FuXi-ENS: A machine learning model for medium-range ensemble weather forecasting

TL;DR

FuXi-ENS advances ML-based ensemble forecasting for medium-range weather by delivering 6-hourly forecasts up to 15 days at $0.25^{\circ}$ resolution and incorporating flow-dependent perturbations via a Variational Autoencoder. Its loss combines $CRPS$ and KL divergence, enabling improved uncertainty representation and outperforming the ECMWF ensemble across multiple deterministic and probabilistic metrics, including extreme-event forecasts. The approach achieves rapid generation (about $10$ seconds per member on an Nvidia $A100$) and demonstrates strong performance in probabilistic TC tracks and a high-impact 2018 heatwave event, highlighting its practical potential for operational forecasting and data assimilation. Overall, FuXi-ENS provides a scalable, high-resolution, probabilistic alternative to conventional NWP ensembles, with significant implications for real-time risk assessment and decision support.

Abstract

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25\textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.

Figures (6)

• Figure 1: Comparison of the globally-averaged latitude-weighted $\textrm{RMSE}$ (first and second rows) as well as normalized $\textrm{RMSE}$ (third and fourth rows) differences of ensemble mean forecasts from the ECMWF ensemble (blue lines) and FuXi-ENS (red lines) for 3 upper-air variables, including $\textrm{Z500}$, $\textrm{T850}$, and $\textrm{WS850}$, and 3 surface variables, such as $\textrm{MSL}$, $\textrm{T2M}$, and $\textrm{WS10M}$, in 15-day forecasts using testing data from 2018. The normalized differences are calculated using the ECMWF ensemble mean as the reference.
• Figure 2: Comparison of normalized differences in globally-averaged, latitude-weighted $\textrm{CRPS}$ (first and second rows), ensemble spread (third and fourth rows), and $\textrm{SSR}$ (fifth and sixth rows) of ensemble forecasts from ECMWF ensemble (blue lines) and FuXi-ENS (red lines) for 6 variables: $\textrm{Z500}$, $\textrm{T850}$, $\textrm{WS850}$, $\textrm{MSL}$, $\textrm{T2M}$, and $\textrm{WS10M}$, in 15-day forecasts using testing data from 2018. The normalized differences are calculated using the ECMWF ensemble mean as the reference.
• Figure 3: Comparison of the ECMWF ensemble (blue lines) and the FuXi-ENS (red lines) on the normalized differences in globally-averaged, latitude-weighted $\textrm{BS}$ for 90th (first row), 95th (second row), 98th (third row), 10th (fourth row), 5th (fifth row), and 2nd (sixth row) percentile events, (second row), and (third row) of for 4 variables: $\textrm{Z500}$ (first column), $\textrm{T850}$ (second column), $\textrm{MSL}$ (third column), and $\textrm{T2M}$ (fourth column), in 15-day forecasts using testing data from 2018.
• Figure 4: Scatter plots comparing $\textrm{AccERROR}_{TC}$ against $\textrm{AccSpread}_TC$, and $\textrm{AT}_{TC}$ against $\textrm{CT}_{TC}$ at a 72-hour forecast lead time for the FuXi-ENS and ECMWF ensemble. In the scatter plots of $\textrm{AccERROR}_{TC}$ against $\textrm{AccSpread}_TC$, each red dot represents an individual forecast, summarized in the format S(M/N), where S is the total number of dots, M is the number above the diagonal, and N is the number below. In the scatter plots of $\textrm{AT}_{TC}$ against $\textrm{CT}_{TC}$, red dots represent individual forecasts, with the blue dots denoting the mean values of red dots within each quadrant. The blue stars indicate the mean values of all forecasts.
• Figure 5: Spatial distributions of $\textrm{T2M}$ generated by FuXi-ENS and ECMWF ensemble during the 2018 Northeast Asia heatwave. The first column displays the ERA5 reanalysis data for 6 UTC on July 23, 2018. Columns 2 through 5 are predictions from FuXi-ENS (first and third rows) and ECMWF ensemble (second and fourth rows), showing the best member (second column), worst member (third column), ensemble mean (fourth column), and ensemble spread (fifth column). The top two rows are forecasts made from 3 days earlier, and the bottom two rows are forecasts made from 11 days earlier. The black contours indicate the $\textrm{Z500}$.