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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 Conclusions and ramifications Some general problems for the future 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) 4D method of assimilation Recently: variant of Kalman filter 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? Goals of Targeted Observing • ‘Better’ forecast in a local domain-difficult to achieve because of random errors • Reduced forecast uncertainty in domainachievable • Need a metric for increased reliabilityrelative entropy (G,S,M,K,DS,N,L) Baumhefner experiments: The wave perspective: models 3 Models: 1D Barotropic 1D Baroclinic 2D Spherical Uncertainty propagation Compare two initial covariances One with uniform uncertainty, the other with locally smaller variance 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 Evolution after 10 days pulse at t=10d variance t-=10d Unstable 1D Linear 2-level QG Pulse at t=10d Variance at t=10d Add downstream U variation to 2-level model x variation of U Pulse at t=3d Variance at t=3d Add downstream U variation to 2-level model Pulse at t=10d Variance at t=10d Relative uncertainty: x-varying U pulse t=3d relative variance t=3d pulse t=10d relative variance t=10d Barotropic vorticity equation with solid body rotation Relative variance at t=4d streamfunction Relative variance at t=20d streamfunction 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 Future: nonlinear problem (Bayes) Parameter estimation