ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting

AI summary

Overview

Research area: Data-driven global weather forecasting (spatiotemporal data analysis / deep learning for atmospheric dynamics).

Technical level: Advanced. The paper assumes familiarity with autoregressive rollout in weather models, Transformer tokenization, mixture-of-experts routing, and reinforcement learning (Q-learning / DQN).

Scope: The paper proposes ARROW, a two-component system — a Multi-Interval Forecasting Model (MIFM) with Ring Positional Encoding and a Shared-Private Mixture-of-Experts, plus a reinforcement-learning Adaptive Rollout Scheduler — and evaluates it on the WeatherBench benchmark against seven baselines.

What This Paper Is About

Existing data-driven weather models learn to predict a fixed short interval (for example 6 hours) and then apply that same model repeatedly to reach long lead times such as 138 hours. The authors argue this paradigm has two flaws: separate models for different time intervals ignore the relationships between time scales and ignore the Earth's spherical geometry, and a fixed rollout schedule cannot adapt to atmospheric evolution, which alternates between gradual change and abrupt transitions. ARROW's goal is a single unified model that forecasts at multiple time intervals and a learned scheduler that chooses which interval to use at each autoregressive step.

Key Contributions

1. ARROW as an adaptive rollout and routing framework. The paper formulates the choice of autoregressive time interval as a decision-making problem that balances error accumulation against the capture of fine-grained atmospheric variations.

2. A Multi-Interval Forecasting Model (MIFM). A single model that predicts across different time intervals. It includes a Shared-Private Mixture-of-Experts (S&P MoE) for multi-scale temporal patterns and Ring Positional Encoding (RPE) to encode the circular latitude structure of the Earth.

3. An Adaptive Rollout Scheduler (AR Scheduler). A Deep Q-Network-based scheduler that, given the current weather state, date and time, and temporal position, selects the next time interval. It is trained jointly with multi-step fine-tuning of the MIFM in an alternating optimization scheme to handle the mutual dependence between the scheduler's policy and the model's parameters.

4. State-of-the-art experimental results. The paper reports that ARROW achieves state-of-the-art performance in global weather forecasting, with improvements of approximately 10% in both RMSE and ACC.

Main Findings

• Overall accuracy: ARROW consistently outperforms all data-driven baselines in both RMSE and ACC on all evaluated days. On average, ARROW achieves improvements of 9.3% in RMSE and 10% in ACC over five days across six atmospheric variables compared to the second-best data-driven models.
• Comparison scope: The main comparison covers a nine-day period from Day 5 to Day 14 across six variables (T2m, U10, V10, TCC, Z500, T850), with lead times at 5-day, 7-day, 9-day and 14-day. Climatology, IFS, Keisler, GraphCast, Pangu-weather, FourcastNet and Stormer are the baselines. IFS is included for reference only and excluded from the overall comparison because its initial states are only available at 00:00 UTC and 12:00 UTC; IFS results also exclude forecasts beyond 10 days and the TCC variable.
• Baseline observations: Deep learning methods perform strongly at short lead times (e.g., 5-day) and in some cases surpass IFS. Keisler performs poorly overall, especially at 9-day and 14-day forecasts, where the paper says its predictions are nearly unusable. GraphCast performs better, which the authors attribute to technical advances such as multi-scale graphs. Neural operator methods lag behind the latest data-driven models. Transformer-based approaches are competitive through computer-vision techniques such as the Swin Transformer.
• Ring Positional Encoding ablation: Replacing RPE with a learnable 2D Positional Encoding (from Dosovitskiy et al., 2020) degrades both RMSE and ACC at the 72-hour lead time. T2m-72h RMSE rises from 1.09 to 1.12, U10-72h from 1.71 to 1.76, and V10-72h from 1.77 to 1.82.
• S&P MoE ablation: Replacing S&P MoE with a single FFN also degrades performance (T2m-72h RMSE 1.13, U10-72h 1.77, V10-72h 1.81), which the authors say underscores the importance of shared and interval-specific representations.
• Auxiliary loss ablations: Removing aux-loss 1 (which encourages divergence between interval noise distributions) gives T2m-72h RMSE 1.15 and ACC 0.89, and removing aux-loss 2 (which pushes the aggregate distribution toward uniform) gives T2m-72h RMSE 1.12 and ACC 0.90. The full pre-trained ARROW reaches T2m-72h RMSE 1.09 and ACC 0.91.
• Rollout strategy comparison: At the 138-hour lead time on T2m and T850, the adaptive strategy outperforms random selection, the naive strategy (repeating a 6-hour interval 23 times), and the greedy strategy used by Pangu-Weather (138h = 24h × 5 + 12h + 6h). Notably, the greedy strategy performs worse than the naive strategy because it cannot capture fine-grained atmospheric variations.
• Case study — Siberian cold wave: ARROW predicted the trajectory of the cold wave that occurred from January 22 to January 27, 2018 and captured temperature variations in East and Central China and several Central Asian countries. It also predicted that a red spot within the marked circle stayed unaffected by the cold wave due to topographic sheltering.
• Case study — cloud cover: For changes in cloud cover from May 10 to May 11, 2018, ARROW accurately predicted global cloud cover one day in advance and identified regions of low cloud cover relevant to photovoltaic power generation.

