Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators

Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.

Huge Ensembles Part II: Properties of a Huge Ensemble of Hindcasts Generated with Spherical Fourier Neural Operators

In Part I, we created an ensemble based on Spherical Fourier Neural Operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires several orders of magnitude fewer computational resources. Here in Part II, we generate a huge ensemble (HENS), with 7,424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. For extreme climate statistics, HENS samples events 4$\sigma$ away from the ensemble mean. At each grid cell, HENS improves the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

Analyzing and Exploring Training Recipes for Large-Scale Transformer-Based Weather Prediction

The rapid rise of deep learning (DL) in numerical weather prediction (NWP) has led to a proliferation of models which forecast atmospheric variables with comparable or superior skill than traditional physics-based NWP. However, among these leading DL models, there is a wide variance in both the training settings and architecture used. Further, the lack of thorough ablation studies makes it hard to discern which components are most critical to success. In this work, we show that it is possible to attain high forecast skill even with relatively off-the-shelf architectures, simple training procedures, and moderate compute budgets. Specifically, we train a minimally modified SwinV2 transformer on ERA5 data, and find that it attains superior forecast skill when compared against IFS. We present some ablations on key aspects of the training pipeline, exploring different loss functions, model sizes and depths, and multi-step fine-tuning to investigate their effect. We also examine the model performance with metrics beyond the typical ACC and RMSE, and investigate how the performance scales with model size.

A Practical Probabilistic Benchmark for AI Weather Models

Since the weather is chaotic, forecasts aim to predict the distribution of future states rather than make a single prediction. Recently, multiple data driven weather models have emerged claiming breakthroughs in skill. However, these have mostly been benchmarked using deterministic skill scores, and little is known about their probabilistic skill. Unfortunately, it is hard to fairly compare AI weather models in a probabilistic sense, since variations in choice of ensemble initialization, definition of state, and noise injection methodology become confounding. Moreover, even obtaining ensemble forecast baselines is a substantial engineering challenge given the data volumes involved. We sidestep both problems by applying a decades-old idea -- lagged ensembles -- whereby an ensemble can be constructed from a moderately-sized library of deterministic forecasts. This allows the first parameter-free intercomparison of leading AI weather models' probabilistic skill against an operational baseline. The results reveal that two leading AI weather models, i.e. GraphCast and Pangu, are tied on the probabilistic CRPS metric even though the former outperforms the latter in deterministic scoring. We also reveal how multiple time-step loss functions, which many data-driven weather models have employed, are counter-productive: they improve deterministic metrics at the cost of increased dissipation, deteriorating probabilistic skill. This is confirmed through ablations applied to a spherical Fourier Neural Operator (SFNO) approach to AI weather forecasting. Separate SFNO ablations modulating effective resolution reveal it has a useful effect on ensemble dispersion relevant to achieving good ensemble calibration. We hope these and forthcoming insights from lagged ensembles can help guide the development of AI weather forecasts and have thus shared the diagnostic code.