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 5 - Application of generalised stability theory to deterministic and statistical prediction
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
Understanding of the stability of deterministic and stochastic dynamical systems has evolved recently from a traditional grounding in the system's normal modes to a more comprehensive foundation in the system's propagator and especially in an appreciation of the role of non-normality of the dynamical operator in determining the system's stability as revealed through the propagator. This set of ideas, which approach stability analysis from a non-modal perspective, will be referred to as generalised stability theory (GST). Some applications of GST to deterministic and statistical forecast are discussed in this review. Perhaps the most familiar of these applications is identifying initial perturbations resulting in greatest error in deterministic error systems, which is in use for ensemble and targeting applications. But of increasing importance is elucidating the role of temporally distributed forcing along the forecast trajectory and obtaining a more comprehensive understanding of the prediction of statistical quantities beyond the horizon of deterministic prediction. The optimal growth concept can be extended to address error growth in non-autonomous systems in which the fundamental mechanism producing error growth can be identified with the necessary non-normality of the system. In this review the influence of model error in both the forcing and the system is examined using the methods of stochastic dynamical systems theory. Deterministic and statistical prediction are separately discussed.
Introduction
The atmosphere and ocean are constantly evolving and the present state of these systems, while notionally deterministically related to previous states, in practice becomes exponentially more difficult to predict as time advances.
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- Predictability of Weather and Climate , pp. 99 - 123Publisher: Cambridge University PressPrint publication year: 2006
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