and resolution-controllable outputs within a unified field-evaluation framework. Furthermore, to maintain coherence across flexible field queries, we design spatial-gradient, temporal-difference, and scale-consistency objectives that regularize regional thermal structures, lead-wise evolution, and cross-resolution agreement. Experiments on the Southeast China 0-6 h ERA5-Land benchmark demonstrate that CSTF achieves the best aggregate deterministic skill, including a 17.0 percent reduction in Bias, with global-scope diagnostics further illustrating flexible lead-time and resolution-controllable inference.

I. INTRODUCTION

Regional T2M forecasting is constrained by fixed lead-time and grid outputs, motivating CSTF’s query-conditioned continuous field formulation. CSTF uses a shared latent weather state and explicit spatial, lead-time, and resolution queries, with coherence-focused supervision and diagnostics.

Motivation

  • Regional temperature forecasts support weather services and decisions because local thermal gradients can matter alongside domain-mean error.Relevant applications include electricity demand management, agricultural planning, public health warning, and urban heat-risk assessment.Source: §I · p. 1

Limitations of fixed-output forecasting

  • Most regional neural forecasters expose discrete products with predefined lead times and output grids, making these choices architectural rather than query variables.Fixed multi-head and sequence-to-sequence models return only the frames specified by their prediction targets or heads.Source: §I · p. 1
  • Autoregressive rollout may accumulate errors, while post-hoc resizing changes the display grid without ensuring consistency across resolutions.These approaches still do not natively evaluate intermediate lead times or alternative grids as evaluations of a common temperature state.Source: §I · p. 1

CSTF formulation

  • CSTF reformulates regional T2M prediction as continuous field evaluation conditioned on spatial coordinates, lead time, and output resolution.The formulation treats time and resolution as model inputs and makes cross-resolution consistency explicitly trainable and diagnosable.Source: §I · pp. 1–2
  • CSTF encodes multivariable ERA5 histories into a shared latent meteorological state and decodes requested T2M fields through coordinate queries.The same framework supports hourly forecasts, intermediate lead-time queries, and resolution-controllable outputs.Source: §I · pp. 1–2

Training and evaluation

  • Coherence-preserving supervision and diagnostics validate fixed-lead skill, continuous lead-time queryability, resolution control, and cross-resolution consistency.The objectives regularize regional thermal structure, lead-wise evolution, and agreement across resolutions.Source: §I · p. 2

II. RELATED WORK

Related work largely uses fixed variables, lead times, and grids for regional temperature prediction, while continuous and coordinate-based models provide relevant precedents. CSTF applies query variables to regional T2M while retaining ERA5-Land verification and a unified forecasting architecture.

Data-driven weather prediction

  • Data-driven weather models have demonstrated skilful high-dimensional forecasting, but most systems still map input histories to predefined variables, lead times, and grids.The related-work discussion positions CSTF as addressing this fixed-output interface for regional T2M prediction.Source: §II · p. 2

Regional temperature prediction

  • Regional temperature prediction is governed by synoptic forcing, advection, radiation, cloud cover, land–sea contrast, topography, and surface heterogeneity.ERA5 supplies dynamically coherent atmospheric context, while ERA5-Land resolves regional thermal gradients relevant to local decisions.Source: §II · p. 2
  • Convolutional encoder–decoders, transformer forecasters, and super-resolution models typically use lead times and grids fixed during training.Post-hoc interpolation changes the display grid without ensuring that different resolutions represent the same temperature state.Source: §II · p. 2

Continuous and coordinate-based modelling

  • Continuous weather models, temporal interpolation methods, coordinate-based neural fields, and operator-learning methods provide precedents for evaluable temporal or spatial representations.These approaches motivate relaxing fixed interfaces through continuous evolution or requested locations and discretizations.Source: §II · p. 2

CSTF formulation

  • CSTF encodes multivariable input history into a latent regional weather state and predicts T2M from lead-time, spatial-coordinate, and output-grid queries.Its objective is accurate supervised integer-lead forecasts plus diagnostic evaluation at non-integer leads and multiple resolutions.Source: Figure 2 · p. 3, A. Problem definition · p. 3

B. Overview

CSTF formulates regional temperature forecasting as shared-state field evaluation rather than independent fixed-grid products. The decoder conditions T2M predictions on requested lead time, coordinates, and resolution while training regularizes consistency across queries.

