Hurricanes over Geological Time

[lpetrich]

This was inspired by the claims of certain people that hurricanes are sent as a punishment for our sins; I decided to explore how far back one can find evidence of hurricanes.

At first thought, one wonders how one is going to learn about hurricanes before there was a historical record of them. But hurricanes produce strong water currents as they travel, which leave effects in sediments.

But first a note on terminology; I'll be using the American term, hurricane, instead of typhoon or tropical cyclone; much of the literature on recent hurricanes uses the latter two terms.

Also, it's helpful to search for "paleo-hurricanes", "paleotempestology" (the study of long-ago storms, especially hurricanes), and "tempestites" (sediment deposits typical of storms, especially hurricanes). The literature describes not only evidence of hurricanes, but also evidence of severe winter midlatitude storms, so we can be confident of evidence of those also.

There is now a sizable literature on sedimentary evidence of North American East Coast and Gulf Coast hurricanes over the Holocene (the last 10,000 years). This includes Lake-Sediment record of late Holocene hurricane activities from coastal Alabama (http://nsstc.uah.edu/aosc/al_hurricanes.htm) and Holocene History of Catastrophic Hurricanes and Fires along the U.S. Gulf Coast (http://gsa.confex.com/gsa/inqu/finalprogram/abstract_54721.htm). Each place on the Gulf Coast has a chance of a direct hit by a Saffir-Simpson Category 4 or 5 hurricane every 300 years (I'm not sure how that's defined). There is also a sizable literature related to hurricanes on China's coast, and even some on hurricanes near Australia.

The February 2007 issue of Geology and GSA Today (http://www.geosociety.org/news/pr/07-02.htm) mentions "Stalagmite stable isotope record of recent tropical cyclone events", Amy Benoit Frappier, Boston College, Geology and Geophysics, Chestnut Hill, MA 02467, USA; et al. Pages 111-114.
Satellite and historical records of tropical cyclone events (tropical storms, hurricanes, and typhoons) are too brief to settle the scientific debate over possible links between climate change and hurricane activity. Paleotempestology, the study of ancient storms, aims to understand the causes of storminess by analyzing records of prehistoric storm activity. Frappier et al. present a new tool for paleotempestology that relies on evidence of hurricane rainfall preserved in caves. Although cave formations (stalagmites) grow relatively slowly, the researchers used a high-precision computer-controlled sampling device to extract an approximately weekly to monthly record of climatic variability from a Belize stalagmite, including individual historical hurricane events. This new technique has the potential to shed new light on hurricane-climate interactions by enabling the reconstruction of storm frequency and intensity even farther in the past than was previously possible.


Looking back into the Pleistocene (1.8 million to 10,000 years ago), there is evidence of hurricane-caused disruption of coral reefs in the Caribbean and nearby, in such papers as Preservation of In Situ Reef Framework in Regions of Low Hurricane Frequency: Pleistocene of Curaçao And Bonaire, Southern Caribbean (http://gsa.confex.com/gsa/2002AM/finalprogram/abstract_41408.htm) and Coral Damage and San Salvador Hurricane History (http://jrscience.wcp.muohio.edu/fieldcourses03/OutlinemarineecologyArticles/CoralDamageandSanSalvador.html).


There is a little bit of literature here and there about storm deposits earlier, like these ones on the Miocene:

Wathne, E., Larsen, E. & Nemec, W. (2002) Miocene tempestites and tsunamites in the Antalya Basin, SW Turkey. In: Abstracts 16th International Sedimentological Congress, pp. 393-394. International Association of Sedimentologists, Rand Afrikaans Univ., Johannesburg.

Molina, Alfaro, Moretti, Soria (1998)
Soft-sediment deformation structures induced by cyclic stress of storm waves in tempestites (Miocene, Guadalquivir Basin, Spain)
Terra Nova 10 (3), 145$150.
doi:10.1046/j.1365-3121.1998.00183.x


The early Cenozoic (Paleogene) had been relatively warm; I've found a paper that suggests that hurricanes had helped stabllize tropical climates back then:

The role of tropical cyclones in maintaing Paleogene climate (http://adsabs.harvard.edu/abs/2005AGUFMPP51C0609V) with abstract
Based on a modern day observational investigation of the effect of tropical cyclones on ocean heat transport, we pursue the conjecture of Emanuel, 2002, that tropical cyclones played an important role in maintaining the most intriguing aspects of Paleogene climate, i.e. the relative stability of tropical climate in the face of substantial high latitude warming. We speculate on what proxy records could be used to test this hypothesis and make concrete predictions of what the pattern of tropical cyclone activity might have been in warm intervals such as the Eocene.

In this report on a2006 Workshop on Tropical Cyclones and Climate (http://iri.columbia.edu/outreach/publication/report/06-02/report06-02.pdf) contains some speculations on how that can happen, like causing the upper layers of the oceans to mix.


Going back to the Mesozoic, we find:

Lowstand tempestites; depositional model for Cretaceous skeletal limestones, Western Interior basin (http://geology.geoscienceworld.org/cgi/content/abstract/24/10/888) in the US Midwest
Late Cretaceous Dinosaurs of the Southeastern United States (http://www.auburn.edu/~kingdat/dinosaur_webpage.htm)
Late Cretaceous (Santonian) Vegetation From The Gulf Coast (http://gsa.confex.com/gsa/2001SE/finalprogram/abstract_4641.htm), mentioning evidence of paleohurricanes
Jurassic-Cretaceous Deposits Of The Central Lhasa Terrane: Implications For The Tectonic Evolution Of Southern Asia Prior To The Indo-Asian Collision (http://gsa.confex.com/gsa/2002AM/finalprogram/abstract_41692.htm) has a brief mention of tempestites
Tiered ichnoassemblages in Jurassic tempestites from Apennines and Southern Alps (http://cat.inist.fr/?aModele=afficheN&cpsidt=13957615), that is, different fossil footprints in different tempestites -- mainly of decapod crustaceans (lobsters, crabs, and the like)
Calcareous tempestites in pelagic facies (Jurassic, Betic Cordilleras, Southern Spain) (http://www.ingentaconnect.com/content/els/00370738/1997/00000109/00000001/art00057)
Storm-dominated deposition of the Lower Jurassic crinoidal limestones in the Kr$$na unit, Western Tatra Mountains, Poland (http://www.springerlink.com/content/y5l5dedq02umt11x/), about crinoid plates getting smashed and ground up by storm currents
Significance of pot and gutter casts in a Middle Triassic carbonate platform, Betic Cordillera, southern Spain (http://www.blackwell-synergy.com/links/doi/10.1046/j.1365-3091.2001.00425.x/abs/), mentioning how some sedimentary layers are likely tempestites
Second day of a geologist field trip, in Bulgaria (http://www.geology.bas.bg/32igc/FTB26SecondDay.html), mentioning tempestites in various Mesozoic rocks
Temporal variation in the wavelength of hummocky cross-stratification: Implications for storm intensity through Mesozoic and Cenozoic (http://www.gsajournals.org/perlserv/?request=get-document&doi=10.1130%2F0091-7613(2001)029%3C0087%3ATVITWO%3E2.0.CO%3B2), concluding a peak intensity of storms in the mid-Cretaceous, when the Earth was a very warm "greenhouse" as opposed to the present-day "icehouse"
The Santonian Age of the Late Cretaceous Period: 85.8 to 83.5 million years ago (http://www.palaeos.com/Mesozoic/Cretaceous/Santonian.html) mentions lots of evidence of abundant storms and hurricanes.


And even further, to the Paleozoic, we find an interesting page that shows reconstructed hurricane paths 350 million years ago in the Carboniferous, Probable influence of geography on the development and global distribution of Tournasian-early Visean age (Waulsortian and Waulsorian-like) mud mounds (http://www.auburn.edu/~kingdat/waulsortian/waulsort.html) It proposes that those mud mounds developed in areas without big storms like hurricanes, which would produce strong currents that would stir up the ocean sediment. This is despite their forming near the Equator, in southern Laurussia (North America + northeastern Europe), which would make them vulnerable to hurricanes. THe hurricane-proofing comes from the narrowness of the Iapetus Ocean between Laurussia and Gondwana -- hurricanes would be confined to it. However, these mud mounds are absent from North China, Tarim, and Kazakhstania, which would have been much more vulnerable to hurricanes; they were surrounded by large expanses of ocean.

Hummocky cross-stratification, tropical hurricanes, and intense winter storms (http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-3091.1985.tb00502.x?journalCode=sed) discusses evidence from the Proterozoic to the present. In the Proterozoic, Paleozoic, Neogene, and Quaternary, which had climates much like the present climate, hurricanes and winter storms had pretty much the distribution in latitude that they do today, but in the warmer and non-glacial Mesozoic and Paleogene, the hurricane belt extended further away from the Equator.

And more:

Storms In The Late Permian And Early Triassic (http://gsa.confex.com/gsa/2001AM/finalprogram/abstract_24207.htm), discussing evidence of more storms and hurricanes then.
Deposition of tempestites in the eastern Rheic strait: evidence from the Upper Palaeozoic of Southern Tuscany (Italy) (http://www.springerlink.com/content/0357n1q2hw3x7077/)
Mud-Dominated Storm Deposits From A Lower Carboniferous Ramp (http://www3.interscience.wiley.com/cgi-bin/abstract/113512564/ABSTRACT?CRETRY=1&SRETRY=0)
Studies of storm deposits in China: a review (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VBJ-3T7F1K8-5&_user=10&_coverDate=11%2F30%2F1997&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=698f335bb1d009fc6c8d9a244374dd81)
Tempestites recorded as variable Pentamerus layers in the Lower Silurian of southern Norway (http://links.jstor.org/sici?sici=0022-3360(198903)63%3A2%3C195%3ATRAVPL%3E2.0.CO%3B2-6) describes how often those brachiopods (a kind of shellfish) were subjected to severe storms: once every 2-3 years in shallower water and 8-10 years in deeper water.
Teachers' Page: BonznStonz: Fossils and Minerals (http://www.bonznstonz.com/teachers.html) (middle of the page) some New York State Silurian-era rocks contain fossils that were buried as a result of long-ago storms.
18 Reasons Why UC Geology Rocks in the Keystone State (http://www.uc.edu/news/NR.asp?id=4590) toward the end it discusses storm-stirred sediments.
Cosmos #4 Heaven & Hell (http://www.uwgb.edu/DutchS/CosmosNotes/cosmos4.htm) mentions some Cambrian sandstone rocks in Wisconsin with big rounded boulders (2-3 m) of quartzite, which had been tossed around and eroded by hurricanes (back then, Wisconsin was near the Equator).
Paleozoic Bedrock of Minnesota (http://www.geo.umn.edu/courses/1004/Spring99/handouts/7.html) briefly mentions tempestites in the late Cambrian to late Ordovician (500 - 450 million years ago), when the place was a shallow tropical sea.
Storms versus tsunamis: Dynamic interplay of sedimentary, diagenetic, and tectonic processes in the Cambrian of Montana (http://www.gsajournals.org/perlserv/?request=get-document&doi=10.1130%2F0091-7613(2002)030%3C0423%3ASVTDIO%3E2.0.CO%3B2) proposes that some sediment layers were generated by tsunamis instead of storms, making them "tsunamites".


