Articles | Volume 19, issue 17
https://doi.org/10.5194/gmd-19-8167-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-19-8167-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A barycenter-based approach for the multi-model ensembling of subseasonal forecasts
Camille Le Coz
CORRESPONDING AUTHOR
LMD/IPSL, École Polytechnique, Institut Polytechnique de Paris, ENS, PSL Research University, Sorbonne Université, CNRS, Palaiseau, France
Alexis Tantet
LMD/IPSL, École Polytechnique, Institut Polytechnique de Paris, ENS, PSL Research University, Sorbonne Université, CNRS, Palaiseau, France
Rémi Flamary
CMAP, Ecole Polytechnique, Institut Polytechnique de Paris, CNRS, Palaiseau, France
Riwal Plougonven
LMD/IPSL, École Polytechnique, Institut Polytechnique de Paris, ENS, PSL Research University, Sorbonne Université, CNRS, Palaiseau, France
Related authors
No articles found.
Giovanni Biagioli, Alexis Aubel, Riwal Plougonven, and Sandrine Bony
EGUsphere, https://doi.org/10.5194/egusphere-2026-4254, https://doi.org/10.5194/egusphere-2026-4254, 2026
This preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).
Short summary
Short summary
Atmospheric waves produce many effects, such as regularly spaced clouds. One such event was sampled by a research aircraft in a recent campaign, as part of a larger wave collection spanning 500 km. The wave left a clear imprint on wind and temperature measurements. We characterize the waves and explain their surprising extent and persistence: the environment created a waveguide from 5–10 km altitude. We then build an easy-to-calculate metric aggregating factors conducive to waveguide emergence.
Phoebe Noble, Haruka Okui, Joan Alexander, Manfred Ern, Neil P. Hindley, Lars Hoffmann, Laura Holt, Annelize van Niekerk, Riwal Plougonven, Inna Polichtchouk, Claudia C. Stephan, Martina Bramberger, Milena Corcos, William Putnam, Christopher Kruse, and Corwin J. Wright
Atmos. Chem. Phys., 26, 7607–7630, https://doi.org/10.5194/acp-26-7607-2026, https://doi.org/10.5194/acp-26-7607-2026, 2026
Short summary
Short summary
Gravity waves are small-scale processes that drive the circulation in the middle and upper atmosphere. In this work, we assess 3 new high-resolution (3-5km horizontal resolution) models against satellite data. Generally, models capture the spatial patterns and represent stratospheric northern hemisphere mountain generated waves well. However, they still underestimate amplitudes globally and struggle with the representation of southern hemispheric convective waves.
Pierre Cadiou, Riwal Plougonven, Aurélien Podglajen, Albert Hertzog, and Alexandra Mac Farlane
Atmos. Chem. Phys., 26, 1665–1684, https://doi.org/10.5194/acp-26-1665-2026, https://doi.org/10.5194/acp-26-1665-2026, 2026
Short summary
Short summary
Winds in the Equatorial region remain difficult to model. We take advantage of long-duration balloon campaigns from 2019 and 2021 to assess errors in winds between 18 and 20 km in a weather forecast model. Large errors persist: one third of the time, the error is larger than 3.5 m per second. This has implications for research studies that calculate air mass trajectories in this transition region between the troposphere and the stratosphere.
Joan Delort Ylla, Alexis Tantet, and Philippe Drobinski
Adv. Geosci., 65, 159–169, https://doi.org/10.5194/adgeo-65-159-2025, https://doi.org/10.5194/adgeo-65-159-2025, 2025
Short summary
Short summary
Understanding how the electricity generation sector reacts to climate change while large shares of wind and solar energies are introduced is of crucial importance to ensure a clean, secure and affordable electricity provision. We find that in a best case scenario, if we account only for climate change impacts on the wind and solar resource coupled to the demand, then climate change tends to have no adverse economic impacts, while it becomes more interesting to invest in solar than wind energy.
