pith. the verified trust layer for science. sign in

arxiv: 2604.16238 · v1 · submitted 2026-04-17 · 💻 cs.LG · physics.ao-ph· stat.ML

Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction

Hannah Guan , Soukayna Mouatadid , Paulo Orenstein , Judah Cohen , Haiyu Dong , Zekun Ni , Jeremy Berman , Genevieve Flaspohler
show 5 more authors
Alex Lu Jakob Schloer Joshua Talib Jonathan A. Weyn Lester Mackey
This is my paper

Pith reviewed 2026-05-10 08:20 UTC · model grok-4.3

classification 💻 cs.LG physics.ao-phstat.ML
keywords probabilistic bias correctionsubseasonal forecastingAI weather modelsdynamical weather modelsforecast skillextreme event predictionmachine learning meteorologybias correction
0
0 comments X p. Extension

The pith

Probabilistic bias correction doubles the subseasonal skill of AI weather forecasts and improves dynamical models for over 90 percent of key targets, winning an international competition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents probabilistic bias correction as a machine learning method that learns to fix systematic errors by studying historical probabilistic forecasts. Subseasonal forecasts from two to six weeks ahead lose accuracy quickly due to biases, limiting their use for planning crops, energy, and disaster response. Applying the method to top ECMWF models doubles the skill of their AI system and raises the dynamical model's performance on 91 percent of pressure targets, 92 percent of temperature targets, and 98 percent of precipitation targets. These improvements produced first-place results in ECMWF's 2025 real-time global forecasting competition across all variables and lead times. The gains support better extreme-event prediction and practical decisions in agriculture, energy, and emergency management.

Core claim

Probabilistic bias correction is a machine learning framework that reduces systematic error in subseasonal forecasts by learning corrections from historical probabilistic forecasts. When applied to the leading dynamical and AI models from ECMWF, it doubles the subseasonal skill of the AI Forecasting System and improves the operationally-debiased dynamical model for 91 percent of pressure, 92 percent of temperature, and 98 percent of precipitation targets. In ECMWF's 2025 real-time forecasting competition, the corrected forecasts placed first for all weather variables and lead times, outperforming dynamical models from six centers, an international multi-model ensemble, the AI Forecasting

What carries the argument

Probabilistic bias correction (PBC), a machine learning framework that learns to correct systematic biases by analyzing historical probabilistic forecasts and applying those adjustments to new predictions.

If this is right

  • More accurate prediction of extreme weather events at 2- to 6-week leads.
  • Improved agricultural planning and water allocation based on extended-range outlooks.
  • Better energy management and disaster preparedness in vulnerable communities.
  • Operational deployment of the corrected forecasts in real-time systems.
  • Outperformance relative to multi-model ensembles and other forecasting teams.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method may extend to other domains where historical probabilistic outputs can inform bias fixes, such as seasonal climate or hydrological forecasts.
  • It highlights that machine learning can complement rather than replace dynamical models by targeting their persistent error patterns.
  • Future tests on longer lead times or different model ensembles could reveal whether the gains hold when forecast uncertainty grows further.
  • Combining PBC with additional ensemble information might yield even sharper improvements in tail-event probabilities.

Load-bearing premise

Corrections learned from historical probabilistic forecasts will generalize to future unseen forecasts without overfitting or introducing new biases at subseasonal lead times.

What would settle it

A new independent test set of subseasonal forecasts where PBC-corrected versions show lower skill than the uncorrected AI or dynamical models for a majority of targets.