Looking back even further, into the Precambrian, I've found:

Extreme winds and waves in the aftermath of a Neoproterozoic glaciation (http://www.snowballearth.org/pdf/Allen_Hoffman_nature03176.pdf), by Philip A. Allen and Paul F. Hoffman.
The most severe excursions in the Earth’s climatic history are thought to be associated with Proterozoic glaciations. According to the ‘Snowball Earth’ hypothesis, the Marinoan glaciation, which ended about 635 million years ago, involved global or nearly global ice cover. At the termination of this glacial period, rapid melting of continental ice sheets must have caused a large rise in sea level. Here we show that sediments deposited during this sea level rise contain remarkable structures that we interpret as giant wave ripples. These structures occur at homologous stratigraphic levels in Australia, Brazil, Canada, Namibia and Svalbard. Our hydrodynamic analysis of these structures suggests maximum wave periods of 21 to 30 seconds, significantly longer than those typical for today’s oceans. The reconstructed wave conditions could only have been generated under sustained high wind velocities exceeding 20 metres per second in fetch-unlimited ocean basins. We propose that these extraordinary wind and wave conditions were characteristic of the climatic transit, and provide observational targets for atmospheric circulation models.
They conclude that these super waves had been produced by super winds, and that these winds were a result of the overall atmospheric circulation between the hot oceans and the cold remaining glaciers, and not anything localized like storms or hurricanes. But from Snowball-Earth research news (http://www.snowballearth.org/news.html),
Extreme winds and waves in glacial aftermath (January, 2005)

Allen, P.A. and Hoffman, P.F., 2005. Extreme winds and waves in the aftermath of a Neoproterozoic glaciation. Nature 433, 123-127.
Jerolmack, D.J. and Mohrig, D., 2005. Formation of Precambrian sediment ripples: Arising from P.A. Allen & P.F. Hoffman Nature 433, 123-127 (2005). Nature, 10.1038/nature04025.
Allen, P.A. and Hoffman, P.F., 2005. Formation of Precambrian sediment ripples: Reply to Jerolmack, D.J. & Mohrig, D. Nature, 10.1038/nature04025.

Sedimentologists from ETH-Zürich and Harvard University interpret “tepee” structures in younger Cryogenian cap dolostones as giant wave ripples, formed by extreme winds and waves in a pan-glacial aftermath. Hindcasting from gravitational wave theory, they suggest that the bedforms were produced at water depths of 200-400 meters by waves with maximum wave periods (21-30 seconds) significantly longer than those prevailing in today’s oceans. The reconstructed wave conditions could only have been generated by sustained wind speeds >20 meters per second (~3 times faster than present trade-wind speeds) in fetch-unlimited ocean basins. In a discussion published on-line, Jerolmack & Mohrig (MIT) suggest that the ripples were formed by hurricanes, not by prevailing winds. In response, the original authors note that multiple generations of ripples have similar azimuthal orientations, whereas hurricanes make landfall at different places and produce variable wind and wave orientations at any given location.


Tsunamis and super-hurricanes after the Acraman asteroid impact (http://www.pir.sa.gov.au/byteserve/minerals/references/mesa_journal/mj_39/mj39_tsunamis_acraman.pdf), by Ian Dyson. That impact had happened about 580 million years ago, and produced a 90-km-diameter crater in what is now southern Australia. Mr. Dyson speculates that that impact had liberated methane from oceanic hydrates, producing global warming and big hurricanes, which in turn produce the telltale storm deposits that he discovered.


Glendonites in Neoproterozoic low-latitude, interglacial, sedimentary rocks, northwest Canada: Insights into the Cryogenian ocean and Precambrian cold-water carbonates (http://geol.queensu.ca/people/narbonne/JamesNarbonneDalrympleKyserGeology2005.pdf), by Noel P. James, Guy M. Narbonne Robert W. Dalrymple and T. Kurtis Kyser. Examining the warm period between the late-Precambrian "Snowball" Sturtian and Marinoan glaciations, they conclude that there is sedimentary evidence of storms -- and possibly hurricanes.

Fazenda Cristal Mesoproterozoic Stromatolites, Bahia State, Brazil (http://www.unb.br/ig/sigep/sitio093/sitio093english.htm) describes evidence of tempestites in the 1.2 billion-year-old Caboclo Formation (Chapada Daiamantina Group).

Stratigraphic architecture of a Paleoproterozoic iron formation depositional system: the Gunflint, Mesabi and Cuyana iron ranges (http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/MQ33432.pdf) mentions some storm deposits in these ca. 1.85-billion-year-old rocks.


It gets more and more difficult to find sedimentary rocks the farther back one goes; in fact, it gets more and more difficult to find any rocks. And the closest I could find is a simulation, An Investigation of the Archean Climate Using the NCAR CCM (http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920014413_1992014413.pdf), and one that did not get into the question of hurricanes or other storms. However, the simulations show that the Earth's atmosphere back then much like what it has now, suggesting that it also had hurricanes and other storms.


I've used the dates from UCMP's geological timescale page (http://www.ucmp.berkeley.edu/help/timeform.html), with some assistance from Palaeos's timescale (http://www.palaeos.com/Timescale/timescale.html)
The literature also contains divisions:
Quaternary: Pleistocene - present
Tertiary: Paleocene - Pliocene
Neogene: Miocene - present
Paleogene: Paleocene - Oligocene

[Ezkerraldean]

so i hear (from the Earth Story series and book on BBC), the indian ocean typhoons only really picked up about 10Ma, due to the growth of the Himalaya. dunno about hurricanes (atlantic tropical storms) though.

[Musing Man]

Impressive effort, seriously.

Now, I'm amazed that lpetrich avoided to transpose all that stuff in one hell of an equation... :D

[lpetrich]

I wonder what Music Man mean by how I "avoided to transpose all that stuff in one hell of an equation..."

Taking a broader view, there has been a fair amount of research into paleoclimates; see Paleoclimatology and Geologic temperature record for brief summaries, and Chris Scotese's climate-history pages (http://www.scotese.com/climate.htm) for a more detailed look, including maps of climate zones and climate indicators, like coal and evaporation deposits and glacial deposits.

The University of Chicago's Paleogeographic Atlas Project (http://pgap.uchicago.edu/) goes into a lot of detail about the paleoclimates of the Jurassic and Permian periods, complete with comparisons with General Circulation Model atmosphere simulations. They find reasonably close agreement, except for the higher latitudes, where the paleoclimatological evidence indicates that these regions are much warmer than what one calculates. However, the authors of these models concede that they had been using a shortcut: they had used the "swamp" approximation of oceans, ignoring ocean-water circulation. And such circulation can keep the high latitudes warm, as the Gulf Stream does for northwestern Europe.

http://upload.wikimedia.org/wikipedia/en/thumb/c/cd/AtmosphCirc2.png/180px-AtmosphCirc2.png (http://upload.wikimedia.org/wikipedia/en/c/cd/AtmosphCirc2.png)
(click on the images here for larger versions)

Here's a rough guide to the Earth's atmospheric circulation: the Sun heats the parts of the Earth near the equator much more than the parts near the poles, which makes air rise at the equator and sink at the poles. This is not the whole story, of course, because the Earth's rotation gets in the way.

Air that has risen at the equator travels away from it, but since the Earth's linear velocity of rotation declines beneath it, the air gets deflected eastward, and at the "horse latitudes" of about 30 degrees latitude, it sinks. It then returns to the equator and gets deflected westward by the Earth's rotation, producing the easterly "trade winds". These loops of atmospheric circulation, one on each side of the equator, are called the "Hadley cells", after their discoverer.

Some of the horse-latitude air goes away from the equator instead of toward it, and gets deflected easterly as a result, producing the "prevailing westerlies". When it gets heated enough, it rises at approximately 60 degrees latitude and returns to the horse latitudes, forming the Ferrel cells. Temperate-zone circulation is more complicated than that, of course, with a continual procession of continent-sized eddies that one can see in weather charts.

Air rising at 60 degrees can continue further away from the equator until it reaches the poles, where it sinks and goes back toward the equator, thus producing the polar cells. As the air does so, it gets deflected westward, making the "polar easterlies".

When air goes up, it lowers the atmospheric pressure a bit, and water in the air can easily condense out of it, making clouds and precipitation. While when air goes down, it raises the atmospheric pressure a bit, and water condenses much less easily. This is why high-pressure zones have much less cloudy and stormy weather than low-pressure zones. This, combined with the Earth's rotation, also explains why northern-hemisphere high-pressure zones rotate clockwise and low-pressure zones rotate counterclockwise. And why southern-hemisphere ones rotate counterclockwise and clockwise, respectively.

The rotation effects I'd mentioned are often called the Coriolis effect.

What's the connection with hurricanes?

http://upload.wikimedia.org/wikipedia/commons/thumb/d/d7/ITCZ_january-july.png/300px-ITCZ_january-july.png (http://upload.wikimedia.org/wikipedia/commons/d/d7/ITCZ_january-july.png)

Where the two Hadley cells meet is called the Intertropical Convergence Zone or ITCZ, which is evident as a line of thunderstorms. It follows the zone of maximum sunlight, the "thermal equator", going northward in northern-hemisphere summer and southward in northern-hemisphere winter (southern-hemisphere winter and summer, respectively).

Where the ITCZ departs from the equator, its thunderstorms get subjected to the Coriolis force, and this can turn them into tropical cyclones, and even hurricanes. This explains why such storms are most common during their hemisphere's summer months.

And it also indicates that one can expect such storms to occur if the Earth's atmospheric circulation and spin-axis tilt are much like what they are today.

But is there evidence of that besides tempestites? Let us now consider what climate patterns result from the atmospheric circulation that I have described.

http://upload.wikimedia.org/wikipedia/en/thumb/c/c2/ClimateMapWorld.png/360px-ClimateMapWorld.png (http://upload.wikimedia.org/wikipedia/en/c/c2/ClimateMapWorld.png)

Near the equator is tropical climates, with lots of rainfall. These can be either everwet (rain all year round) or summerwet (rains mainly in the summer, from the ITCZ being present at that place at that time).

The next zone is subtropical deserts; the Earth has two desert belts approximately centered on the horse latitudes (30 degrees).

