Annual Cycle and the Prediction of Interannual Variability

1. Annual Cycle and the Prediction of Interannual Variability Zhaohua Wu Center for Ocean-Land Atmosphere Studies Calverton, Maryland, USA

2. MY CONFESSION Climate Test Bed Seminar Series, NOAA

3. OUTLINE • Speculations (preliminary thoughts) • Climate variability of different timescales are driven by different physical mechanisms • Variability associated with one physical mechanism is more predictable than the total variability • Justifications • Annual cycle and anomaly • Prediction in a new paradigm Climate Test Bed Seminar Series, NOAA

4. TYPICAL DATA Climate Test Bed Seminar Series, NOAA

5. Random forcing climate data AN ANALOGUE High frequency oscillation Low frequency oscillation Climate Test Bed Seminar Series, NOAA

6. DIFFICULTY IN PREDICTION Climate Test Bed Seminar Series, NOAA

7. ADVANTAGES OF SEPARATION Climate Test Bed Seminar Series, NOAA

8. Delayed term related to Kelvin wave reflection at the eastern boundary Local instability Nonlinear damping Background climatology ENSO MODELS • Delayed Oscillator Climate Test Bed Seminar Series, NOAA

9. SOLUTIONS OF THE FORCED DELAYED OSCILLATION MODEL Climate Test Bed Seminar Series, NOAA

10. AM/FM SINGNAL Climate Test Bed Seminar Series, NOAA

11. anomaly data annual cycle PREDICTION OF ANOMALY • Anomaly • Prediction model The matrix M and the anomaly are dependent on the definition of annual cycle. The matrix M is very sensitive to high frequency component of quasi-periodic signal, leading to the difficulty of prediction Climate Test Bed Seminar Series, NOAA

12. ANNUAL CYCLE IN ANOMALY Note: After removing climatological annual cycle, we still see locally in the anomaly a sort of annual cycle. Then, what is the annual cycle? Climate Test Bed Seminar Series, NOAA

13. FORCED LORENZ MODEL Climate Test Bed Seminar Series, NOAA

14. PROBLEMS with AMS DEFINITION • Numerous versions of annual cycle • Assuming the climate system is stationary • Implying the climate system is linear • Implying the later evolution of climate system can change what has already happened Climate Test Bed Seminar Series, NOAA

15. DEFINITION OF MAC From data analysis perspective, AC is “An adaptively and intrinsically determined temporally local component of the climate data which contains frequency and amplitude modulations and has quasi-annual period” (Amplitude frequency modulated annual cycle, or MAC) Climate Test Bed Seminar Series, NOAA

16. A B C D t THE ULTIMATE CONSTRAINOF DATA ANALYSIS • Data analysis should be temporally local, for • Later evolution can not change the past • What matter to a dynamic system’s future evolution are its initial condition and boundary condition Climate Test Bed Seminar Series, NOAA

17. METHOD FOR EXTRACTING MAC • The Ensemble Empirical Mode Decomposition (EEMD) • Based on the Empirical Mode Decomposition, a method based on the principles of adaptiveness and temporal locality • A natural dyadic filter based on data characteristics • Mimicking a multiple observation scenario for singly observed data by adding noise to the data and averaging out the added noise through ensemble approach • A noise-assisted data analysis (NADA) method Climate Test Bed Seminar Series, NOAA

18. Chirp Waves Norden E Huang EXTREMA & ENVELOPES Climate Test Bed Seminar Series, NOAA

19. signal source 1 signal source 2 receiver EMPIRICAL MODE DECOMPOSITION & HILBERT-HUANG TRANSFORM Overall Signal Climate Test Bed Seminar Series, NOAA

20. EMPIRICAL MODE DECOMP. Climate Test Bed Seminar Series, NOAA

21. EMD SEPARATION Climate Test Bed Seminar Series, NOAA

22. LENGTH-OF-DAY Climate Test Bed Seminar Series, NOAA

23. SOME KNOWN CYCLES Climate Test Bed Seminar Series, NOAA

24. CHANGE OF OUR UNDERSTANDING • The phase of ENSO Interannual variability does not locked to annual cycle • ENSO phase locking to annual cycle may be only a result of phase locking of the “residual annual cycle” contained in the traditional anomaly to annual cycle itself Climate Test Bed Seminar Series, NOAA

25. PHASE LOCKING “Warm ENSO events tend to peaking in winter season”? Note: From traditional anomaly, the phase locking can not be determined directly; rather, it is determined indirectly through examining the standard deviation of individual month: if the interannual variability tends to peak in a particular month, the standard deviation of the anomaly at that particular month is larger. Climate Test Bed Seminar Series, NOAA

26. EVIDENCE OF LOCKING Climate Test Bed Seminar Series, NOAA

27. ANOMALIES wrt TAC AND MAC Climate Test Bed Seminar Series, NOAA

28. PHASE LOCKING? Climate Test Bed Seminar Series, NOAA

29. SCATTERED ENSO EVENTS Climate Test Bed Seminar Series, NOAA

30. ENSO MODELS • Models with intermediate complexity • Specified climatology has an annual forcing term ~ almost always peaking in a particular season • When perpetual monthly (e.g., jan, jul) climatology specified ~ not peaking at a particular season • Delayed Oscillator Delayed term related to Kelvin wave reflection at the eastern boundary Local instability Nonlinear damping Background climatology Climate Test Bed Seminar Series, NOAA

31. SOLUTIONS OF THE FORCED DELAYED OSCILLATION MODEL Climate Test Bed Seminar Series, NOAA

32. “SPRING BARRIER” • The “spring barrier” appeared in the prediction of traditional anomaly . • When anomaly is defined with respect to MAC, “spring barrier” disappear Climate Test Bed Seminar Series, NOAA

33. SPRING BARRIER PROBLEM Climate Test Bed Seminar Series, NOAA

34. SPRING BARRIER REDUCED Climate Test Bed Seminar Series, NOAA

35. MAC & ITS FREQUENCY Climate Test Bed Seminar Series, NOAA

36. ALTERNATIVE PREDICTION SCHEME Ai,predictedis a relatively slowly varying quantity, easier to predict Climate Test Bed Seminar Series, NOAA

37. SCHEMATIC ILLUSTRATION Climate Test Bed Seminar Series, NOAA

38. RETROSPECTIVE PREDICTION Climate Test Bed Seminar Series, NOAA

39. FURTHER WORKS(SEEKING HELPS FROM YOU) • End problem in EMD/EEMD • Understanding physical causes of envelope changes • Systematic error correction Conclusion: I believe there are promising aspects of this new approach. Climate Test Bed Seminar Series, NOAA