read the original abstract

Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in physics-based dynamical models and data-driven artificial intelligence (AI) models. However, model skill drops precipitously at subseasonal timescales (2 - 6 weeks ahead), due to compounding errors and persistent biases. To counter this degradation, we introduce probabilistic bias correction (PBC), a machine learning framework that substantially reduces systematic error by learning to correct historical probabilistic forecasts. When applied to the leading dynamical and AI models from the European Centre for Medium-Range Weather Forecasts (ECMWF), PBC doubles the subseasonal skill of the AI Forecasting System and improves the skill of the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. We designed PBC for operational deployment, and, in ECMWF's 2025 real-time forecasting competition, its global forecasts placed first for all weather variables and lead times, outperforming the dynamical models from six operational forecasting centers, an international dynamical multi-model ensemble, ECMWF's AI Forecasting System, and the forecasting systems of 34 teams worldwide. These probabilistic skill gains translate into more accurate prediction of extreme events and have the potential to improve agricultural planning, energy management, and disaster preparedness in vulnerable communities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript introduces Probabilistic Bias Correction (PBC), a machine learning framework that learns to correct systematic biases from historical probabilistic forecasts. Applied to ECMWF dynamical and AI subseasonal models, PBC is reported to double the skill of the AI Forecasting System and improve the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. The method was deployed in ECMWF's 2025 real-time forecasting competition, where the resulting global forecasts ranked first across all variables and lead times, outperforming dynamical models from six centers, a multi-model ensemble, the ECMWF AI system, and 34 other teams.

Significance. If the performance claims hold, the work is significant for operational meteorology. Subseasonal forecasting remains a low-skill regime critical for agriculture, energy, and disaster preparedness; a generalizable bias-correction approach that improves both physics-based and AI models, enhances extreme-event prediction, and succeeds in a blind real-time competition supplies strong evidence of practical utility. The use of an independent competition as out-of-sample validation is a notable strength.

minor comments (3)
  1. Abstract: the claim that PBC 'doubles the subseasonal skill' of the AI system should explicitly name the skill metric (e.g., CRPSS, ACC) and the exact baseline value against which the doubling is measured.
  2. Results: the reported improvement percentages (91%, 92%, 98%) would benefit from accompanying sample sizes, definitions of 'targets,' and statistical significance or confidence intervals to allow readers to gauge robustness.
  3. Methods: while the supervised learning setup appears standard, a concise description of the PBC model architecture, input features, training period, and any regularization used would aid reproducibility without altering the central claims.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately reflects the core contributions of Probabilistic Bias Correction (PBC) in improving both ECMWF dynamical and AI subseasonal forecasts, with notable gains in skill and its first-place performance in the 2025 real-time competition. We appreciate the recognition of the work's significance for operational meteorology and the value of the independent competition as out-of-sample validation.

Circularity Check

0 steps flagged

No significant circularity detected in derivation or claims

full rationale

The paper presents PBC as a supervised machine-learning bias-correction framework trained on historical probabilistic forecasts and evaluated on independent future periods, including a real-time 2025 ECMWF competition. No equations or method steps reduce the reported skill gains to fitted parameters by construction, self-referential definitions, or load-bearing self-citations. The central results (doubling AI skill, 91-98% target improvements, first-place competition ranking) rest on standard out-of-sample verification rather than tautological renaming or imported uniqueness theorems. This is a normal non-circular empirical ML paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on the assumption that systematic biases in probabilistic forecasts are learnable from historical data and transferable to future forecasts.

axioms (1)
  • domain assumption Historical probabilistic forecasts contain systematic biases that can be corrected by machine learning without introducing new errors at subseasonal leads.
    Core premise of the PBC framework as described in the abstract.

pith-pipeline@v0.9.0 · 5609 in / 1132 out tokens · 74854 ms · 2026-05-10T08:20:13.841874+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references · 23 canonical work pages

  1. [1]

    URL https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/ met.1654

    White, C.J., Carlsen, H., Robertson, A.W., Klein, R.J.T., Lazo, J.K., Kumar, A., Vitart, F., Perez, E., Ray, A.J., Murray, V ., Bharwani, S., MacLeod, D., James, R., Fleming, L., Morse, A.P., Eggen, B., Graham, R., Kjellström, E., Becker, E., Pegion, K.V ., Holbrook, N.J., McEvoy, D., Depledge, M., Perkins-Kirkpatrick, S., Brown, T.J., Street, R., Jones, ...

    work page doi:10.1002/met.1654 2017

  2. [2]

    npj Climate Atmos

    Vitart, F., Robertson, A.: The sub-seasonal to seasonal prediction project (S2S) and the prediction of extreme events. npj Climate Atmos. Sci., 1, 3 (2018)