Milena Corcos, Albert Hertzog, Riwal Plougonven, and Aurélien Podglajen
Atmos. Chem. Phys., 23, 6923–6939, https://doi.org/10.5194/acp-23-6923-2023, https://doi.org/10.5194/acp-23-6923-2023, 2023
Short summary
Short summary
The role of gravity waves on tropical cirrus clouds and air-parcel dehydration was studied using the combination of Lagrangian observations of temperature fluctuations from superpressure balloons and a 1.5D model. The inclusion of the gravity waves to a reference simulation of a slow ascent around the cold-point tropopause drastically increases ice-crystal density, cloud fraction, and air-parcel dehydration, and it produces a crystal size distribution that agrees better with observations.
Richard Wilson, Clara Pitois, Aurélien Podglajen, Albert Hertzog, Milena Corcos, and Riwal Plougonven
Atmos. Meas. Tech., 16, 311–330, https://doi.org/10.5194/amt-16-311-2023, https://doi.org/10.5194/amt-16-311-2023, 2023
Short summary
Short summary
Strateole-2 is an French–US initiative designed to study atmospheric events in the tropical upper troposphere–lower stratosphere. In this work, data from several superpressure balloons, capable of staying aloft at an altitude of 18–20 km for over 3 months, were used. The present article describes methods to detect the occurrence of atmospheric turbulence – one efficient process impacting the properties of the atmosphere composition via stirring and mixing.
Cameron Bertossa, Peter Hitchcock, Arthur DeGaetano, and Riwal Plougonven
EGUsphere, https://doi.org/10.5194/egusphere-2022-601, https://doi.org/10.5194/egusphere-2022-601, 2022
Preprint archived
Short summary
Short summary
This work has identified characteristic spatial and temporal scales for non-Gaussian outbreaks in forecasts, specifically, bimodality. Methodology is introduced which allows one to connect meteorological phenomena to bimodal outbreaks. Large-scale circulation interacting with local processes is uncovered as a frequent ingredient to such outbreaks. These insights not only provide a deeper understanding of the dynamical processes involved, but also have drastic implications for forecast skill.
Cameron Bertossa, Peter Hitchcock, Arthur DeGaetano, and Riwal Plougonven
Weather Clim. Dynam., 2, 1209–1224, https://doi.org/10.5194/wcd-2-1209-2021, https://doi.org/10.5194/wcd-2-1209-2021, 2021
Short summary
Short summary
While the assumption of Gaussianity leads to many simplifications, ensemble forecasts often exhibit non-Gaussian distributions. This work has systematically identified the presence of a specific case of
non-Gaussianity, bimodality. It has been found that bimodality occurs in a large portion of global 2 m temperature forecasts. This has drastic implications on forecast skill as the minimum probability in a bimodal distribution often lies at the maximum probability of a Gaussian distribution.
Cited articles
Agueh, M. and Carlier, G.: Barycenters in the Wasserstein Space, SIAM J. Math. Anal., 43, 904–924, https://doi.org/10.1137/100805741, 2011. a, b
Alessandri, A., Borrelli, A., Navarra, A., Arribas, A., Déqué, M., Rogel, P., and Weisheimer, A.: Evaluation of Probabilistic Quality and Value of the ENSEMBLES Multimodel Seasonal Forecasts: Comparison with DEMETER, Mon. Weather Rev., 139, 581–607, https://doi.org/10.1175/2010MWR3417.1, 2011. a
