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TSSM: Triaxial State Space Model for Global Station Weather Forecasting with Temporal-Variable-Historical Modeling

The paper proposes TSSM, a novel Triaxial State Space Model that integrates period-aligned historical data to effectively capture long-term weather patterns and correlations, achieving state-of-the-art performance in global station weather forecasting with significant improvements in accuracy, extreme event prediction, and robustness to missing observations.

Original authors: Songru Yang, Zili Liu, Tao Han, Ben Fei, Fenghua Ling, Lei Bai, Chang Liu, Xiangyang Ji, Zhenwei Shi, Zhengxia Zou

Published 2026-07-16

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CC BY 4.0

Original authors: Songru Yang, Zili Liu, Tao Han, Ben Fei, Fenghua Ling, Lei Bai, Chang Liu, Xiangyang Ji, Zhenwei Shi, Zhengxia Zou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to predict the weather by only looking out your window for the last hour. You might guess if it's about to rain based on the clouds right now, but you'd miss the bigger picture: that it's usually stormy this time of year, or that a specific wind pattern tends to happen every July. This is the challenge of Global Station Weather Forecasting (GSWF). It's the science of predicting local weather conditions—like temperature, wind speed, and pressure—at specific spots on Earth, rather than just looking at a giant map of the whole planet. Scientists have been using powerful computers and complex math to do this for decades, but there's a catch: weather is chaotic. It changes fast, and if you only look at the "recent past," your predictions can go wildly wrong, especially when trying to forecast days ahead or when a massive storm is coming. The big question has been: How do we teach a computer to remember not just what happened yesterday, but what happened on this exact day last year, the year before, and so on?

Enter the Triaxial State Space Model (TSSM), a new approach that treats weather forecasting less like reading a short story and more like flipping through a giant, organized photo album of the past. Instead of just staring at a short "look-back window" of recent data, TSSM organizes weather records into a three-dimensional stack: time, different weather variables (like wind and rain), and history. Think of it like this: if you want to know what the weather will be like in Qingdao, China, next Tuesday, TSSM doesn't just look at the last few days. It pulls up the weather from every Tuesday in July for the past ten years, aligning them perfectly. It sees that while the weather is chaotic day-to-day, it follows a reliable rhythm when you compare the same month, day, and hour across different years.

The paper proposes that by using this "historical axis," the model can learn the long-term patterns of the atmosphere that short-term models miss. The researchers built a system that scans this data in three directions: along the timeline (what's happening now), across the variables (how wind affects pressure), and down the history (how this specific date has behaved in the past). They tested this on Weather-5K, a massive dataset containing hourly records from over 5,000 weather stations worldwide. The results were striking. TSSM didn't just get the average temperature right; it was much better at predicting extreme events, like sudden heatwaves or heavy storms, which are the hardest to forecast. In fact, the model showed a 61% improvement in predicting these extreme events compared to previous methods.

One of the most impressive findings is how the model handles mistakes. When predicting far into the future, old methods often make a small error, then use that wrong prediction to guess the next step, causing the error to snowball until the forecast is useless. TSSM, however, uses the historical data as a "reality check" at every step. Even if the model drifts off course, the long-term historical patterns pull it back. This allowed TSSM to maintain high accuracy even when forecasting 240 hours (10 days) ahead, a feat where other models usually fail. Furthermore, the model proved incredibly tough when data was missing. In real life, weather stations often lose signal or break. When the researchers simulated 80% of the data being missing, TSSM still kept 95.7% of its accuracy, whereas other methods dropped to less than half their performance.

The authors suggest that this approach offers a "nearly free lunch" for better forecasting: by simply reorganizing how we look at historical data, we can capture complex weather dynamics without needing massive new supercomputers. While the model does show a trade-off—sometimes prioritizing extreme event detection over perfect average accuracy—it offers a robust new way to handle the chaos of the atmosphere. By anchoring short-term guesses in long-term history, TSSM suggests that the key to predicting the future might just be remembering the past a little better.

Technical Summary: TSSM for Global Station Weather Forecasting

Problem Statement
Global Station Weather Forecasting (GSWF) is critical for localized and extreme weather prediction. However, existing data-driven methods, which typically formulate GSWF as multivariate time series forecasting, rely heavily on short-term temporal look-back windows. The authors argue that these methods suffer from "myopic assumptions" and an over-reliance on limited historical windows, which are insufficient to capture the inherently non-stationary, cross-scale periodic nature of atmospheric dynamics. Consequently, current approaches struggle with extreme event prediction, exhibit severe error accumulation in iterative long-horizon forecasting, and lack robustness when faced with missing observations or partial data.