    2018

  3. [3]

    Bulletin of the American Meteorological Society101(6), 869–896 (2020) https://doi.org/10.1175/BAMS-D-19-0037.1

    Merryfield, W.J., Baehr, J., Batté, L., Becker, E.J., Butler, A.H., Coelho, C.A.S., Danabasoglu, G., Dirmeyer, P.A., Doblas-Reyes, F.J., Domeisen, D.I.V ., Ferranti, L., Ilynia, T., Kumar, A., Müller, W.A., Rixen, M., Robertson, A.W., Smith, D.M., Takaya, Y ., Tuma, M., Vitart, F., White, C.J., Alvarez, M.S., Ardilouze, C., Attard, H., Baggett, C., Balmas...

    work page doi:10.1175/bams-d-19-0037.1 2020

  4. [4]

    Nature525(7567), 47–55 (2015)

    Bauer, P., Thorpe, A., Brunet, G.: The quiet revolution of numerical weather prediction. Nature525(7567), 47–55 (2015)

    2015

  5. [5]

    Bulletin of the American Meteorological Society105(6), 864–883 (2024) https://doi.org/10.1175/BAMS-D-23-0162.1

    Ben Bouallègue, Z., Clare, M.C.A., Magnusson, L., Gascón, E., Maier-Gerber, M., Janousek, M., Rodwell, M., Pinault, F., Dramsch, J.S., Lang, S.T.K., Raoult, B., Rabier, F., Chevallier, M., Sandu, I., Dueben, P., Chantry, M., Pappenberger, F.: The rise of data-driven weather forecasting: A first statistical assessment of machine learning– based weather for...

    work page doi:10.1175/bams-d-23-0162.1 2024

  6. [6]

    Nature619(7970), 533–538 (2023)

    Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., Tian, Q.: Accurate medium-range global weather forecasting with 3d neural networks. Nature619(7970), 533–538 (2023)

    2023

  7. [7]

    Learning skillful medium-range global weather forecasting

    Lam, R., Sanchez-Gonzalez, A., Willson, M., Wirnsberger, P., Fortunato, M., Alet, F., Ravuri, S., Ewalds, T., Eaton-Rosen, Z., Hu, W., Merose, A., Hoyer, S., Holland, G., Vinyals, O., Stott, J., Pritzel, A., Mohamed, S., Battaglia, P.: Learning skillful medium-range global weather forecasting. Science382(6677), 1416–1421 (2023) https://doi.org/10.1126/sci...

    work page doi:10.1126/science.adi2336 2023

  8. [8]

    Nature641, 1180–1187 (2025) https://doi.org/10

    Bodnar, C., Bruinsma, W.P., Lucic, A., Stanley, M., Allen, A., Brandstetter, J., Garvan, P., Riechert, M., Weyn, J.A., Dong, H., Gupta, J.K., Thambiratnam, K., Archibald, A.T., Wu, C.-C., Heider, E., Welling, M., Turner, R.E., Perdikaris, P.: A foundation model for the Earth system. Nature641, 1180–1187 (2025) https://doi.org/10. 1038/s41586-025-09005-y

    2025

  9. [9]

    npj Climate and Atmospheric Science6(1), 190 (2023)

    Chen, L., Zhong, X., Zhang, F., Cheng, Y ., Xu, Y ., Qi, Y ., Li, H.: Fuxi: a cascade machine learning forecasting system for 15-day global weather forecast. npj Climate and Atmospheric Science6(1), 190 (2023)

    2023

  10. [10]

    WeatherBench 2: A benchmark for the next generation of data-driven global weather models.J

    Rasp, S., Hoyer, S., Merose, A., Langmore, I., Battaglia, P., Russell, T., Sanchez-Gonzalez, A., Yang, V ., Carver, R., Agrawal, S., Chantry, M., Ben Bouallegue, Z., Dueben, P., Bromberg, C., Sisk, J., Barrington, L., Bell, A., Sha, F.: Weatherbench 2: A benchmark for the next generation of data-driven global weather models. Journal of Advances in Modelin...

