On the Applications of HHT to Climate Studies

1. On the Applications of HHT to Climate Studies Norden E. Huang Research Center for Adaptive Data Analysis National Central University

2. History of HHT 1998: The Empirical Mode Decomposition Method and the Hilbert Spectrum for Non-stationary Time Series Analysis, Proc. Roy. Soc. London, A454, 903-995. The invention of the basic method of EMD, and Hilbert transform for determining the Instantaneous Frequency and energy. 1999: A New View of Nonlinear Water Waves – The Hilbert Spectrum, Ann. Rev. Fluid Mech. 31, 417-457. Introduction of the intermittence in decomposition. 2003: A confidence Limit for the Empirical mode decomposition and the Hilbert spectral analysis, Proc. of Roy. Soc. London, A459, 2317-2345. Establishment of a confidence limit without the ergodic assumption. 2004: A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method, Proc. Roy. Soc. London, A460, 1597-1611 Defined statistical significance and predictability. 2007: On the trend, detrending, and variability of nonlinear and nonstationary time series. Proc. Natl. Acad. Sci., 104, 14,889-14,894. The correct adaptive trend determination method 2009: On Ensemble Empirical Mode Decomposition. Advances in Adaptive Data Analysis 1, 1-41. 2009: On instantaneous Frequency. Advances in Adaptive Data Analysis (in press)

3. Current Efforts and Applications • Non-destructive Evaluation for Structural Health Monitoring • (DOT, NSWC, DFRC/NASA, KSC/NASA Shuttle, THSR) • Vibration, speech, and acoustic signal analyses • (FBI, and DARPA) • Earthquake Engineering • (DOT) • Bio-medical applications • (Harvard, Johns Hopkins, UCSD, NIH, NTU, VHT, AS) • Climate changes • (NASA Goddard, NOAA, CCSP) • Cosmological Gravity Wave • (NASA Goddard) • Financial market data analysis • (NCU) • Theoretical foundations • (Princeton University and Caltech)

4. Climate studies Climate[ME climat < LL clima < Gr. klima : region, zone < base of klinein, to slope (or incline); the slope of earth from equator toward the pole]: the study of the trend and the fluctuations of the regional and long term averaged weather patterns. The activities include • Data Analysis • Physical Processes • Modeling

5. Problems HHT could help • Data Analysis • Trend and cycle • How to remove annual cycle • What is trend • Climate variation scales • Tectonic scale • Glacial scale • Global fluctuations • Modeling • validation

6. Data Processing and Data Analysis • Processing[proces < L. Processus < pp of Procedere = Proceed: pro- forward + cedere, to go] : A particular method of doing something. • Data Processing >>>> Mathematically meaningful parameters • Analysis[Gr. ana, up, throughout + lysis, a loosing] : A separating of any whole into its parts, especially with an examination of the parts to find out their nature, proportion, function, interrelationship etc. • Data Analysis >>>> Physical understandings

7. A Plea for Adaptive Approaches The job of a scientist is to listen carefully to nature, not to tell nature how to behave. Richard Feynman To listen is to use adaptive method and let the data sing, and not to force the data to fit preconceived modes.

8. Problems HHT could help • Data Analysis • Trend and cycle • How to remove annual cycle • What is trend • Climate variation scales • Tectonic scale • Glacial scale • Global fluctuations • Modeling • validation

9. CO2 Data Analysis Wu, Zhaohua, E. K. Schneider, B. P. Kirtman, E.S. Sarachik, N.E. Huang and C. J. Tucker, 2009: Amplitude-Frequency Modulated Annual Cycle: An Alternative Reference Frame for Climate Anomaly (to appear Climate Dynamics).

