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 8 - Approximating optimal state estimation
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
Minimising forecast error requires accurately specifying the initial state from which the forecast is made by optimally using available observing resources to obtain the most accurate possible analysis. The Kalman filter accomplishes this for linear systems and experience shows that the extended Kalman filter also performs well in non-linear systems. Unfortunately, the Kalman filter and the extended Kalman filter require computation of the time-dependent error covariance matrix which presents a daunting computational burden. However, the dynamically relevant dimension of the forecast error system is generally far smaller than the full state dimension of the forecast model which suggests the use of reduced order error models to obtain near optimal state estimators. A method is described and illustrated for implementing a Kalman filter on a reduced order approximation of the forecast error system. This reduced order system is obtained by balanced truncation of the Hankel operator representation of the full error system. As an example application a reduced order Kalman filter is constructed for a time-dependent quasi-geostrophic storm track model. The accuracy of the state identification by the reduced order Kalman filter is assessed and comparison made with the state estimate obtained by the full Kalman filter and with the estimate obtained using an approximation to 4D-Var. The accuracy assessment is facilitated by formulating the state estimation methods as observer systems. A practical approximation to the reduced order Kalman filter that utilises 4D-Var algorithms is examined.
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- Predictability of Weather and Climate , pp. 181 - 216Publisher: Cambridge University PressPrint publication year: 2006
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