Downscaling weather forecasts from Low- to High-Resolution with Diffusion Models
Authors: Joffrey Dumont Le Brazidec, Simon Lang, Martin Leutbecher, Baudouin Raoult, Gert Mertes, Florian Pinault, Aristofanis Tsiringakis, Pedro Maciel, Ana Prieto Nemesio, Jan Polster, Cathal O Brien, Matthew Chantry
Organizations: European Centre for Medium-Range Weather Forecasts (ECMWF)
We introduce a probabilistic diffusion-based method for global atmospheric downscaling implemented within the Anemoi framework. The approach transforms low-resolution ensemble forecasts into high-resolution ensembles by learning the conditional distribution of finer-scale residuals, defined as the difference between the high-resolution fields and the interpolated low-resolution inputs. The system is trained on reforecast pairs from ECMWF IFS, using coarse fields at 100 km to reconstruct fine-scale variability at 30 km resolution. The bulk of the training focuses on recovering small-scale structures, while fine-tuning in high-noise regimes enables the generation of extremes. Evaluation against the medium-range IFS ensemble target shows that the model increases probabilistic skill (FCRPS) for surface variables, reproduces target power spectra at small scales, captures physically consistent multivariate relationships such as wind-pressure coupling, and generates extreme values consistent with those of the target ensemble in tropical cyclones.
Figures & tables
Figure 1: Hurricanes Idalia and Franklin as seen in the subseasonal ensemble forecast (eefo, O96 resolution) and its AI-based downscaling to O320 resolution. The background field in each panel shows the low-resolution O96 input, while the inset (black frame) shows the corresponding downscaled O320 prediction from the diffusion model. Top: mean sea level pressure (hPa). Bottom: 10-metre wind speed (m/s). Initialisation date: 29 August 2023, +24 h lead time (valid 30 August 2023), ensemble member 6. The downscaled fields resolve the tight inner-core structure of both tropical cyclones — including the pressure minima and eyewall wind maxima — that is absent from the coarse input.
Field / Weather variable
Level
Input/Target
Normalisation
Geopotential, horizontal and vertical wind components, temperature, specific humidity
10m wind (u, v), 2m temperature, 2m dewpoint temperature, surface pressure, skin temperature, mean sea level pressure, total column water
Surface
Input: low-res Target: high-res
Standardised
Land–sea mask, orography, cosine/sine of local time of day, day of year, latitude, longitude, insolation,
Surface
Input: high-res
Not normalised
Table 1: Meteorological fields, levels, and normalisation used for training Anemoi-D 2 .
Figure 2: Schematic of the diffusion-based downscaling model. At each denoising step, the model takes as input on the O320 grid: (i) the current noisy residual estimate, (ii) static and temporal forcing fields, and (iii) the coarse O96 atmospheric fields interpolated to O320 ( D96→320 ). These features are processed by an encoder–processor–decoder graph neural network: the encoder projects information from O320 to the hidden grid, the processor applies 16 successive graph-transformer layers on the hidden graph, and the decoder projects the result back to O320. In the lower panel, the pink boxes represent these three consecutive components. The model output is a prediction of the residual on O320, which is added to the interpolated coarse field to reconstruct the final high-resolution field.
Figure 3: Receptive field of the GNN processor for a randomly selected node (red). The figure shows how many nodes receive its information after 2, 10, and 16 message-passing layers—that is, across the corresponding 2-, 10-, and 16-hop neighborhoods. The graph structure is fixed; only the range of information propagation increases.
Stage
Steps
Noise setup
Objective
1
106
EDM lognormal noise distribution ( Karras et al., 2022 ) with mean −1.2 and standard deviation 1.2
Base training
2
105
Higher-noise fine-tuning with a Karras-style schedule, using ρ=7 , σmax=10000 , and Smax=10000
Improve generation from strongly degraded states and better capture extremes
Table 2: Summary of the two-stage training procedure.
Figure 4: Fair Continuous Ranked Probability Score (FCRPS) for 2-metre temperature (left) and 10-metre wind speed (right) over the Northern Hemisphere extratropics, from forecast day 1 to 10 (20240201–20240225), evaluated against SYNOP station observations. Comparison between the downscaled ensemble forecast, the IFS medium-range ensemble forecast, and the subseasonal ensemble forecast (input).
Figure 5: Subseasonal ensemble forecast first member (first column), medium-range ensemble forecast first member (second column), and downscaling with the diffusion model of two subseasonal members (third and fourth columns, with the third corresponding to downscaling of the first column). Results are shown for the Amazon rainforest at lead time 24h. Rows display 10u, 10v, 2t, and T850. The diffusion model generates stochastic and physically consistent small-scale features.