Backhoff-Veraguas, J., Fontbona, J., Rios, G., and Tobar, F.: Bayesian learning with Wasserstein barycenters*, ESAIM: PS, 26, 436–472, https://doi.org/10.1051/ps/2022015, 2022. a
Becker, E., van den Dool, H., and Zhang, Q.: Predictability and Forecast Skill in NMME, J. Climate, 27, 5891–5906, https://doi.org/10.1175/JCLI-D-13-00597.1, 2014. a
Bertino, L., Evensen, G., and Wackernagel, H.: Sequential Data Assimilation Techniques in Oceanography, Int. Stat. Rev., 71, 223–241, https://doi.org/10.1111/j.1751-5823.2003.tb00194.x, 2003. a
Casanova, S. and Ahrens, B.: On the Weighting of Multimodel Ensembles in Seasonal and Short-Range Weather Forecasting, Mon. Weather Rev., 137, 3811–3822, https://doi.org/10.1175/2009MWR2893.1, 2009. a, b
DelSole, T., Yang, X., and Tippett, M. K.: Is unequal weighting significantly better than equal weighting for multi-model forecasting?, Q. J. Roy. Meteor. Soc., 139, 176–183, https://doi.org/10.1002/qj.1961, 2013. a
Eade, R., Smith, D., Scaife, A., Wallace, E., Dunstone, N., Hermanson, L., and Robinson, N.: Do seasonal-to-decadal climate predictions underestimate the predictability of the real world?, Geophys. Res. Lett., 41, 5620–5628, https://doi.org/10.1002/2014GL061146, 2014. a
Ferrone, A., Mastrangelo, D., and Malguzzi, P.: Multimodel probabilistic prediction of 2 m-temperature anomalies on the monthly timescale, Adv. Sci. Res., 14, 123–129, https://doi.org/10.5194/asr-14-123-2017, 2017. a, b
Flamary, R., Lounici, K., and Ferrari, A.: Concentration bounds for linear Monge mapping estimation and optimal transport domain adaptation, arXiv [preprint], https://arxiv.org/abs/1905.10155 (last access: 12 February 2020), 2020. a
Fortin, V., Abaza, M., Anctil, F., and Turcotte, R.: Why Should Ensemble Spread Match the RMSE of the Ensemble Mean?, J. Hydrometeorol., 15, 1708–1713, https://doi.org/10.1175/JHM-D-14-0008.1, 2014. a
Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs, L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A. M., Gu, W., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S. D., Sienkiewicz, M., and Zhao, B.: The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2), J. Climate, 30, 5419–5454, https://doi.org/10.1175/JCLI-D-16-0758.1, 2017. a
Global Modeling and Assimilation Office (GMAO): MERRA-2 statD_2d_slv_Nx: 2d, Daily, Aggregated Statistics, Single-Level, Assimilation, Single-Level Diagnostics V5.12.4, Greenbelt, MD, USA, Goddard Earth Sciences Data and Information Services Center (GES DISC) [data set], https://doi.org/10.5067/9SC1VNTWGWV3, 2015a. a
Global Modeling and Assimilation Office (GMAO): MERRA-2 inst1_2d_asm_Nx: 2d, 1-Hourly, Instantaneous, Single-Level, Assimilation, Single-Level Diagnostics V5.12.4, Greenbelt, MD, USA, Goddard Earth Sciences Data and Information Services Center (GES DISC) [data set], https://doi.org/10.5067/3Z173KIE2TPD, 2015b. a
Global Modeling and Assimilation Office (GMAO): MERRA-2 inst3_3d_asm_Np: 3d, 3-Hourly, Instantaneous, Pressure-Level, Assimilation, Assimilated Meteorological Fields V5.12.4, Greenbelt, MD, USA, Goddard Earth Sciences Data and Information Services Center (GES DISC) [data set], https://doi.org/10.5067/QBZ6MG944HW0, 2015c. a
