1. Chaos: The enemy of seasonal forecasting! Richard Washington University of Oxford rwashing@nimbus.geog.ox.ac.uk

2. DETERMINISTIC FORECAST Climate Model Initial conditions

3. DETERMINISTIC FORECAST Climate Model Initial conditions

4. DETERMINISTIC FORECAST Climate Model Initial conditions Realisation of weather will be different from observed After a few days…..

5. DETERMINISTIC FORECAST Climate Model Initial conditions BEWARE THE BUTTERFLY!

6. Climate Model

7. Initial conditions

8. Climate Model Initial conditions

9. ENSEMBLE FORECAST Climate Model Initial conditions

10. Very Low Skill Very High Skill

12. Sensitivity to initial conditions……. How can we better understand this?

13. The Game of Pinball

14. Is the trajectory of the ball predictable? Is the system predictable? How long will the ball stay on the board?

15. How many seconds does it take for the ball to vanish?

17. The system is fixed: nothing changes from the release of one ball to the next…. The gradient of the board is the same The strength of the magnets is the same The position of the magnets is the same

18. So, why is the system unpredictable?

19. Only the initial position of the ball changes from one release to the next:

20. System is sensitive to initial conditions……. The atmosphere in the mid latitudes never forgets the initial conditions

21. Understanding the problem graphically……

22. y=2x+1 y=x 2 +1 Graphical solutions To simple equations

23. .............1.............2.............3 Take a system of 3 equations System is simpler than the atmosphere….

25. COLD & WETHOT & DRY

26. Evolution over 7 days……

27. COLD & WETHOT & DRY 1 2 3 4 5 6 7

28. Evolution over 7 days…… day 1: cold and wet day 2: hot and dry day 3: hot and dry day 4: hot and dry day 5: hot and dry day 6: hot and dry day 7: cold and wet COLD & WET HOT & DRY 1 2 3 4 5 6 7

29. Evolution over 7 days…… Sensitivity to initial conditions

30. Experiment A Evolution over 7 days……

31. COLD & WETHOT & DRY 2 1 1 34 5 7 6

32. Evolution over 7 days…… day 1: hot and dry day 2 hot and dry day 3: hot and dry day 4: hot and dry day 5: hot and dry day 6: hot and dry day 7: hot and dry

33. Experiment B Evolution over 7 days……

34. COLD & WETHOT & DRY 2 1 3 4 5 6 7

35. Evolution over 7 days…… day 1: hot and dry day 2: cold and wet day 3: cold and wet day 4: cold and wet day 5: cold and wet day 6: cold and wet day 7: cold and wet

36. Experiment AExperiment B day 1: hot and dry day 2: hot and dry day 3: hot and dry day 4: hot and dry day 5: hot and dry day 6: hot and dry day 7: hot and dry day 1: hot and dry day 2: cold and wet day 3: cold and wet day 4: cold and wet day 5: cold and wet day 6: cold and wet day 7: cold and wet

37. COLD & WETHOT & DRY 2 1 3 4 5 6 7 2 3 5 6 7 4

38. Lorenz Attractor illustrates how the atmosphere: is sensitive to infenitismally small initial conditions..... 7 days = hot and dry 7 days = cold and wet BUT Initial conditions A = B Weather/climate tends to modes or patterns of variability

39. How can we quantify this sensitivity to initial conditions? How can we establish modes of atmospheric variability?

42. How chaotic is the atmosphere?

43. Experimental Design- Pills and Patients t1 t2 t3 t4 ? ? ?? ? ? ? ? ?? ??

44. Experimental Design- Pills and Patients t1 t2 t3 t4 RESULT????

45. Experimental Design- SST and Climate t1 t2 t3 t4 RESULT SST

47. Experiment 1Experiment 2

48. 123

49. Very Low Skill Very High Skill

50. What variance is common to each model run? What variance is unique to each model run? Forced Vs Free variance Forced Vs Free manifold Signal Vs Chaos

51. Simplest Case: Forced Vs Free Manifold single variable (rainfall) single model grid box Total Variance = forced variance + internal variability

52. Step 1: Estimate Internal Variability computed as variance of each datum from its ensemble mean N = number of years of forcing (92 years) n = number of experiments (6) X = ensemble mean for ith year

53. Step 2: Estimate variance of ensemble means computed as variance of the ensemble mean from the mean of all the data

54. variance ensemble = variance due to forcing + 1/n variance due to internal variability Step 3: Estimate variance due to Forcing by SST

55. Actual Experiment UK Met Office Model: HADAM2A Forced with SST (GISST data set) 1904-1996 6 model runs = 6 twentieth centuries! 6 unique initial conditions

56. What variance is common to each model run? What variance is unique to each model run? Forced Vs Free variance Forced Vs Free manifold Signal Vs Chaos

57. JFM % forced rainfall variance

58. JAS % forced rainfall variance

59. Chaos – the enemy of seasonal forecasting! Like many systems, the atmosphere is sensitive to initial conditions The same forcing due to SST can produce a different outcome if the starting conditions are different But the tropics is the least chaotic part of the atmosphere We can design methods to overcome the problem partially…e.g. ensemble forecasting

60. Readings Lorenz, E.N. 1995: The essence of chaos, UCL Press Rowell,-D.-P. et al 1995: Variability of summer rainfall over tropical north Africa (1906-92) : observations and modelling. Quarterly-Journal,-Royal-Meteorological- Society. 121(523), pp 669-704. Palmer T.N 1998: Nonlinear dynamics and climate change, Bulletin of the American Met Society, 79, 7, 1411-1423. Washington, R. 2000: Quantifying chaos in the atmosphere, Progress in Physical Geography.