physics.ao-phAug 27, 2026
SaveBridging short- and medium-range weather forecasting with machine learning
Organizations: Physical Sciences Laboratory (PSL), National Oceanic and Atmospheric Administration (NOAA), Boulder, CO, USA · Nansen Environmental and Remote Sensing Center, Bergen, Norway · Bjerknes Center for Climate Research, Bergen, Norway · Earth Prediction Innovation Center (EPIC) · Cooperative Institute for Research in Environmental Sciences (CIRES) at the University of Colorado Boulder, Boulder, CO, USA · Global Systems Laboratory (GSL), National Oceanic and Atmospheric Administration (NOAA), Boulder, CO, USA
Abstract
The National Oceanic and Atmospheric Administration (NOAA) employs independent prediction systems for distinct forecast products. While some separation is practical, we argue that combining short- and medium-range weather into a single prediction system would provide the public with a useful distillation of global weather and its impacts. To this end, we present Nested-EAGLE (Experimental Artificial intelligence Global and Limited-area Ensemble): a 0.25° global weather model with a 6 km refinement over the Contiguous United States (CONUS). The model achieves significantly lower mean-squared error in near-surface and low-level quantities over CONUS compared to NOAA's Global Forecast System and High-Resolution Rapid Refresh (HRRR), while remaining competitive throughout the rest of the global atmosphere. We show that the skill gains for near-surface fields stem from incorporating high-resolution regional analysis data into training through the nesting process. Forecasts of precipitation amounts are less skillful than those from HRRR, owing to deterministic training. However, we show that Nested-EAGLE provides the most accurate forecasts of storm locations at longer leads, despite blurred extrema. Our results motivate future work to extend the skill gains beyond CONUS and improve precipitation representation.
Figures & tables
Figure 1: Illustration of Nested-EAGLE. The model operates on a state space composed of HRRR data over CONUS, conservatively regridded to 6 km resolution, and GFS data everywhere else on the globe at 0.25 ∘ resolution. For a given timestamp , Nested-EAGLE is initialized with this nested state at and hours, and makes a prediction 6 hours into the future. The model is parameterized by a deep neural network that consists of a graph-transformer encoder and decoder, and a sliding-window transformer processor. The processor acts on a latent mesh that is essentially a coarsened version of the nested data space, with relatively higher resolution over CONUS than elsewhere. The figure shows the latent mesh nodes in gray, and an example attention window passing over the high-resolution CONUS region given a query node over Boulder, Colorado. Additionally, the figure illustrates that Nested-EAGLE diagnoses some quantities, like accumulated precipitation shown here, which are not provided as inputs. For this figure, we used = 0600 UTC 8 March 2023. See Section 5.1 for more design details and Section S5 for more snapshots of several variables from a sample forecast.
Figure 2: RMSE against in situ observations over CONUS during the test period. The model forecasts were first conservatively regridded to the same 6 km resolution Lambert conformal conic projection that Nested-EAGLE employs over CONUS, then bilinearly interpolated to the observation locations. See Figure S2 for an evaluation of more quantities and vertical levels, and Section S1.1 for a quantification of skill differences in terms of lead time. Lines show the median over 293 forecasts and shading the 95% confidence interval.
Figure 3: RMSE against in situ observations over Europe during the test period. The European region is defined as a simple latitude-longitude box from 35 ∘ N–75 ∘ N and 25 ∘ W–65 ∘ E. All datasets operate on a 0.25 ∘ latitude-longitude grid in this region, so they are not regridded prior to observation-location interpolation. See Figure S3 for an evaluation of more quantities and vertical levels. Lines show the median over 293 forecasts and shading the 95% confidence interval.
Figure 4: RMSE over CONUS. Similar to Figure 2 , but with additional experiments using swapped initial conditions. The additional purple dashed line shows the RMSE of Nested-EAGLE when it is initialized with GFS data only at inference time, which we call Nested-EAGLE(GFS IC), where IC denotes the initial conditions. The gray dashed line shows the opposite: during inference ML-GFS-Base is fed initial conditions that have HRRR data over CONUS for ML-GFS-Base(G+H IC), where G+H denotes combined GFS and HRRR initial conditions. For this figure, all datasets were conservatively regridded to a 0.25 ∘ resolution and evaluated over an approximate CONUS latitude-longitude box from 20 ∘ N–55 ∘ N and 135 ∘ W–50 ∘ W. Lines show the median over 293 forecasts and shading the 95% confidence interval.