Gnassounou, T., Flamary, R., and Gramfort, A.: Convolution Monge Mapping Normalization for learning on sleep data, in: Advances in Neural Information Processing Systems, edited by: Oh, A., Naumann, T., Globerson, A., Saenko, K., Hardt, M., and Levine, S., vol. 36, Curran Associates, Inc., 10457–10476, https://proceedings.neurips.cc/paper_files/paper/2023/file/21718991f6acf19a42376b5c7a8668c5-Paper-Conference.pdf, 2023. a, b
Gneiting, T. and Raftery, A. E.: Strictly Proper Scoring Rules, Prediction, and Estimation, J. Am. Stat. Assoc., 102, 359–378, https://doi.org/10.1198/016214506000001437, 2007. a
Gneiting, T., Raftery, A. E., Westveld, A. H., and Goldman, T.: Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation, Mon. Weather Rev., 133, 1098–1118, https://doi.org/10.1175/MWR2904.1, 2005. a
Gonzalez, P. L. M., Brayshaw, D. J., and Ziel, F.: A new approach to extended-range multimodel forecasting: Sequential learning algorithms, Q. J. Roy. Meteor. Soc., 147, 4269–4282, https://doi.org/10.1002/qj.4177, 2021. a
Goutham, N., Plougonven, R., Omrani, H., Parey, S., Tankov, P., Tantet, A., Hitchcock, P., and Drobinski, P.: How Skillful Are the European Subseasonal Predictions of Wind Speed and Surface Temperature?, Mon. Weather Rev., 150, 1621–1637, https://doi.org/10.1175/MWR-D-21-0207.1, 2022. a, b
Hagedorn, R., Doblas-Reyes, F. J., and Palmer, T.: The rationale behind the success of multi-model ensembles in seasonal forecasting – I. Basic concept, Tellus A, 57, 219–233, https://doi.org/10.3402/tellusa.v57i3.14657, 2005. a, b, c, d
Hagedorn, R., Buizza, R., Hamill, T. M., Leutbecher, M., and Palmer, T. N.: Comparing TIGGE multimodel forecasts with reforecast-calibrated ECMWF ensemble forecasts, Q. J. Roy. Meteor. Soc., 138, 1814–1827, https://doi.org/10.1002/qj.1895, 2012. a, b
Hamill, T. M.: Verification of TIGGE Multimodel and ECMWF Reforecast-Calibrated Probabilistic Precipitation Forecasts over the Contiguous United States, Mon. Weather Rev., 140, 2232–2252, https://doi.org/10.1175/MWR-D-11-00220.1, 2012. a, b
Haughton, N., Abramowitz, G., Pitman, A., and Phipps, S. J.: Weighting climate model ensembles for mean and variance estimates, Clim. Dynam., 45, 3169–3181, https://doi.org/10.1007/s00382-015-2531-3, 2015. a
Heizenreder, D., Trepte, S., and Denhard, M.: SRNWP-PEPS: A regional multi-model ensemble in Europe, The European Forecaster: Newsletter of the WGCEF, 11, 2006. a
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., Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.-N.: The ERA5 global reanalysis, Q. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020. a
Kalnay, E.: Atmospheric modeling, data assimilation and predictability, Cambridge University Press, https://doi.org/10.1017/CBO9780511802270, 2003. a
Karpechko, A. Y., Charlton-Perez, A., Balmaseda, M., Tyrrell, N., and Vitart, F.: Predicting Sudden Stratospheric Warming 2018 and Its Climate Impacts With a Multimodel Ensemble, Geophys. Res. Lett., 45, 13538–13546, https://doi.org/10.1029/2018GL081091, 2018. a, b
Kharin, V. V. and Zwiers, F. W.: Climate Predictions with Multimodel Ensembles, J. Climate, 15, 793–799, https://doi.org/10.1175/1520-0442(2002)015<0793:CPWME>2.0.CO;2, 2002. a, b
Kioutsioukis, I. and Galmarini, S.: De praeceptis ferendis: good practice in multi-model ensembles, Atmos. Chem. Phys., 14, 11791–11815, https://doi.org/10.5194/acp-14-11791-2014, 2014. a