    work page doi:10.1029/2023ms004019 2023

  11. [11]

    Nature Communications15(1), 6425 (2024) https://doi.org/10.1038/s41467-024-50714-1

    Chen, L., Zhong, X., Li, H., Wu, J., Lu, B., Chen, D., Xie, S.-P., Wu, L., Chao, Q., Lin, C., Hu, Z., Qi, Y .: A machine learning model that outperforms conventional global subseasonal forecast models. Nature Communications15(1), 6425 (2024) https://doi.org/10.1038/s41467-024-50714-1

    work page doi:10.1038/s41467-024-50714-1 2024

  12. [12]

    Advances in Neural Information Processing Systems37, 43715–43729 (2024)

    Nathaniel, J., Qu, Y ., Nguyen, T., Yu, S., Busecke, J., Grover, A., Gentine, P.: Chaosbench: A multi-channel, physics-based benchmark for subseasonal-to-seasonal climate prediction. Advances in Neural Information Processing Systems37, 43715–43729 (2024)

    2024

  13. [13]

    Bulletin of the World Meteorological Organization61(2), 23 (2012)

    Vitart, F., Robertson, A.W., Anderson, D.L.: Subseasonal to seasonal prediction project: Bridging the gap between weather and climate. Bulletin of the World Meteorological Organization61(2), 23 (2012)

    2012

  14. [14]

    Eos106(2025) https://doi.org/10.1029/2025EO250389

    Richter, J.H., Joseph, E.: Scientists must join forces to solve forecasting’s predictability desert. Eos106(2025) https://doi.org/10.1029/2025EO250389

    work page doi:10.1029/2025eo250389 2025

  15. [15]

    In preparation (2026)

    Schloer, J., Tietsche, S., Roberts, C., Vitart, F.: AIFS-SUBS: Adapting the AIFS for Sub-Seasonal Prediction. In preparation (2026)

    2026

  16. [16]

    part i: Effect on deterministic forecasts

    Tuppi, L., Ekblom, M., Ollinaho, P., Järvinen, H.: Simultaneous optimization of 20 key parameters of the inte- grated forecasting system of ecmwf using openifs. part i: Effect on deterministic forecasts. Monthly weather review151(6), 1325–1346 (2023)

    2023

  17. [17]

    Machine Learning: Earth1(1), 010701 (2025) https://doi.org/10.1088/ 3049-4753/adf649 15

    Loegel, O., Talib, J., Vitart, F., Hoffmann, J., Chantry, M.: The ai weather quest: an international competi- tion for sub-seasonal forecasting with ai. Machine Learning: Earth1(1), 010701 (2025) https://doi.org/10.1088/ 3049-4753/adf649 15

    2025

  18. [18]

    Proceedings of the National Academy of Sciences123(16), 2523372123 (2026) https://doi.org/10.1073/pnas.2523372123 https://www.pnas.org/doi/pdf/10.1073/pnas.2523372123

    Shrader, J.G., Thies, S., Bakkensen, L., Linsenmeier, M., Lemoine, D.: Weather forecasts become more important for reducing mortality as the climate warms. Proceedings of the National Academy of Sciences123(16), 2523372123 (2026) https://doi.org/10.1073/pnas.2523372123 https://www.pnas.org/doi/pdf/10.1073/pnas.2523372123

    work page doi:10.1073/pnas.2523372123 2026

  19. [19]

    Journal of the Atmospheric Sciences20(2), 130–141 (1963)

    Lorenz, E.N.: Deterministic nonperiodic flow. Journal of the Atmospheric Sciences20(2), 130–141 (1963)

    1963

  20. [20]

    Tellus21(3), 289–307 (1969)

    Lorenz, E.N.: The predictability of a flow which possesses many scales of motion. Tellus21(3), 289–307 (1969)

    1969

  21. [21]

    Science310(5746), 248–249 (2005)

    Gneiting, T., Raftery, A.E.: Weather forecasting with ensemble methods. Science310(5746), 248–249 (2005)

