cs.AIOct 19, 2026
SaveGlobal probabilistic forecasting of air pollution
Organizations: Department of Computational Engineering, LUT University, Lahti, Finland · Institute for Atmospheric and Earth System Research, University of Helsinki, Helsinki, Finland · Atmospheric Modelling Centre Lahti (AMC-Lahti), Lahti, Finland
Abstract
Fine particulate matter (PM2.5) refers to particulate matter with an aerodynamic diameter of 2.5 micrometre or less. It comes from human activities, such as traffic and industry, and from wildfires, desert dust and gases emitted by vegetation. Short-term exposure to it accounts for about a million deaths a year. Operational forecasts run on grids tens of kilometres wide, which hide the pollution breathed by nearly two hundred million people a day. Machine learning has transformed weather forecasting, but data-driven forecasts of air pollution still blur extremes and lose skill as the air travels. Here we introduce Foehn, a generative model that learns from global kilometre-scale estimates of PM2.5 and computes where the air comes from. Over a year of retrospective forecasts, it outperforms the operational forecast at three stations in four and forecasts at the scale of this hidden exposure. Its ensembles are calibrated, and their mean detects local pollution extremes four days ahead as well as the operational forecast does one day ahead. Such forecasts could warn the millions whom coarse maps miss, once kilometre-scale data are available in real time.
Figures & tables
Fig. 1: Foehn computes where the air comes from and learns what it carries. a , Computed transport, without learned parameters. The three-dimensional forecast wind (shown at 850 hPa, 00 UTC on 20 January 2022, the start day) drives FLEXGREEN. FLEXGREEN releases particles in every 0.5 ∘ land cell over the target day and follows them back to the start day. On the way, it sums the emissions that the air takes up: the anthropogenic emissions (purple; black carbon shown) and those of the fires of the start day. Lines, 5-day back-trajectories of the air reaching 18 cities on 25 January 2022, blue near the ground and pink aloft. b , Learned tracers. An encoder turns the start day (PM 2.5 at 0.25 ∘ and fires) into 32 tracers. Each place reads them where its air was on the start day, in the mixed layer. c , Generator. A conditional flow-matching network turns a noise field into a 1 km forecast in four sampling steps (red axis), for each lead time (blue axis). It is conditioned on the start day at 1 km (lens: Delhi), the forecast weather (2-m temperature and wind shown) and 44 transport maps: the tracers of b , the emission terms of a , the share of air from aloft, its survival and the advected PM 2.5 (three shown, 5 days ahead). Discs, one member of the forecast issued on 20 January 2022 for 21, 22 and 27 January, from noise ( ) to forecast ( ). The three intermediate discs blend the two at the flow times reached after the first three steps (0.03, 0.17 and 0.53). Each noise field gives one ensemble member. Colour scale, daily PM 2.5 (µg m -3 ).
Fig. 2: Even a perfect 40 km forecast cannot warn millions of people a day who breathe polluted air. a , Number of residents per day in 2022 whose 1 km grid cell was above the World Health Organization (WHO) 24-h interim target 3 (37.5 µg m -3 ) while the mean of the surrounding 40 km cell was below it, mapped per 40 km cell: people whom even a perfect 40 km forecast could not warn (1 km estimates of the Global High Air Pollutants dataset, GHAP, and population, without any forecast). b – d , Beijing–Tianjin on 21 January 2022, the most polluted day of the year for the world’s population: daily PM 2.5 in GHAP with the contour of 75 µg m -3 , WHO interim target 1 ( b ); the same field averaged over 40 km cells, the size of the cells of the CAMS forecast, which is what a perfect 40 km forecast gives ( c ); and the residents above 75 µg m -3 seen (grey) or hidden (pink) by the 40 km cells ( d ). e , Of the person-days of 2022 above each threshold in the residents’ 1 km grid cell, the share in 40 km cells whose mean is below it, by region: the WHO 24-h guideline level (15 µg m -3 ; light) and interim targets 3 (37.5 µg m -3 ) and 1 (75 µg m -3 ; dark); same data as a . A bar is shown when the region has at least one billion person-days above its threshold.
Fig. 3: Foehn forecasts all inhabited land at 1 km and resolves basins that the operational grid blurs. a , Foehn’s forecast of daily PM 2.5 (ensemble mean of four members) issued at the end of 20 January 2022 for 21 January, the day of 2022 with the highest population-weighted PM 2.5 . b , The forecast of a in four polluted basins, each monitored by a different official network (1, Delhi, Central Pollution Control Board of India; 2, Po Valley, European Environment Agency; 3, Los Angeles, US Environmental Protection Agency; 4, Seoul, AirKorea). Shown are the CAMS forecast issued at the same time (00 UTC run of 21 January, 0.4 ∘ grid), Foehn at 1 km and the 1 km estimates (GHAP, made after the fact, not a forecast), with the measurements of that day at the stations in the same colours. Numbers, root-mean-square error (RMSE) over 2022 at the stations of each basin, 1 day ahead, on identical station-days. Aurora and the error against the estimates in four regions are shown in Extended Data Fig. 5 .