Just outside these deserts are winterwet "Mediterranean" climates; in the winter, these places become temperate-like, while in the summer, these places become subtropical-like.

And beyond these are temperate climates, which are usually fairly wet.

Near the poles, the air is very dry; this makes the polar regions icy deserts.


And what do we find from paleoclimate research?

Evidence of this pattern of climate zones for as long as we can find sufficiently detailed and well-distributed climate-sensitive features. Chris Scotese has several maps of climate evidence, as does the University of Chicago team, and I've found this paper about climate evidence for the last 300 million years:

Tracing the tropics across land and sea: Permian to present (http://www.blackwell-synergy.com/doi/abs/10.1080/00241160310004657)
The continuity through the past 300 million years of key tropical sediment types, namely coals, evaporites, reefs and carbonates, is examined. Physical controls for their geographical distributions are related to the Hadley cell circulation, and its effects on rainfall and ocean circulation. Climate modelling studies are reviewed in this context, as are biogeographical studies of key fossil groups. Low-latitude peats and coals represent everwet climates related to the Intertropical Convergence Zone near the Equator, as well as coastal diurnal rainfall systems elsewhere in the tropics and subtropics. The incidence of tropical coals and rainforests through time is variable, being least common during the interval of Pangean monsoonal climates. Evaporites represent the descending limbs of the Hadley cells and are centred at 10° to 40° north and south in latitudes that today show an excess of evaporation over precipitation. These deposits coincide with the deserts as well as seasonally rainy climates, and their latitudinal ranges seem to have been relatively constant through time. Reefs also can be related to the Hadley circulation. They thrive within the regions of clear water associated with broad areas of downwelling which are displaced toward the western portions of tropical oceans. These dynamic features are ultimately driven by the subtropical high-pressure cells which are the surface signature of the subsiding branches of the Hadley circulation. Carbonates occupy the same areas, but extend into higher latitudes in regions where terrestrial surface gradients are low and clastic runoff from the land is minimal. We argue that the palaeo-latitudinal record of all these climate-sensitive sediment types is broadly similar to their environments and latitudes of formation today, implying that dynamic effects of atmospheric and oceanic circulation control their distribution, rather than temperature gradients that would expand or contract through time.

[drewjmore]

I vote for a sticky. Fascinating.

[just saw the light]

Cool stuff! Thanks

[Rymmie1981]

I'm not sure why, but this makes me happy. I like powerful ammunition for my theological gunfights. Ok, I do know why this makes me happy. Move along now.

[llanitedave]

Alright, now how would the somewhat faster rotation velocity of Earth during the Precambrian eras play into all this? Stronger coriolis? More powerful trade winds? More or fewer Hadley cells?

[lpetrich]

First, about a Mediterranean climate. It may be a result of the tropical Hadley circulation moving toward whichever hemisphere is currently experiencing summer; that would account for subtropical-arid summer and temperate-humid winter.

And that moving tropical circulation is what makes the monsoons -- notice how the ITCZ moves over the year.

As to the Coriolis force, since it is a function of rotation, it increases with increasing rotation rate (duh!).

There was, in fact, a simulation of Archean climates and weather patterns that I had mention earlier: An Investigation of the Archean Climate Using the NCAR CCM (http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920014413_1992014413.pdf)

I will now summarize the results. The simulations covered several features of the Archean Earth; faster rotation, a fainter Sun, and less exposed land area. These features were handled in various combinations in order to work out which features make which climate effects.

The faster-rotation ones used a period of 14 hours instead of the present-day 24 hours (23 h 56 m 4 s with respect to the stars). And the less-sunlight ones used a solar luminosity at Earth of 90% of its present-day value.

The greater rotation rate means that atmospheric eddies were smaller and more numerous; there are more temperate high and low spots, and also warm and cold fronts.

It also means that the Hadley circulation is smaller, extended to 20 instead of 30 degrees from the Equator. The temperate Ferrel cells move equatorward by 10 degrees, but stay 30 degrees in size. The Earth's faster rotation deflects the winds more, making them come down sooner. And the smaller gradient means that the Hadley-circulation winds go down by a factor of 1.2 - 1.5.

This also means that the poleward transfer of heat is less efficient, making the poles colder and the tropics to midlatitudes warmer. Cloudiness decreases everywhere, but precipitation is a more complicated story. Relative to the present, it slightly increases at the Equator and decreases in subtropical and nearby temperate latitudes. But relative to the situation of a global ocean and less sunlight, it increases.


It would be interesting to run circulation-model calculations for the other Solar System objects with substantial atmospheres:
Venus
Mars
Jupiter
Saturn
Titan
Uranus
Neptune
Triton
Pluto

And a quick search revealed circulation-model calculations for several of these objects, with varying degrees of success.

[llanitedave]

This is a fascinating topic. Another model I'd dearly love to see is for an earthlike planet with a reduced axial tilt but an increased orbital ellipticity. The seasons there would be less a matter of tilt geometry and more a matter of increased or decreased solar heating. I intuitively imagine that seasons would be more globally consistent but I can't decide whether the "rainy season" would occur near perihelion, when evaporation rates and energy input is at maximum, or near aphelion, when the atmosphere is cooling and stored water vapor is condensing on a large scale.

If I had the background to do that kind of study myself, I would!

[wjs3]

lpetrich:

I am a relatively new poster here (even though I lurked for a while), so I'd like to apologize if this is a derail at all. I hope it's not.

Really great posts. I have some background in meteorology and it was fun to read about hadley cells, the ITCZ and the like. If tropical cyclones come up here again, I'll look forward to participating.

FWIW, for a class I took on tropical weather, I wrote this (http://www.personal.psu.edu/wjs203/Assignment%202/Meteo%20241_assignment_2_intro.htm) assignment on large scale tropical phenomena, like the ITCZ. If anyone reading your posts is interested in learning more about the tropics, I thought it might help.

Best--

WJS3

[RAFH]

I'm not sure why, but this makes me happy. I like powerful ammunition for my theological gunfights. Ok, I do know why this makes me happy. Move along now.

It just makes me happy. A sense of wonder even.

Thanks Ipetrich. I love to think about ancient storms raging across ancient seas and lands. Cripes, this could devolve into a whole new dream sequence. I can hardly wait.

[Barefoot Bree]

(That's LPetrich, in lower case, not IPetrich. Just fyi.)

[David B]

JUst a heads up to myself to get back to this thread at my leisure.

I don't usually like very long OPs, but climatology is something I'm interested in, ant there seems a lot of potential to do some serious learning here.

David B

[lpetrich]

llanitedave, Darren Williams (http://physics.bd.psu.edu/faculty/williams/) and others have done some calculations of that, and in the case that you have in mind, the Earth would be rainiest at aphelion, when its oceans are still warm from the perihelion heating.

This brings to mind how well we can follow back in time the Earth's spin and orbit parameters. Since hurricanes form as a result of the ITCZ departing from the Equator far enough to allow the Earth's rotation to start clusters of thunderstorms spinning, hurricanes are thus dependent on the Earth having a significant obliquity, a significant angle between its equatorial and orbit planes. It is now about 23.45 degrees; it currently varies between 21.5 and 24.5 degrees as a result of perturbations of the orientation of the Earth's orbit plane. But was that always the case over geological time?

There is geological evidence of various astronomical cycles, and that can be used to help answer this question.

Coral animals, shelled mollusks, stromatolite-making cyanobacteria, and other such organisms leave behind evidence of such cycles in the structures that they produce. Also, sediment deposition at coastlines can change between high-tide and low-tide forms, producing "tidal rhythmites".

One can find not only the numbers of days in the month and the year, but also some additional orbit features of the Moon. Its orbit is inclined to the Ecliptic by about 5.15 degrees and its orbit's eccentricity is 0.055. Furthermore, as a result of the Sun's gravity perturbing its orbit, its line of nodes, where its orbit plane and Ecliptic intersect, precesses backward with a period of 18.67 years, while its major-axis direction precesses forward with a period of 8.85 years. The Sun also makes lots of small periodic effects in the Moon's orbit, but I won't discuss them further here. For more details, see Orbit of the Moon.

The Moon's orbit plane's inclination to the Earth's equator thus oscillates between 18.3 and 28.6 degrees, and the lunar tide is about 40% greater at the Moon's perigee than its apogee (tidal effects go as the inverse cube of the distance).

The nice thing is that, if one can extract the line-of-nodes or the major-axis precession rates, one has some additional data that one can use to check one's reconstructions, because one can calculate these rates from the length of the month and the year. To lowest order, the angular velocities are:

(line of nodes) = - (3/4)*(Earth orbit)2/(Moon orbit)
(major axis) = + (3/4)*(Earth orbit)2/(Moon orbit)

omitting higher-order terms; terms proportional to (Earth orbit)3/(Moon orbit)2, (Earth orbit)4/(Moon orbit)3, and so forth. The lowest-order result gives a period of 17.83 years, which is close to the actual result for the line of nodes, but is twice that for the major axis. Adding the next few higher-order terms gives much better results in both cases.

This discrepancy had greatly bothered Sir Isaac Newton, because it looked like a failure for his otherwise-successful physical theorizing; it was supposedly the only problem that made his head ache. But his successors were eventually able to continue the calculations to higher orders of approximation, which had a merciful analgesic effect.

That said, it has been very difficult for me to find a reasonably comprehensive collection of inferred numbers of days per month and year over geological time, despite the sizable amount of research on this question. I've found results like there being 400 days in the year in the Devonian Period, but not much more.

This is a result of the tides that the Sun and the Moon produce on the Earth; as a result, the Earth is slowly spinning down and the Moon is slowly spiraling away. The rates of spindown and outspiral have varied in the past, partially as a result of the presence or absence of shallow seas like the Bering Sea, which can have slosh-period resonances with the tides.

But it has been hard for me to find anything on determining the Earth's obliquity from growth rings or rhythmite layers or the like. However, I have discovered a lot of speculation that the late-Precambrian ice ages, with their near-equatorial ice sheets, was due to the Earth having a high obliquity at the time, sort of like what Uranus now has. Climate simulations reveal that the tropics would have been relatively cool, and that the polar areas would have alternated between very hot summers and very cold winters.

[llanitedave]

Thanks for the links and the insights, Ipetrich. This is a topic that never gets old.

Regarding the Earth's obliquity during the late Precambrian, doesn't this idea conflict with the Rare Earth claim of Ward and Brownlee, among others, that the moon's tidal influence helps stabilize the earth's axial tilt? If anything, during those periods when the Earth rotated faster, it's equatorial bulge would have been larger, and when the moon was closer, it's interaction with that bulge would have been greater. This would tend to make the Earth's obliquity even less inclined to wobble greatly than it is today.

