SOON: Symmetric Orthogonal Operator Network for Global Subseasonal-to-Seasonal Climate Forecasting

TL;DR

SOON tackles global S2S forecasting by explicitly decoupling zonal wave propagation from meridional transport through an anisotropic latitudinal-ring embedding and a stack of Symmetric Operator Blocks that mimic Strang splitting. The Zonal Operator and Meridional Operator operate in tandem within a symmetric, time-reversal framework, achieving third-order local truncation error and reducing long-horizon error accumulation. Across ERA5, SOON delivers state-of-the-art accuracy and computational efficiency, outperforming both operational NWP systems and data-driven baselines, especially for the challenging weeks 5–6 window. The work advances physically grounded neural forecasting by preserving spectral fidelity with RMSNorm, maintaining energy-conserving dynamics, and offering scalable global forecasts suitable for operational contexts.

Abstract

Accurate global Subseasonal-to-Seasonal (S2S) climate forecasting is critical for disaster preparedness and resource management, yet it remains challenging due to chaotic atmospheric dynamics. Existing models predominantly treat atmospheric fields as isotropic images, conflating the distinct physical processes of zonal wave propagation and meridional transport, and leading to suboptimal modeling of anisotropic dynamics. In this paper, we propose the Symmetric Orthogonal Operator Network (SOON) for global S2S climate forecasting. It couples: (1) an Anisotropic Embedding strategy that tokenizes the global grid into latitudinal rings, preserving the integrity of zonal periodic structures; and (2) a stack of SOON Blocks that models the alternating interaction of Zonal and Meridional Operators via a symmetric decomposition, structurally mitigating discretization errors inherent in long-term integration. Extensive experiments on the Earth Reanalysis 5 dataset demonstrate that SOON establishes a new state-of-the-art, significantly outperforming existing methods in both forecasting accuracy and computational efficiency.

Figures (23)

• Figure 1: The anisotropic nature of global atmospheric dynamics. Global atmospheric circulation is governed by the coupling of two orthogonal physical processes: Zonal Dynamics, dominated by periodic wave propagation (e.g., planetary Rossby waves), and Meridional Transport, driven by the north-south exchange of heat and momentum (e.g., eddy heat fluxes).
• Figure 2: The main architecture of our proposed SOON. The Anisotropic Embedding projects atmospheric initial states into latitudinal ring tokens by compressing the longitudinal dimension into feature channels. These tokens are then evolved through a backbone of several stacked SOON Blocks. Specifically, each block sequentially applies two weight-shared Zonal Operators and a Meridional Operator to explicitly decouple wave propagation and transport dynamics. Finally, a Decoder maps the evolved features to bi-weekly forecast fields.
• Figure 3: The global RMSE distribution of $t850$ with lead times weeks 3-4 in the testing set.
• Figure 4: RMSE variation across latitudinal bands. SOON demonstrates superior accuracy, achieving the lowest errors near the poles.
• Figure 5: RMSE comparison between SOON and data-driven models on variable $z$ and $t$ across different pressure levels.

Theorems & Definitions (10)

• Theorem 3.1: Local Truncation Error of SOON Block
• proof
• Proposition 3.2
• Proposition 3.3: Spectral Fidelity of RMSNorm
• proof
• proof
• Remark 3.1: Significance in S2S Forecasting
• proof
• proof
• Remark 3.2: Physical Implication for S2S Forecasting