Perspective Paper on Lorenz (1982): “Atmospheric Predictability Experiments with a Large Numerical Model”

Linus Magnusson

doi:10.16993/tellus.4141

Perspective Paper on Lorenz (1982): “Atmospheric Predictability Experiments with a Large Numerical Model”

Tellus

Volume 79 (2026): Issue 1

By: Linus Magnusson

Open Access

|Aug 2026

Bauer, P., Thorpe, A., & Brunet, G. (2015). The quiet revolution of numerical weather prediction. Nature, 525, 47–55. 10.1038/nature14956
Open DOI Search in Google Scholar Back to article
Baumgart, M., Riemer, M., Wirth, V., Teubler, F., & Lang, S. T. K. (2018). Potential-vorticity dynamics of forecast errors: a quantitative case study. Monthly Weather Review, 146, 1405–1425. 10.1175/MWR-D-17-0196.1
Open DOI Search in Google Scholar Back to article
Bengtsson, L. K., Magnusson, L., & Källén, E. (2008). Independent estimations of the asymptotic variability in an ensemble forecast system. Monthly Weather Review, 136, 4105–4112. 10.1175/2008MWR2526.1
Open DOI Search in Google Scholar Back to article
Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., & Tian, Q. (2023). Accurate medium-range global weather forecasting with 3D neural networks. Nature, 619, 533–538. 10.1038/s41586-023-06185-3
Open DOI Search in Google Scholar Back to article
Boffetta, G., Giuliani, P., Paladin, G., & Vulpiani, A. (1998). An extension of the Lyapunov analysis for the predictability problem. Journal of the Atmospheric Sciences, 55, 3409–3416. 10.1175/1520-0469(1998)055<;3409:AEOTLA>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Burridge, D. M., & Källén, E. (Eds.) (1984). Problems and prospects in long and medium range weather forecasting. Springer. 10.1007/978-3-642-82132-5
Open DOI Search in Google Scholar Back to article
Charney, J. G., Fleagle, R. G., Riehl, H., Lally, V. E., & Wark, D. Q. (1966). The feasibility of a global observation and analysis experiment. BAMS, 47, 200–220.
Search in Google Scholar Back to article
Dalcher, A., & Kalnay, E. (1987). Error growth and predictability in operational ECMWF forecasts. Tellus A, 39, 474–491. 10.3402/tellusa.v39i5.11774
Open DOI Search in Google Scholar Back to article
Grams, C. M., Magnusson, L., & Madonna, E. (2018). An atmospheric-dynamics perspective on the amplification and propagation of forecast error in numerical weather prediction models: a case study. Quarterly Journal of the Royal Meteorological Society, 144, 2577–2591. 10.1002/qj.3353
Open DOI Search in Google Scholar Back to article
Haiden, T., Janousek, M., Vitart, F., Prates, F., Maier-Gerber, M., Li, C. W. Y., & Chevallier, M. (2025). Evaluation of ECMWF forecasts. ECMWF Technical Memorandum 931.
Search in Google Scholar Back to article
Hauser, S., Cavallo, S. M., Magnusson, L., Martin, J. E., & Parsons, D. B. (2026). Exceptionally poor and good medium-range forecasts of the large-scale circulation over Europe in ERA5 reforecasts. Quarterly Journal of the Royal Meteorological Society, 152, e70117. 10.1002/qj.70117
Open DOI Search in Google Scholar Back to article
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. et al. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146, 1999–2049. 10.1002/qj.3803
Open DOI Search in Google Scholar Back to article
Hoskins, B. J., & Karoly, D. J. (1981). The steady linear response of a spherical atmosphere to thermal and orographic forcing. Journal of the Atmospheric Sciences, 38, 1179–1196. 10.1175/1520-0469(1981)038<;1179:TSLROA>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Judt, F. (2018). Insights into atmospheric predictability through global convection-permitting model simulations. Journal of the Atmospheric Sciences, 75, 1477–1497. 10.1175/JAS-D-17-0343.1
Open DOI Search in Google Scholar Back to article
Judt, F. (2020). Atmospheric predictability of the tropics, middle latitudes, and polar regions explored through global storm-resolving simulations. Journal of the Atmospheric Sciences, 77, 257–276. 10.1175/JAS-D-19-0116.1
Open DOI Search in Google Scholar Back to article
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. (2023). Learning skillful medium-range global weather forecasting. Science, 382, 1416–1421. 10.1126/science.adi2336
Open DOI Search in Google Scholar Back to article
