Generative assimilation and prediction for weather and climate

TL;DR

Generative Assimilation and Prediction (GAP) is introduced, a unified deep generative framework for assimilation and prediction of both weather and climate that is competitive with state-of-the-art ensemble assimilation, probabilistic weather forecast and seasonal prediction, yields stable millennial simulations, and reproduces climate variability from daily to decadal time scales.

Abstract

Machine learning models have shown great success in predicting weather up to two weeks ahead, outperforming process-based benchmarks. However, existing approaches mostly focus on the prediction task, and do not incorporate the necessary data assimilation. Moreover, these models suffer from error accumulation in long roll-outs, limiting their applicability to seasonal predictions or climate projections. Here, we introduce Generative Assimilation and Prediction (GAP), a unified deep generative framework for assimilation and prediction of both weather and climate. By learning to quantify the probabilistic distribution of atmospheric states under observational, predictive, and external forcing constraints, GAP excels in a broad range of weather-climate related tasks, including data assimilation, seamless prediction, and climate simulation. In particular, GAP is competitive with state-of-the-art ensemble assimilation, probabilistic weather forecast and seasonal prediction, yields stable millennial simulations, and reproduces climate variability from daily to decadal time scales.

Figures (6)

• Figure 1: Schematic of the generative assimilation and prediction (GAP) framework. A, Evolution of atmospheric state probability distributions, illustrating the Probabilistic Assimilation and Prediction (PAP) ideology. A logarithmic timeline is adopted to highlight the duality between assimilation and prediction that we aim to unify. During assimilation (left), observations progressively constrain the climatological distribution, narrowing possible states. During prediction (right), uncertainty evolves through distinct phases: weather forecasting (up to around two weeks) shows growing uncertainty until deterministic predictions lose utility; seasonal prediction (up to around 1-2 years) maintains predictability below climatological levels through low-frequency climate process constraints; and climate prediction (beyond 1-2 years) shows complete dissipation of initial condition information while external forcings modify the underlying climatological distribution. B-D, Practical implementation of GAP. B, Assimilation phase implementation: given state estimates sampled from $p(\mathbf{X}_t|\mathbf{X}_{t-\Delta t},\mathbf{O}_t)$ -- the probability distribution of the current state $\mathbf{X}_t$ conditioned on previous state $\mathbf{X}_{t-\Delta t}$ (or climatological distribution if $\mathbf{X}_{t-\Delta t}$ were unavailable) and current observations $\mathbf{O}_t$ -- we use a forecasting model $\mathbf{M}$ to generate preliminary predictions, which together with observations $\mathbf{O}_{t+\Delta t}$ guide subsequent probabilistic state estimation for $p(\mathbf{X}_{t+\Delta t}|\mathbf{X}_{t},\mathbf{O}_{t+\Delta t})$. C, Transition point marking the end of assimilation and beginning of prediction, where forecasts proceed without observational input while yielding predicted observations via $p(\mathbf{O}|\mathbf{X})$. D, Prediction phase implementation: preliminary model predictions are combined with climatological priors to sample possible states across weather to climate timescales, maintaining physical consistency throughout.
• Figure 2: Multi-scale evaluation of GAP's climatological representation. A, Grid-point scale comparison between ERA5 and GAP using 2-meter temperature statistics (mean, variance, minimum, and maximum). Stippled areas indicate regions where GAP's generated distributions are statistically indistinguishable from ERA5 at the 95% confidence level according to the Kolmogorov-Smirnov test. B, Leading empirical orthogonal function (EOF) of 500hPa geopotential height, revealing GAP's accurate reproduction of the Northern Annular Mode pattern. C, Hadley cell circulation represented by mass streamfunction (contours) and zonal-mean winds (colors) as a function of pressure and latitude. Solid (dashed) contours indicate positive (negative) values of the stream function, with contour intervals set to $2 \times 10^{10} \, \text{kg/s}$. D, Spatial power spectral density as function of wavelength for 2-meter temperature, showing the characteristic power law decay from global to local scales. E, Vertical profiles of ageostrophic-to-geostrophic wind ratio in the extra-tropics ($|\text{lat}| \geq 20^\circ$), demonstrating preservation of fundamental atmospheric balance conditions.
• Figure 3: Evaluation of GAP's data assimilation capabilities. A-D, Spatial patterns of specific humidity and geopotential height from ERA5 (ground truth), IFS-HRES analysis (operational benchmark), GAP-OSSE (perfect observations), and GAP-OBS (real observations), demonstrating comparable accuracy between GAP and operational systems. E-H, Ensemble standard deviation and error patterns from GAP-OSSE and GAP-OBS, showing strong correspondence between predicted uncertainty (spread) and actual error, indicating reliable uncertainty quantification. I, RMSE statistics as a function of distance from observation points through the assimilation window, illustrating how error (deep colors) and ensemble variance (shallow colors) decrease near observations and increase with distance. J, RMSE skill at different observation density levels through the assimilation window for GAP ensemble (blue line with shading) and IFS-HRES analysis (black line), showing progressive acceleration in convergence as observation density increases from climatological levels to $10^4$ observational points.
• Figure 4: GAP's ensemble forecasts of high-impact weather events. A, 3-day forecast of typhoon In-Fa (July 28, 2021), showing wind speed (color shading) and geopotential height (contours) at 500hpa from ERA5 reference, GAP ensemble mean, standard deviation, ensemble mean prediction error, and individual ensemble members. B, 10-day forecast of an atmospheric river hitting California (April 12, 2023), displaying 850hPa geopotential height (contours) and specific humidity (color shading). C, 21-day forecast of a European heatwave (June 23, 2023), showing 2-meter temperature anomalies (color shading) and 500hPa geopotential height (contours). D, 42-day forecast of the Madden-Julian Oscillation (January 20 to March 1, 2023), presenting Hovmöller diagram of zonal wind anomalies at 850hPa (color shading) across tropical latitudes (0-45$^\circ$S) and longitudes (0-180$^\circ$E).
• Figure 5: Evaluation of GAP's performance across assimilation and prediction tasks. A, Comparing GAP assimilation versus IFS-HRES initial conditions across multiple variables, pressure levels, and assimilation times, with blue/red cells indicating reduced/increased assimilation error compared to IFS-HRES analysis (measured by relative RMSE difference, see SI Sec. C.1). B-D, Quantitative comparison of medium-range forecast skill between GAP, IFS-ENS, NeuralGCM-ENS, Pangu, and GraphCast, showing: B, anomaly correlation coefficient (deterministic skill); C, continuous ranked probability score (probabilistic skill); and D, spread-skill ratio (uncertainty calibration). E-J, Spatial distribution of seasonal prediction skill for 2-meter temperature at 2-month (E-G) and 3-month (H-J) lead times, comparing GAP without SST forcing (E,H), $\text{GAP}_{\text{SAP}}$ with SST anomaly persistence (F,I), and ECMWF's SEAS5 (G,J). Latitude-weighted mean ACC values are indicated at the top of each panel.