I'm reluctant to accept a number of Ward and Brownlee's speculations, but this one at least seems to be reasonable.

[unrealist42]

It is interesting that 2 years ago a hurricane came ashore in Brazil for the first time.

[wjs3]

It is interesting that 2 years ago a hurricane came ashore in Brazil for the first time.

Speaking of hurricanes/tropical cyclones in the south atlantic...

Here's an image sent to me by a friend who works at the national hurricane cenrter. The image is from 800z on 2/23/2006. There's what appears to be a very small tropical cyclone (at least based on the satellite) that is located off of the south coast of Brazil (first time posting an image. I hope this works):

http://i165.photobucket.com/albums/u54/spin3232/Satelite230220060800Z.jpg

The NHC was serious enough about this system that they opened an "invest"--the first step in declaring a system as active--at the Navy site dedicated to do so (Sorry, the NRL deletes the archives on any storms that don't get named!)

This season, again, there was a storm that looked "subtropical" (characteristics of a tropical and mid latitude cyclone). One such storm popped up around Feb 9, 2007 according to my notes (can't find a satellite image right now).

I'm not sure where the scientific community is on this--whether the hypothesis is that:

1) With observation tools available today, we now observe more south Atlantic hurricanes though the south Atlantic is no more active
2) Given the overall multi-decadal oscillation's active phase in the north Atlantic, the south Atlantic is active too
3) Something is changing climatologically that's causing more frequent tropical cyclones in the south Atlantic (other than the multi-decadal oscillation).

Best--

WJS3

WJS3

[lpetrich]

Regarding the Earth's obliquity during the late Precambrian, doesn't this idea conflict with the Rare Earth claim of Ward and Brownlee, among others, that the moon's tidal influence helps stabilize the earth's axial tilt? If anything, during those periods when the Earth rotated faster, it's equatorial bulge would have been larger, and when the moon was closer, it's interaction with that bulge would have been greater. This would tend to make the Earth's obliquity even less inclined to wobble greatly than it is today.
Indeed the Moon's tides help stabilize the Earth's spin-axis orientation -- the Sun's alone may be too weak to do so. So let us calculate the rate of tidal precession. We find that it is:
\frac{d \vec n}{dt} = 3 \frac{C - A}{C\omega} \frac{GM}{r^3} (\vec n \cdot \hat r) (\hat r \times \vec n)

where L is the angular momentum, A and C are the equatorial and polar moments of inertia, n is the direction of the north pole, \omega is the rotation rate, M is the mass of the tide maker and r is its distance away. Since the Earth and the Moon continually move, this will cause monthly and yearly and Moon-nodal-period wobbles in the Earth's spin-axis position: the nutation. However, there will also be cumulative precession effects, and that is what we are looking for. Doing the integration yields
\frac{d \vec n}{dt} = - \frac32 \frac{C - A}{C\omega} \frac{GM}{a^3} \frac{1 - (3/2)\sin^2 i}{(1-e^2)^{3/2}} (\vec n \cdot \vec n') (\vec n' \times \vec n)

for an orbit with major axis a, eccentricity e, and inclination i to an average orbit with north-pole direction n'. I put in i to take into account the Moon, with its orbit whose line of nodes continually precesses; it is 0 for the Earth's orbit around the Sun.

At first sight, it may seem that the Earth's precession rate was less in the past, when its rotation rate was greater. But the faster rotation may mean more flattening, and thus a bigger "handle" for the Sun's and Moon's gravitational forces to hold onto it and precess it.

How does it work out? The Earth's shape is largely determined by its rotation and its resulting hydrostatic equilibrium. The Earth's gravitational potential and centrifugal potentials are
V_g = - \frac{GM}{r}\left( 1 - J_2 \left(\frac{R}{r}\right)^2 \frac{3 (\hat r \cdot \vec n)^2 - 1}{2} - \dots \right) ;\ V_c = - \frac12 \omega^2 r^2 (1 - (\hat r \cdot \vec n)^2)

where J2 is the second gravitational moment and R is the equatorial radius. It is given by
J_2 M R^2 = \frac32 (C - A)

Since the total potential, Vg + Vc, must be constant at the surface, we find for flattening f = (R-Rpolar)/R that, to lowest approximation,
f = \frac12 \frac{R^3 \omega^2}{GM} + \frac32 J_2

The moment J2 must be found from the interior flattening; it is given to lowest approximation by
J_2 M R^2 = \frac{2}{15} \int \rho r^4 \left(5f + r \frac{df}{dr}\right) dr

One can find f in the interior using hydrostatic equilibrium, which gives, to lowest approximation, Clairaut's equation:
\frac{d^2 f}{dr^2} + \frac{8\pi \rho r^2}{M(r)} \frac{df}{dr} + \left( \frac{4\pi \rho r^3}{3M(r)} - 1 \right) \frac{6f}{r^2} = 0 ;\ \frac{dM(r)}{dr} = 4\pi \rho r^2

These equations look like a nightmare, but the linearity of Clairaut's equation and the J2 equation mean that J2 is proportional to the surface flattening, and therefore to the square of the rotation rate.

Thus, the precession rate becomes proportional to the rotation rate, meaning that the Earth had a more stable precession then than now. It was easier for the Earth to avoid resonances in its orbit-parameter variations. And as a result, the Earth's obliquity likely did not change much over much of its history.

ETA: the values are:
flattening = 2.983 * 10-3
J2 = 1.083 * 10-3

[premjan]

We are getting possibly more than the usual number of small rainstorms here in the UAE - wonder if there is a climate shift due to the neighboring Iranian mountains / global warming.

[lpetrich]

No idea, premjan. You might want to search for UAE weather records so you can see if that's really unusual; weather does vary from year to year. Back to some interior-structure calculations:

Oops, a correction:
J_2 M R^2 = \frac{2}{15} \int 4 \pi \rho r^4 \left(5f + r \frac{df}{dr}\right) dr

It's possible to derive some results in a few special cases where it is relatively easy to find solutions.

Constant-density case (much like the Earth and other terrestrial planets and moons):
J_2 = \frac25 f ;\ f = \frac54 \frac{R^3 \omega^2}{GM} ;\ J_2 = \frac12 \frac{R^3 \omega^2}{GM}

Pressure proportional to the square of the density (more like Jupiter; the radius becomes independent of the central density, and there are some other simplifications):
J_2 = \frac{2(15 - \pi^2)}{45\pi^2} f ;\ f = \frac{15}{2\pi^2} \frac{R^3 \omega^2}{GM} ;\ J_2 = \frac{15 - \pi^2}{3\pi^2} \frac{R^3 \omega^2}{GM}

Numerically, this J2 is approximately (1/43.3) f; the compressibility lets the planet be centrally concentrated.

The Earth's J2 is about 1/3 its flattening, meaning that the Earth is somewhat centrally concentrated, which agrees with what we find from the travel times of earthquake waves through the Earth's interior.

ETA: here's a table of J2/f for the planets that there's data on in this Solar-System directory (http://www.indwes.edu/faculty/bcupp/solarsys/ss.htm) (taken from NASA's planetary fact sheets (http://nssdc.gsfc.nasa.gov/planetary/planetfact.html) and The Nine Planets (http://www.nineplanets.org/)):
Earth: 0.323
Mars: 0.303
Jupiter: 0.227
Saturn: 0.166
Uranus: 0.146
Neptune: 0.200

And while we are on the subject of the other planets, note that the four gas-giant planets have atmospheric circulations somewhat similar to Earth's, but with more Hadley and Ferrel cells (equator - Hadley - Ferrel - Hadley - Ferrel - ... - pole).

This is especially apparent on Jupiter, which has a banded appearance, with the light bands (zones) being upwelling, low-pressure zones, and the dark bands (belts) being downwelling, high-pressure zones. Jupiter's atmosphere also has lots of eddies, with the biggest being the Great Red Spot. That feature has been present for at least the last couple of centuries, but unlike Earth hurricanes, it has stayed at approximately constant latitude.

Saturn and Neptune also have a banded appearance, though fainter than Jupiter's, but Uranus does not, possibly as a result of its high obliquity (98 degrees).

[lpetrich]

Oops again :(

For pressure = (density)^2, J_2 = \frac{2(15 - \pi^2)}{45} f No \pi^2 in the denominator. This makes J2 = 0.228 f

This value is very close to Jupiter's value, interestingly enough. I now turn to the other big atmospheres.

The atmosphere of Venus has a very thick and hot, with a surface pressure 92 times Earth's. It owes its high temperatures, 500 C at its surface, to the Greenhouse Effect; since it traps much of its infrared glow, it has to be very hot before it can radiate enough to be in equilibrium with the incoming sunlight. This gives the atmosphere plenty of thermal inertia; this keeps its temperature relatively constant despite its long solar day of 117 Earth days.

Venus has a layer of sulfuric-acid clouds whos tops are at 80 km, with a temperature of -76 C and a pressure of 0.005 * Earth's surface's pressure; that layer is thick enough to keep most of the incoming sunlight from reaching the surface.

Not surprisingly, winds are very weak on Venus's surface, about 1 m/s. But above the clouds, they reach 95 m/s, circling the planet about every 4 days. This superrotation continues to be mysterious.


Turning to Mars, it has a circulation much like Earth's, as discussed in Mars General Circulation Modeling Group at NASA Ames (http://www-mgcm.arc.nasa.gov/mgcm/HTML/research.html). It has Hadley cells, midlatitude storms, etc., though, of course, no hurricanes.


There has even been some work on Titan's atmosphere: Numerical simulation of the general circulation of the atmosphere of Titan (http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=11538593&dopt=Abstract). Its rotation is synchronous with its orbit around Saturn, giving it a period of about 16 days. However, the simulations discovered superrotation in its atmosphere also; about 100 m/s near Titan's equator.

[premjan]

As well as having an effect on temperatures, Thomas said climate change could also be a cause of the apparent decline in the average amount of rainfall in the country.

Since 1998, there has been less than the average annual rainfall figure of 93mm every year except last year.

"This has been the longest period of below-average rainfall recorded here. As temperatures change, they can have a knock-on effect on all weather conditions," he said.
http://archive.gulfnews.com/articles/07/04/01/10115057.html
Apparently the amount of rain is up only for the last year and this year though I do estimate that we are having more storms.