Figure 5: Spatial RMSE between Nested-EAGLE and Nested-EAGLE(GFS IC), where differences are restricted to the HRRR subdomain for clarity. The figure shows the spatial distribution of errors between the green and purple dashed lines in Figure 4 . At forecast hour 0 (top rows, left), differences are entirely due to differences in GFS and HRRR analyses. After 6 hours (top rows, middle), the figure shows the difference between Nested-EAGLE with and without HRRR data over CONUS after a single forecast step. By 30 hours (top rows, right), the differences are negligible. The spatial RMSE represents the average over 293 forecasts. For a visual reference, the bottom row shows HRRR orography and the absolute value of differences between HRRR and GFS orography, regridded to 6 km resolution.
Figure 6: FSS against AORC over CONUS during the test period, shown as a function of the absolute amplitude (mm/6h). A value of 1 indicates a perfect FSS, i.e., higher is better. Lines show the mean over 1,426 forecasts and shading the 95% confidence interval.
Figure 7: FSS against AORC over CONUS during the test period, shown as a function of percentile represented by each model. As in Figure 6 , a value of 1 indicates a perfect FSS, i.e., higher is better. Lines show the mean over 1,426 forecasts and shading the 95% confidence interval.
| Prognostic Fields (Inputs & Outputs) 3D Atmospheric 2D Geopotential Height Surface Pressure Zonal Wind 10m Zonal Wind Meridional Wind 10m Meridional Wind Vertical Velocity Surface Temperature Temperature 2m Temperature Specific Humidity 2m Specific Humidity | Forcing Fields (Inputs Only) Time Varying Static Solar Insolation Land-Sea Mask Cosine & Sine of Latitude Orography Cosine & Sine of Longitude Cosine & Sine of Julian Day Cosine & Sine of Local Time Diagnostic Fields (Outputs Only) 6 hour Accumulated Precipitation 80m Zonal Wind 80m Meridional Wind |
Table 1: State space definition. The 3D atmospheric fields are represented on 12 pressure levels: 100, 150, 200, 250, 300, 400, 500, 600, 700, 850, 925, and 1000 hPa. All fields are normalized by their Z-score ( ) with the following exceptions. Specific Humidity, 2m Specific Humidity, and Accumulated Precipitation are normalized by the standard deviation ( ). Orography is normalized by its maximum value ( ), and all other forcing fields are not normalized. Specific Humidity, 2m Specific Humidity, and Accumulated Precipitation are bounded to positive values with , following Moldovan et al. (2026) .
Figure 8: 10 day forecasts after initialization at 0000 UTC 9 March 2023 from prototypes using different latent meshes and processor architectures. The left panel comes from a model with a graph-transformer processor acting on an icosahedral multimesh with 158 km and 20 km resolutions globally and over CONUS, respectively. The right panel comes from a model with a sliding-window transformer processor and a latent mesh with 2 ∘ and 30 km resolutions globally and over CONUS, respectively. Note that both forecasts stem from earlier prototypes trained on GFS data regridded to 1 ∘ and HRRR data regridded to 15 km resolutions.
| Hyperparameter | Stage A | Stage B | Stage C |
|---|---|---|---|
| Optimization Iterations | 60,000 | 5,760 | 5,760 |
| Epochs | 82 | 8 | 8 |
| Linear Warmup Steps | 1,000 | 100 | 100 |
| Maximum Effective Learning Rate | |||
| Minimum Learning Rate | |||
| Autoregressive Rollout Steps | 1 | 2 | 2–4 |
Table 2: Training Schedule . All stages used a batch size of 16, and our 8 year training dataset has 11,616 samples, resulting in about 726 optimization iterations (or batches) per epoch in Stage A. We used an AdamW optimizer ( Loshchilov and Hutter, 2019 ) with parameters . The loss is a weighted MSE function, where the loss over the target subregion is upweighted to 10% of the total loss; see Section S2.1 for details on this choice. Training required approximately 45 hours of wall-clock time on the National Energy Research Scientific Computing Center’s (NERSC) Perlmutter machine, using 16 nodes each with 4 A100s and 40 GB of GPU RAM per A100. We distributed the model across a single node, i.e., 4 GPUs per model instance.
Figure 9: 24 hours of conventional observational coverage on 7 December 2024. Observations over the U.S. and Europe are colored in blue and orange, respectively, as these subregions are discussed in Sections 2.1 and 2.2 . Observations everywhere else are indicated by gray dots.
| 10 m Wind Speed | 2 m Temperature | 2 m Specific Humidity | |||||||
| Lead Time | ML-GFS-Base | HRRR | GFS | ML-GFS-Base | HRRR | GFS | ML-GFS-Base | HRRR | GFS |
| 0 h | |||||||||
| 12 h | |||||||||
| 24 h | |||||||||
| 36 h | |||||||||
| 48 h | |||||||||
Table S1: Lead time gain for the near-surface fields. Each value indicates the lead time gain ( , see Equation 1 ) that Nested-EAGLE has for a given model and variable. Positive values indicate the additional lead time that Nested-EAGLE has lower RMSE than the listed model. Gray values indicate statistically insignificant differences between the median RMSE, based on the 293 forecasts described in the main text and a 95% confidence interval.
| 850 hPa Temperature | 500 hPa Geopotential Height | 250 hPa Wind Speed | |||||||
| Lead Time | ML-GFS-Base | HRRR | GFS | ML-GFS-Base | HRRR | GFS | ML-GFS-Base | HRRR | GFS |
| 0 h | |||||||||
| 12 h | |||||||||
| 24 h | |||||||||
| 36 h | |||||||||
| 48 h | |||||||||
Table S2: Lead time gain for the atmospheric fields. Otherwise, same as Table S1 .