Fig. 4: Each member of Foehn’s ensemble keeps the sharp structure of a haze episode that the operational forecasts smooth away. Daily PM 2.5 on 25 January 2022, the peak of the haze over the North China Plain. a – g , The 1 km estimates ( a ) and the forecasts issued 1 day ahead: three of Foehn’s 16 members ( b – d ), Foehn’s ensemble mean ( e ) and the CAMS ( f ) and Aurora ( g ) forecasts issued at the same time, on their 0.4 ∘ grid. h , Variance per decade of wavelength of each field over the panel area (radially averaged power spectrum). i – o , p , The same, issued 5 days ahead. q – t , Probability of exceeding 75 µg m -3 (WHO 24-h interim target 1) from Foehn’s 16 members, issued 7, 5, 3 and 1 days ahead; black contour, 75 µg m -3 in the estimates. u , Daily mean (UTC day) of the measurements at the 12 monitors of the China National Environmental Monitoring Centre (CNEMC) in central Beijing in January 2022 (circles), GHAP at their grid cells (grey dotted) and the forecasts issued 1 day earlier: Foehn’s 16 members (band, minimum to maximum; line, ensemble mean) and the CAMS forecast issued at the same time (black); light blue dashed, Foehn’s ensemble mean issued 3 days earlier.
Fig. 5: The computed transport traces a dust episode to its origin, and its gain fades as the start day loses influence. a – d , GHAP daily PM 2.5 at 1 km over the central Sahel on 13–16 May 2022 and, on each of the first 3 days, where the air reaching Kano (star) on 16 May was then (black dots), from the FLEXGREEN Green’s functions of the forecasts started on 13 ( a ), 14 ( b ) and 15 May ( c ). e – g , Foehn’s probability of PM 2.5 above 100 µg m -3 on 16 May at 1 km, from its 16 members, in the forecasts issued 3 ( e ), 2 ( f ) and 1 day ( g ) before; compare with d . h – j , Why the gain of the computed transport fades with lead time (all land, 2022). h , Where the air arriving on the target day was on the start day: in the mixed layer (blue) or higher up or farther back (pink), by lead time. i , The same share 3 days ahead, place by place: where the start day still matters. j , Reduction of the continuous ranked probability score (CRPS) against the 1 km estimates brought by the computed transport: violins, for each start day; dots and bars, over all forecasts, with 95% intervals.
Fig. 6: Five days ahead, Foehn places the smoke of the 2022 Gironde fires over a bird reserve. The La Teste-de-Buch and Landiras fires, which started on 12 July 2022, burnt about 18,000 hectares in the Gironde that month 52 ; the La Teste fire burnt beside the Réserve Ornithologique du Teich (open circle), a bird reserve on the Arcachon basin; star, Bordeaux. a , GHAP daily PM 2.5 at 1 km on 18 July, the smokiest day at the reserve; triangles, the fire cells of the day in the Global Fire Assimilation System (GFAS); circles, the European Environment Agency (EEA) stations, coloured by their measurement. b – e , Foehn’s probability of PM 2.5 above 25 µg m -3 (WHO interim target 4) on 18 July, from its 16 members, issued 7 ( b , 11 July, before the fires ignited), 6 ( c ), 5 ( d ) and 1 day ( e ) before; triangles, the fire cells in the inputs of each forecast; black contour, 25 µg m -3 in GHAP on 18 July. f , GHAP daily PM 2.5 over the 20 km surroundings of the reserve, 13–26 July (shading, days with fire cells over the two fires; dashed, 25 µg m -3 ). g , Foehn’s probability of exceeding 25 µg m -3 over the same surroundings by target day (columns) and lead time (rows); numbers, probabilities of 0.19 and above; grey, no forecast in this evaluation. h , The 16 members over the same surroundings for 18 July, by lead time (bars, ensemble mean; dotted, GHAP; dashed, 25 µg m -3 ).
Extended Data Fig. 1: Over Europe, Foehn is 26 times faster than Aurora, with a 35% lower error at 1 km. a , Power of the forecast error relative to the power of the GHAP anomaly, by wavelength, at 0.25 ∘ over central Europe (61 start days of 2022, three days ahead): below one, skill at that wavelength; at one, no skill; above one, structure in the wrong place. b , The same at 1 km on the regional window from Paris to Florence, for the models trained natively at 1 km and for the continental 0.25 ∘ models interpolated to 1 km. c , RMSE at 1 km (mean over leads one to four days, Europe 2022) against the time to produce one member of one forecast on one MI250X compute die; the marker area is the peak GPU memory. Foehn is 26 times faster than Aurora with 35% lower error; the inset enlarges the boxed region.