Methodology: Triaxial State Space Model (TSSM)
To address these limitations, the paper proposes the Triaxial State Space Model (TSSM), which introduces a "Temporal-Variable-Historical" paradigm. Instead of treating weather forecasting solely as a function of recent history, TSSM incorporates period-aligned historical data (same month/day/hour across previous years) to compensate for long-term patterns beyond the immediate look-back window.

The core components of the methodology include:

Triaxial Data Reorganization:
The authors restructure conventional 2D time-variable data into a 3D tensor ( $T \times V \times H$ ) representing Temporal, Variable, and Historical axes. Multivariate weather series from previous years are stacked along the historical axis, aligned by relative timestamps (month, day, hour). This creates a "history-enhanced" input without requiring external data sources.
Causal Forecasting Framework:
The model employs a dual-causality mechanism. To predict the future window of the current year ( $h$ ), the model utilizes look-back windows from years $0$ to $h$ and future windows from years $0$ to $h-1$ . This ensures that information flows unidirectionally: short-term patterns in the look-back window dynamically calibrate long-term historical evolution, while long-term backgrounds constrain short-term predictions. This design prevents future data leakage and supports iterative forecasting.
Triaxial Scanning Mechanisms:
Leveraging the directed scanning capabilities of State Space Models (SSMs), TSSM processes the 3D tensor through three dedicated branches:
- T-Scan (Temporal): Captures short-term dynamics and temporal dependencies within the look-back window using bidirectional scanning.
- V-Scan (Variable): Models inter-variable correlations. To ensure the model learns content-based interactions rather than positional biases, the variable order is randomly shuffled during processing.
- H-Scan (Historical): Captures long-term evolutionary patterns and deviations from historical averages. Crucially, this branch scans for "anomalies" (deviations from the historical mean) to specifically enhance the detection of extreme weather events.
Hierarchically Shared Structure:
The architecture utilizes a hierarchical structure with shared weights to process weather features at multiple temporal resolutions (from seasonal patterns to extreme events). This design expands the historical receptive field and helps align patterns that may be temporally misaligned across different years.

Key Contributions

Paradigm Shift: The paper extends GSWF from a standard temporal-variable framework to a Temporal-Variable-Historical paradigm, effectively utilizing period-aligned historical data to model long-term evolution and cross-scale periodicity.
Novel Architecture: The introduction of TSSM with specific scanning modules (T-Scan, V-Scan, H-Scan) that efficiently model axial dependencies while maintaining linear complexity despite multiplied data dimensions.
Robustness and Efficiency: The method provides a solution for iterative forecasting with reduced error accumulation and demonstrates robustness to missing observations by leveraging historical context, all without requiring complex generative frameworks or massive parameter scales.

Experimental Results
The authors evaluated TSSM on Weather-5K, the largest station weather dataset to date (5,000+ stations, 10 years of hourly data), as well as hydrological and general time series datasets.

Accuracy and Extreme Events: On Weather-5K, TSSM achieved a 10% gain in overall accuracy and a 61% gain in extreme event metrics (SEDI) compared to state-of-the-art baselines. It secured the best or second-best results on 88% of the 72 evaluated metrics.
Long-Horizon Forecasting: The model showed significant advantages in long-horizon settings, achieving a 37.5% gain at 240 hours. In iterative forecasting (e.g., 48h $\times$ 5), it reached a 103.5% gain over direct long-horizon forecasting, with cumulative iterative error remaining below 4.3%.
Robustness to Missing Data: Under an 80% missing observation rate, TSSM retained over 90% of its performance, whereas baseline methods degraded by more than 50%.
Generalizability: The method achieved 95% best or second-best results on human-involved datasets (hydrological and general time series), demonstrating its applicability beyond pure meteorological data.
Efficiency: Despite using only 5M parameters, TSSM outperformed the 120M parameter foundation model (Chronos2) by 61% in overall improvement, suggesting that task-specific design is more critical than scale for station-level forecasting.

Significance and Claims
The paper claims that TSSM offers a "nearly free lunch" for comprehensive performance gains by integrating historical context into the forecasting pipeline. The authors posit that the primary limitation of existing methods is their reliance on short-term windows, which fails to capture the physical structures and long-range dependencies essential for accurate weather prediction. By explicitly modeling historical evolution and anomalies, TSSM provides a more reliable solution for localized weather systems, particularly in scenarios involving extreme events, long-term forecasting, and data scarcity. The work suggests that future weather forecasting should move beyond the "look-back window" constraint to embrace a broader, period-aligned historical perspective.

Technical Summary: TSSM for Global Station Weather Forecasting

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