SEEDS: Emulation of Weather Forecast Ensembles with Diffusion Models

TL;DR

Uncertainty quantification in numerical weather prediction is challenged by the computational cost of large ensembles. SEEDS proposes diffusion-model emulation to generate weather-like ensembles conditioned on a small number of seeds, enabling both generative ensemble emulation and generative post-processing that can match or exceed physics-based ensembles in predictive skill and tail coverage, at a fraction of the computational cost. The approach uses a high-capacity axial-attention Transformer score model trained on two decades of GEFS reforecasts and ERA5 data, producing $N$ samples conditioned on $K$ seeds with throughput suitable for tens of thousands of members. This diffusion-based, scalable sampler offers a practical path to massive ensemble generation and bias correction, with potential extensions to climate projections and climate risk assessment.

Abstract

Uncertainty quantification is crucial to decision-making. A prominent example is probabilistic forecasting in numerical weather prediction. The dominant approach to representing uncertainty in weather forecasting is to generate an ensemble of forecasts. This is done by running many physics-based simulations under different conditions, which is a computationally costly process. We propose to amortize the computational cost by emulating these forecasts with deep generative diffusion models learned from historical data. The learned models are highly scalable with respect to high-performance computing accelerators and can sample hundreds to tens of thousands of realistic weather forecasts at low cost. When designed to emulate operational ensemble forecasts, the generated ones are similar to physics-based ensembles in important statistical properties and predictive skill. When designed to correct biases present in the operational forecasting system, the generated ensembles show improved probabilistic forecast metrics. They are more reliable and forecast probabilities of extreme weather events more accurately. While this work demonstrates the utility of the methodology by focusing on weather forecasting, the generative artificial intelligence methodology can be extended for uncertainty quantification in climate modeling, where we believe the generation of very large ensembles of climate projections will play an increasingly important role in climate risk assessment.

Figures (27)

• Figure 1: Illustration of the target distributions of generative ensemble emulation (gefs-full) and post-processing (Mixture). Shown are the histograms (bars: frequencies with 12 shared bins, curves: Gaussian kernel density estimators fit to the bars), i.e., the empirical distributions of the surface temperature near Mountain View, CA on 2021/07/04 in the GEFS and ERA5 ensembles. The goal common to both tasks is to generate additional ensemble members to capture the statistics of the desired distribution conditioned on a few GEFS samples. Note the small "bump" at the temperature of 287K in the mixture distribution.
• Figure 2: Maps of total column vertically-integrated water vapor ($kg/m^2$) for 2022/07/14, as captured by (top left) the ERA5 reanalysis, (top right and middle row) 5 members of the gefs-full forecast issued with a 7-day lead time, and (bottom) 3 samples from seeds-gee. The top 2 GEFS forecasts were used to seed the seeds-gee sampler.
• Figure 3: Visualization of spatial coherence in forecasted weather charts for 2022/07/14, with a 7-day lead time. The contours are for mean sea level pressure (dashed lines mark isobars below 1010 hPa) while the heatmap depicts the geopotential height at the 500 hPa pressure level. Row 1: ERA5 reanalysis, then 2 forecast members from gefs-full used as seeds to our model. Row 2--3: Other forecast members from gefs-full. Row 4--5: 8 samples drawn from seeds-gee. Row 6: Samples from a pointwise Gaussian model parameterized by the gefs-full ensemble mean and variance.
• Figure 4: The energy spectra of several global atmospheric variables for January of 2022 from the ERA5 reanalysis (thick black), members of the gefs-full 7-day forecast (orange), and samples from seeds-gee (green). The forecasts for each day are re-gridded to a latitude-longitude rectangular grid of the same angular resolution prior to computing the spectra. The computed spectra are averaged over the entire month. Each ensemble member is plotted separately.
• Figure 5: Generated ensembles provide better statistical coverage of the extreme heat event over Portugal. Each plot displays 16,384 generated forecasts from our method, extrapolating from the two seeding forecasts randomly taken from the operational forecasts. Contour curves of iso-probability are also shown. The first row is from seeds-gee and the second from seeds-gpp. seeds-gpp characterizes the event best. Most notably, in the two rightmost plots of the bottom row, seeds-gpp is able to generate well-dispersed forecast envelopes that cover the extreme event, despite the two seeding ones deviating substantially from the observed event.