Kirtman, B. P., Min, D., Infanti, J. M., Kinter, J. L., Paolino, D. A., Zhang, Q., van den Dool, H., Saha, S., Mendez, M. P., Becker, E., Peng, P., Tripp, P., Huang, J., DeWitt, D. G., Tippett, M. K., Barnston, A. G., Li, S., Rosati, A., Schubert, S. D., Rienecker, M., Suarez, M., Li, Z. E., Marshak, J., Lim, Y.-K., Tribbia, J., Pegion, K., Merryfield, W. J., Denis, B., and Wood, E. F.: The North American Multimodel Ensemble: Phase-1 Seasonal-to-Interannual Prediction; Phase-2 toward Developing Intraseasonal Prediction, B. Am. Meteorol. Soc., 95, 585–601, https://doi.org/10.1175/BAMS-D-12-00050.1, 2014. a
Knutti, R., Sedláček, J., Sanderson, B. M., Lorenz, R., Fischer, E. M., and Eyring, V.: A climate model projection weighting scheme accounting for performance and interdependence, Geophys. Res. Lett., 44, 1909–1918, https://doi.org/10.1002/2016GL072012, 2017. a
Le Coz, C., Tantet, A., Flamary, R., and Plougonven, R.: Code for “A barycenter-based approach for the multi-model ensembling of subseasonal forecasts”, Zenodo [code], https://doi.org/10.5281/zenodo.15058503, 2025a. a
Le Coz, C., Tantet, A., Flamary, R., and Plougonven, R.: Pre-processed data for “A barycenter-based approach for the multi-model ensembling of subseasonal forecasts”, Zenodo [data set], https://doi.org/10.5281/zenodo.15038871, 2025b. a
Leung, L. R., Hamlet, A. F., Lettenmaier, D. P., and Kumar, A.: Simulations of the ENSO Hydroclimate Signals in the Pacific Northwest Columbia River Basin, B. Am. Meteorol. Soc., 80, 2313–2330, https://doi.org/10.1175/1520-0477(1999)080<2313:SOTEHS>2.0.CO;2, 1999. a
Lussana, C., Nipen, T. N., Seierstad, I. A., and Elo, C. A.: Ensemble-based statistical interpolation with Gaussian anamorphosis for the spatial analysis of precipitation, Nonlin. Processes Geophys., 28, 61–91, https://doi.org/10.5194/npg-28-61-2021, 2021. a
Manrique-Suñén, A., Gonzalez-Reviriego, N., Torralba, V., Cortesi, N., and Doblas-Reyes, F. J.: Choices in the Verification of S2S Forecasts and Their Implications for Climate Services, Mon. Weather Rev., 148, 3995–4008, https://doi.org/10.1175/MWR-D-20-0067.1, 2020. a
Manzanas, R., Gutiérrez, J. M., Bhend, J., Hemri, S., Doblas-Reyes, F. J., Torralba, V., Penabad, E., and Brookshaw, A.: Bias adjustment and ensemble recalibration methods for seasonal forecasting: a comprehensive intercomparison using the C3S dataset, Clim. Dynam., 53, 1287–1305, https://doi.org/10.1007/s00382-019-04640-4, 2019. a
Materia, S., Ángel G. Muñoz, Álvarez Castro, M. C., Mason, S. J., Vitart, F., and Gualdi, S.: Multimodel Subseasonal Forecasts of Spring Cold Spells: Potential Value for the Hazelnut Agribusiness, Weather Forecast, 35, 237–254, https://doi.org/10.1175/WAF-D-19-0086.1, 2020. a, b
Matheson, J. E. and Winkler, R. L.: Scoring Rules for Continuous Probability Distributions, Manage. Sci., 22, 1087–1096, http://www.jstor.org/stable/2629907, 1976. a
Ning, L., Carli, F. P., Ebtehaj, A. M., Foufoula-Georgiou, E., and Georgiou, T. T.: Coping with model error in variational data assimilation using optimal mass transport, Water Resour. Res., 50, 5817–5830, https://doi.org/10.1002/2013WR014966, 2014. a