B. Overview

  • CSTF encodes multi-variable ERA5 histories into a shared latent regional weather state before decoding requested temperature fields.The shared state avoids separate product-specific mappings for different forecast products.Source: B. Overview · p. 3, C. Query-conditioned field model · p. 4
  • The decoder evaluates T2M using explicit lead-time, spatial-coordinate, and output-resolution queries.This makes each forecast product an evaluation of the same encoded atmospheric state under a specified query.Source: B. Overview · p. 3, C. Query-conditioned field model · p. 4
  • Training combines deterministic, spatial-gradient, temporal-difference, and scale-consistency objectives to regularize accuracy, thermal structure, temporal evolution, and cross-resolution agreement.Source: B. Overview · p. 3

D. Multi-scale meteorological encoder

The encoder constructs a lead-time- and resolution-independent meteorological state, while the decoder uses spatial, temporal, and sampling-density queries to generate fields directly at requested grids.

D. Multi-scale meteorological encoder

  • The state encoder aggregates multi-variable ERA5 history into regional weather features while preserving thermal gradients and broader meteorological cues.The state remains independent of any fixed lead time or output resolution.Source: D. Multi-scale meteorological encoder · p. 4
  • CSTF represents forecast time with a sinusoidal lead-time embedding that supports both supervised integer leads and non-integer diagnostic queries.Examples of non-integer queries include 0.5 h and 4.5 h.Source: E. Lead-time and resolution queries · p. 4
  • Requested grids are encoded through normalized spatial locations together with sampling density, because coordinates alone do not distinguish sparse from dense sampling.Source: E. Lead-time and resolution queries · p. 4
  • The decoder interpolates the latent state to the requested grid and conditions predictions on local features, coordinates, resolution, and lead time.Fields such as 96×96, 128×128, and 192 × 192 are generated by direct evaluation rather than resizing a fixed-grid forecast.Source: F. Coordinate decoder · p. 4

G. Training objective

CSTF anchors predictions to supervised ERA5-Land targets and adds regularizers for scale agreement, regional thermal structure, and short-range temporal evolution.

G. Training objective

  • The supervised forecast loss anchors CSTF predictions to available ERA5-Land references.Source: G. Training objective · p. 4
  • The scale-consistency loss matches direct low-resolution queries with area-downsampled base-grid queries.This encourages different resolution evaluations of the same atmospheric state to agree after aggregation.Source: G. Training objective · p. 4
  • The spatial-gradient loss regularizes finite-difference T2M gradients to discourage oversmoothing.Source: G. Training objective · p. 4
  • Table I compares RMSE and MAE at each supervised forecast lead, with lower values indicating better accuracy.The table highlights the best result in each column and underlines the second-best result.Source: Table I · p. 5
  • Table II compares aggregate integer-lead forecasting using RMSE, MAE, bias magnitude, and spatial correlation.Lower is better for the error and bias measures, while higher is better for correlation.Source: Table II · p. 5
  • The temporal-difference loss aligns frame-to-frame temperature changes to constrain short-range evolution.Source: G. Training objective · p. 5

H. Inference and diagnostic queries

CSTF uses the same evaluator for lead-time and grid-size queries, validating integer leads against references and diagnosing non-integer leads and cross-resolution consistency separately.

H. Inference and diagnostic queries

A. Implementation Details

CSTF is evaluated for deterministic hourly T2M forecasting on the Southeast China benchmark, with quantitative comparisons against established baselines and qualitative inspection of regional errors.

