1. SOES 6047 Global Climate Cycles L21: Orbital parameters from geological data
Dr. Heiko Pälike

2. Last “orbital” lecture:
Orbital time scale calibrations:
get an overview of what orbital time scale calibration & tuning is
get an overview of how time scale calibration is done
appreciate the improved accuracy that orbital time scale calibrations yield in the older parts of the geological record
appreciate that current (non-orbitally calibrated) time scales rely on a few well dated radiometric dates

3. Objectives & learning outcomes
appreciate that one can use the geological record to improve orbital (and Earth System) models
learn that the orbital variations of the Earth are partially controlled by its own physics (“the Earth model”)
understand the terms “tidal dissipation” and “dynamical ellipticity”, and their relevance to insolation calculations
appreciate the nature and implications of chaos in solar system calculations
learn how geological records can be used to constrain the chaotic nature of insolation calculations

4. Lecture outline
The Earth model: Earth & climate processes that affect the orbital motion around the Sun
Examples how these parameters have been extracted from deep sea records
Chaos in the Solar System: do we care?
How to improve astronomical models with geological data

5. Some references
Berger, A. & Loutre, M. F. (1991), ‘Insolation values for the climate of the last years’, Quaternary Science Reviews 10, 297–317.
Berger, A. & Loutre, M. F., ‘Astronomical forcing through geological time’, Orbital forcing and cyclic sequences (IAS Special Publication), P. L. de Boer & D. G. Smith, eds. (Blackwell Scientific, 1994), vol. 19, 15–24.
Bills, B. G. & Ray, R. D. (1999), ‘Lunar orbital evolution: A synthesis of recent results’, Geophysical Research Letters 26, 3045– 3048.
Hilgen, F. J., et al. (1993), ‘Evaluation of the astronomically calibrated time scale for the late Pliocene and earliest Pleistocene’, Paleoceanography 8, 549–565.
Imbrie, J., et al., ‘The orbital theory of Pleistocene climate: Support from a revised chronology of the marine O record’, Milankovitch and Climate, Part 1, A. L. Berger et al., eds. (Reidel Publishing Company, 1984), 269–305.
Laskar, J. (1999), ‘The limits of Earth orbital calculations for geological time-scale use’, Philos. Trans. R. Soc. London Ser. A 357, 1735–1759.
Laskar, J., Joutel, F., & Boudin, F. (1993), ‘Orbital, Precessional, and Insolation Quantities for the Earth from -20 Myr to +10 Myr’, Astron. Astrophys. 270, 522–533.
Laskar, J., et al. (2004), ‘A long term numerical solution for the insolation quantities of the Earth’, Astron. Astrophys. 428, 261– 285. Astronomical solution available from (May 2004).
Levrard, B. & Laskar, J. (2003), ‘Climate friction and the Earth’s obliquity’, Geophysical Journal International 154, 970–990.
Lourens, L. J., Wehausen, R., & Brumsack, H. J. (2001), ‘Geological constraints on tidal dissipation and dynamical ellipticity of the Earth over the past three million years’, Nature 409, 1029–1033.
Lourens, L. J., et al. (1996), ‘Evaluation of the Plio-Pleistocene astronomical timescale’, Paleoceanography 11, 391–413.
Pälike, H., Laskar, J., & Shackleton, N. J. (2004), ‘Geologic constraints on the chaotic diffusion of the solar system’, Geology
Pälike, H. & Shackleton, N. J. (2000), ‘Constraints on astronomical parameters from the geological record for the last 25 Myr’, Earth Planet. Sci. Lett. 182, 1–14.
Pisias, N. G. & Moore, T. C. (1981), ‘The evolution of Pleistocene climate: a time series approach’, Earth and Planetary Science Letters 52, 450–458.

6. Introduction
The accuracy for relative age scales based on astronomical age calibrations for the late Neogene is conceptually assumed to be better than one half of the shortest cycle length considered
Further back in geological time, astronomical age calibrations have a much smaller fractional error than radiometric age determinations (Lecture 13)
BUT:
how accurate can we be at the precession cycle level?
what determines the uncertainty on short time scales?
Uncertainties from:
The Earth’s climate machine (phase lags behind forcing)
The Earth recorder (bioturbation, post-depositional effects)
The astronomy

7. Determination of phase lags
Milankovitch postulated that it is summer insolation variations at around 65°N that have the largest influence on NH glacial- interglacial cycles
Imbrie (1984) ran a very simple ice-sheet model, that was based on an overall 17kyr time constant using radiometric ages for glacial cycles, and resulted in a phase lag of ice-sheet development behind insolation of about ~5 kyr for climatic precession, and ~8 kyr for obliquity (slightly improved model by Pisias, 1990)
Hilgen et al. refined these estimates using the youngest sapropel layer S1 (radiometrically dated between 7-10 kyr calendar year age)
found shorter time lag of 3 kyr for climatic precession, 6kyr for obliquity
Any additional errors?

