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
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
pulse at
t=10d
variance
t-=10d

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

14. Add downstream U variation to 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
pulse
t=3d
relative
variance
t=3d
pulse
t=10d
relative
variance
t=10d

17. Barotropic vorticity equation with 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