Palmer, T. N., Alessandri, A., Andersen, U., Cantelaube, P., Davey, M., Délécluse, P., Déqué, M., Díez, E., Doblas-Reyes, F. J., Feddersen, H., Graham, R., Gualdi, S., Guérémy, J.-F., Hagedorn, R., Hoshen, M., Keenlyside, N., Latif, M., Lazar, A., Maisonnave, E., Marletto, V., Morse, A. P., Orfila, B., Rogel, P., Terres, J.-M., and Thomson, M. C.: Development of a European Multimodel Ensemble System for Seasonal-to-Interannual Prediction (DEMETER), B. Am. Meteorol. Soc., 85, 853–872, https://doi.org/10.1175/BAMS-85-6-853, 2004. a
Papayiannis, G. I., Galanis, G. N., and Yannacopoulos, A. N.: Model aggregation using optimal transport and applications in wind speed forecasting, Environmetrics, 29, e2531, https://doi.org/10.1002/env.2531, 2018. a
Pegion, K., Kirtman, B. P., Becker, E., Collins, D. C., LaJoie, E., Burgman, R., Bell, R., DelSole, T., Min, D., Zhu, Y., Li, W., Sinsky, E., Guan, H., Gottschalck, J., Metzger, E. J., Barton, N. P., Achuthavarier, D., Marshak, J., Koster, R. D., Lin, H., Gagnon, N., Bell, M., Tippett, M. K., Robertson, A. W., Sun, S., Benjamin, S. G., Green, B. W., Bleck, R., and Kim, H.: The Subseasonal Experiment (SubX): A Multimodel Subseasonal Prediction Experiment, B. Am. Meteorol. Soc., 100, 2043–2060, https://doi.org/10.1175/BAMS-D-18-0270.1, 2019. a, b
Peyré, G. and Cuturi, M.: Computational Optimal Transport, arXiv [preprint], https://doi.org/10.48550/arXiv.1803.00567, 2020. a, b
Raftery, A. E., Gneiting, T., Balabdaoui, F., and Polakowski, M.: Using Bayesian Model Averaging to Calibrate Forecast Ensembles, Mon. Weather Rev., 133, 1155–1174, https://doi.org/10.1175/MWR2906.1, 2005. a, b
Rajagopalan, B., Lall, U., and Zebiak, S. E.: Categorical Climate Forecasts through Regularization and Optimal Combination of Multiple GCM Ensembles, Mon. Weather Rev., 130, 1792–1811, https://doi.org/10.1175/1520-0493(2002)130<1792:CCFTRA>2.0.CO;2, 2002. a
Robertson, A. W., Lall, U., Zebiak, S. E., and Goddard, L.: Improved Combination of Multiple Atmospheric GCM Ensembles for Seasonal Prediction, Mon. Weather Rev., 132, 2732–2744, https://doi.org/10.1175/MWR2818.1, 2004. a, b
Robin, Y., Yiou, P., and Naveau, P.: Detecting changes in forced climate attractors with Wasserstein distance, Nonlin. Processes Geophys., 24, 393–405, https://doi.org/10.5194/npg-24-393-2017, 2017. a
Robin, Y., Vrac, M., Naveau, P., and Yiou, P.: Multivariate stochastic bias corrections with optimal transport, Hydrol. Earth Syst. Sci., 23, 773–786, https://doi.org/10.5194/hess-23-773-2019, 2019. a
Santambrogio, F.: Progress in Nonlinear Differential Equations and Their Applications, in: Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling, vol. 87, Birkhäuser, Cham, https://doi.org/10.1007/978-3-319-20828-2, 2015. a, b
Schulzweida, U.: CDO User Guide, https://doi.org/10.5281/zenodo.7112925, 2022. a
Smith, D. M., Scaife, A. A., Boer, G. J., Caian, M., Doblas-Reyes, F. J., Guemas, V., Hawkins, E., Hazeleger, W., Hermanson, L., Ho, C. K., Ishii, M., Kharin, V., Kimoto, M., Kirtman, B., Lean, J., Matei, D., Merryfield, W. J., Müller, W. A., Pohlmann, H., Rosati, A., Wouters, B., and Wyser, K.: Real-time multi-model decadal climate predictions, Clim. Dynam., 41, 2875–2888, https://doi.org/10.1007/s00382-012-1600-0, 2013. a
Specq, D., Batté, L., Déqué, M., and Ardilouze, C.: Multimodel Forecasting of Precipitation at Subseasonal Timescales Over the Southwest Tropical Pacific, Earth and Space Science, 7, e2019EA001003, https://doi.org/10.1029/2019EA001003, 2020. a, b, c, d
