1. Looking for Climate Signals in Ice Cores Santa Fe, 2011 Gerald R. North Thanks to Petr Chylek for the data and encouragement. g-north@tamu.edu

2. Two simulated time series of length of the time series: N=1000 This time series has a signal of amplitude 0.3 and period of 11y period added: can you see it? Pure white noise N(0, 1) Pure white noise N(0, 1) + 0.3 Sin[2  t/11]

3. Periodogram: Square of the Discrete Fourier Transform. 2 std above mean We can reduce sampling noise by smoothing the periodogram 10.82y Note: 9 out of 500 lines (2.2%) exceed 2 std Pure white noise N(0, 1) + 0.3 Sin[2  t/11]

4. Here is a 25 line (box car) moving average of the periodogram. Error bar is divided by 5. 12.5y Note the bias in frequency of the line Pure white noise N(0, 1) + 0.3 Sin[2  t/11]

5. Another way: Sort the periodogram into bins with 25 lines in each: 11y peak disappears! Pure white noise N(0, 1) + 0.3 Sin[2  t/11]

6. A better approach: Use the lag window method 0 0 This step to 0 is too abrupt time To reduce the effects of the sharp transition at the beginning and end of the time series we apply the window by: Parzen’s Lag Window

7. 10.83y 2 std above mean Pure white noise N(0, 1) + 0.3 Sin[2  t/11]

8. Example: white noise (  =1) with a sharp peak of amplitude 0.3 at period 11 y Pure white noise N(0, 1) + 0.3 Sin[2  t/11] Moral: Lag Window (Parzen’s here) is good for sharp lines + noise

9. Amplitude of the 11y oscillation in TSI: 0.07% Sun Spots and Total Solar Irradiance

10. 25.04 -> period of 10.49 years

11. Estimated Response to 10y Cycle 0.1% TSI Forcing based on a simple energy balance climate model with a slab (mixed layer) ocean (North, Stevens, Wu, 2004) Plausibility of seeing the 11y cycle in surface temperature data

12. 90% confidence intervals Simultaneous detection of solar cycle, volcanic, aerosol, greenhouse gases North, G. R. and Q. Wu, 2001: Detecting climate signals using space-time EOFs. J. Climate, 14, 1839-1862. 36 global sites20 tropical sites Noise-forced

13. Top-Down influence of the solar cycle on temperatures. Coughlin & Tung, 2004. Comment: this effect adds to the surface effect (EBM). They used Empirical Mode Decomposition

14. 10.7y Here is a simulation of white noise background (0, 1) with a 0.05 amplitude sine wave. The white noise is about the variance from year to year in South Greenland. This shows that it is plausible to detect a signal of this strength. The result is robust; I did the simulation many times. The other peaks jump around, but the 11y peak stays relatively fixed.

15. Dye3 Core Results Comments: the Dye 3 site is close to the coast and should reflect AMO, NAO and other activities. But we might look for the 11y cycle as well. The data are 18 O which probably indicates temperature at the time of deposition. But it may indicate other things such as North American storm tracks, etc. Dye3

16. Conceptual Model: the time series is an AR1 process with possible additive sharp lines. Ideal AR1 spectral density Parzen Window To get the period of oscillation, divide the abscissa into 3600 Dye 3 Spectral Density.

17. 20 bandwidths (expect 1 peak to exceed --- in 20 BWs) 19.6 14.210.3 95% if freq is known a priori 42.1 Dye 3 (South Greenland) analysis for N=3600 years, using the Parzen Window

18. 11yr Band-Passed Time Series

19. Sunspots From Foukal’s book, attributed to Eddy Band-Passed Taylor Dome Time Series Delaygue&Bard, 2011 10 Be 14 C I have no great confidence in my Dye 3 reconstruction (sampling error issues).

20. Taylor Dome: 600 yr Record http://nsidc.org/data/docs/agdc/nsidc0108_wahlen/index.html Taylor Dome Data personally communicated by Petr Chylek

21. 10.3 20.0 5 bandwidths (expect 1 peak to exceed --- in 20 BWs) Taylor Dome (Antarctica) analysis for N=600 years, using the Parzen Window

22. Robert G. Currie Papers Currie uses Max Entropy Spectral Analysis to detect the Lunar Tidal (18.6y) and Solar Cycle Peaks in North America Station (and other) data. He pools hundreds of records to increase signal to noise.

23. More from Currie ( 1996)

24. The M2 (18.6y) tidal constituent. Amplitude is indicated by color, and the white lines are co-tidal differing by 1 hr. The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6 hour period.

25. Surely the solar cycle and the tidal contributions are tiny perturbations in the time series. How could these be important in the spectral analysis? Answer: the tidal 18.6y signal is common to all station time series and coherent (deterministic, nearly same phase at all sites). When we add thousands of records together to form an average, most of the natural variability cancels out, but not the coherent signal. Could this explain the 18 year cycle in the Berkeley record for the 1800s? The tides are big where BEST has data. Answer: the 10.5y signal is from a single time series but the record is 60 cycles long (Taylor Dome) and 360 cycles long (Dye 3) A deterministic peak in a periodogram grows as the record grows, but the noise does not. Thoughts:

26. Conclusions Response to 10.5y solar cycle and surface temperature appears to be real. Surface response appears to be larger than EBM simulation (probable top-down contribution) There could be a tidal signal (18.6y) in the data. There is not much evidence for a long term AMO (pure tone at 60 or 70y) in this study.

27. Supplementary Slide follow

28. global average Nature 1994 First Notice of AMO actually named AMO by Richard Kerr, Science

29. Bartlett WindowDye 3 N=3600y mdofBWPeaks (y) 501661089.9, 12.9 200442710.1, 14.1 4002013.510.4

30. Dye 3Parzen Window N=3600y 10.5y mdofBWPeaks (y) 5034713310.5 4008316.710.4

31. Taylor DomeBartlett Window mdofBWPeaks (y) 5034369.8, 19.4 100171810.1, 20.4

32. Taylor DomeParzen Windows mdofBWPeaks (y) 5034229.7, 18.5 2008.55.610.3, 21.1