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Waves, Information and Local Predictability

Waves, Information and Local Predictability. IPAM Workshop Presentation By Joseph Tribbia NCAR. Waves, information and local predictability: Outline. History Motivation Goals of targeted observing (Un)certainty prediction and flow Analysis of simple basic flows

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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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