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  • Cited by 66
  • Print publication year: 2006
  • Online publication date: December 2009

Chapter 3 - Predictability – a problem partly solved

Summary

Ed Lorenz, pioneer of chaos theory, presented this work at an earlier ECMWF workshop on predictability. The paper, which has never been published externally, presents what is widely known as the Lorenz 1996 model. Ed was unable to come to the 2002 meeting, but we decided it would be proper to acknowledge Ed's unrivalled contribution to the field of weather and climate predictability by publishing his 1996 paper in this volume.

The difference between the state that a system is assumed or predicted to possess, and the state that it actually possesses or will possess, constitutes the error in specifying or forecasting the state. We identify the rate at which an error will typically grow or decay, as the range of prediction increases, as the key factor in determining the extent to which a system is predictable. The long-term average factor by which an infinitesimal error will amplify or diminish, per unit time, is the leading Lyapunov number; its logarithm, denoted by λ1, is the leading Lyapunov exponent. Instantaneous growth rates can differ appreciably from the average.

With the aid of some simple models, we describe situations where errors behave as would be expected from a knowledge of λ1, and other situations, particularly in the earliest and latest stages of growth, where their behaviour is systematically different. Slow growth in the latest stages may be especially relevant to the long-range predictability of the atmosphere.

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References
Charney, J. G., Fleagle, R. G., Lally, V. E., Riehl, H. and Wark, D. Q. (1966). The feasibility of a global observation and analysis experiment. Bull. Am. Meteorol. Soc., 47, 200–20
Farrell, B. F. (1989). Optimal excitation of baroclinic waves. J. Atmos. Sci., 46, 1193–206
Kalnay, E. and Dalcher, A. (1987). Forecasting forecast skill. Mon. Weather Rev., 115, 349–56
Leith, C. E. (1965). Lagrangian advection in an atmospheric model. In WMO-IUGG Symposium on Research and Development Aspects of Long-range Forecasting, WMO Technical Note 66, 168–76
Lorenz, E. N. (1969a). The predictability of a flow which possesses many scales of motion. Tellus, 21, 289–307
Lorenz, E. N. (1969b). Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci., 26, 636–46
Lorenz, E. N. (1982). Atmospheric predictability experiments with a large numerical model. Tellus, 34, 505–13
Lorenz, E. N. (1993). The Essence of Chaos. University of Washington Press
Mintz, Y. (1965). Very long-term global integration of the primitive equations of atmospheric motion. In WMO-IUGG Symposium on Research and Development Aspects of Long-range Forecasting, WMO Technical Note 66, 141–67
Palmer, T. N. (1988). Medium and extended range predictability and stability of the Pacific/North American mode. Quart. J. Roy. Meteor. Soc., 114, 691–713
Simmons, A. J., Mureau, R. and Petroliagis, T. (1995). Error growth and estimates of predictability from the ECMWF forecasting system. Quart. J. Roy. Meteor. Soc., 121, 1739–1771
Smagorinsky, J. (1965). Implications of dynamic modelling of the general circulation on long-range forecasting. In WMO-IUGG Symposium on Research and Development Aspects of Long-range Forecasting, WMO Technical Note 66, 131–7
Smagorinsky, J. (1969). Problems and promises of deterministic extended range forecasting. Bull. Am. Meteorol. Soc., 50, 286–311
Thompson, P. D. (1957). Uncertainty of initial state as a factor in the predictability of large-scale atmospheric flow patterns. Tellus, 9, 275–95
Toth, Z. and Kalnay, E. (1993). Ensemble forecasting at NMC: the generation of perturbations. Bull. Am. Meteorol. Soc., 74, 2317–30
Zebiak, S. E. and Cane, M. A. (1987). A model El Niño-Southern Oscillation. Mon. Weather Rev., 115, 2262–78