Global kilometre-scale forecasts of fine particulate matter
Daily PM2.5 from all its sources (traffic, industry, heating, agriculture, desert dust, sea salt and fires) for every inhabited place on Earth at 1 km, from one day to a week ahead, as a calibrated ensemble. Foehn learns from the first global 1 km record of PM2.5, generates whole continents in one pass by flow matching, and computes rather than learns the transport of the air with FLEXGREEN, a GPU re-implementation of the backward mode of the FLEXPART particle model.
Click or tap anywhere on land. FLEXGREEN followed the air that arrived there on 21 January 2022 backwards through the forecast wind for seven days: each dot is a particle of that air, where it was one to seven days before. Blue, it was near the ground, in the mixed layer, on that day; pink, it was higher up. The numbers are computed for the place you choose, from the same Green's functions that Foehn's forecasts use.
Choose a place on the map.
Kheder A., Boy M. & Liu Z.-S. Global probabilistic forecasting of air pollution. arXiv:2610.25941, 2026 — abstract · PDF.
About a million deaths a year are attributable to short-term exposure to fine particulate matter (PM2.5), whatever its source: traffic, industry, heating, agriculture, desert dust or fires. Yet PM2.5 varies from street to street, while forecasts use grids tens of kilometres wide. Machine learning has transformed weather forecasting, but two problems keep it from the scale at which air pollution harms. Kilometre-scale fields are too large to forecast in one piece, and the peaks that matter for health are smoothed away by standard training or arrive with distant air. Here we show that both can be solved. Our model, Foehn, learns from the first global record of daily PM2.5 at kilometre scale, forecasts continent-sized windows in one pass by flow matching, and computes the transport of the air with a particle model driven by the weather forecast. In retrospective forecasts for 2022, it produced calibrated, seamless kilometre-scale ensembles over all inhabited land, up to a week ahead. At thousands of stations not used to train or select it, they were more accurate than the operational forecast issued at the same time, caught local extremes more reliably and reached people whom coarse grids hide. Computing what physics knows, and learning the rest, makes forecasts accurate, inexpensive and interpretable.
The PM2.5 that reaches a place is set by what the arriving air contained and by what happened to it on the way. Foehn separates the two.
FLEXGREEN, computed transport. A GPU re-implementation of the backward mode of the FLEXPART particle model releases particles in every 0.5° land cell on the target day and follows them backwards in the three-dimensional forecast wind, with turbulence and removal. The result is the Green's function of the transport: where the arriving air was on the start day, at which height, and how much of its aerosol survived. It has no learned parameter.
A generative network for what the air carries. The network reads the start-day fields where the physics says the air was, and generates the 1 km field of the target day by flow matching; each noise field gives one ensemble member, and whole continents are produced in one pass with no visible seam.
The forecasts of the three case studies of the preprint, as issued: choose a case, a target day and how many days before the forecast was issued, and compare Foehn's ensemble with the 1 km reference estimates (GHAP, made after the fact) and the CAMS operational forecast issued at the same time. Every panel is a genuine output of the final model (16 members, 1 km); nothing is recomputed in the browser. The address bar follows your selection, so a view can be shared.
Retrospective forecasts for 2022, made with the archived operational weather forecasts, scored against the 1 km estimates over all land and at 6,324 monitoring stations never used to train or select the model. Click a figure for full resolution.
Foehn produces a global field at 1 km without visible seams, assembled from twenty-one overlapping continent-sized windows. Shown: the forecast issued for 21 January 2022, the day of the year with the highest population-weighted PM2.5. At 1 km it resolves what the 40 km grid of the operational forecast blurs.
Flow matching keeps the detail that a squared error averages away: each member reproduces the plain, the mountains and the cities of the January 2022 haze over the North China Plain, and the spread of the ensemble matches its error at every lead time.
Even a perfect 40 km forecast would miss 186 million people a day above 37.5 µg m−3, the WHO interim target 3. Foehn forecasts at the scale at which they can be warned: one day ahead, it warned 43 % of them, and it catches local extremes markedly better than the operational systems.
Every forecast comes with its Green's functions, which show where the arriving air was: here, the Saharan dust that reached Kano, Nigeria, on 16 May 2022. Computing the transport helps most in the first days, while the start day still matters.
Five days ahead, Foehn put the smoke of the Gironde fires of July 2022 over the forest of the Landes and the Teich bird reserve, giving the reserve about a one-in-three chance of exceeding 25 µg m−3.
The design was chosen in a controlled benchmark over Europe: five spatiotemporal networks retrained with exactly the inputs of Foehn's flow-matching network (its European 0.25° version), against the CAMS operational forecast, Aurora and climatology. Europe, 2022; scores averaged over lead times of 1 to 4 days and three training seeds.
RMSE in µg m−3 (lower is better); CSI of exceedances of 25 µg m−3 (higher is better); inference: one member of one forecast on one AMD MI250X compute die. Foehn's network was the most accurate in 35 of 36 combinations of score, lead time and set of days (all days, the 10 % most polluted days and documented transport episodes).
| Model | RMSE, 0.25° | RMSE, 1 km | RMSE, 2,971 EEA stations | CSI, > 25 µg m−3 | Inference (s) | GPU memory (GB) |
|---|---|---|---|---|---|---|
| Foehn (flow matching, European 0.25° version) | 5.07 | 5.47 | 11.23 | 0.421 | 0.231 | 0.15 |
| Foehn without the learned transport layer | 5.12 | 5.52 | 11.25 | 0.413 | 0.045 | 0.15 |
| ConvLSTM | 5.26 | 5.68 | 11.32 | 0.398 | 0.011 | 0.72 |
| Earthformer | 5.40 | 5.82 | 11.34 | 0.392 | 0.006 | 0.42 |
| SimVP | 5.49 | 5.92 | 11.39 | 0.379 | 0.010 | 0.10 |
| TopoFlow | 5.54 | 5.96 | 11.42 | 0.388 | 0.010 | 0.43 |
| ClimaX | 5.76 | 6.19 | 11.49 | 0.359 | 0.010 | 0.95 |
| Aurora | 7.98 | 8.44 | 12.20 | 0.212 | 6.0 | 20.40 |
| CAMS operational forecast | 8.43 | 8.86 | 12.12 | 0.204 | – | – |
| Climatology | 7.70 | 8.13 | 12.14 | 0.238 | – | – |
What Foehn is, and is not, in its present form.
| Code (MIT licence) | github.com/AmmarKheder/Foehn — FLEXGREEN, data preparation, training, calibration, inference, evaluation, and every figure of the preprint. |
| Trained weights | Available to the editors and referees; released with the code upon publication. |
| Target and inputs | GHAP daily 1 km PM2.5 (Wei et al., Zenodo); ECMWF IFS HRES forecasts (WeatherBench 2); ERA5; CAMS global forecasts and analyses, GFAS and CAMS-GLOB-ANT (Copernicus Atmosphere Data Store); GHS-POP population. |
| Evaluation stations | EEA, CNEMC, US EPA AQS, AirKorea, NIES Japan, CPCB India (partly through OpenAQ). Stations are used for evaluation only. |
@article{kheder2026foehn,
title = {Global kilometre-scale forecasts of fine particulate matter},
author = {Kheder, Ammar and Boy, Michael and Liu, Zhi-Song},
year = {2026},
note = {Manuscript submitted}
}Questions and problems: GitHub issues · ammar.kheder@lut.fi