    2005

  22. [22]

    Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, applied meteorology and physical oceanography128(581), 747–774 (2002)

    Palmer, T.N.: The economic value of ensemble forecasts as a tool for risk assessment: From days to decades. Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, applied meteorology and physical oceanography128(581), 747–774 (2002)

    2002

  23. [23]

    Weather81(3), 82–88 (2026)

    Mylne, K.: Probability forecasts–part 1: ensembles and probabilistic forecasts. Weather81(3), 82–88 (2026)

    2026

  24. [24]

    Quarterly Journal of the Royal Meteorological Society145, 12–24 (2019)

    Palmer, T.: The ECMWF ensemble prediction system: Looking back (more than) 25 years and projecting forward 25 years. Quarterly Journal of the Royal Meteorological Society145, 12–24 (2019)

    2019

  25. [25]

    Probabilistic weather forecasting with machine learning

    Price, I., Sanchez-Gonzalez, A., Alet, F., Andersson, T.R., El-Kadi, A., Masters, D., Ewalds, T., Stott, J., Mohamed, S., Battaglia, P., Lam, R., Willson, M.: Probabilistic weather forecasting with machine learning. Nature637, 84–90 (2025) https://doi.org/10.1038/s41586-024-08252-9

    work page doi:10.1038/s41586-024-08252-9 2025

  26. [26]

    Journal of Geophysical Research: Atmospheres 115(D24) (2010)

    Stephens, G.L., L’Ecuyer, T., Forbes, R., Gettelmen, A., Golaz, J.-C., Bodas-Salcedo, A., Suzuki, K., Gabriel, P., Haynes, J.: Dreary state of precipitation in global models. Journal of Geophysical Research: Atmospheres 115(D24) (2010)

    2010

  27. [27]

    Nature Communications14(1) (2023) https://doi.org/10.1038/ s41467-023-38874-y

    Mouatadid, S., Orenstein, P., Flaspohler, G., Cohen, J., Oprescu, M., Fraenkel, E., Mackey, L.: Adaptive bias correction for improved subseasonal forecasting. Nature Communications14(1) (2023) https://doi.org/10.1038/ s41467-023-38874-y

    2023

  28. [28]

    Monthly Weather Review135(1), 118–124 (2007) https://doi.org/10.1175/MWR3280.1

    Weigel, A.P., Liniger, M.A., Appenzeller, C.: The discrete brier and ranked probability skill scores. Monthly Weather Review135(1), 118–124 (2007) https://doi.org/10.1175/MWR3280.1

    work page doi:10.1175/mwr3280.1 2007

  29. [29]

    Artificial Intelligence for the Earth Systems 3(1), 230027 (2024) https://doi.org/10.1175/AIES-D-23-0027.1

    Bouallègue, Z.B., Weyn, J.A., Clare, M.C.A., Dramsch, J., Dueben, P., Chantry, M.: Improving medium-range ensemble weather forecasts with hierarchical ensemble transformers. Artificial Intelligence for the Earth Systems 3(1), 230027 (2024) https://doi.org/10.1175/AIES-D-23-0027.1

    work page doi:10.1175/aies-d-23-0027.1 2024

  30. [30]

    Daniels, M

    Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., De Chiara, G., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., ...

    work page doi:10.1002/qj.3803 1999

  31. [31]

    Climate Dynamics52(9), 5451–5475 (2019)

    Andrade, F.M., Coelho, C.A.S., Cavalcanti, I.F.A.: Global precipitation hindcast quality assessment of the subseasonal to seasonal (s2s) prediction project models. Climate Dynamics52(9), 5451–5475 (2019)

    2019

  32. [32]

    Domeisen, D.I.V ., White, C.J., Afargan-Gerstman, H., G. Muñoz, Janiga, M.A., Vitart, F., Wulff, C.O., Antoine, S., Ardilouze, C., Batté, L., Bloomfield, H.C., Brayshaw, D.J., Camargo, S.J., Charlton-Pérez, A., Collins, D., Cowan, T., Mar Chaves, M., Ferranti, L., Gómez, R., González, P.L.M., Romero, C.G., Infanti, J.M., Karozis, S., Kim, H., Kolstad, E.W...