Extended Data Fig. 2: Over Europe, Foehn’s network is more accurate than five networks retrained with identical inputs, the CAMS forecast and Aurora. Root-mean-square error of the forecasts of 2022 against the 0.25 ∘ block means ( a ), the 1 km pixels ( b ) and 2,971 European Environment Agency stations ( c ), and critical success index of exceedances of 25 µg m -3 ( d ), versus lead time: Foehn’s flow-matching network (its 0.25 ∘ European version) with and without the learned transport layer, ConvLSTM, Earthformer, SimVP, TopoFlow and ClimaX retrained with identical inputs, the CAMS operational forecast, Aurora and climatology. Means over three seeds.
Extended Data Fig. 3: Over Europe, Foehn scores better than each other system in 319 of 324 comparisons, on all days, polluted days and transported episodes. Scorecard of the change of Foehn’s score relative to each system (rows), for the root-mean-square error (RMSE), the continuous ranked probability score (CRPS; absolute error for point forecasts) and the critical success index of exceedances of 25 µg m -3 (CSI, sign reversed so that blue always means Foehn better), one to four days ahead, over Europe in 2022 at 0.25 ∘ : on all days (left), on the 10% of days with the largest polluted area (centre) and during the four documented transported episodes (right). Means over three seeds; Foehn is better in 319 of the 324 cells, and the five others are within 2%. Systems as in Extended Data Fig. 2 .
Extended Data Fig. 4: Coarse grids hide whole cities from warnings, and Foehn’s kilometre-scale forecasts detect local extremes earlier and with more value. a – c , Cairo on 2 January 2022 and d – f , Santiago de Chile on 20 June 2022, the largest hidden city-days of Africa and of the Americas among twenty large cities fixed in advance (Methods), as in Fig. 2 b–d: GHAP at 1 km with the contour of 75 µg m -3 , the same field on 40 km cells, and the residents above 75 µg m -3 seen (grey) or hidden (pink) by the 40 km cells. Around Cairo, 16.6 million residents were above the threshold and every one of them hidden; around Santiago, 5.8 million, all hidden, the basin of the city averaged with the surrounding slopes of the Andes and the coastal range. g , h , Detection of local extremes over land in 2022, the days above the local 99th percentile of 2017–2020: symmetric extremal dependence index (SEDI) by lead time ( g ; the CAMS and Aurora forecasts cover 4 days) and by region 1 day ahead ( h ), for Foehn’s ensemble mean and the CAMS and Aurora 4 forecasts issued at the same time. i , j , Retrospective potential relative economic value of warnings of days above the local 95th ( i ) and 99th ( j ) percentiles at the monitoring stations, against the ratio of the cost of protection to the loss avoided, 1 day (solid) and 3 days ahead (dashed).
Extended Data Fig. 5: On 21 January 2022, Foehn resolves at 1 km the structure of four polluted regions that the 0.4 ∘ forecasts blur. Daily mean PM 2.5 on 21 January 2022 over the North China Plain, the Indo-Gangetic Plain around Delhi, the Po Valley, and Seoul and the Han basin (regions chosen before the comparison): the 1 km estimates (first column), the CAMS forecast and Aurora issued at 00 UTC on 21 January (0.4 ∘ ), Foehn’s ensemble mean issued at the end of 20 January (1 km), and Foehn minus the reference. Each row has its own colour range (2nd–98th percentiles of the reference). Numbers: mean absolute error (MAE, µg m -3 ) and spatial correlation against the reference over the land pixels of the panel, the 0.4 ∘ forecasts read at the 1 km pixels.
Extended Data Fig. 6: At the stations of six official networks, Foehn’s error 4 days ahead is 12% lower than that of the CAMS forecast and 17% lower than Aurora’s. a – f , Root-mean-square error (RMSE) of the daily PM 2.5 forecasts of 2022 by lead time at the stations of each official network, on identical station-days: Foehn (ensemble mean at the 1 km pixel of the station), the CAMS forecast and Aurora issued at the same time (end of the start day), and the climatology of the 1 km estimates at the station pixel (grey dashed; Methods); the bias of Foehn, CAMS and Aurora one day ahead is written in each panel (µg m -3 ). Read at the station pixel on the same day, the 1 km estimates themselves have an RMSE of 2.4 ( a ), 2.6 ( b ), 11.2 ( c ), 8.5 ( d ), 6.6 ( e ) and 36.5 µg m -3 ( f ; Methods). Over all stations, Foehn’s RMSE four days ahead is 14.4 µg m -3 , against 16.4 for the CAMS forecast and 17.3 for Aurora, 12% (95% interval 7–19%) and 17% (13–22%) lower. g , All 6,324 stations: Foehn read at its 1 km pixel and averaged to 0.25 ∘ and 0.5 ∘ before being read like the baselines (equal resolution); averaged to 0.5 ∘ , its error one day ahead is 13.5 µg m -3 . h , Ratio of the ensemble spread to the RMSE of the ensemble mean by lead time: the 1 km model on the validation year 2021 against the 1 km estimates (four members, every eighth start day), after (solid) and before (dashed) the CRPS training, and Foehn trained in Aurora’s protocol on May–November 2022 against the CAMS analysis (eight members); 1 for a calibrated ensemble.