8. Additional uncertainties
For insolation, which month is controlling global climate cycles?
Example: for each consecutive month, offset between insolation series of about ~2 kyr (12 months, ~24 kyr)
(W/m^2)
Age (kyr)
Example: May and July mid-monthly insolation at 65°N, July lags May by ca. 4 kyr for climatic precession
Graphs produced by Heiko Palike, University of Southampton using AnalySeries software

9. Geological hints for phase lags ..
Using the thickness variations of sapropel layers S6-S9 as proxy for the strength of insolation variations, Lourens et al. (1996) suggest a shorter obliquity time lag of 3 kyr
thick
thin
thick
thin
Reproduced by permission of American
Geophysical Union: Lourens L.J.,
Antonarakou A., Hilgen F.J., Van Hoof A.
A.M., Vergnaud-Grazzini C., Zachariasse
W.J., Evaluation of the Plio-Pleistocene as
tronomical timescale. Paleoceanography,
v. 11(4), p April 1996.
Copyrigh [1996] American Geophysical
Union.

10. Any other complications?
YES!
In addition to the complications of the climate machine and the Earth’s recorder, there is also uncertainty about the astronomical calculations
The astronomical calculations of the Earth’s orbit around the Sun can be split into a
Earth-physics dependency .... the “Earth Model” (“tidal dissipation”,“dynamical ellipticity”, “climate friction”)
Long-term interaction between all the planets, independent of the Earth&Moon, but leading to long-term chaotic variations of the astronomical patterns
Can we constrain these two uncertainties with geological data?

11. Tidal dissipation E M lunar semimajor axis (103 km) ocean model
Reproduced by permission of American Geophysical Union: Bills, B. G., and R. D. Ray, Lunar
orbital evolution: A synthesis of recent results, Geophys. Res. Lett., v. 26(19), p. 3045–3048.
16 July Copyrigh [1999] American Geophysical Union. E M
tide delay ~ 610s
tidal bulge
breaking couple
receeding
3.8 cm/year
Bills & Ray, G.R.L., Oct.1999
400
ocean model
350
lunar semimajor axis (103 km)
300
Observables:
present day lunar retreat (laser ranging)
change of length of day from ancient corals, shells, tidal laminates
relationship of astronomical frequencies in geological records
350
present rate
-1500
-1000
-500
time b.p.(106 yr)
datapoints from tidal rhythmites
Figure produced by Heiko Palike, University of Southampton
The difference between a model with current day slowdown and no slowdown for obliquity cycles (41k period) is very small and would be: no slowdown: ~487 cycles over 20Myr current slowdown: ~491 cycles over 20Myr BUT: important effect on interference pattern with climatic precession

12. Influence of tidal dissipation on cycle pattern:
Three different astronomical solutions
Berger (no dissipation)
Laskar (no dissipation)
Laskar w. present day dissipation
Graph produced by Heiko Palike, University of Southampton

13. Are there observables to constrain tidal dissipation?
Have to be very careful to avoid circular argument when dealing with “tuned” data sets
Problem: very small, but systematic, difference between models with and without tidal dissipation
-> Need highest-quality data, and ideally very long time series from same site
accumulated effect bigger further back in time, but larger dating uncertainties ....
In 2000: two studies who tried this with different approaches:
Lourens et al. (2001): use short but high quality data from Mediterranean
Pälike et al. (2000): use interference pattern approach with data from ODP Leg 154 (Ceara Rise)

14. Results from ODP Leg 967 Source of data: eastern Mediterranean Sea
Method: Comparing very high
Resolution elemental data to
Astronomical solutions.
Reprinted by permission from Macmillan Publishers Ltd: Lourens, L.J., Wehausen, R., Brumsack,
H.J. (2001) Geological Constraints on tidal dissapation and dynamical ellipticity of the Earth over
the past three million years. Nature, v. 409, p (Copyright 2001) Not under CC licence
general principle: fix phase relationship for either obliquity OR climatic precession
other phase then determined (fixed) by data

15. Lourens et al. (2001) Results
Reprinted by permission from Macmillan Publishers Ltd: Lourens, L.J.,
Wehausen, R., Brumsack, H.J. (2001) Geological Constraints on
tidal dissapation and dynamical ellipticity of the Earth over the past t
hree million years. Nature, v. 409, p (Copyright 2001)
Not under CC licence
Their conclusion: At ~3 Ma: best fitting solution with present day dynamical ellipticity but only 50% of present day tidal dissipation. BUT: present day slow-down rate gives only a slightly worse fit!

