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 4 - The Liouville equation and atmospheric predictability
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
Introduction and motivation
It is widely recognised that weather forecasts made with dynamical models of the atmosphere are inherently uncertain. Such uncertainty of forecasts produced with numerical weather prediction (NWP) models arises primarily from two sources: from imperfect knowledge of the initial model conditions and from imperfections in the model formulation itself. The recognition of the potential importance of accurate initial model conditions and an accurate model formulation dates back to times even prior to operational NWP (Bjerknes, 1904; Thompson, 1957). In the context of NWP, the importance of these error sources in degrading the quality of forecasts was demonstrated to arise because errors introduced in atmospheric models are, in general, growing (Lorenz, 1982, 1963, 1993, this volume), which at the same time implies that the predictability of the atmosphere is subject to limitations (Errico et al., 2002). An example of the amplification of small errors in the initial conditions, or, equivalently, the divergence of initially nearby trajectories is given in Figure 4.1, for the system discussed by Lorenz (1984). The uncertainty introduced into forecasts through uncertain initial model conditions, and uncertainties in model formulations, has been the subject of numerous studies carried out in parallel with the continuous development of NWP models (e.g. Leith, 1974; Epstein, 1969; Palmer, 2000, this volume, Buizza, this volume).
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- Predictability of Weather and Climate , pp. 59 - 98Publisher: Cambridge University PressPrint publication year: 2006
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