# Sub-seasonal forecasting with a large ensemble of deep-learning weather prediction models

arXiv: https://arxiv.org/abs/2102.05107 · HTML: https://mlsanity.com/paper/2102.05107/

## Key facts

- Cited by 79 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 9 Feb 2021.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Improving data-driven global weather prediction using deep convolutional neural networks on a cubed sphere](https://mlsanity.com/paper/2003.11927/) (2020)
- [Physically Interpretable Neural Networks for the Geosciences: Applications to Earth System Variability](https://mlsanity.com/paper/1912.01752/) (2019)
- [Improving Subseasonal Forecasting in the Western U.S. with Machine Learning](https://mlsanity.com/paper/1809.07394/) (2018)
- [Evaluation, Tuning and Interpretation of Neural Networks for Meteorological Applications](https://mlsanity.com/paper/2005.03126/) (2020)
- [Ensemble methods for neural network-based weather forecasts](https://mlsanity.com/paper/2002.05398/) (2020)

## Built on by (most cited first, 30 of 79)

- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2208.05419/) (2022)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Mamba-ND: Selective State Space Modeling for Multi-Dimensional Data](https://mlsanity.com/paper/2402.05892/) (2024)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction](https://mlsanity.com/paper/2402.00712/) (2024)
- [AtmoRep: A stochastic model of atmosphere dynamics using large scale representation learning](https://mlsanity.com/paper/2308.13280/) (2023)
- [A posteriori learning for quasi-geostrophic turbulence parametrization](https://mlsanity.com/paper/2204.03911/) (2022)
- [On the Foundations of Earth and Climate Foundation Models](https://mlsanity.com/paper/2405.04285/) (2024)
- [Prithvi WxC: Foundation Model for Weather and Climate](https://mlsanity.com/paper/2409.13598/) (2024)
- [Continuous Ensemble Weather Forecasting with Diffusion models](https://mlsanity.com/paper/2410.05431/) (2024)
- [Advancing Parsimonious Deep Learning Weather Prediction using the HEALPix Mesh](https://mlsanity.com/paper/2311.06253/) (2023)
- [ClimateSet: A Large-Scale Climate Model Dataset for Machine Learning](https://mlsanity.com/paper/2311.03721/) (2023)
- [A Practical Probabilistic Benchmark for AI Weather Models](https://mlsanity.com/paper/2401.15305/) (2024)
- [SubseasonalClimateUSA: A Dataset for Subseasonal Forecasting and Benchmarking](https://mlsanity.com/paper/2109.10399/) (2021)
- [Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model](https://mlsanity.com/paper/2406.08632/) (2024)
- [Probabilistic Emulation of a Global Climate Model with Spherical DYffusion](https://mlsanity.com/paper/2406.14798/) (2024)
- [Adaptive Bias Correction for Improved Subseasonal Forecasting](https://mlsanity.com/paper/2209.10666/) (2022)
- [Combining distribution-based neural networks to predict weather forecast probabilities](https://mlsanity.com/paper/2103.14430/) (2021)
- [Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators](https://mlsanity.com/paper/2408.03100/) (2024)
- [WeatherBench Probability: A benchmark dataset for probabilistic medium-range weather forecasting along with deep learning baseline models](https://mlsanity.com/paper/2205.00865/) (2022)
- [Towards physically consistent data-driven weather forecasting: Integrating data assimilation with equivariance-preserving deep spatial transformers](https://mlsanity.com/paper/2103.09360/) (2021)
- [Validating Deep Learning Weather Forecast Models on Recent High-Impact Extreme Events](https://mlsanity.com/paper/2404.17652/) (2024)
- [CirT: Global Subseasonal-to-Seasonal Forecasting with Geometry-inspired Transformer](https://mlsanity.com/paper/2502.19750/) (2025)
- [Global Extreme Heat Forecasting Using Neural Weather Models](https://mlsanity.com/paper/2205.10972/) (2022)

## Abstract (arXiv)

We present an ensemble prediction system using a Deep Learning Weather Prediction (DLWP) model that recursively predicts key atmospheric variables with six-hour time resolution. This model uses convolutional neural networks (CNNs) on a cubed sphere grid to produce global forecasts. The approach is computationally efficient, requiring just three minutes on a single GPU to produce a 320-member set of six-week forecasts at 1.4deg resolution. Ensemble spread is primarily produced by randomizing the CNN training process to create a set of 32 DLWP models with slightly different learned weights. Although our DLWP model does not forecast precipitation, it does forecast total column water vapor, and it gives a reasonable 4.5-day deterministic forecast of Hurricane Irma. In addition to simulating mid-latitude weather systems, it spontaneously generates tropical cyclones in a one-year free-running simulation. Averaged globally and over a two-year test set, the ensemble mean RMSE retains skill relative to climatology beyond two-weeks, with anomaly correlation coefficients remaining above 0.6 through six days. Our primary application is to subseasonal-to-seasonal (S2S) forecasting at lead times from two to six weeks. Current forecast systems have low skill in predicting one- or 2-week-average weather patterns at S2S time scales. The continuous ranked probability score (CRPS) and the ranked probability skill score (RPSS) show that the DLWP ensemble is only modestly inferior in performance to the European Centre for Medium Range Weather Forecasts (ECMWF) S2S ensemble over land at lead times of 4 and 5-6 weeks. At shorter lead times, the ECMWF ensemble performs better than DLWP.