Lecture Notes

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Data Assimilation

PDF iconData assimilation concepts and methods

By F Bouttier and P Courtier

Contents

  1. Basic concepts of data assimilation
  2. The state vector, control space and observations
  3. The modelling of errors
  4. Statistical interpolation with least-squares estimation
  5. A simple scalar illustration of least-squares estimation
  6. Models of error covariances
  7. Optimal interpolation (OI) analysis
  8. Three-dimensional variational analysis (3D-Var)
  9. 1D-Var and other variational analysis systems
  10. Four-dimensional variational assimilation (4D-Var)
  11. Estimating the quality of the analyses Implementation techniques
  12. Dual formulation of 3D/4D-Var (PSAS)
  13. The extended Kalman filter (EKF)
  14. Conclusion
  15. Appendix
    • A. A primer on linear algebra
    • B. Practical adjoint coding
    • C. Exercises
    • D. Main symbols
  16. References

PDF iconAssimilation Algorithms

By EV Holm

Contents

  1. Basic concepts
  2. Variational data assimilation
  3. Common assimilation algorithms
  4. References

PDF iconAssimilation techniques (3): 3dVar

By M Fisher

Contents

  1. Introduction
  2. The incremental method
  3. The background cost function
  4. References

PDF iconAssimilation techniques (4): 4dVar

By M Fisher

Contents     

  1. Introduction
  2. Comparison between the ECMWF 3dVar and 4dVar systems
  3. The current operational configuration of 4dVar
  4. Increments from a single observation
  5. A cautionary example
  6. References

PDF iconAssimilation techniques (5): Approximate Kalman Filters and Singular Vectors

By M Fisher

Contents

  1. Introduction
  2. Why is the Kalman filter impractical for very large systems?
  3. The ensemble Kalman filter
  4. Subspaces, projections and Hessian singular vectors
  5. The ECMWF reduced-rank Kalman filter
  6. Examples
  7. References

PDF iconA data assimilation tutorial based on the Lorenz-95 system

By M Leutbecher

Contents

  1. Introduction
  2. Data assimilation experiments
  3. Outlook
  4. References

PDF iconAdaptive observations, the Hessian metric and singular vectors

By M Leutbecher

Contents

  1. Introduction
  2. Adaptive observations in the Lorenz 95 system - Methodology
  3. Adaptive observations in the Lorenz 95 system - Results
  4. Reduced rank prediction of forecast error variance reductions in an operational NWP context
  5. Discussion
  6. Conclusions
  7. References

PDF iconObservation Impact on the Short Range Forecast

By C Cardinali

Contents

  1. Introduction
  2. Observational Impact on the Forecast
  3. Results
  4. Conclusion
  5. References

PDF iconObservation influence diagnostic of a data assimilation system

By C Cardinali

Contents

  1. Introduction
  2. Classical Statistical Definitions of Influence Matrix and Self-Sensitivity
  3. Observational Influence and Self-Sensitivity for a DA Scheme
  4. Results 
  5. Conclusions
  6. Appendix:
    • A. Influence Matrix Calculation in Weighted Regression Data Assim. Scheme
    • B. Approximate calculation of self-sensitivity in a large variational analysis system
  7. References

PDF iconObservations and diagnostic tools for data assimilation

By H Järvinen

Contents

  1. Observational preprocessing
  2. The observation screening
  3. Use of feedback information
  4. Diagnostic tools for an assimilation system
  5. References

PDF iconThe control of gravity waves in data assimilation

By A Simmons

Contents

  1. Introduction
  2. Non-linear normal-mode initialization
  3. Control of gravity waves in the ECMWF variational data assimilation
  4. Digital filtering
  5. Appendix
    • A. Definition of operators for the ECMWF vertical finite-difference scheme
    • B. The Lamb wave
    • C. The non-recursive implementation of the recursive filter
  6. References

PDF iconPrinciples of remote sensing of atmospheric parameters from space

By R Rizzi (revised by R Saunders)