Experimental setup

  • The benchmark uses a three-hour, nine-variable ERA5 history to predict six hourly ERA5-Land T2M fields over Southeast China.The main grid is 128 × 128, with deterministic metrics reported for supervised integer leads.Source: A. Implementation Details · p. 5

Baseline comparisons

  • CSTF is compared with SMAAT-UNet, EarthFormer, ARROW-style forecasting, and Weather-RF/FREUD-style forecasting under matched protocols.Controlled CSTF variants remove selected objective terms.Source: A. Implementation Details · p. 5

Deterministic results

  • ARROW attains slightly lower errors at the first two leads, while CSTF achieves the best skill from t+3 h through t+6 h.This lead-wise comparison indicates stronger later-horizon performance for CSTF on the benchmark.Source: B. Regional deterministic forecast · p. 5
  • CSTF obtains the lowest average RMSE, MAE, and bias and the highest spatial correlation among the compared methods.Relative to ARROW-style forecasting, RMSE decreases from 1.203°C to 1.123°C and MAE from 0.838°C to 0.811°C.Source: B. Regional deterministic forecast · p. 5

Qualitative analysis

  • Qualitative forecasts show coherent regional thermal structures, with larger errors mainly confined to localized areas.Figure 3 compares input context, integer-lead predictions, ERA5-Land references, and absolute-error maps.Source: B. Regional deterministic forecast · p. 6, Figure 3 · p. 6

C. Global diagnostic visualization

Global-scope diagnostics examine whether CSTF preserves coherent temperature fields while supporting continuous lead-time and resolution queries beyond the supervised regional benchmark.

Global diagnostic visualization

  • The global visualization compares ERA5-Land references, CSTF predictions, and absolute-error maps under a Robinson projection with polar insets.The diagnostic inspects large-scale thermal coherence and spatial error patterns rather than providing quantitative global comparisons.Source: C. Global diagnostic visualization · p. 6, Figure 4 · p. 6

Continuous lead-time query

  • Integer lead queries are compared with ERA5-Land targets, whereas half-hour queries are reported as forecast-only diagnostics because the target split is hourly.The queried lead times include both supervised integer leads and non-integer leads.Source: D. Continuous lead-time query · p. 6
  • Regional temperature structures evolve smoothly across queried lead times, with corresponding global diagnostic views provided.The same query interface is examined at integer and non-integer lead times.Source: D. Continuous lead-time query · p. 6

Resolution-controllable inference

  • CSTF directly decodes temperature fields at requested output grids rather than resizing a fixed-grid prediction.The resulting panels preserve the main thermal patterns across query resolutions.Source: E. Resolution-controllable prediction · p. 6
  • Cross-resolution evaluation aggregates non-base queries to a common reference grid to test consistency separately from ERA5-Land verification.This diagnostic isolates the behavior of the resolution-query training signal under controlled ablations.Source: F. Scale-consistency analysis · p. 6

G. Ablation Studies

Ablation studies test the contribution of CSTF’s auxiliary objectives to lead-wise accuracy, temporal evolution, thermal structure, and cross-resolution coherence.

Lead-wise objective ablation

  • The full objective improves RMSE and MAE across all supervised leads, with larger gains at longer horizons.The reported variants remove auxiliary losses or retain spatial-gradient and temporal-difference terms while removing scale consistency.Source: G. Ablation Studies · p. 6

Query diagnostics

  • Continuous lead-time figures query the same trained model at 0.5, 2, 4.5, and 6 hours.The 0.5 h and 4.5 h queries are non-integer forecast-only diagnostics, while 2 h and 6 h align with supervised hourly targets.Source: Figure 5 · p. 7

Global diagnostics

  • Global diagnostic visualizations extend continuous lead-time and resolution queries beyond the regional benchmark.The global views use Robinson or orthographic projections with the same query-conditioned model.Source: Figure 6 · p. 7, Figure 8 · p. 7

