Dual-Scale Temporal Fusion Reveals Structured Predictability in Subseasonal-to-Seasonal Temperature Prediction

Technical Summary: Dual-Scale Temporal Fusion for Subseasonal-to-Seasonal Temperature Prediction

Problem Statement
Subseasonal-to-seasonal (S2S) temperature forecasting (30–90 days) represents a critical gap between medium-range weather prediction and seasonal outlooks. While essential for agriculture, energy planning, and risk management, forecast reliability in this window is limited. Current understanding often attributes skill degradation primarily to forecast lead time (a monotonic decay), which fails to fully explain the complex spatiotemporal patterns of predictability. The challenge lies in bridging the rapid decay of initial condition signals with the slow emergence of boundary-forced signals, all while accounting for seasonal and regional heterogeneity.

Methodology
The authors propose a Dual-Scale Temporal Fusion Framework designed to explicitly separate and recombine distinct temporal components of climate data. The architecture (Fig. 1) consists of the following key modules:

1. Dual Generators (Temporal Decomposition):

   • Interannual Context: A branch processing calendar-aligned historical climate data (same day of the year across previous years) to capture long-term, low-frequency patterns.
   • Recent Dynamics: A branch processing lead-time-matched recent weather states to capture short-term evolution.
   • These branches are implemented as parallel U-Net-style encoder-decoder networks with skip connections.

2. Spatially Adaptive Temporal Fusion:

   • Instead of fixed weighting, the model predicts a spatially resolved fusion weight map ($\lambda$).
   • This $\lambda$-map dynamically modulates the contribution of the interannual context versus recent dynamics at each grid point.
   • The fusion is conditioned on input fields but does not take lead time ($\tau$) as an explicit direct input, allowing the model to learn how temporal weighting shifts based on seasonal regimes and geographic difficulty rather than just horizon length.

3. Lead-Conditioned Refinement:

   • A residual refinement network processes the fused output.
   • Normalized lead time ($\tau$) is encoded as a conditioning map injected into intermediate layers, allowing the network to adjust corrections based on the forecast horizon without altering the primary fusion mechanism.

4. Topology-Aware Structural Constraints:

   • To address spatial artifacts and improve coherence, the model incorporates topological descriptors (critical-point types, scalar magnitudes, saddle-level contours) as auxiliary input channels.
   • A consistency loss is applied during training to preserve large-scale spatial organization, particularly over complex terrain.

5. Training and Data:

   • Data: Daily mean 2-m air temperature from ERA5 reanalysis over the Continental United States (CONUS) from 2010–2024 (2010–2019 for training, 2020–2024 for testing).
   • Objective: A composite loss function combining pixel-level reconstruction, structural similarity, adversarial consistency, and topological regularization (activated after a warm-up period).

Key Results

• Dual-Scale Efficacy: The dual-scale fusion model consistently outperforms single-scale variants (relying solely on history or recent dynamics) in terms of RMSE and spatial correlation across the 30–90-day window (Fig. 2B).
• Seasonal vs. Lead-Time Dominance: Forecast errors exhibit a pronounced seasonal organization. Winter (DJF) errors are significantly larger and more spatially heterogeneous than summer (JJA) errors. The seasonal contrast in error magnitude exceeds the variation caused by lead time within the same season (Fig. 3).
• Adaptive Fusion Weights ($\lambda$):
  • Winter: The model learns to assign higher weights to interannual context ($\lambda \to 1$) in high-latitude and complex terrain regions where predictability is lowest.
  • Summer: Weights are more balanced ($\lambda \approx 0.5$) across the domain.
  • Regime Dependence: In winter, $\lambda$ increases monotonically with local RMSE, indicating the model relies more on historical context when recent dynamics are unreliable. In summer, $\lambda$ is stable across error bins. Crucially, $\lambda$ does not vary systematically with lead time, suggesting that the seasonal regime and local difficulty drive the fusion strategy more than the forecast horizon itself (Fig. 4).
• Topology-Aware Improvements: Incorporating topological constraints reduces RMSE and eliminates grid-aligned artifacts seen in non-topological baselines. It enhances the coherence of large-scale patterns and regional gradients, particularly in complex terrain (Fig. 5).
• Benchmarking: The model demonstrates performance comparable to the external stochastic AI foundation model Swift (up to 75 days) while maintaining stable error behavior across the full 30–90-day window (Fig. 2C).

Significance and Claims
The paper reframes S2S predictability not as a simple function of decaying lead time, but as a structured, multi-scale phenomenon driven by the interplay of temporal components, spatial heterogeneity, and pattern coherence.

• Structured Predictability: The authors define "structured predictability" as the explicit representation of temporal decomposition (interannual vs. recent), spatial heterogeneity (region-dependent weighting), and geometric coherence (topological constraints).
• Interpretability: The learned fusion weights ($\lambda$) provide an interpretable indicator of when and where interannual climate context offers a stabilizing benefit over recent weather evolution. This reveals that the model adapts to physical challenges (e.g., baroclinic instability in winter) by shifting reliance to historical baselines.
• Practical Utility: The framework offers a mechanism to stabilize forecasts in difficult regimes (winter, complex terrain) without sacrificing performance in more predictable regimes. By moving beyond uniform horizon-based modeling, the approach provides a foundation for more interpretable and robust S2S forecasting systems.

The authors note limitations, including the lack of explicit quantification of connections to specific climate modes (e.g., MJO), the scarcity of public benchmarks for the full 30–90-day window, and the current focus on a single variable (temperature) and regional domain. They suggest future work could extend this to multi-variable Earth system modeling and explicit connections to teleconnection patterns.