Contents

  1. Introduction
  2. Absorption and transmission of monochromatic radiation
  3. Black-body radiation
  4. Emissivity, Kirchoff law and local thermodynamical equilibrium
  5. The equation for radiative transfer
  6. Spectral distribution of radiance leaving the atmosphere
  7. Modelling the interaction
  8. Line shapes and the absorption coefficient
  9. Continuum absorption
  10. Integration over frequency
  11. The direct problem
  12. References
PDF iconInversion methods for satellite sounding data

By J Eyre

Contents

  1. Basic ideas
  2. Temperature profile inversion methods
  3. Constituent profile inversion
  4. Clouds
  5. Satellite sounding in numerical weather prediction
  6. References

PDF iconIntroduction to microwave radiative transfer

By P Bauer

Contents

  1. Radiative transfer
  2. Radiative transfer models
  3. Atmospheric absorption
  4. Surface emission / reflection
  5. Hydrometeors
  6. Fast models
  7. Outstanding issues
  8. References

PDF iconMicrowave radiative transfer modeling in clouds and precipitation - Part I

By P Bauer

Contents

  1. Introduction
  2. Microwave radiative transfer
  3. Radiative transfer models
  4. Optical properties
  5. References

PDF iconMicrowave radiative transfer modeling in clouds and precipitation - Part II

By E Moreau, P Bauer and F Chevallier

Contents

  1. Introduction
  2. Edington vs Doubling-Adding model
  3. Comparison with other models
  4. References

PDF iconLand surface assimilation

By J-F Mahmouf and P Viterbo

Contents

  1. Introduction
  2. Design of land surface parametrizations
  3. Introduction to land surface assimilation
  4. Simple land surface initialisation methods
  5. Soil moisture initialisation using SYNOP observations
  6. Other techniques to initial soil moisture
  7. Initialisation of other land surface quantities
  8. Conclusions
  9. References

Numerical Methods

PDF iconAtmospheric Waves

By M Miller

Contents

  1. Introduction
  2. Basic equations
  3. Exact solutions of the linearized equations
  4. Simplified solutions to the linearized equations - filtering approximations
  5. Surface gravity waves
  6. Equatorial waves
  7. Summary diagram and modelling implications
  8. References

PDF iconProperties of the equations of motion

By M Cullen

Contents

  1. Introduction
  2. Observed behaviour
  3. Toy problems
  4. Shallow water equations
  5. Three dimensional equations
  6. Averaged equations
  7. Summary
  8. References

PDF iconNumerical methods

By RW Riddaway and M Hortal

Contents

  1. Some introductory ideas
  2. Finite differences
  3. The non-linear advection equation
  4. Towards the primitive equations
  5. The semi-Lagrangian technique
  6. The spectral method
  7. The finite-element technique
  8. Solving the algebraic equations
  9. References

PDF iconAdiabatic formulation of large-scale models of the atmosphere: Finite schemes for the horizontal discretization

By AJ Simmons

Contents

  1. Introduction
  2. Distribution of grid points
  3. Staggering of variables
  4. Conservation and Eulerian advection schemes
  5. Treatment of the poles
  6. References

PDF iconAdiabatic formulation of models

By T Davies

Contents

  1. Introduction
  2. Governing equations
  3. Horizontal discretization
  4. Vertical coordinates
  5. Vertical discretization
  6. References

PDF iconThe wave model

By P Janssen

Contents

  1. Derivation of the energy balance equation
  2. The WAM model
  3. Benefits for atmospheric modelling
  4. References

Parametrization

PDF iconThe general problem of parametrization

By M Tiedtke

Contents

  1. Introduction
  2. The spectrum of atmospheric motions
  3. The non-parametrized equations
  4. Principles of parametrization
  5. References

PDF iconParametrization of non-convective condensation processes

By M Tiedtke

Contents

  1. Thermodynamics of moist air
  2. Cloud physical processes
  3. Parametrization of non-convective processes and precipitation processes in numerical models
  4. References

PDF iconAtmospheric moist convection

By P Bechtold

Contents

  1. The nature of moist convection
  2. Parameterization of convection
  3. The IFS convection parameterization
  4. Forecasting - case studies
  5. Appendix 
    • Simple wave types and quasi-geostrophic adjustment
  6. References