Methodology in Plain English

Stage 1 — One-step pre-training of the MIFM. The initial weather state is converted into tokens. Ring Positional Encoding is added so the model respects the Earth's circular latitude structure rather than treating the globe as a flat image; the authors note the circularity property deliberately does not apply to the longitude dimensions because longitude is not circular after equirectangular projection. These weather embeddings are combined with the embedded time interval and passed through N "Arch blocks." Each block contains a Shared-Private Mixture-of-Experts: one shared feed-forward network handles patterns common to all intervals, while M private feed-forward networks handle interval-specific patterns. A gating mechanism, perturbed with learned noise, decides which private experts each token is routed to. Two auxiliary cross-entropy losses are added: one encourages different intervals to use different experts, and the other encourages balanced use of all experts so the model does not collapse onto a few of them. The training target is the weather change over the interval rather than the absolute future state, and the model is trained with a randomized dynamics forecasting loss so a single model handles all intervals.

Stage 2 — Multi-step fine-tuning of the AR Scheduler. The authors build a weather forecasting environment containing the pre-trained ARROW model and the same weather dataset. The state space contains the current predicted weather state, the date and time, and the temporal position (travel time, remaining time, target lead time). The action space is the discrete set of available intervals: {6h, 12h, 24h}. The reward is the negative latitude-weighted RMSE at each step, plus a penalty term ω that discourages overly long trajectories. A Deep Q-Network takes the concatenated temporal and weather embeddings through a multi-head self-attention module and outputs a value estimate for each state-action pair, trained with a standard temporal-difference loss using a target network and a main network.

Because fine-tuning the model changes the environment and therefore invalidates the policy, the authors treat this as a bi-level optimization problem, which they say cannot easily be optimized jointly. They resolve it with an alternating optimization algorithm that updates the value estimator and the fine-tuned model in turn, so both gradually converge.

Why This Matters

Impact on research. The paper claims to be the first data-driven weather forecasting method to consider adaptive rollout — a learned, state-dependent choice of time step analogous to adaptive time-stepping solvers used in numerical weather prediction. It offers a unifying single-model alternative to maintaining separate models per interval, and it connects weather forecasting to reinforcement learning in a concrete formulation.

Real-world applications (as named in the paper):

• Energy, including renewable energy and photovoltaic power scheduling, for which cloud cover (TCC) prediction provides decision support.
• Agriculture, which the paper cites as a key sector supported by global weather forecasting.
• Economics and individual travel planning.
• Air quality and traffic flow prediction, where temperature serves as an important auxiliary covariate.

Industry relevance. Weather forecasting is computationally expensive under traditional numerical weather prediction, and the paper positions data-driven models as a practical alternative. The one-day-ahead cloud cover result and the cold wave case study map directly onto operational decisions in power generation and severe-weather response.

Future Directions

• Applying reinforcement learning to local weather forecasting rather than only global forecasting.
• Investigating physics-guided approaches, as the authors state they plan to explore.
• Determining whether the adaptive rollout scheduler generalizes to finer or additional interval choices beyond the {6h, 12h, 24h} action space used here.
• Improving weaker baselines and methods: the paper highlights that graph neural networks (GraphCast) show promise and that Keisler performs poorly at longer lead times, leaving open questions about which architecture families best complement adaptive rollout.

Target Audience

Researchers and graduate students in machine learning and spatiotemporal data analysis, meteorological and climate modeling groups working with data-driven forecasting, and practitioners in reinforcement learning interested in real-world control and scheduling applications. The mixture-of-experts design and the DQN-based scheduler are also relevant to those working on routing and adaptive computation in Transformers.

Authors’ abstract

Weather forecasting is a fundamental task in spatiotemporal data analysis, with broad applications across a wide range of domains. Existing data-driven forecasting methods typically model atmospheric dynamics over a fixed short time interval, e.g., 6 hours, and rely on naive autoregression-based rollout for long-term forecasting, e.g., 5 days. However, this paradigm suffers from two key limitations: (1) it often inadequately models the spatial and multi-scale temporal dependencies inherent in global weather systems, and (2) the rollout strategy struggles to balance error accumulation with the capture of fine-grained atmospheric variations. In this study, we propose ARROW, an Adaptive-Rollout Multi-scale temporal Routing method for Global Weather Forecasting. To contend with the first limitation, we construct a multi-interval forecasting model that forecasts weather across different time intervals. Within the model, the Shared-Private Mixture-of-Experts captures both shared patterns and specific characteristics of atmospheric dynamics across different time scales, while Ring Positional Encoding accurately encodes the circular latitude structure of the Earth when representing spatial information. For the second limitation, we develop an adaptive rollout scheduler based on reinforcement learning, which selects the most suitable time interval to forecast according to the current weather state. Experimental results demonstrate that ARROW achieves state-of-the-art performance in global weather forecasting, establishing a promising paradigm in this field.