Exploring the Origin of the Two-Week Predictability Limit:A Revisit of Lorenz’s Predictability Studies in the 1960s

This study aims to revisit Lorenz's pioneering work from the 1960s and delve into the origin of the two-week predictability limit of the atmosphere. This report specifically focuses on five of Lorenz's papers published in 1969 using three different approaches, the Charney et al. report in 1966, and the Global Atmospheric Research Program (GARP) report in 1969.

The dynamical approach involved conducting numerical experiments using various general circulation models, such as those of Leith, Mintz-Arakawa, and Smagorinsky. Experimental results indicated different rates of error growth and doubling times. A doubling time of five days within the Mintz-Arakawa model suggested a predictability limit of approximately two weeks. However, a reanalysis of numerical results suggests that doubling time estimates may reflect an instability for a model equilibrium state rather than atmospheric instability.

The empirical approach employed analogues to estimate error growth. Lorenz reported a doubling time of eight days, but adjusted estimates using the quadratic and cubic hypotheses. Due to its reliance on a limited number of observations and the validity of the two hypotheses, this approach has faced criticism.

The dynamical-empirical approach introduced the Lorenz 1969 model. The model revealed a dependence of predictability on scales. However, the model failed to reproduce nonlinear chaotic behavior and it could not contain baroclinic instability, which is a major energy source of the atmosphere.

The study emphasizes the importance of accurately revisiting and interpreting earlier experiments to bridge the gap between theoretical predictability limits and practical model capabilities. The study also acknowledges advancements in numerical models and data assimilation systems that have demonstrated promising, long-range simulations surpassing the two-week predictability limit.

Website: https://bwshen.sdsu.edu

Selected References

1. Charney, J. G., R. G. Fleagle, V. E. Lally, H. Riehl, and D. Q. Wark, 1966: The feasibility of a global observation and analysis experiment. Bull. Amer. Meteor. Soc., 47, 200–220.
2. GARP, 1969: GARP topics. Bull. Amer. Meteor. Soc., 50, 136–141.
3. Lorenz, E.N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130–141.
4. Lorenz, E. N., 1969a: Studies of atmospheric predictability. [Part 1] [Part 2] [Part 3] [Part 4] Final Report, February, Statistical Forecasting Project. Air Force Research Laboratories, Office of Aerospace Research, USAF,Bedford, MA, 145 pp.
5. Lorenz, E. N., 1969b: Three approaches to atmospheric predictability. Bull. Amer. Meteor. Soc., 50, 345-351.
6. Lorenz, E. N., 1969c: Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci., 26, 636-646.
7. Lorenz, E. N., 1969d: The predictability of a flow which possesses many scales of motion. Tellus, 21, 19 pp.
8. Lorenz, E. N., 1969e: How much better can weather prediction become? MIT Technology Review, July/August, 39-49.
9. Lorenz, E. N., 1969f: The nature of the global circulation of the atmosphere: a present view. The Global Circulation of the Atmosphere, London, Roy. Meteor. Soc., 3-23.
10. Lorenz, E., 1972: Limits of meteorological predictability. Prepared for the American Meteorological Society, February. (unpublished, available from https://eapsweb.mit.edu/sites/default/files/Limits_of_Meteorological_Predictability_Feb1972.pdf)
11. Shen, B.-W., R. A. Pielke Sr., X. Zeng, and X. Zeng, 2023b: Lorenz’s View on the Predictability Limit. Encyclopedia 2023, 3(3), 887-899; https://doi.org/10.3390/encyclopedia3030063
12. Shen, B.-W., 2023: A Review of Lorenz's Models from 1960 to 2008. International Journal of Bifurcation and Chaos. Proof version available from ResearchGate https://doi.org/10.13140/RG.2.2.24115.81446 (invited, accepted, 1 August 2023; to Appear)
13. Shen, B.-W., R. A. Pielke Sr. and X. Zeng, 2023a: The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Special Issue on Multistability, Multiscale Predictability, and Sensitivity in Numerical Models. [Editorial] Atmosphere 2023, 14(8), 1279; https://doi.org/10.3390/atmos14081279 (22 journal pages)
14. Shen, B.-W.; Pielke, R.A., Sr.; Zeng, X.; Baik, J.-J.; Faghih-Naini, S.; Cui, J.; Atlas, R. 2021: Is Weather Chaotic? Coexistence of Chaos and Order within a Generalized Lorenz Model. Bull. Am. Meteorol. Soc., 2, E148–E158. https://doi.org/10.1175/BAMS-D-19-0165.1