[lpetrich]

I've looked for what global-warming simulations predict about precipitation, and details are much more difficult to find than for temperatures. But I've found:

Tropical drying trends in global warming models and observations (http://www.atmos.ucla.edu/~csi/RESEARCH/ar4prec.html):
Climate models agree on tropical drying amplitudes under global warming, and on a drier Caribbean-Central American region
(see also: PNAS paper links)

Precipitation changes associated with global warming simulations have proven much more difficult to characterize and corroborate than surface temperature changes. Analysis of an ensemble of coupled GCMs from the IPCC 4AR shows large inter-model agreement on a measurement of the overall amplitude of the precipitation decreases that occur at the margins of the convective zones, with percent error bars of magnitude similar to those for the tropical warming itself (Fig. 1). This agreement appears to be unprecedented for a precipitation-related global warming quantity. There is also general agreement on increases in precipitation near the centers of convective zones. Two related mechanisms hypothesized to be responsible for these changes have been previously identified in earlier publications by this research group: the "upped-ante" mechanism for drought tendency and the "anomalous gross moist stability" or "rich-get-richer" mechanism.
The article then discusses how the Caribbean / Central-American area has gotten drier as a result of global warming, and will continue to do so.

Since Dubai has latitude 25d 16m, about the latitude of Key West, Florida (24d 33m), it is likely that it is getting drier for the same reasons.

Another paper which finds the same sort of result is Tropical and subtropical precipitation changes under global warming (http://adsabs.harvard.edu/abs/2006AGUFM.A31G..04N):
The upped-ante mechanism can produce sharp reductions in rainfall on the margins of convergence zones, in regions where there is inflow from neighboring nonconvective regions. The rich-get-richer mechanism produces precipitation increases in the the regions with large climatological moisture convergence and drought in the subtropics.

When climate model precipitation changes are evaluated by measures motivated by these mechanisms, an ensemble of 10 models is found to agree on the overall amplitude of the regional precipitation changes, both for decreases on the margins of the convective zones and in the subtropics, and for increases in the interior.
Thus, wet areas will become wetter and dry areas drier.


This subtropical drying will coexist with bigger tropical storms and hurricanes, according to Global Warming and Hurricanes (http://www.research.noaa.gov/spotlite/archive/spot_gfdl.html) and similar simulations:
The strongest hurricanes in the present climate may be upstaged by even more intense hurricanes over the next century as the earth's climate is warmed by increasing levels of greenhouse gases in the atmosphere. Most hurricanes do not reach their maximum potential intensity before weakening over land or cooler ocean regions. However, those storms that do approach their upper-limit intensity are expected to be slightly stronger in the warmer climate due to the higher sea surface temperatures.

According to a new simulation study by a group of scientists at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL), a 5-12% increase in wind speeds for the strongest hurricanes (typhoons) in the northwest tropical Pacific is projected if tropical sea surfaces warm by a little over 2°C (Figure 1). Recent preliminary findings indicate that these results may apply to the other tropical cyclone basins as well. Such an increase in the upper-limit intensity of hurricanes with global warming was suggested on theoretical grounds a decade ago, but the NOAA investigation is the first to examine the question using a hurricane prediction model that can simulate realistic hurricane structures.
The article then described how they used a fine grid for the simulated hurricanes that was fit inside of the coarse grid of an overall climate model.

http://www.research.noaa.gov/spotlite/archive/images/intensities_t.gif
The peak shifts from 68 to 73 m/s - 245 to 263 km/hr - 152 to 163 mi/hr.


Elsewhere, I've found Simulation of Global Warming with the MRI Coupled Model (http://www.mri-jma.go.jp/Dep/cl/cl4/GW/GW.html); it reproduces present climate fairly well, but some of its details are rather off -- it predicts more tropical rain and in different patterns than what one actually observes.

Another site that describes that work: Simulation of Global Warming in MRI (http://jcbmac.chem.brown.edu/baird/Chem22i/GlWarmMod/GOIN.html); it includes a Model Description (http://jcbmac.chem.brown.edu/baird/Chem22i/GlWarmMod/model.html).


Finally, I must mention Global Warming Art (http://www.globalwarmingart.com), a site with a big collection of climate-change diagrams, like:

Past Temperatures (http://www.globalwarmingart.com/wiki/Temperature_Gallery) - from the present to the Cambrian
Carbon Dioxide (http://www.globalwarmingart.com/wiki/Carbon_Dioxide_Gallery) - including fossil-fuel consumption details
Sea Level (http://www.globalwarmingart.com/wiki/Sea_Level_Gallery) - how it's changed
Glaciers (http://www.globalwarmingart.com/wiki/Glacier_Gallery) - how they are shrinking
Future Changes (http://www.globalwarmingart.com/wiki/Predictions_of_Future_Change_Gallery)

And a list of All images (http://www.globalwarmingart.com/wiki/List_of_all_images)

[lpetrich]

I will now consider how one can infer various details of the Earth's orbit in the past. It may seem like something very difficult to do, but it turns out that there are ways of doing so.

The Earth is not alone in the Solar System, and neither it nor the Sun are perfectly spherical. This means that the Earth's path around the Sun will depart from a perfect Keplerian ellipse. The Earth already does so as a result of the Moon being in orbit around it; the Earth-Moon barycenter is about 4700 km away from the Earth's center, about 3/4 of its average radius of 6371 km. But the Earth-Moon barycenter, however, does travel in a close approximation of a Keplerian ellipse.

The Earth's oblateness produces an effect that is about J2(RE/aE)2 or 2*10-12.

(E = Earth, J2 is the coefficient of the lowest-order oblateness gravitational effect, R = equatorial radius, and a = semimajor axis)

The Earth and the Moon being separate objects produce an effect that is about (mM/mE)(aM/aE)2 or 8*10-8.

(M = Moon, m = mass)

General-relativistic "post-Newtonian" effects produce an effect that is about (GmS)/(aEc2) or 10-8.

(S = Sun, G = gravitational constant, c = speed of light in a vacuum)

The Sun's oblateness produces a gravitational effect that has been difficult to measure, but from its observed oblateness of 9*10-6 and its being centrally concentration, one infers that its J2 value is somewhere around 10-6. This yields an effect of about 2*10-11.

But the Solar System contains more than the Sun, the Earth, and the Moon, and a precise calculation shows that the effects of the other planets on the Earth's orbit are approximately
Jupiter 5*10-6
Venus 4*10-6
Saturn 3*10-7
Mars 2*10-7
Mercury 3*10-8
Uranus 5*10-9
Neptune 10-9

So Jupiter and Venus have the largest effects on the Earth's orbit, totaling about 10-5. This means that the Earth's orbit should be perturbed on timescales of about 70,000 years, which is very fast by geological standards, almost as fast as the Earth's spin precession, with its period of about 23,000 years.

Needless to say, these other planets's orbits get perturbed, and the result is a rather complicated coupled system. However, the planets' orbits are nearly circular and coplanar, which enables one to expand in powers of the eccentricity and inclination, thus getting some convenient simplifications.

A complication is that when the inclination becomes small, the position of the line of nodes (where the orbit plane intersects the reference plane) becomes poorly defined, and when the eccentricity becomes small, the position of the line of apsides (closest and farthest positions) becomes poorly defined. But there is a way around that, which is to define variables

h = e \sin \varpi ;\ k = e \cos \varpi ;\ p = \sin i \, \sin \Omega ;\ q = \sin i \, \cos \Omega
where
e = \text{eccentricity} ;\ \varpi = \text{longitude of the periapsis}
i = \text{inclination} ;\ \Omega = \text{longitude of the ascending node}

To lowest order, and also ignoring orbit-resonance effects, we find these equations of motion for planet i, summed over planets j:

\frac{dh_i}{dt} = + \frac12 n_i a_i \sum_{j \ne i} \frac{m_j}{M} ( B_1(a_i,a_j) k_i - B_2(a_i,a_j) k_j )
\frac{dk_i}{dt} = + \frac12 n_i a_i \sum_{j \ne i} \frac{m_j}{M} ( B_1(a_i,a_j) h_i - B_2(a_i,a_j) h_j )
\frac{dp_i}{dt} = - \frac12 n_i a_i \sum_{j \ne i} \frac{m_j}{M} B_1(a_i,a_j) (q_i - q_j )
\frac{dq_i}{dt} = + \frac12 n_i a_i \sum_{j \ne i} \frac{m_j}{M} B_1(a_i,a_j) (p_i - p_j )

where
B_p(a_i,a_j) = \frac{1}{\pi} \int_0^\pi \frac{a_i a_j \cos (p \phi)}{(a_1^2 + a_2^2 - 2 a_1 a_2 \cos \phi)^{3/2}} d\phi

and
n = \sqrt{\frac{GM}{a^3}}

a planet's "mean motion" or mean angular velocity, and M is the Sun's mass.

Note that all the apsidal precessions are forward and all the node precessions are backward, the latter being like the Earth's spin-axis precession.

The integrals for the B's are elliptic integrals, but they can be done numerically without much trouble. I've calculated oscillation periods for each of the modes, and I also estimate which planets that have the largest oscillations in those periods:

Eccentricity
1: 58000 yrs - Saturn, Jupiter, Mars
2: 72000 yrs - Mars, Venus, Earth
3: 75000 yrs - Mars, Earth, Venus
4: 180000 yrs - Mercury, Venus, Earth
5: 240000 yrs - Mercury, Venus, Earth
6: 350000 yrs - Uranus, Jupiter, Saturn, Mercury, Venus, Mars, Earth
7: 480000 yrs - Uranus, Neptune, Jupiter, Saturn, Mars, Earth, Mercury, Venus
8: 2000000 yrs - Neptune, Uranus, Saturn, Jupiter

Inclination
1: 50000 yrs - Saturn, Mars, Jupiter, Earth, Uranus
2: 69000 yrs - Mars, Venus, Earth, Mercury
3: 73000 yrs - Mars, Venus, Earth, Mercury
4: 200000 yrs - Mercury, Venus, Earth, Mars
5: 250000 yrs - Mercury, Venus, Earth, Mars
6: 440000 yrs - Uranus, Mercury, Neptune, Venus, Earth, Mars, Jupiter, Saturn
7: 1900000 yrs - Neptune, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus

There is also an infinite-period inclination mode that corresponds to the orientation of the Solar System's "invariable plane", the plane perpendicular to its angular-momentum vector. It is inclined 1.58 degrees to the Earth's orbit and has an ascending node of 108 degrees.

I have also attempted to estimate how much the various modes contribute to the various orbits' eccentricities and inclinations. For the Earth, the biggest eccentricity contributors are modes 2, 3, 4, and 6, and the biggest inclination contribor is mode 2.

I have attempted to check my calculations against some more precise calculation in the professional literature ("orbit91"), and I find that the eccentricity starts getting noticeable discrepancies at only 50,000 years, indicating some flaw somewhere.