Extended Data Fig. 7: Trained in Aurora’s own setup, Foehn’s design has a lower error than Aurora 3 and 5 days ahead, with 131 times fewer parameters. Foehn-CAMS has Foehn’s design (computed transport, learned tracers, flow-matching network; 9.9 million parameters) but is trained on the 0.4 ∘ CAMS analyses with the inputs of Aurora’s air-pollution model (1.3 billion parameters) and forecasts the instantaneous near-surface PM 2.5 every 12 h up to five days. a , Forecasts initialized at 00 UTC on 1 September 2022, one and five days ahead: Foehn-CAMS (ensemble mean of eight members), Aurora run from the same analyses, the operational CAMS forecast, and the CAMS analysis, the truth of the benchmark; shown over land, scored over the whole domain (84 ∘ N–60 ∘ S; numbers: latitude-weighted RMSE of each map, µg m -3 ). b , Latitude-weighted RMSE (top) and continuous ranked probability score (bottom) against the CAMS analysis by lead time, for the forecasts initialized at 00 UTC from May to November 2022 (214 initializations) and valid at 00 UTC, over the whole domain and four continents. The CRPS of Foehn-CAMS is the fair CRPS of its eight members; for the deterministic Aurora and CAMS forecasts it reduces to the absolute error. Grey dashed, climatology: the CAMS analyses of 2018–2021 at the same hour within 15 days of the calendar day (their mean for the RMSE, the 124 of them as an ensemble for the CRPS). Insets, the RMSE three to five days ahead. Six regions at 12-hour steps, with the intervals of the differences, are in Extended Data Fig. 8 .
Extended Data Fig. 8: In Aurora’s setup, Foehn’s error 3 days ahead is lower than Aurora’s over 79% of the Earth’s surface and about half of the land. a – f , Near-surface PM 2.5 on 4 September 2022 at 00 UTC forecast three days earlier, over six regions: the CAMS analysis (truth), Foehn-CAMS (ensemble mean), Aurora and the CAMS forecast, shown over land, with the latitude-weighted RMSE of each map over the region (µg m -3 ); right, the latitude-weighted RMSE of the region by lead time at 12-hour steps over May–November 2022 (214 initializations), with the climatology of the CAMS analyses of 2018–2021 (grey dashed), and beside it the days three to five (shaded) enlarged, with the change of Foehn-CAMS’s RMSE relative to Aurora three days ahead and its 95% interval (7-day moving-block bootstrap over initializations; blue when the interval excludes zero). Three days ahead, Foehn-CAMS’s error is lower than Aurora’s over 79% of the Earth’s surface but over about half of the land area.
Extended Data Fig. 9: The computed transport adds skill at short lead times, and the emissions taken up along the way add it at longer ones. a – f , Gain in the accuracy of the ensemble mean (reduction of the root-mean-square error, RMSE, against the 1 km estimates, on identical 0.25 ∘ land cells and days of 2022) brought by the computed transport (blue: the base model relative to the same network trained without the transport inputs) and by the emissions taken up along the back-trajectories (red: the model with the six anthropogenic emission channels relative to the base model trained without them), by lead time, in six of the nine regions of the evaluation (the other three in Methods); shading, 95% intervals (paired moving-block bootstrap over start days); the background marks which contribution gains more, and the dotted line the lead time at which the emissions overtake the transport (East Asia, 3.9 days; South America, 3.8 days). g – i , The RMSE itself, by lead time, for the base model and the model with emissions, in Europe, North America and East Asia. j , Ratio of the ensemble spread to the RMSE of the ensemble mean over all regions together, by lead time, for the two models. Both comparisons are between models before the calibration training (Methods).
Extended Data Fig. 10: Over Europe, a network trained at 1 km and applied tile by tile leaves seams that Foehn’s tile-free network avoids. One-day forecast of PM 2.5 at 1 km: the 1 km estimates, the target ( a ), Earthformer trained at 1 km and applied tile by tile ( b ) and the tile-free flow-matching network of Foehn ( c ); arrows mark tile edges, and the root-mean-square error of each forecast is shown. d , Mean jump of the forecast across tile edges divided by the jump elsewhere, over Europe (1, no seam).
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