    work page doi:10.1175/bams-d-20-0221.1 2022

  33. [33]

    https://web.archive.org/web/20260222173505/ https://confluence.ecmwf.int/display/FUG/Section+5.3.2+SUBS-M-climate%2C+the+sub-seasonal+model+ climate

    ECMWF: SUBS-M-climate, the sub-seasonal model climate. https://web.archive.org/web/20260222173505/ https://confluence.ecmwf.int/display/FUG/Section+5.3.2+SUBS-M-climate%2C+the+sub-seasonal+model+ climate. Accessed: 2026-02-22

    work page arXiv 2026

  34. [34]

    Quarterly Journal of the Royal Meteorological Society141(688), 807–818 (2015)

    Van Schaeybroeck, B., Vannitsem, S.: Ensemble post-processing using member-by-member approaches: Theoretical aspects. Quarterly Journal of the Royal Meteorological Society141(688), 807–818 (2015)

    2015

  35. [35]

    ECMWF Newsletter164, 28–33 (2020) https://doi.org/10.21957/vb78ui92dj

    Vannitsem, S., Demaeyer, J.: Statistical post-processing of ensemble forecasts at the belgian met service. ECMWF Newsletter164, 28–33 (2020) https://doi.org/10.21957/vb78ui92dj

    work page doi:10.21957/vb78ui92dj 2020

  36. [36]

    doi:10.1175/MWR2904.1

    Gneiting, T., Raftery, A.E., Westveld, A.H., Goldman, T.: Calibrated probabilistic forecasting using ensemble model output statistics and minimum crps estimation. Monthly Weather Review133(5), 1098–1118 (2005) https: //doi.org/10.1175/MWR2904.1

    work page doi:10.1175/mwr2904.1 2005

  37. [37]

    Journal of Hydrology , author =

    Li, W., Pan, B., Xia, J., Duan, Q.: Convolutional neural network-based statistical post-processing of ensemble precipitation forecasts. Journal of Hydrology605, 127301 (2022) https://doi.org/10.1016/j.jhydrol.2021.127301

    work page doi:10.1016/j.jhydrol.2021.127301 2022

  38. [38]

    arXiv preprint arXiv:2106.13924 (2021)

    Finn, T.S.: Self-attentive ensemble transformer: Representing ensemble interactions in neural networks for earth system models. arXiv preprint arXiv:2106.13924 (2021)

    work page arXiv 2021

  39. [39]

    Accessed: 2026-04-15 (2026)

    European Centre for Medium-Range Weather Forecasts (ECMWF): AI Weather Quest Leaderboards. Accessed: 2026-04-15 (2026). https://aiweatherquest.ecmwf.int/leaderboards/

    2026

  40. [40]

    ECMWF Science Blog (2026)

    Talib, J., Loegel, O., Vitart, F., Hoffmann, J., Schloer, J.: The AI Weather Quest: spotlighting the best of machine learning sub-seasonal prediction. ECMWF Science Blog (2026). https://doi.org/10.21957/0fddea4898 . https: //www.ecmwf.int/en/about/media-centre/science-blog/2026/ai-weather-quest-2026

    work page doi:10.21957/0fddea4898 2026

  41. [41]

    Khyathi Raghavi Chandu, Linjie Li, Anas Awadalla, Ximing Lu, Jae Sung Park, Jack Hessel, Lijuan Wang, and Yejin Choi

    Brier, G.W.: Verification of forecasts expressed in terms of probability. Monthly Weather Review78(1), 1–3 (1950) https://doi.org/10.1175/1520-0493(1950)078<0001:VOFEIT>2.0.CO;2

    work page doi:10.1175/1520-0493(1950)078 1950

  42. [42]

    In: Proceedings of the 3rd International Conference on Information Systems for Crisis Response and Management (ISCRAM)

