Modulated Adaptive Fourier Neural Operators for Temporal Interpolation of Weather Forecasts

Weather and climate data are often available at limited temporal resolution, either due to storage limitations, or in the case of weather forecast models based on deep learning, their inherently long time steps. The coarse temporal resolution makes it difficult to capture rapidly evolving weather events. To address this limitation, we introduce an interpolation model that reconstructs the atmospheric state between two points in time for which the state is known. The model makes use of a novel network layer that modifies the adaptive Fourier neural operator (AFNO), which has been previously used in weather prediction and other applications of machine learning to physics problems. The modulated AFNO (ModAFNO) layer takes an embedding, here computed from the interpolation target time, as an additional input and applies a learned shift-scale operation inside the AFNO layers to adapt them to the target time. Thus, one model can be used to produce all intermediate time steps. Trained to interpolate between two time steps 6 h apart, the ModAFNO-based interpolation model produces 1 h resolution intermediate time steps that are visually nearly indistinguishable from the actual corresponding 1 h resolution data. The model reduces the RMSE loss of reconstructing the intermediate steps by approximately 50% compared to linear interpolation. We also demonstrate its ability to reproduce the statistics of extreme weather events such as hurricanes and heat waves better than 6 h resolution data. The ModAFNO layer is generic and is expected to be applicable to other problems, including weather forecasting with tunable lead time.

Kilometer-Scale Convection Allowing Model Emulation using Generative Diffusion Modeling

Storm-scale convection-allowing models (CAMs) are an important tool for predicting the evolution of thunderstorms and mesoscale convective systems that result in damaging extreme weather. By explicitly resolving convective dynamics within the atmosphere they afford meteorologists the nuance needed to provide outlook on hazard. Deep learning models have thus far not proven skilful at km-scale atmospheric simulation, despite being competitive at coarser resolution with state-of-the-art global, medium-range weather forecasting. We present a generative diffusion model called StormCast, which emulates the high-resolution rapid refresh (HRRR) model-NOAA's state-of-the-art 3km operational CAM. StormCast autoregressively predicts 99 state variables at km scale using a 1-hour time step, with dense vertical resolution in the atmospheric boundary layer, conditioned on 26 synoptic variables. We present evidence of successfully learnt km-scale dynamics including competitive 1-6 hour forecast skill for composite radar reflectivity alongside physically realistic convective cluster evolution, moist updrafts, and cold pool morphology. StormCast predictions maintain realistic power spectra for multiple predicted variables across multi-hour forecasts. Together, these results establish the potential for autoregressive ML to emulate CAMs -- opening up new km-scale frontiers for regional ML weather prediction and future climate hazard dynamical downscaling.

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.

Generative Data Assimilation of Sparse Weather Station Observations at Kilometer Scales

Data assimilation of observational data into full atmospheric states is essential for weather forecast model initialization. Recently, methods for deep generative data assimilation have been proposed which allow for using new input data without retraining the model. They could also dramatically accelerate the costly data assimilation process used in operational regional weather models. Here, in a central US testbed, we demonstrate the viability of score-based data assimilation in the context of realistically complex km-scale weather. We train an unconditional diffusion model to generate snapshots of a state-of-the-art km-scale analysis product, the High Resolution Rapid Refresh. Then, using score-based data assimilation to incorporate sparse weather station data, the model produces maps of precipitation and surface winds. The generated fields display physically plausible structures, such as gust fronts, and sensitivity tests confirm learnt physics through multivariate relationships. Preliminary skill analysis shows the approach already outperforms a naive baseline of the High-Resolution Rapid Refresh system itself. By incorporating observations from 40 weather stations, 10\% lower RMSEs on left-out stations are attained. Despite some lingering imperfections such as insufficiently disperse ensemble DA estimates, we find the results overall an encouraging proof of concept, and the first at km-scale. It is a ripe time to explore extensions that combine increasingly ambitious regional state generators with an increasing set of in situ, ground-based, and satellite remote sensing data streams.

Coupled Ocean-Atmosphere Dynamics in a Machine Learning Earth System Model

Seasonal climate forecasts are socioeconomically important for managing the impacts of extreme weather events and for planning in sectors like agriculture and energy. Climate predictability on seasonal timescales is tied to boundary effects of the ocean on the atmosphere and coupled interactions in the ocean-atmosphere system. We present the Ocean-linked-atmosphere (Ola) model, a high-resolution (0.25{\deg}) Artificial Intelligence/ Machine Learning (AI/ML) coupled earth-system model which separately models the ocean and atmosphere dynamics using an autoregressive Spherical Fourier Neural Operator architecture, with a view towards enabling fast, accurate, large ensemble forecasts on the seasonal timescale. We find that Ola exhibits learned characteristics of ocean-atmosphere coupled dynamics including tropical oceanic waves with appropriate phase speeds, and an internally generated El Ni\~no/Southern Oscillation (ENSO) having realistic amplitude, geographic structure, and vertical structure within the ocean mixed layer. We present initial evidence of skill in forecasting the ENSO which compares favorably to the SPEAR model of the Geophysical Fluid Dynamics Laboratory.

DiffObs: Generative Diffusion for Global Forecasting of Satellite Observations

This work presents an autoregressive generative diffusion model (DiffObs) to predict the global evolution of daily precipitation, trained on a satellite observational product, and assessed with domain-specific diagnostics. The model is trained to probabilistically forecast day-ahead precipitation. Nonetheless, it is stable for multi-month rollouts, which reveal a qualitatively realistic superposition of convectively coupled wave modes in the tropics. Cross-spectral analysis confirms successful generation of low frequency variations associated with the Madden--Julian oscillation, which regulates most subseasonal to seasonal predictability in the observed atmosphere, and convectively coupled moist Kelvin waves with approximately correct dispersion relationships. Despite secondary issues and biases, the results affirm the potential for a next generation of global diffusion models trained on increasingly sparse, and increasingly direct and differentiated observations of the world, for practical applications in subseasonal and climate prediction.

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.

Generative Residual Diffusion Modeling for Km-scale Atmospheric Downscaling

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a km-scale downscaling diffusion model is presented as a cost effective alternative. The model is trained from a regional high-resolution weather model over Taiwan, and conditioned on ERA5 reanalysis data. To address the downscaling uncertainties, large resolution ratios (25km to 2km), different physics involved at different scales and predict channels that are not in the input data, we employ a two-step approach (\textit{ResDiff}) where a (UNet) regression predicts the mean in the first step and a diffusion model predicts the residual in the second step. \textit{ResDiff} exhibits encouraging skill in bulk RMSE and CRPS scores. The predicted spectra and distributions from ResDiff faithfully recover important power law relationships regulating damaging wind and rain extremes. Case studies of coherent weather phenomena reveal appropriate multivariate relationships reminiscent of learnt physics. This includes the sharp wind and temperature variations that co-locate with intense rainfall in a cold front, and the extreme winds and rainfall bands that surround the eyewall of typhoons. Some evidence of simultaneous bias correction is found. A first attempt at downscaling directly from an operational global forecast model successfully retains many of these benefits. The implication is that a new era of fully end-to-end, global-to-regional machine learning weather prediction is likely near at hand.