Testing the Limit of Atmospheric Predictability with a Machine Learning Weather Model

TL;DR

The paper challenges the conventional atmospheric predictability limit by using a differentiable machine-learning weather model, GraphCast, to optimally perturb initial conditions and conduct gradient-based forecast optimization. Across 2020 data, the approach achieves substantial reductions in forecast error at 10 days and extends skill beyond 30 days, with the method showing robust improvements that persist even when tested in a different model, Pangu-Weather. The results imply that, with highly accurate initial conditions, deterministic forecasts can remain skillful longer than traditionally thought, reflecting a mix of analysis-error reduction and model-bias correction. This has practical implications for forecast practice and motivates further integration of ML-based optimization with physics-based models, including coupled atmosphere–ocean systems.

Abstract

Atmospheric predictability research has long held that the limit of skillful deterministic weather forecasts is about 14 days. We challenge this limit using GraphCast, a machine-learning weather model, by optimizing forecast initial conditions using gradient-based techniques for twice-daily forecasts spanning 2020. This approach yields an average error reduction of 86% at 10 days, with skill lasting beyond 30 days. Mean optimal initial-condition perturbations reveal large-scale, spatially coherent corrections to ERA5, primarily reflecting an intensification of the Hadley circulation. Forecasts using GraphCast-optimal initial conditions in the Pangu-Weather model achieve a 21% error reduction, peaking at 4 days, indicating that analysis corrections reflect a combination of both model bias and a reduction in analysis error. These results demonstrate that, given accurate initial conditions, skillful deterministic forecasts are consistently achievable far beyond two weeks, challenging long-standing assumptions about the limits of atmospheric predictability.

Figures (8)

• Figure 1: Weighted mean squared error as detailed in Eq. \ref{['loss_equation']} for all 732 control forecasts (black), 14-day optimized forecasts (green), and 32-day optimized forecasts (orange) during 2020.
• Figure 2: Sample-mean optimal perturbations averaged over 732 cases for (a) 850 hPa temperature, (b) 700 hPa specific humidity, (c) 500 hPa pressure vertical velocity (negative values indicate rising air); and (d) 850 hPa temperature sample standard deviation. Gray solid (dashed) contours represent the corresponding positive (negative) sample-mean values for ERA5.
• Figure 3: ERA5 2020 climatological anomaly and optimal perturbation autocorrelation as a function of lag for geopotential (Z500), temperature (T850), and zonal wind (U500) at their respective pressure levels. Solid lines represent the global mean autocorrelation for the optimal perturbations while dashed lines show the ERA5 anomaly global mean autocorrelation. The first correlation value is computed at 12 hours, consistent with the twice-daily optimization.
• Figure 4: Mean, median, and interquartile range (25th--75th percentiles) of the relative change in mean squared error for Pangu-Weather forecasts using 732 GraphCast-optimized initial conditions. The control forecasts use 1.0° ERA5 data interpolated to a 0.25° grid for an equal comparison.
• Figure S1: Visualization of the optimization process. A forecast is computed from an initial condition x(0) for a selected lead time (t). The derivative of the global loss function (Eq. \ref{['loss_equation']}) is taken with respect to the difference between the computed forecast and a verification dataset (i.e., ERA5). The optimization is repeated i times and then the process proceeds to Round 2 (R2) where the forecast is lengthened by a multiple of t. See Methods for additional details.