Waves Information and Local Predictability IPAM Workshop Presentation

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)

4 D 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: 1 D Barotropic 1 D Baroclinic 2 D Spherical

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

How does relative certainty propagate? • Simplest example: 1 D 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=10 d variance t-=10 d

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

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

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

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

Barotropic vorticity equation with solid body rotation Relative variance at t=4 d streamfunction Relative variance at t=20 d 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