Lang, S., Alexe, M., Chantry, M., Dramsch, J., Pinault, F., Raoult, B., Clare, M. C. A., Lessig, C., Maier-Gerber, M., Magnusson, L., Ben Bouallègue, Z., Nemesio, A. P., Dueben, P. D., Brown, A., Pappenberger, F., & Rabier, F. (2024). AIFS: ECMWF’s data-driven forecasting system. arXiv. 10.48550/arXiv.2406.01465
Open DOI Search in Google Scholar Back to article
Leith, C. E. (1978). Objective methods for weather prediction. Annual Review of Fluid Mechanics, 10, 107–128. 10.1146/annurev.fl.10.010178.000543
Open DOI Search in Google Scholar Back to article
Leutbecher, M. et al. (2017). Stochastic representations of model uncertainties at ECMWF: state of the art and future vision. Quarterly Journal of the Royal Meteorological Society, 143, 2315–2339. 10.1002/qj.3094
Open DOI Search in Google Scholar Back to article
Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20, 130–141. 10.1175/1520-0469(1963)020<;0130:DNF>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Lorenz, E. N. (1969a). The predictability of a flow which possesses many scales of motion. Tellus, 21, 289–307. 10.3402/tellusa.v21i3.10086
Open DOI Search in Google Scholar Back to article
Lorenz, E. N. (1969b). Atmospheric predictability as revealed by naturally occurring analogues. Journal of the Atmospheric Sciences, 26, 636–646. 10.1175/1520-0469(1969)026<;0636:APARBN>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Lorenz, E. N. (1982). Atmospheric predictability experiments with a large numerical model. Tellus, 34, 505–513. 10.1111/j.2153-3490.1982.tb01839.x
Open DOI Search in Google Scholar Back to article
Magnusson, L. (2017). Diagnostic methods for understanding the origin of forecast errors. Quarterly Journal of the Royal Meteorological Society, 143, 2129–2142. 10.1002/qj.3072
Open DOI Search in Google Scholar Back to article
Magnusson, L., & Källén, E. (2013). Factors influencing skill improvements in the ECMWF forecasting system. Monthly Weather Review, 141, 3142–3153. 10.1175/MWR-D-12-00318.1
Open DOI Search in Google Scholar Back to article
Magnusson, L., Nycander, J., & Källén, E. (2009). Flow-dependent versus flow-independent initial perturbations for ensemble prediction. Tellus A, 61, 194–209. 10.1111/j.1600-0870.2008.00385.x
Open DOI Search in Google Scholar Back to article
Majumdar, S. J. et al. (2021) Multiscale forecasting of high-impact weather: current status and future challenges. Bulletin of the American Meteorological Society, 102, E635–E659. 10.1175/BAMS-D-20-0111.1
Open DOI Search in Google Scholar Back to article
McTaggart-Cowan, R. et al. (2026) WP-MIP: An artificial intelligence, hybrid and physically based model intercomparison project for weather prediction. arXiv. 10.5194/ems2026-598
Open DOI Search in Google Scholar Back to article
Moldovan, G., Pinnington, E., Prieto Nemesio, A., Lang, S., Ben Bouallègue, Z., Dramsch, J., Alexe, M., Santa Cruz, M., Hahner, S., Cook, H., Theissen, H., Clare, M., O’Brien, C., Polster, J., Magnusson, L., Mertes, G., Pinault, F., Raoult, B., de Rosnay, P., Forbes, R., & Chantry, M. (2026). AIFS 1.1.0: an update to ECMWF’s machine-learned weather forecast model AIFS. EGUsphere, accepted. 10.5194/egusphere-2025-4716
Open DOI Search in Google Scholar Back to article
Murphy, A. H. (1988). Skill scores based on the mean square error and their relationships to the correlation coefficient. Monthly Weather Review, 116, 2417–2424. 10.1175/1520-0493(1988)116<;2417:SSBOTM>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Nicolis, C., Vannitsem, S., & Royer, J.-F. (1995). Short-range predictability of the atmosphere: mechanisms for superexponential error growth. Quarterly Journal of the Royal Meteorological Society, 121, 705–722. 10.1002/qj.49712152312
Open DOI Search in Google Scholar Back to article
Palmer, T. N. (1993). Extended-range atmospheric prediction and the Lorenz model. Bulletin of the American Meteorological Society, 74, 49–65. 10.1175/1520-0477(1993)074<;0049:ERAPAT>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Peña, M., & Kalnay, E. (2004). Separating fast and slow modes in coupled chaotic systems. Nonlinear Processes in Geophysics, 11, 319–327. 10.5194/npg-11-319-2004
Open DOI Search in Google Scholar Back to article
Rabier, F., Järvinen, H., Klinker, E., Mahfouf, J.-F., & Simmons, A. (2000). The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics. Quarterly Journal of the Royal Meteorological Society, 126, 1143–1170. 10.1002/qj.49712656415
Open DOI Search in Google Scholar Back to article