    De Groeve, T., Peter, T., Annunziato, A., Vernaccini, L.: Global disaster alert and coordination system. In: Proceedings of the 3rd International Conference on Information Systems for Crisis Response and Management (ISCRAM). ISCRAM, Newark, NJ, USA (2006)

    2006

  43. [43]

    Bulletin of the American Meteorological Society98(1), 163–173 (2017) https://doi.org/10

    Vitart, F., Ardilouze, C., Bonet, A., Brookshaw, A., Chen, M., Codorean, C., Déqué, M., Ferranti, L., Fucile, E., Fuentes, M., Hendon, H., Hodgson, J., Kang, H.-S., Kumar, A., Lin, H., Liu, G., Liu, X., Malguzzi, P., Mallas, I., Manoussakis, M., Mastrangelo, D., MacLachlan, C., McLean, P., Minami, A., Mladek, R., Nakazawa, T., Najm, S., Nie, Y ., Rixen, M...

    2017

  44. [44]

    https://iridl.ldeo.columbia.edu/SOURCES/ .ECMWF/.S2S/.ECMF/ (2026)

    ECMWF S2S data: ECMWF S2S ECMF: ECMWF Ensemble. https://iridl.ldeo.columbia.edu/SOURCES/ .ECMWF/.S2S/.ECMF/ (2026)

    2026

  45. [45]

    Hugging Face (2025)

    Zhong, X.: FuXi-S2S (Revision f63dc2e). Hugging Face (2025). https://doi.org/10.57967/hf/4277 . https: //huggingface.co/datasets/FudanFuXi/FuXi-S2S

    work page doi:10.57967/hf/4277 2025

  46. [46]

    Aifs–ecmwf’s data-driven forecasting system.arXiv preprint arXiv:2406.01465, 2024

    Lang, S., Alexe, M., Chantry, M., Dramsch, J., Pinault, F., Raoult, B., Clare, M.C.A., Lessig, C., Maier-Gerber, M., Magnusson, L., Bouallègue, Z.B., Nemesio, A.P., Dueben, P.D., Brown, A., Pappenberger, F., Rabier, F.: AIFS - ECMWF’s Data-Driven Forecasting System. arXiv (2024). https://doi.org/10.48550/arXiv.2406.01465

    work page doi:10.48550/arxiv.2406.01465 2024

  47. [47]

    AIFS-CRPS: Ensemble forecasting using a model trained with a loss function based on the Continuous Ranked Probability Score

    Lang, S., Alexe, M., Clare, M.C.A., Roberts, C., Adewoyin, R., Bouallègue, Z.B., Chantry, M., Dramsch, J., Dueben, P.D., Hahner, S., Maciel, P., Prieto-Nemesio, A., O’Brien, C., Pinault, F., Polster, J., Raoult, B., Tietsche, S., Leutbecher, M.: AIFS-CRPS: Ensemble Forecasting Using a Model Trained with a Loss Function Based on the Continuous Ranked Proba...

    work page doi:10.48550/arxiv.2412.15832 2024

  48. [48]

    Mathematical 17 Programming47(1), 425–439 (1990)

    Best, M.J., Chakravarti, N.: Active set algorithms for isotonic regression; a unifying framework. Mathematical 17 Programming47(1), 425–439 (1990)

    1990

  49. [49]

    https://aiweatherquest.ecmwf.int/team/cmaandfdu/

    Lu, B., Li, H., Chen, L., Zhong, X., Wu, J., Zhao, C., Zhou, C., Zhao, Y ., Hu, J., Xin, Y .: CMAandFDU Team Page – AI Weather Quest. https://aiweatherquest.ecmwf.int/team/cmaandfdu/. Accessed: April 14, 2026

    2026

  50. [50]

    https://aiweatherquest.ecmwf.int/team/lp/

    Lu, P.: LP Team Page – AI Weather Quest. https://aiweatherquest.ecmwf.int/team/lp/. Accessed: April 14, 2026 Acknowledgements PO is supported by FAPERJ (Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro) grant SEI-260003/020673/2025. JC is supported by National Science Foundation grant no. AGS-2140909. JS and JT are supported w...

    2026