Figure S1: Global RMSE. RMSE against in situ observations over the globe.
Figure S2: CONUS RMSE. Same as Figure S1 , except restricted to 20 ∘ N–55 ∘ N and 135 ∘ W–50 ∘ W. The difference between this figure and Figure 2 is that more variables are shown here, and that this evaluation is carried out at 0.25 ∘ resolution, not 6 km.
Figure S3: Europe RMSE. Same as Figure S1 , except restricted to 35 ∘ N–75 ∘ N and 25 ∘ W–65 ∘ E. The only difference between this figure and Figure 3 is that more variables are shown here.
Figure S4: Northern Hemisphere RMSE. Same as Figure S1 , except restricted to 20 ∘ N–80 ∘ N.
Figure S5: Tropics RMSE. Same as Figure S1 , except restricted to 20 ∘ S–20 ∘ N.
Figure S6: Southern Hemisphere RMSE. Same as Figure S1 , except restricted to 80 ∘ S–20 ∘ S.
Figure S7: Polar North RMSE. Same as Figure S1 , except restricted to 60 ∘ N–90 ∘ N.
Figure S8: Polar South RMSE. Same as Figure S1 , except restricted to 90 ∘ S–60 ∘ S.
Figure S9: LAM loss fraction sensitivity tests. RMSE against HRRR analysis. Each color indicates the percentage of loss dedicated to the LAM region (i.e., HRRR subdomain) during training. Note that “none” refers to the case where no reweighting is performed, so the region takes on a weighting based purely on the spatial extent of the HRRR domain relative to the globe, which is about 3.4%. Lines show the mean over 158 forecasts and shading the 95% confidence interval.
Figure S10: Attention window size sensitivity test. RMSE against in situ observations. The colors indicate the number of latent mesh nodes in the westward and eastward directions from a query point during attention computations (see visualization in Figure 1 ). Lines show the median over 158 forecasts and shading the 95% confidence interval.
Figure S11: Training iterations sensitivity test. RMSE against HRRR analysis. The colors indicate the number of optimization iterations taken during training, where each iteration consists of a single 6 hour forecast step. Lines show the mean over 158 forecasts and shading the 95% confidence interval.
Figure S12: Latent channels sensitivity test. RMSE against HRRR analysis. The colors indicate the number of channels used in the latent space, i.e., the width of the neural network. Lines show the mean over 158 forecasts and shading the 95% confidence interval.
Figure S13: Pressure scaling sensitivity test. RMSE against HRRR analysis. The colors indicate whether pressure scaling was used in the loss function or not. Lines show the mean over 158 forecasts and shading the 95% confidence interval.
Figure S14: Sensitivity to number of initial states. MAE against in situ observations. The color indicates the number of initial states used. We use MAE here since it is less sensitive to outliers that dominate the 2m specific humidity signal. Lines show the median over 158 forecasts and shading the 95% confidence interval.
Figure S15: Attribution of perturbed 2m temperature bias to orography differences. The left panel shows Pearson’s from an OLS regression and Spearman’s , where both indicate the correlation between 2m temperature bias (i.e., signed error averaged over initial conditions) and orography differences between Nested-EAGLE and Nested-EAGLE(GFS IC). The right panel shows the lapse rates implied by the regression analyses, which are fairly close to the standard reference value in the troposphere. We computed the OLS regression over all 6 km grid cells, whereas we evaluated the Theil-Sen fit over a random sample of 8,000 grid cells, from which we estimated the 95% confidence interval.
Figure S16: Monthly mean 6 hour accumulated precipitation, March 2023. Produced with a 24 hour lead time and valid during March 2023.
Figure S17: Monthly mean 6 hour accumulated precipitation, August 2023. Produced with a 24 hour lead time and valid during August 2023.
Figure S18: 10m wind speed . = 0600 UTC 8 March 2023.
Figure S19: 2m temperature . = 0600 UTC 8 March 2023.
Figure S20: 2m specific humidity . = 0600 UTC 8 March 2023.
Figure S21: Accumulated precipitation . = 0600 UTC 8 March 2023.