Rodwell, M. J., Lang, S. T. K., Ingleby, N. B., Bormann, N., Hólm, E., Rabier, F., Richardson, D. S., & Yamaguchi, M. (2016). Reliability in ensemble data assimilation. Quarterly Journal of the Royal Meteorological Society, 142, 443–454. 10.1002/qj.2663
Open DOI Search in Google Scholar Back to article
Rodwell, M. J., Magnusson, L., Bauer, P., Bechtold, P., Bonavita, M., Cardinali, C., Diamantakis, M., Earnshaw, P., Garcia-Mendez, A., Isaksen, L., Källén, E., Klocke, D., Lopez, P., McNally, T., Persson, A., Prates, F., & Wedi, N. (2013). Characteristics of occasional poor medium-range weather forecasts for Europe. Bulletin of the American Meteorological Society, 94, 1393–1405. 10.1175/BAMS-D-12-00099.1
Open DOI Search in Google Scholar Back to article
Rotunno, R., & Snyder, C. (2008). A generalization of Lorenz’s model for the predictability of flows with many scales of motion. Journal of the Atmospheric Sciences, 65, 1063–1076. 10.1175/2007JAS2449.1
Open DOI Search in Google Scholar Back to article
Saetra, Ø., Hersbach, H., Bidlot, J., & Richardson, D. S. (2004). Effects of observation errors on the statistics for ensemble spread and reliability. Monthly Weather Review, 132, 1487–1501. 10.1175/1520-0493(2004)132<;1487:EOOEOT>2.0.CO;2
Open DOI Search in Google Scholar Back to article
Selz, T. (2019). Estimating the intrinsic limit of predictability using a stochastic convection scheme. Journal of the Atmospheric Sciences, 76, 757–765. 10.1175/JAS-D-17-0373.1
Open DOI Search in Google Scholar Back to article
Selz, T., & Craig, G. C. (2023). Can artificial intelligence-based weather prediction models simulate the butterfly effect? Geophysical Research Letters, 50, e2023GL105747. 10.1029/2023GL105747
Open DOI Search in Google Scholar Back to article
Selz, T., & Craig, G. C. (2025). Can AI-based weather prediction models simulate the butterfly effect? The role of architecture and implementation. ESS Open Archive. 10.22541/essoar.176556004.46250262/v1
Open DOI Search in Google Scholar Back to article
Simmons, A. J., & Hollingsworth, A. (2002). Some aspects of the improvement in skill of numerical weather prediction. Quarterly Journal of the Royal Meteorological Society, 128, 647–677. 10.1256/003590002321042135
Open DOI Search in Google Scholar Back to article
Simmons, A.J., Mureau, R., & Petroliagis, T. (1995), Error growth and estimates of predictability from the ECMWF forecasting system. Q.J.R. Meteorol. Soc., 121, 1739–1771. 10.1002/qj.49712152711
Open DOI Search in Google Scholar Back to article
Stan, C., Straus, D. M., Frederiksen, J. S., Lin, H., Maloney, E. D., & Schumacher, C. (2017). Review of tropical–extratropical teleconnections on intraseasonal time scales. Reviews of Geophysics, 55, 902–937. 10.1002/2016RG000538
Open DOI Search in Google Scholar Back to article
Stroe, R., & Royer, J.-F. (1993). Comparison of different error growth formulas and predictability estimation in numerical extended-range forecasts. Annals of Geophysics, 11, 296–316.
Search in Google Scholar Back to article
Sun, Y. Q., & Zhang, F. (2020). A new theoretical framework for understanding multiscale atmospheric predictability. Journal of the Atmospheric Sciences, 77, 2297–2309. 10.1175/JAS-D-19-0271.1
Open DOI Search in Google Scholar Back to article
Vonich, P. T., & Hakim, G. J. (2025). Testing the limit of atmospheric predictability with a machine-learning weather model. arXiv, arXiv:2504. 10.1175/AIES-D-26-0009.1
Open DOI Search in Google Scholar Back to article
Žagar, N., Horvat, M., Zaplotnik, Ž., & Magnusson, L. (2017). Scale-dependent estimates of the growth of forecast uncertainties in a global prediction system. Tellus A, 69, 1287492. 10.1080/16000870.2017.1287492
Open DOI Search in Google Scholar Back to article
Zhang, F., Bei, N., Rotunno, R., Snyder, C., & Epifanio, C. C. (2007). Mesoscale predictability of moist baroclinic waves: convection-permitting experiments and multistage error growth dynamics. Journal of the Atmospheric Sciences, 64, 3579–3594. 10.1175/JAS4028.1
Open DOI Search in Google Scholar Back to article
Zhang, F., Sun, Y. Q., Magnusson, L., Buizza, R., Lin, S.-J., Chen, J.-H., & Emanuel, K. (2019). What is the predictability limit of midlatitude weather? Journal of the Atmospheric Sciences, 76, 1077–1091. 10.1175/JAS-D-18-0269.1
Open DOI Search in Google Scholar Back to article