Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- Chapter 1 Predictability of weather and climate: from theory to practice
- Chapter 2 Predictability from a dynamical meteorological perspective
- Chapter 3 Predictability – a problem partly solved
- Chapter 4 The Liouville equation and atmospheric predictability
- Chapter 5 Application of generalised stability theory to deterministic and statistical prediction
- Chapter 6 Ensemble-based atmospheric data assimilation
- Chapter 7 Ensemble forecasting and data assimilation: two problems with the same solution?
- Chapter 8 Approximating optimal state estimation
- Chapter 9 Predictability past, predictability present
- Chapter 10 Predictability of coupled processes
- Chapter 11 Predictability of tropical intraseasonal variability
- Chapter 12 Predictability of seasonal climate variations: a pedagogical review
- Chapter 13 Predictability of the North Atlantic thermohaline circulation
- Chapter 14 On the predictability of flow-regime properties on interannual to interdecadal timescales
- Chapter 15 Model error in weather and climate forecasting
- Chapter 16 Observations, assimilation and the improvement of global weather prediction – some results from operational forecasting and ERA-40
- Chapter 17 The ECMWF Ensemble Prediction System
- Chapter 18 Limited-area ensemble forecasting: the COSMO-LEPS system
- Chapter 19 Operational seasonal prediction
- Chapter 20 Weather and seasonal climate forecasts using the superensemble approach
- Chapter 21 Predictability and targeted observations
- Chapter 22 The attributes of forecast systems: a general framework for the evaluation and calibration of weather forecasts
- Chapter 23 Predictability from a forecast provider's perspective
- Chapter 24 Ensemble forecasts: can they provide useful early warnings?
- Chapter 25 Predictability and economic value
- Chapter 26 A three-tier overlapping prediction scheme: tools for strategic and tactical decisions in the developing world
- Chapter 27 DEMETER and the application of seasonal forecasts
- Index
- Plate section
- References
Chapter 3 - Predictability – a problem partly solved
Published online by Cambridge University Press: 03 December 2009
Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- Chapter 1 Predictability of weather and climate: from theory to practice
- Chapter 2 Predictability from a dynamical meteorological perspective
- Chapter 3 Predictability – a problem partly solved
- Chapter 4 The Liouville equation and atmospheric predictability
- Chapter 5 Application of generalised stability theory to deterministic and statistical prediction
- Chapter 6 Ensemble-based atmospheric data assimilation
- Chapter 7 Ensemble forecasting and data assimilation: two problems with the same solution?
- Chapter 8 Approximating optimal state estimation
- Chapter 9 Predictability past, predictability present
- Chapter 10 Predictability of coupled processes
- Chapter 11 Predictability of tropical intraseasonal variability
- Chapter 12 Predictability of seasonal climate variations: a pedagogical review
- Chapter 13 Predictability of the North Atlantic thermohaline circulation
- Chapter 14 On the predictability of flow-regime properties on interannual to interdecadal timescales
- Chapter 15 Model error in weather and climate forecasting
- Chapter 16 Observations, assimilation and the improvement of global weather prediction – some results from operational forecasting and ERA-40
- Chapter 17 The ECMWF Ensemble Prediction System
- Chapter 18 Limited-area ensemble forecasting: the COSMO-LEPS system
- Chapter 19 Operational seasonal prediction
- Chapter 20 Weather and seasonal climate forecasts using the superensemble approach
- Chapter 21 Predictability and targeted observations
- Chapter 22 The attributes of forecast systems: a general framework for the evaluation and calibration of weather forecasts
- Chapter 23 Predictability from a forecast provider's perspective
- Chapter 24 Ensemble forecasts: can they provide useful early warnings?
- Chapter 25 Predictability and economic value
- Chapter 26 A three-tier overlapping prediction scheme: tools for strategic and tactical decisions in the developing world
- Chapter 27 DEMETER and the application of seasonal forecasts
- Index
- Plate section
- References
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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- Predictability of Weather and Climate , pp. 40 - 58Publisher: Cambridge University PressPrint publication year: 2006
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