Scale-consistency ablation

  • Removing the scale-consistency term increases cross-resolution error after aggregation.This supports the role of scale consistency in coherent resolution-query prediction.Source: G. Ablation Studies · p. 7

Objective-term ablation

  • The full objective provides balanced gains in aggregate accuracy, thermal-structure fidelity, and scale coherence.Table V summarizes the combined effects of the objective terms on the Southeast China test split.Source: G. Ablation Studies · p. 7, Table V · p. 7

Query diagnostics

  • Resolution-controllable figures decode fixed inputs and lead-time queries at 96×96, 128×128, 160×160, and 192×192 grids.The outputs use direct resolution-conditioned decoding rather than post-hoc resizing.Source: Figure 7 · p. 7

APPENDIX

The appendix extends deterministic and query-specific evidence through additional global and regional visualizations, implementation details, and quantitative diagnostics.

Supplementary organization

  • The supplementary material adds implementation details, extended temperature forecast case studies, and query, training, benchmark, and ablation diagnostics.These materials are organized across Sections A–C.Source: APPENDIX · p. 10

Objective details

  • The spatial-gradient objective penalizes mismatches in local thermal contrasts, while the temporal-difference objective aligns adjacent-lead temperature changes.Together they target regional structure and short-range warming or cooling tendencies.Source: A. Additional Implementation Details · p. 10

Deterministic case studies

  • Additional deterministic figures separate supervised-hourly forecast coherence from later lead-time and resolution-query interrogation.The appendix uses these visualizations to distinguish standard forecast behavior from flexible field evaluation.Source: B. Additional Temperature Forecast… · p. 10

Global case studies

Regional case studies

  • The Southeast China case reports absolute-error maps at each integer lead time and overlays spatial RMSE computed against ERA5-Land over valid land pixels.This exposes where discrepancies emerge across the 0–6 h forecast horizon.Source: B. Additional Temperature Forecast… · p. 10

Query diagnostics

  • Appendix query diagnostics cover regional and global continuous lead-time and resolution-conditioned behavior, while Figure 15 compiles quantitative checks.The checks include optimization, deterministic skill, lead-wise degradation, cross-resolution consistency, and objective ablations.Source: C. Additional Query and Quantitative… · pp. 10–11

D. Extended Objective-Term Ablation

The extended ablation isolates the spatial-gradient and temporal-difference regularizers under a controlled experimental setup. Removing either term degrades lead-wise deterministic skill, while the diagnostics examine accuracy, scale consistency, and query behavior across lead times and resolutions.

Controlled ablation design

  • Table III compares full-objective CSTF with variants removing the spatial-gradient or temporal-difference loss under identical architecture, inputs, split, selection, and evaluation settings.The controlled variants complement the main-text ablation of the scale-consistency term.Source: D. Extended Objective-Term Ablation · p. 11

Ablation results

  • Removing Lgrad produces the largest deterioration in lead-wise deterministic skill, especially at longer lead times.The result indicates that spatial-gradient preservation is important for maintaining regional temperature structure.Source: D. Extended Objective-Term Ablation · pp. 11–12

Diagnostic coverage

  • The diagnostic figures cover lead-wise error maps, continuous lead-time queries, resolution-conditioned queries, global-scope evaluations, and training and ablation behavior.These views inspect spatial error growth, temporal smoothness, resolution consistency, global thermal evolution, and optimization stability.Source: Figure 10 · p. 12, Figure 11 · p. 13, Figure 12 · p. 14

Ablation results

  • Removing Ltemp increases RMSE and MAE across all supervised leads, although its degradation is smaller than removing Lgrad.This supports a role for temporal-difference supervision in stabilizing short-range forecast evolution.Source: D. Extended Objective-Term Ablation · p. 12

Ablation interpretation

  • Together with the scale-consistency ablation, the results indicate complementary regularization of spatial structure, lead-wise evolution, and cross-resolution coherence.The complete objective is assessed through controlled term removals.Source: D. Extended Objective-Term Ablation · pp. 11–12

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