PDF iconAtmospheric thermodynamics

By P Bechtold

Contents

  1. Ideal gas law
  2. First law of thermodynamics
  3. Second law of thermodynamics
  4. Enthalpy
  5. State functions and Maxwell relations
  6. Humidity variables
  7. Virtual temperature
  8. Reversible adiabatic transformation without phase change
  9. Reversible adiabatic transformation with phase change
  10. Clausius Clapeyron equation
  11. Ways of reaching saturation
  12. Energy diagrams - Tephigram
  13. Saturation adjustment - numerical procedure
  14. References

PDF iconImproved middle atmosphere climate and forecasts in the ECMWF model through a non-orographic gravity wave drag parametrization

By A Orr, P Bechtold, J Scinocca, M Ern and M Janizkova

Contents

  1. Introduction
  2. The S03 gravity wave scheme
  3. Climate experiments, parameter settings, and validating data
  4. The extratropical temperature structure and circulation
  5. Planetary waves
  6. Tropical oscillations
  7. Parametrized and resolved momentum flux
  8. High resolution middle atmosphere forecast error and analysis
  9. Summary and discussion
  10. References

PDF iconThe mass-flux approach to the parametrization of deep convection

By D Gregory

Contents

  1. Introduction
  2. The need for parametrization
  3. Mass-flux theory of convection
  4. Evaluation of mass-flux theory
  5. Evaluation of convective schemes using cloud-resolving models
  6. Concluding comments
  7. References

PDF iconSensitivity of general circulation model performance to convective parametrization

By D Gregory

Contents

  1. Introduction
  2. The importance of shallow convection
  3. Sensitivity of climate simulations to the parametrization of deep convection
  4. Summary
  5. References

PDF iconThe parametrization of cloud cover

By AM Tompkins

Contents

  1. Introduction
  2. Background
  3. Relative humidity schemes
  4. Statistical schemes
  5. The ECMWF prognostic cloud cover scheme
  6. Summary
  7. References

PDF iconThe parametrization of the planetary boundary layer

By A Beljaars

Contents

  1. Introduction
  2. Similarity theory and surface fluxes
  3. PBL schemes for atmospheric models
  4. List of symbols
  5. References

PDF iconA review of parametrization schemes for land surface processes

By P Viterbo

Contents

  1. Introduction
  2. General remarks
  3. Soil energy and water budget
  4. Examples of parametrization schemes
  5. Subgrid-scale heterogeneity
  6. Validation and intercomparison
  7. Initial values
  8. Snow modelling
  9. Conclusions
  10. References

PDF iconThe role of the land surface in the climate system

By P Viterbo

Contents

  1. Introduction
  2. Surface energy and water budget
  3. Time scales and the role of soil moisture
  4. Impact of land surface on weather: A brief literature survey
  5. Examples from ECMWF recent experience
  6. Conclusions
  7. References

PDF iconTheory of linear gravity waves

By T Palmer

Contents

  1. Simple properties of internal gravity waves
  2. Gravity-wave drag
  3. References

PDF iconSubgrid-scale orographic drag

By MJ Miller

Contents

  1. General principles
  2. Description of the scheme
  3. Specification of subgrid-scale orography
  4. Appendix
    • A. List of symbols

PDF iconRadiation transfer

By J-J Morcette

Contents

  1. Introduction: An historical perspective
  2. The Earth's radiative balance and its implications
  3. The theory of radiation transfer
  4. Radiation schemes in use at ECMWF
  5. Comparisons with observations
  6. Conclusions and perspective
  7. References

Predictability

PDF iconChaos and weather prediction

By R Buizza

Contents

  1. Introduction
  2. The Lorenz system
  3. Numerical weather prediction
  4. Sources of forecast error
  5. The ECMWF Ensemble Prediction System
  6. Targeted observations
  7. Summary and future developments
  8. Conclusion
  9. Acknowledgements
  10. References

PDF iconPredicting uncertainty in forecasts of weather and climate

By T Palmer

Contents

  1. Introduction
  2. The Liouville equation
  3. The probability density function of initial error
  4. Representing uncertainty in model formulation
  5. Error growth in the linear and nonlinear phase
  6. Applications of singular vectors
  7. Forecasting uncertainty by ensemble predictions
  8. Verifying forecasts of uncertainty
  9. The economic value of predicting uncertainty
  10. Concluding remarks