Takaya, Y.: Forecast System Design, Configuration, and Complexity, in: Sub-Seasonal to Seasonal Prediction, Chapt. 12, edited by: Robertson, A. W. and Vitart, F., Elsevier, 245–259, https://doi.org/10.1016/B978-0-12-811714-9.00012-7, 2019. a
Vigaud, N., Robertson, A. W., and Tippett, M. K.: Multimodel Ensembling of Subseasonal Precipitation Forecasts over North America, Mon. Weather Rev., 145, 3913–3928, https://doi.org/10.1175/MWR-D-17-0092.1, 2017. a, b, c
Vigaud, N., Tippett, M. K., Yuan, J., Robertson, A. W., and Acharya, N.: Spatial Correction of Multimodel Ensemble Subseasonal Precipitation Forecasts over North America Using Local Laplacian Eigenfunctions, Mon. Weather Rev., 148, 523–539, https://doi.org/10.1175/MWR-D-19-0134.1, 2020. a, b
Vissio, G. and Lucarini, V.: Evaluating a stochastic parametrization for a fast–slow system using the Wasserstein distance, Nonlin. Processes Geophys., 25, 413–427, https://doi.org/10.5194/npg-25-413-2018, 2018. a
Vissio, G., Lembo, V., Lucarini, V., and Ghil, M.: Evaluating the Performance of Climate Models Based on Wasserstein Distance, Geophys. Res. Lett., 47, e2020GL089385, https://doi.org/10.1029/2020GL089385, 2020. a
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., Robertson, A. W., Ruti, P., Sun, C., Takaya, Y., Tolstykh, M., Venuti, F., Waliser, D., Woolnough, S., Wu, T., Won, D.-J., Xiao, H., Zaripov, R., and Zhang, L.: The Subseasonal to Seasonal (S2S) Prediction Project Database, B. Am. Meteorol. Soc., 98, 163–173, https://doi.org/10.1175/BAMS-D-16-0017.1, 2017. a, b, c, d, e
Wang, Y., Ren, H.-L., Zhou, F., Fu, J.-X., Chen, Q.-L., Wu, J., Jie, W.-H., and Zhang, P.-Q.: Multi-Model Ensemble Sub-Seasonal Forecasting of Precipitation over the Maritime Continent in Boreal Summer, Atmosphere, 11, https://doi.org/10.3390/atmos11050515, 2020. a, b
Wilcoxon, F.: Individual Comparisons by Ranking Methods, Biometrics Bull., 1, 80–83, http://www.jstor.org/stable/3001968, 1945. a
Wilks, D. S.: Forecast Verification, in: Statistical Methods in the Atmospheric Sciences, Chapt. 9, 4 edn., edited by: Wilks, D. S., Elsevier, 369–483, https://doi.org/10.1016/B978-0-12-815823-4.00009-2, 2019. a, b, c
Zheng, C., Chang, E. K.-M., Kim, H., Zhang, M., and Wang, W.: Subseasonal to Seasonal Prediction of Wintertime Northern Hemisphere Extratropical Cyclone Activity by S2S and NMME Models, J. Geophys. Res.-Atmos., 124, 12057–12077, https://doi.org/10.1029/2019JD031252, 2019. a, b, c
Zhou, X., Zhu, Y., Hou, D., Fu, B., Li, W., Guan, H., Sinsky, E., Kolczynski, W., Xue, X., Luo, Y., Peng, J., Yang, B., Tallapragada, V., and Pegion, P.: The Development of the NCEP Global Ensemble Forecast System Version 12, Weather Forecast, 37, 1069–1084, https://doi.org/10.1175/WAF-D-21-0112.1, 2022. a
Short summary
We explore an alternative framework for constructing multi-model ensembles by formulating ensemble combination as a barycenter problem. We compare the L2 barycenter (equivalent to pooling) with the Wasserstein barycenter (more precisely its Gaussian approximation). Both have the same ensemble mean but differ in how they represent forecasts uncertainty. In terms of Continuous Ranked Probability Score, the Wasserstein barycenter outperforms more often while performing similarly on average.
We explore an alternative framework for constructing multi-model ensembles by formulating...