I then did Fourier transforms of the professionally-calculated results and my results, and found that the most prominent periods are nevertheless close to what I'd calculated (M = mine, P = professional):

M: 14.1 - 355000 yrs
P: 12.4 - 403000 yrs
M/P amp: 1.07
Modes: 4 - 6

M: 40.4 - 124000 yrs
P: 39.5 - 127000 yrs
M/P amp: 1.36
Modes: 2 - 4, 3 - 4

M: 54.3 - 92100 yrs
P: 52.0 - 96200 yrs
M/P amp: 1.34
Modes: 2 - 6, 3 - 6

Note that these are "beat" frequencies between the different modes, like between modes 4 and 6 for the longest one.

Turning to the inclination, the orbit91 dataset does not contain inclination changes explicitly, but it does tabulate the Earth's obliquity (equator-ecliptic angle). Working with those, and using a precession period of 25700 years, I find:

P: 94.1 - 53700 years - 49300 years
Rel. Amp: 0.34
Mode: 1

P: 122.7 - 40700 years - 69600 years
Rel. Amp: 1
Mode: 2

P: 168.2 - 29700 years - 190000 years
Rel. Amp: 0.13
Mode: 4

P: 172.5 - 29000 years - 227000 years
Rel. Amp: 0.15
Mode: 5

Periods: obliquity, Earth orbit
Before each period, the location of the Fourier-transform peak


As I stated earlier, I had ignored orbital resonances, and Jupiter and Saturn are close to a 5:2 orbital resonance, with Jupiter making a little less than 5 orbits for every 2 orbits by Saturn. Using Jupiter and Saturn periods of 11.86223 and 29.4577 years, I find that every 59.58 years, Jupiter and Saturn are in the same relative positions, but advanced 8.1 degrees. And that this advancing has a period of 8800 years. And this may produce forced eccentricity and inclination effects large enough to throw off my calculations.

[lpetrich]

I now turn to the question of what additional effects these orbit-element variations have, like effects on the Earth's spin-axis precession. If the Earth's orbital plane stayed fixed, then the Earth's spin axis would make a circle around the Earth's orbit axis. But the Earth's orbital plane is not fixed; it oscillates about a degree or so, and the Earth's precession tries to track this oscillation. But this tracking is imperfect, and the Earth's obliquity (spin-axis orbit-axis angle) is thus induced to oscillate, going between 21.5 and 24.5 degrees.

But as Ward and Brownlee had asked in "Rare Earth", what if the Earth did not have its Moon? In that case, the Earth's spin-axis precession would be much slower, and comparable in rate to those orbit-element oscillations. Doing a precise calculation reveals that the Moon contributes about 68% of the Earth's precession, and that Moonlessness would increase the Earth's precession period from 25700 years to 80600 years. This is close to the periods of inclination modes 1, 2, and 3, especially 3.

And the absence of the Moon would mean less tidal drag, and thus a faster-rotating Earth. As I'd calculated earlier, the precession rate is approximately proportional to the rotation rate for hydrostatic equlibrium, and the Earth's precession would fall on modes 3, 2, or 1 if its rotation period was 21.9, 20.6, or 17.2 hours.

And when it does so, that will make a resonance, complete with amplified obliquity oscillations; the Earth's average obliquity may even become significantly changed. And if the Earth's obliquity starts to approach 90 degrees, the Earth's climate will get changed rather drastically. Midlatitudes and polar regions would have 24-hour daytime in the summer and 24-hour nighttime in the winter, making summers very hot and winters very cold, at least inside the contnents.

Ward and Brownlee thus propose that it is fortunate that the Earth has its Moon, because otherwise it would be very difficult for complex land organisms to thrive. And indeed we find in the geological record that the Earth has had climate zones similar to the present-day Earth's since at least the mid-Paleozoic, suggesting that the Earth's obliquity has not changed by very much over that time.


Something similar may have happened to Mars in the past. Mars's obliquity is currently 25.19 degrees (Earth's is 23.45 deg), and its precession period is currently around 175,000 (Earth) years (93,000 Mars years). That period is amidst the various mode periods, meaning that Mars may have gone through precession resonances in the past as it was spinning down from tidal drag. In fact, it is now close to the mode 4 inclination period, meaning that it may now be in such a resonance.

And is there evidence for such obliquity variations? As described in Martian Gully Mystery Solved? (http://www.lawrencehallofscience.org/pass/passv06/marsobliquity.html), astronomers François Costard and François Forget of the University of Paris have proposed that that is the case, pointing to relatively recent Martian erosion features at high latitudes and at poleward-facing slopes. When the obliquity is high, the summer-hemisphere pole's CO2 would have sublimated, thickening the atmosphere and heating Mars up. And the sunlight would have come from a poleward rather than from an equatorward direction.


And something simular could have happened to Uranus also, as discussed in How Uranus got its tilt (http://www.planetary.org/blog/article/00000553/). From Views of the Solar System (http://www.solarviews.com), the obliquities of Jupiter, Saturn, Uranus, and Neptune are 3.13, 25.33, 97.86, and 29.56 degrees. While Jupiter's is what one would most readily expect from Solar-System formation, the other three Jovian planets have much more tilted axes, and Uranus an on-its-side tilt.

That article discussed a paper by Adrián Brunini, Origin of the obliquities of the giant planets in mutual interactions in the early Solar System (http://www.nature.com/nature/journal/v440/n7088/abs/nature04577.html), Nature, vol. 440, pp. 1163-1165 (27 April 2006). According to that paper's scenario, Jupiter, Saturn, Uranus, and Neptune started out at distances of 5, 8, 13, and 14 astronomical units. As they grew and swept up outer-Solar-System material and interacted with each other, Jupiter and Saturn passed through a 2:1 resonance which made the orbits of Uranus and Neptune much more eccentric. But after a few million years, the outer planets settle down, with Uranus and Neptune moving farther outward and Saturn, Uranus, and Neptune acquiring their axial tilts.

Their satellites are not a real problem for this hypothesis, since their orbits would have followed their primaries' equators as they precessed.


Finally, although good numbers have been hard for me to find, I've found some other calculated mode periods in Milankovitch Theory and Climate (http://www.ldeo.columbia.edu/~polsen/nbcp/cmintro.html); that page's numbers are, alongside mine:

Eccentricity:
2: 72340 / 72000 yrs
3: 74630 / 75000 yrs
4: 173800 / 180000 yrs
5: 231600 / 240000 yrs
6: 350000 / 305000 yrs

Inclination:
2: 68750 / 69000 yrs
3: 73020 / 73000 yrs

[lpetrich]

Are there finer-grained effects on climate? Such effects have been speculated about for decades; one of the first was Serbian civil engineer and geophysicist Milutin Milanković, more usually spelled by English speakers as Milutin Milankovitch, in 1920. Thus, the orbital and spin cycles I've been describing are sometimes called Milankovitch cycles.

There has been a lot of controversy over how well the cycles match the geological record of Pleistocene ice ages, as well as controversy over how the orbital and spin effects get magnified to produce the climate changes attributed to them. Furthermore, glaciers slowly and steadily advance during each Ice Age, but quickly and fully retreat during each interglacial.

But in outline, here is what happens:

When the Earth's obliquity is low, summers are mild, meaning less snow melting. Thus, the glaciers advance.

But when the Earth's obliquity is high, summers are hot, meaning more snow melting. Thus, the glaciers retreat.

At the present, the Earth's obliquity is 23.45 degrees; it ranges between 22.08 and 24.54 degrees, with an average of 23.34 degrees (Orbit91 solution). The biggest inclination variation is due to inclination mode #2, and its period relative to the Earth's precession is about 41,000 years.

The eccentricity/perihelion effect is more complicated. The eccentricity vector precesses forward, though at least three modes prominently contribute (#2, #4, and #6). However, the Earth's spin precesses backward much faster, and relative to the Earth's spin, their forward precession has periods of around 20,000 years.

When the Earth is at perihelion during the northern-hemisphere summer, that hemisphere gets hot summers and cold winters, while the southern hemisphere gets mild summers and winters. While when the Earth is at perihelion during the northern-hemisphere winter, it is the northern hemisphere that gets mild summers and winters, and the southern hemisphere that gets hot summers and cold winters.

This effect is modulated by eccentricity variations, which are more complicated from the interaction of several similar-amplitude modes. The Earth's orbit's mean, median, minimum, and maximum eccentricity are 0.0275, 0.0270, 0.0003, and 0.0571 (Orbit91), and is now 0.0167. Its periods are typically 100,000 - 400,000 years.

At first thought, it seems that eccentricity effects will produce an Ice Age in one hemisphere and an interglacial in the other hemisphere, but the Earth has an asymmetric land distribution which nevertheless enables this effect to give the Earth ice ages.

Why is land distribution significant? Large glaciers can much more readily form on land than on the ocean, because the ocean has much greater thermal inertia and because it can transport heat by convection (ocean currents). And so we find at the present time that the South Pole, which is in land, is covered by a much thicker layer of ice than the North Pole, which is in sea.

At the present time, the northern hemisphere has much more midlatitude land than the southern hemisphere, enabling large glaciers to form on that land; during much of the Paleozoic, however, much of the Earth's midlatitude land area was in the southern hemisphere instead. So at the present time, the eccentricity/perihelion effect will make ice ages when the Earth is at perihelion during northern-hemisphere winter and the eccentricity is average to relatively high.

Milankovitch cycles were not taken very seriously for a long time, because it can be difficult to study the comings and goings of the Ice Age continental glaciers from their land effects -- those glaciers tend to destroy the evidence of what their predecessors had done.

But in the late 1960's, it became possible to measure oxygen-isotope abundances in fossil-plankton shells in cores from drilling in ocean floors. The reason that this is important for climate studies is because the lighter isotopes of oxygen evaporate more readily than its heavier isotopes, and the formation of large glaciers requires the evaporation of a lot of seawater, enriching the remainder in the heavier isotopes. When the glaciers melt, the oceans become enriched in lighter isotopes again. This is not a large effect (about 1 part in 1000), but it can nevertheless be detected. I note in passing that the oxygen has three stable isotopes, O16, O17 (0.03%), and O18 (0.2%), and that most measurements are of O18 relative to O16.

And in 1976, Hays, Imbrie, and Shackleton discovered evidence of the Milankovitch cycles in some seafloor cores for the last 800,000 years or so. And since then, the climatic effects of Milankovitch cycles have been an actively-researched subject.