16. Change of cycle periods
The slope of these depends on the tidal dissipation !
• Α different approach is to consider the slowly evolving frequency variations (obliquity & climatic precession) over longer stretches of time
Figure produced by Heiko Palike, University of Southampton

17. Figure produced by Heiko Palike, University of Southampton
More useful examples
note effect of the Earth’s precession slow-down for astronomical models that take into consideration the effect of tidal dissipation ....
Figure produced by Heiko Palike, University of Southampton

18. Determining precession slow-down with interference method
general principle: use interference pattern between two close frequencies (Example: Piano tuning)
Figures produced by Heiko Palike, University of Southampton
An example of the interference pattern between two
Close frequencies e.g. piano tuning
Redrawn from Pälike & Shackleton (2000)

19. Results from Leg 154 interference study
Conclusion from this study: The best fitting solution La93(ell=0.999, td=1.004) from the data is indistinguishable from present-day values within error for (at least) the past 25 Myr.
This plot in Figure 7 shows the best
fitting solution over the time interval
0–11.5 Ma and 17.5–25 Ma. The
interval over which we consider the
geological data to be good is indicated
by the solid part of curve b. Follow
link in reference below to see figure
and full article.
Palike H., Shackleton N.J. (2000) Constraints on
astronomical parametres from the geological record
for the last 25 Myr. Earth and Planetary Science
Letters, v. 182, p

20. Chaos in the Solar System
one final complication in our quest for more accurate astronomical age calibrations is severe:
contrary to Newton’s statement that the Solar System will carry on working like a clock-work for eternity, Laskar (1990) established that the dynamics of orbital elements in the solar system are not fixed for all times, but rather unpredictable over tens of millions of years
This does not so much affect the average cycle period, but instead the longer amplitude modulation terms which are the “fingerprint” of an astronomical solution
Example: Chaos in the solar system leads to diffusion (exponential) of accuracy: If the relative position of a planet is known with a relative error of 10-9 at present, this error increases to 10-8 after 10 Myr, and to 1!!! after 100 Myr.
What are the limits, then, of astronomical calculations for time- scale calibration use? (the answer is in Laskar 1999, 2004)

21. Examples for chaotic orbits ...
The chaotic nature of the solar system has consequences on how far back we can calculate orbits with confidence
It directly affects the fundamental frequencies (remember Lecture. 10 ???)
Courtesy of: Laskar J. (1999) The limits of earth orbital
calculations for geological time-scale use. Philosophical
Transactions of the Royal Society (A). 357,
J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A. C. M. Correia, and B. Levrard. A
long-term numerical solution for the insolation quantities of the Earth. Astronomy
and Astrophysics v. 428, p 261–285. (2004) Reproduced with permission © ESO.

22. Model with no chaotic transition
climatic precession
obliquity
short eccentricity
long eccentricity
~1.2 My
~2.4 My
Figure produced by Heiko Palike, University of Southampton

23. Model with chaotic transition
climatic precession
~2.4 My
obliquity
~1.2 My
~2.4 My
short eccentricity
~2.4 My
long eccentricity
Figure produced by Heiko Palike, University of Southampton

24. Can we test for chaos with geological data ?
Due to the exponential increase of errors in astronomical models with time, we can turn this to our advantage ...
IF we can find one or more of chaotic transitions in the geological record in the past, THEN it would be possible to extremely increase the accuracy of astronomical models AND fundamental constants (gravity!)
IF we can exclude for a certain time interval that there has been a chaotic transition, THEN we have a weaker constraint that still excludes many of the “wrong” models, and extends the time over which the models might be valid
This test was done with high-quality geological data from ODP Legs 154 and

25. Chaotic solar system: amplitude modulations
Courtesy of GSA. Palike H., Laskar J., Shackleton N.J. (2004) Geological constraints on the chaotic diffusion of the solar system. Geology, v. 32, p

26. Extracting obliquity modulations
Courtesy of GSA. Palike H., Laskar J., Shackleton N.J. (2004) Geological constraints on the chaotic diffusion of the solar system. Geology, v. 32, p

27. Extracting eccentricity modulations
Courtesy of GSA. Palike H., Laskar J., Shackleton N.J. (2004) Geological constraints on the chaotic diffusion of the solar system. Geology, v. 32, p

28. Findings:
Exciting: We CAN say something about astronomy and physics from deep sea mud!
Over last +30 Myr, no evidence in geological data for originally “postdicted” transition to have taken place
New astronomical calculation La2004 preferred by data over older solution La1993 which contained a chaotic transition at around 25 Ma
Good news: Astronomer says that if no transition over past 30 Myr, then probably also not for past 50 Myr >>> Easier to extend astronomical calibration of geological time scale!

29. Key point summary
Geological data, in the right circumstances, potentially record not just global climate cycles, but also much more intricate patterns of the astronomical patterns
Turning the principle of geological time scale calibration with astronomical models around, we can also EXTRACT astronomical parameters from geological data ---- Exciting!
These parameters (tidal dissipation, dynamical ellipticity, chaotic nature) need to be constrained in order to extend the astronomically calibrated geological time scale!
At least for the past 25 Myr, tidal dissipation appears to have been similar to today’s values
No chaotic transition during past 30 Myr recorded

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