10. MAUNA LOA CO2

11. WAVELET DECOMP.

12. WAVELET NANAC

13. EEMD DECOMP.

14. WAVELET DECOMP.

15. STATISTICS

16. Observations • Decomposition with a priori basis produces components with wave form similar to the basis adopted. • Decomposition with adaptive basis produces components with wave form retaining the physical properties of the underlying processes. • Adaptive basis could be used as filters that would preserve the intrinsic properties of the variation in the data, useful for studying change in growth seasons.

17. Problems HHT could help • Data Analysis • Trend and cycle • How to remove annual cycle • What is trend • Climate variation scales • Tectonic scale • Glacial scale • Global fluctuations • Modeling • validation

18. The State-of-the-Arts“One economist’s trend is another economist’s cycle”Engle, R. F. and Granger, C. W. J. 1991 Long-run Economic Relationships. Cambridge University Press. • Simple trend – straight line • Stochastic trend – straight line for each quarter

19. IPCC Global Mean Temperature Trend

20. PhilosophicalProblem Anticipated 名不正則言不順 言不順則事不成 ——孔夫子

21. OnDefinition Without a proper definition, logic discourse would be impossible.Without logic discourse, nothing can be accomplished.Confucius

22. Definition of the Trend Within the given data span, the trend is an intrinsically fitted monotonic function, or a function in which there can be at most one extremum. The trend should be an intrinsic and local property of the data; it is determined by the same mechanisms that generate the data. Being local, it has to associate with a local length scale, and be valid only within that length span, and be part of a full wave length. The method determining the trend should be intrinsic. Being intrinsic, the method for defining the trend has to be adaptive. All traditional trend determination methods are extrinsic.

23. Definition of Detrend and Variability Within the given data span, detrend is an operation to remove the trend. Within the given data span, the Variability is the residue of the data after the removal of the trend. As the trend should be intrinsic and local properties of the data; Detrend and Variability are also local properties. Being local, they have to associate with a local length scale, and be valid only within part of a full local wave length. The method determining the trend should be intrinsic. Being intrinsic, the method for defining the trend has to be adaptive. All traditional trend determination methods are extrinsic and/or subjective.

24. Global Temperature Anomaly Annual Data from 1856 to 2003

25. Global Temperature Anomaly 1856 to 2003

26. IMF Mean of 10 Sifts : CC(1000, I)

27. Mean IMF

28. STD IMF

29. Statistical Significance Test

30. Data and Trend C6

31. Rate of Change Overall Trends : EMD and Linear

32. Variability with Respect to Overall trend

33. Data and Trends: C5:6

34. Trend Period C5

35. Rate of Change Trend C5:6

36. Variability with Respect to 65-Year trend

37. How are GSTA data derived? Noise Reduction Using Global Surface Temperature Anomaly data 1856 to 2003

38. Jones (2003) Monthly GSTA Data

39. Jones (2003) 12 Monthly GSTA Data

40. Jones (2003) 12 Monthly GSTA Data

41. Jones (2003) GSTA Data Seasonal Variation

42. Jones (2003) GSTA Data Seasonal Variance

43. Jones Monthly GSTA Data : Fourier Spectrum

44. Observations • Annual data is actually the mean of 12:1 down sample set of the original monthly data. • In spite of the removal of climatologic mean, there still is a seasonal peak (1 cycle / year). • Seasonal Variation and Variance are somewhat irregular. • Data contain no information beyond yearly frequency, for higher frequency part of the Fourier spectrum is essentially flat. • Decide to filtered the Data with HHT before down sample.

45. Need a Filter to Remove Alias • Traditional Fourier filter is inadequate: • Removal of Harmonics will distort the fundaments • Noise spikes are local in time; signals local in time have broad spectral band • HHT is an adaptive filter working in time space rather than frequency space.

46. Jones Monthly GSTA Data : IMF

47. Jones Monthly GSTA Data : IMF Smoothed

48. Jones Monthly GSTA Data & HHT Smoothed

49. Jones Monthly GSTA Data : Fourier Spectrum Data & Smoothed

50. 12 Monthly GSTA Data HHT Smoothed