Some references:
NOAA Paleoclimatology: Astronomical Theory of Climate Change (http://www.ncdc.noaa.gov/paleo/milankovitch.html)
U.S. Naval Observatory: Astronomical Applications Department: The Seasons and the Earth's Orbit - Milankovitch Cycles (http://aa.usno.navy.mil/faq/docs/seasons_orbit.html)
Climate, Astronomical Forcing, and Chaos (http://www.ldeo.columbia.edu/~polsen/nbcp/cmintro.html)
Long-term solutions for the insolation quantities of the Earth - Jacques Laskar (http://syrte.obspm.fr/iauJD16/laskar.pdf) (big PDF)
Climate Forcing Data (http://www.ncdc.noaa.gov/paleo/forcing.html)
Berger and Loutre: Orbit91 (ftp://ftp.ncdc.noaa.gov/pub/data/paleo/insolation/)
Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing (http://www.ncdc.noaa.gov/paleo/pubs/huybers2006b/huybers2006b.html)
Laskar: Astronomical Solutions for Earth Paleoclimates (http://www.imcce.fr/Equipes/ASD/insola/earth/earth.html)
Laskar: Astronomical Solutions for Martian Paleoclimates (http://www.imcce.fr/Equipes/ASD/insola/mars/mars.html) - has some nice graphs of Mars's obliquity over time; it varies much more than the Earth's, and it is difficult to follow past about 20 million years
Secular variations of the planetary orbits (French acronym: VSOP) - solution for the planets' orbit elements and positions that is good for the last few thousand years.

Now still more numbers. From this graph of Milankovitch cycles (http://en.wikipedia.org/wiki/Image:Milankovitch_Variations.png), I get these periods:

Periapsis longitude relative to the Earth's vernal equinox, and "absolute" position:
19 kyr -> 73 kyr -> #2,
22 kyr -> 150 kyr -> #4
24 kyr -> 360 kyr -> #6

Obliquity variations:
41 kyr - 69 kyr - #2

Eccentricity variations ("beat" periods):
95 kyr -> #4 - #6
125 kyr -> #2 - #4
400 kyr -> #2 - #6

[fragment]

This is a nice summary of the orbital effects on climate, lpetrich.

[lpetrich]

I will now look past the Pleistocene and its ice ages to see if there is evidence of spin/orbit astronomical cycles in earlier times. If there is, then that can provide constraints on planet-orbit sizes, shapes, and orientations, and also the Earth's obliquity.

To lowest order, the oscillation modes of the eccentricity and the inclination have periods and relative amplitudes that are functions only of the planets' major axes and distance. However, to higher order, there will be terms in planet resonances, like the Jupiter-Saturn 2:5 one, and higher powers of the eccentricity and the inclination. These will have the effect of making the modes' overall amplitudes and phases change over time relative to their lowest-order values.

A serious problem is the possibility of dynamical chaos. This is much misunderstood, because dynamical chaos does not mean absolute unpredictability. Chaotic systems are usually predictable over short timespans, and their long-term behavior often shows overall regularity, but precise prediction over the long term is extremely difficult, and is impossible in practice due to measurement errors in the initial conditions and parameter values, roundoff errors in the calculations, and errors in the numerical-integration algorithms used.

Roundoff error is because computers use a finite number of digits to represent numbers; while more digits mean greater accuracy, they also mean more computation time.

Numerical-integration algorithms produce error because they use a finite number of points in each step. Imagine approximating a curve with a polygon - the more polygon vertices you use, the better the approximation gets, but it is still an approximation. And the same is true if you use finite-order polynomials in some parameter instead of lines; the approximation becomes better, but it is still an approximation.


Back to dynamical chaos. One works out predictability by tracking the system from two slightly different sets of initial conditions. You then finds the distance between the state-variable values as you advance in time; if they increase exponentially, this increase is evidence of dynamical chaos. The increase rate is called the Lyapunov (or Liapunov) exponent, and the timescale for increase the Lyapunov time:
Lyapunov exponent (rather technical), also at Wolfram MathWorld (http://mathworld.wolfram.com/LyapunovCharacteristicExponent.html)
Dynamical Chaos theory (rather technical), also at Wolfram Mathworld (http://mathworld.wolfram.com/Chaos.html)


Numerical integration of the planets' motion typically results in a Lyapunov time of around 10 million years; this means that it is difficult to get past about 50 or 60 million years:

Jacques Laskar's results for the Solar System (http://syrte.obspm.fr/iauJD16/laskar.pdf)
Chaos in the Solar System (http://www.imcce.fr/Equipes/ASD/preprints/prep.2003/th2002_laskar.pdf), Jacques Laskar
Chaos and stability in the Solar System (http://www.pnas.org/cgi/reprint/98/22/12342.pdf), PNAS 2001, vol. 98, no. 22, p. 12342; Renu Malhotra, Matthew Holman, and Takashi Ito


Chaos can also happen to planets' spin axes.

The Moon's presence makes the Earth's spin axis precess much faster than the Sun does; this makes its precession much faster than the orbit-element oscillations, thus avoiding resonances and thus keeping its obliquity variations small.

However, as a result of the Earth's orbit's chaos, the Earth's precession is weakly chaotic; it stays in a narrow obliquity range, but past a few orbit Lyapunov times, its phase (direction of the vernal equinox) becomes difficult to predict. However, it is also difficult to predict that phase over such long timespans because of uncertainties in the amount of tidal drag, glaciation, etc.

But as the Moon spirals away from the Earth, and as the Earth itself spins down, its Earth's precession will become slower and slower, and it will interact with its orbit oscillations. The Earth's precession will then become strongly chaotic, getting obliquities going up to as much as 85 degrees.


The Earth might even go the way of Venus; Jacques Laskar has proposed that Venus got its retrograde rotation as a result of its precession having been chaotic some time in the past. Venus's slow rotation, however, is a result of tidal drag from tides produced by the Sun in its thick atmosphere.


And Mars? Astronomical Solutions for Martian Paleoclimates (http://www.imcce.fr/Equipes/ASD/insola/mars/mars.html), by Jacques Laskar et al. features some simulations of Mars's precession.

Its obliquity had oscillated between 15 and 35 degrees until about 5 million years ago; before that, it had oscillated between 25 and 45 degrees. Mars's obliquity-oscillation amplitude also goes from 2 to 10 to 6 to 10 to 2 again over 2.5 million years. Its eccentricity had oscillated between 0.05 - 0.03 and 0.11 - 0.12 with the same period, with eccentricity and obliquity amplitude being inversely correlated (low eccentricity - high obliquity; high eccentricity - low obliquity).

Going past 20 million years revealed a clear sign of chaos: five runs produced five different obliquity-variation patterns, ranging to going up to an average of 50 degrees to going down to an average of 10 degrees.


So Mars's obliquity will be difficult to predict for most of the Solar System's history, but its being chaotic suggests that it has had periods of high obliquity, which could well have produced summers hot enough to melt water.

Mars's poles now have icecaps on them, and they have a layered structure that suggests climate cycles. But it is difficult to say much more than that without further research, like landing rovers on them. Such a mission will be very challenging; Mars's poles experience nighttime for several months, meaning that a rover either has to flee to more equatorial latitudes or else have a non-solar power source that can sustain it during that time.


And the Earth? I'll be getting back to it in my next post after taking this detour in this post to show what we are up against.

[llanitedave]

I've got this thread saved to my desktop. Too much good stuff here to let it get away.

[lpetrich]

An interlude: some numbers on the Earth's rotation period and the Moon's revolution period, courtesy of Geological Constraints on the Precambrian History of Earth’s Rotation and the Moon’s Orbit (http://www.eos.ubc.ca/~mjelline/453website/eosc453/E_prints/1999RG900016.pdf), by George E. Williams.

In much of his paper, he discussed some numbers obtained from some tidal rhythmites at Elatina and Reynella in south Australia near Adelaide from the late Proterozoic, about 620 million years ago. These ocean-shore deposits were affected by the tides, which gave them a layered structure. I had been reluctant to mention them earlier here, because they imply that the Earth had had hardly any spindown from then until the Devonian. But I have now concluded that these results' error bars are large enough to permit a a nonzero spindown rate that approximately fits the Earth's present-day rotation.

Results extracted from the data, compared to present-day results; I've underlined the primary results, those directly from the data:

Lunar (Moon-relative) days per synodic (Sun-relative) month: 29.5 +- 0.5 / 28.53
Solar (Sun-relative) days per synodic month: 30.5 +- 0.5 / 29.53
Solar days per sidereal (star-relative) month: 28.3 +- 0.5 / 27.32
Synodic months per year: 13.1 +- 0.1 / 12.37
Apsidal period (forward precession of the line of apsides): 9.7 +- 0.1 / 8.85
Nodal period (backward precession of the line of nodes): 19.5 +- 0.5 / 18.61
Solar days per year: 400 +- 7 / 365.24
Sidereal (star-relative) days per year: 401 +- 7 / 366.24
Solar-day length (hours): 21.9 +- 0.4 / 24.00
Moon's semimajor axis (Earth equatorial radii: 6378 km): 58.16 +- 0.30 / 60.27
Lunar recession rate (cm/yr): 2.17 +- 0.31 (average from then to present) / 3.82 +- 0.07 (measured)

I have Estimated the Earth's spin-precession period for that time; I find that it decreased from 25700 years to around 22000 years. This would mean that the Earth's spin precession was more stable back then than it is today.

And there is a clue as to the Earth's obliquity back then: the observability of the Moon's nodal period, combined with Elatina's near-equatorial paleolatitude of about 10 degrees north. This means that the Earth must have had a significant obliquity, one large enough to give the Moon's orbit a significant inclination to the Earth's equator. At the present time, that inclination varies from 18.3 degrees to 28.6 degrees as the Moon's line of nodes precesses backwards around the Ecliptic; that would be enough to make the nodal effect noticeable. However, I have not found any attempts to estimate the inclination and obliquity sizes friom the Elatina deposits' variations.

But an obliquity similar in size to its present-day value can account for the observed annual and semiannual effects, which can come from both tides and nontidal seasonal-climate effects. The Earth's orbit eccentricity can also produce tidal and seasonal-climate effects, but distinguishing that effect from obliquity effects can be difficult.

That aside, the Moon's orbit eccentricity has a noticeable effect, one large enough to enable measurement of its apsidal period. Its eccentricity may have been close to its present-day value of 0.055.

The Elatina tidal rhythmites were deposited over a period of about 60 years, and it was toward the end of a Snowball Earth (http://www.snowballearth.org/overview.html) period, or at least a Slushball Earth period.


Referring back to the OP, the similar obliquity and rotation rate likely mean that hurricanes were as common in the Elatina deposits' time as they are today, at least during interglacials. Their preferred spawning locations, however, would almost certainly be different due to the different locations of the continents and the resulting different locations of the ITCZ.


There are some older rhythmites that are known to exist and have been examined for evidence of the aforementioned astronomical cycles; Dr. Williams mentioned:

The Big Cottonwood Formation in Utah from 900 mya
The Weeli Wolli Banded Iron Formation in western Australia from 2450 mya

Published results for Big Cottonwood are flawed, while the literature on Weeli Wolli features two different interpretations of that BIF's banding.

Neither formation has as much detail has the Elatina deposits, or at least has they have not been studied as closely as Elatina has been studied, which limits their usefulness.