Figure 6: Subseasonal ensemble forecast first member (first column), medium-range ensemble forecast first member (second column), and downscaling with the diffusion model of two subseasonal members (third and fourth columns, with the third corresponding to downscaling of the first column). Results are shown for the Himalayas at lead time 24h. Rows display 10u, 10v, 2t, and T850. The diffusion model generates physically consistent small-scale features.
Figure 7: Comparison of global amplitude spectra of weather variables from the subseasonal forecasts, the medium-range forecasts, and the downscaled subseasonal forecasts. The spectra are evaluated over the full globe at forecast day 6 and are based on 31 forecast initialisation dates and 10 ensemble members per date, corresponding to a sample of 310 forecasts.
Figure 8: Normalised pdfs of mean sea level pressure (980–1015 hPa) and 10-meter wind speed (0–30 m/s) for Hurricane Idalia across ensemble members, initialized on 26-30 August 2023, with a 1 to 5-days lead time. The pdfs represent the distributions of gridpoint values within the cyclone region, normalised by the corresponding distribution of the operational analysis. They are shown for the target IFS medium-range ensemble forecasts, the input IFS subseasonal ensemble forecasts, and the downscaled reconstructions (before and after finetuning). The accompanying map illustrates Idalia’s track from 27 to 31 August 2023, marking stages from tropical depression to major hurricane. Idalia cyclone track is adapted from NOAA/NHC https://www.nhc.noaa.gov/data/tcr/index.php?season=2023&basin=atl .
Figure 9: Mean sea level pressure (985–1015 hPa) and wind speed (0–30 m/s) for tropical cyclone Idalia for three ensemble members at 24-hour lead time, initialized on 28 August 2023. The first column shows the target IFS medium-range ensemble forecast MSLP, the second column displays the input IFS subseasonal ensemble forecast MSLP, and the third and fourth columns present the MSLP and wind fields, respectively, reconstructed through downscaling of the IFS subseasonal ensemble forecast.
Figure 10: Normalised pdfs of mean sea level pressure (960–1015 hPa) and 10-meter wind speed (0–30 m/s) for Hurricane Hilary across ensemble members, initialized on 16-20 August 2023, with a 1 to 5-days lead time. The pdfs represent the distributions of gridpoint values within the cyclone region (approximately the dashed orange line), normalised by the corresponding distribution of the operational analysis. They are shown for the target IFS medium-range ensemble forecasts, the input IFS subseasonal ensemble forecasts, and the downscaled reconstructions (before and after finetuning). The map illustrates the cyclone’s track from 16 to 20 August 2023, marking stages from tropical depression to major hurricane. Hilary cyclone track is adapted from NOAA/NHC https://www.nhc.noaa.gov/data/tcr/index.php?season=2023&basin=epac .
Figure 11: Local fields of mean sea level pressure (960–1015 hPa) and wind speed (0–30 m/s) for Tropical Cyclone Hilary across ensemble members at 24-hour lead time, initialized on 17 August 2023. The first column shows the target IFS medium-range ensemble forecast MSLP, the second column displays the input IFS subseasonal ensemble forecast MSLP, and the third and fourth columns present the MSLP and wind fields, respectively, reconstructed through downscaling of the IFS subseasonal ensemble forecast.
Weather forecasting predicts future atmospheric conditions, from local storms to global patterns, using physical models, observations, and machine learning.
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Decisions about heat, frost and flooding are made locally, yet reanalyses and climate models resolve tens of kilometres. Generative downscalers add kilometre-scale detail with uncertainty, but are tied to a grid, costly to sample and lack a tractable likelihood. Here we introduce CD-FFM, a functional flow-matching model that treats the high-resolution field as a continuous random field that one model can query at any location and resolution. Its velocity acts pointwise, so spatial variability comes from a noise prior fitted to the observed spectrum and every observation has an exact likelihood. Downscaling ERA5 to 1 km daily temperature over Fennoscandia, CD-FFM lowers the continuous ranked probability score by 27-31% against regression and 12-18% against a forty-times larger neural operator in each of three test years, and outperforms a CorrDiff-style diffusion model while sampling about fifty times faster. The same model transfers to precipitation and makes large kilometre-scale ensembles affordable.
Zhi-Song Liu, Helmi Toropainen, Ammar Kheder +1
Department of Computational Engineering, LUT University, Lappeenranta, Finland. · Institute for Atmospheric and Earth System Research (INAR), University of Helsinki, Helsinki, Finland. · Atmospheric Modelling Center, Lahti (AMC-Lahti), Lahti, Finland.