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Waves, Information and Local Predictability

This presentation by Joseph Tribbia from NCAR discusses the history, motivation, goals of targeted observing, uncertainty prediction, and analysis of simple basic flows in relation to waves, information, and local predictability. The presentation also explores the conclusions, ramifications, and future challenges in the field.

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Waves, Information and Local Predictability

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  1. Waves, Information and Local Predictability IPAM Workshop Presentation By Joseph Tribbia NCAR

  2. Waves, information and local predictability: Outline • History • Motivation • Goals of targeted observing • (Un)certainty prediction and flow • Analysis of simple basic flows • Conclusions and ramifications • Some general problems for the future

  3. Brief history of data assimilation • NWP requires initial conditions • Interpolation of observations (Panofsky,Cressman, Doos) • Statistical interpolation (Gandin, Rutherford, Schlatter) • Four-dimensional assimilation (Thompson, Charney, Peterson, Ghil, Talagrand)

  4. 4D method of assimilation

  5. Recently: variant of Kalman filter

  6. Motivation • Lorenz and Emanuel (1998): invented the field of adaptive observing • Suppose one wants to improve Thursday’s forecast in LA, where should one observe the atmosphere today?

  7. Goals of Targeted Observing • ‘Better’ forecast in a local domain-difficult to achieve because of random errors • Reduced forecast uncertainty in domain-achievable • Need a metric for increased reliability-relative entropy (G,S,M,K,DS,N,L)

  8. Baumhefner experiments:

  9. The wave perspective: models 3 Models: 1D Barotropic 1D Baroclinic 2D Spherical

  10. Uncertainty propagation Compare two initial covariances One with uniform uncertainty, the other with locally smaller variance

  11. How does relative certainty propagate? • Simplest example: 1D Rossby wave context • compare pulse (mean) propagation (group velocity) with (co)variance propagation pulse t=0 var t=o

  12. Evolution after 10 days variance t-=10d pulse at t=10d

  13. Unstable 1D Linear 2-level QG Pulse at t=10d Variance at t=10d

  14. Add downstream U variationto 2-level model x variation of U Pulse at t=3d Variance at t=3d

  15. Add downstream U variation to 2-level model Pulse at t=10d Variance at t=10d

  16. Relative uncertainty: x-varying U relative variance t=3d pulse t=3d pulse t=10d relative variance t=10d

  17. Barotropic vorticity equationwith solid body rotation Relative variance at t=4d streamfunction Relative variance at t=20d streamfunction

  18. Conclusions and ramifications • Pulse perturbations and error variance differences propagate similarly if weighted properly • Aspects of variance propagation ascribed to nonlinearity may be ‘weighted ‘ wave dispersion • Group velocity gives a wave dynamic perspective to adaptive observing strategies

  19. Future: nonlinear problem (Bayes)

  20. Parameter estimation

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