ETA: some more:

Tidal rhythmites and their implications (http://www.mantleplumes.org/WebDocuments/MazumderESR2004.pdf), by Rajat Mazumder and Makoto Arima
Implications of lunar orbital peridicity from the Chaibasa tidal rhythmite (India) of late Paleoproterozoic age (http://www.mantleplumes.org/WebDocuments/GEOY-32-10-841.pdf), by Rajat Mazumder

They discussed the Chaibasa formation near Tata, eastern India; it is a late Paleoproterozoic (2100-1600 mya) rhythmite sandstone. They found good agreement with the second of Williams's two interpretations of the Weeli Wolli results:

Lunar days per synodic month: 32 / 31.1 +- 1.5 / 28.53
Solar days per synodic month: 33 / 32.1 +- 1.5 / 29.53

However, it was difficult to identify longer cycles in the Chaibasa deposits.

[lpetrich]

Now for what I'd promised earlier.

The authors of Climate, Forcing, and Astronomical Chaos (http://www.ldeo.columbia.edu/~polsen/nbcp/cmintro.html) note:
However, the fact that most of the frequencies thought to be important to paleoclimate studies are derived from combinations of a relatively few fundamental frequencies is a very powerful potential tool for getting celestial mechanical information directly out the geological record. Using a time scale derived by tuning to the most stable of the eccentricity cycles, the 404 ky cycle (see Laskar, this report, and Olsen, this report) the other long eccentricity cycles can be identified and their component g frequencies solved for (e. g. Olsen and Kent, 1999a). The very long length of the Newark basin and other Triassic-Jurassic basin cyclical records makes it possible to see such long cycles, and because of this it is possible to determine the fundamental periods. A similar procedure could be used for the obliquity cycle modulators. Because the eccentricity cycles and obliquity modulators are linked (see Laskar, this report), results from cores recovered in tropical regions where precision is dominant (i.e. the Newark basin cores), make predictions for the obliquity signal that can be tested by cores containing a strong obliquity response, most likely from the high latitudes. The geological record can this constrain celestial mechanical values for the past. Finally, by extending the procedure outlined above, it may be possible to obtain the phases and even amplitudes of the g and s values for the Triassic-Jurassic eventually allowing the construction of an insolation curve for the Earth Mesozoic.

I have searched for other such evidence of pre-Pleistocene climate cycles, and I've found:

The Pliocene Paradox (http://www.aos.princeton.edu/WWWPUBLIC/gphlder/pliopar.pdf) is about why the Earth was so warm when its landmass configuration and other such features were not different from what they were like in the Quaternary (Pleistocene - Recent). This includes a permament El Niño warm current configuration in the tropical oceans.
Up to 3 Ma there was a persistence of mild winters in central
Canada and the northeastern United States, droughts in Indonesia, and torrential rains along the coasts of California and Peru, and in eastern equatorial Africa. The onset of dry conditions in the latter region around 3 Ma favored the evolution of African hominids.
They note that the Milankovitch-cycle effects start getting amplified at about 3 Mya, and that glacial debris starts appearing in the north Pacific at about 2.7 Mya; the ice ages started at about that time, and grew strong over the last 1 million years.

So could glaciers' higher reflectance of light be an important positive-feedback mechanism? The more glaciers, the more light reflected, the less light absorbed; the less glaciers, the less light reflected, the more light absorbed.

Expression of Milankovitch Cycles in Mid-Pliocene Strata of the Productive Series, Azerbaijan (http://aapg.confex.com/aapg/sl2003/techprogram/paper_79375.htm) finds evidence of the perihelion-precession and eccentricity cycles.
Conference on Milankovitch cycles over the past 5 million years (http://cdsagenda5.ictp.trieste.it/full_display.php?smr=0&ida=a06238)
Breakthrough Made in Dating of the Geological Record (http://www.agu.org/sci_soc/eos96336.html) discusses fitting of sediment variations in Greece and Italy to eccentricity cycles, finding a good fit all the way back to 12.2 million years, in the middle of the Miocene. They plan to go even further back, to 17 million years.
Color Alternations in Cores (http://www-odp.tamu.edu/publications/188_IR/chap_03/c3_10.htm)
Principal Results (continued): Site 1165: Continental Rise (Wild Drift) (http://www-odp.tamu.edu/publications/prelim/188_prel/188s1165.html)
Evidence of Milankovitch cycles at Prydz Bay, Antarctica, going back to the early Miocene, over 20 million years ago.

Erik De Sonville's Astrochronology Intro (http://users.skynet.be/erik.desonville/en/astro.paleo.htm)
Orbitally induced climate and geochemical variability across the Oligocene-Miocene boundary (http://www.es.ucsc.edu/~jzachos/pubs/PZFT00.pdf) - 23 mya.
A Cyclostratigraphic Analysis of the Eocene-Oligocene Boundary GSSP, Massignano, Italy (http://www.carleton.edu/departments/GEOL/Resources/comps/CompsPDFfiles/2006CompsPapers/Brown2006.pdf) - evidence of Milankovitch cycles from 34 mya.
Calibrating Oligocene Eustasy to Oxygen Isotope Data (http://www.cosis.net/abstracts/EAE03/13654/EAE03-J-13654.pdf) (abstract) - evidence of Milankovitch cycles from Oligocene New Jersey sediments.
Milankovitch Cyclicity: A Tool for Determining the Stratigraphic Evolution of the Late Neogene Offshore Central California Margin (http://adsabs.harvard.edu/abs/2005AGUFMPP11B1460H) - 5 mya Santa Maria basin, central California continental shelf.
Intute search results for "Milankovitch" (http://www.intute.ac.uk/cgi-bin/search_harvester.pl?term1=Milankovitch&subject=sciences)
Climate change linked to anomaly in Earth's orbit (http://spaceflightnow.com/news/n0104/16anomaly/), really an unusual coincidence of cycle phases at the Oligocene-Miocene boundary, 23 Mya. It caused a cold snap that produced glaciers in Antarctica.

So it looks like we may soon get a Milankovitch chronology for most of the Cenozoic, a timespan that is only a few orbit-element Lyapunov times. This means that one can successfully integrate back in time from the present day over most of the Cenozoic, meaning that we potentially have an additional check on radiometric dates.

I'll be getting to some pre-Cenozoic evidence in my next post -- I've discovered a surprising amount of it for the Mesozoic.

[llanitedave]

Keep it coming, Ipetrich. We're listening.

[lpetrich]

Going into the Mesozoic, I've found:

Rates and Kinematics of Folding based on Mylankovitch Rhythms in Cretaceous Carbonates, NE Mexico (http://www.searchanddiscovery.net/documents/abstracts/annual2003/extend/80522.PDF) - evidence of the 20-kyr and 41-kyr cycles.
Late Cretaceous Precessional Cycles in Double Time: A Warm-Earth Milankovitch Response (http://www.sciencemag.org/cgi/content/abstract/261/5127/1431)
http://geology.geoscienceworld.org/cgi/content/abstract/30/4/291]Global correlation of Cenomanian (Upper Cretaceous) sequences: Evidence for Milankovitch control on sea level (http://gsa.confex.com/gsa/2005AM/finalprogram/abstract_91401.htm) - evidence for the 400-kyr eccentricity cycle from 94-100 Mya.
Milankovitch Cyclicity Revealed By Mineral-Magnetic Data From Mid-Cretaceous Oceanic Anoxic Events 1a and 1b, DSDP Site 398, North Atlantic Ocean (http://gsa.confex.com/gsa/2006AM/finalprogram/abstract_114753.htm) - evidence of cycles during those events, which were at ~120 Mya (Early Aptian) and ~112 Mya (Aptian/Albian).
Milankovitch cycles and palaeoproductivity in the mid-Cretaceous at Demerara Rise, ODP Leg 207 (http://www.cosis.net/abstracts/EGU06/07476/EGU06-A-07476.pdf?PHPSESSID=249a471eac7cc7b4c96d70b1bd11bd90) - 112 - 89 Mya (Albian to Turonian)
A Milankovitch Timescale for the Mid Cretaceous of the Vocontian Basin, SE France (http://www.cosis.net/abstracts/EGU04/07393/EGU04-A-07393.pdf) - 124-94 Mya (Aptian, Albian, and Cenomanian). Selected regions examined closely are dominated by the precession and short eccentricity cycles, while the overall formation has evidence of 400 kyr and 2.4 Myr eccentricity cycles. Furthermore, the 400-kyr cycles coincide with sediment cycles that are associated with sea-level changes; there is evidence for that elsewhere.
Milankovitch climatic origin of mid-Cretaceous black shale rhythms in central Italy (http://www.nature.com/nature/journal/v321/n6072/abs/321739a0.html) - 100 Mya; the eccentricity and precession cycles account for most of the variations.
Milankovitch-Based Correlation and Timing of Depositional Cyclicity Across the Early Cretaceous Platform, NE Mexico: Climate Variations Encoded by Rock Magnetics (http://gsa.confex.com/gsa/2005AM/finalprogram/abstract_91401.htm) - evidence of the main Milankovitch periods: 405kyr, 123kyr, 51.2kyr, 39.4kyr, 22.5kyr, 18.6kyr.
Milankovitch cyclicity and rock-magnetic signatures of palaeoclimatic change in the Early Cretaceous Biancone Formation of the Southern Alps, Italy (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WD3-45JK4SK-4&_user=10&_coverDate=04%2F30%2F1999&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=41388e830d63ca9fe3468b1caa6f0e25)

Milankovitch Cycles in Upper Jurassic and Lower Cretaceous Radiolarites of the Equatorial Pacific: Spectral Analysis and Sedimentation Rate Curves (http://www-odp.tamu.edu/publications/129_SR/VOLUME/CHAPTERS/sr129_30.pdf) (Alain J. Molinie and James G. Ogg) - 165-136 Mya (Callovian - Valanginian) - evidence of the eccentricity periods of 413 kyr, 123 kyr, and 95 kyr.
Towards an Astronomically Calibrated Timescale for the Jurassic (http://gsa.confex.com/gsa/2006AM/finalprogram/abstract_113743.htm) - proposal for looking for evidence of Milankovitch cycles in various Jurassic sedimentary deposits.
Strategies for assessing Early-Middle (Pliensbachian-Aalenian) Jurassic cyclochronologies (http://earth.geology.yale.edu/~jjpark/hinnovpark1999.pdf) (Linda A. Hinnov, Jeffrey J. Park) - 190-172 Mya - discusses some sediments in northern Italy in rather gory detail, finding evidence of periapsis-precession cycles in the older ones and obliquity cycles in the younger ones. This was connected to various overall climate changes, like "major hydrologic shifts on land, widespread oceanic anoxia, and evidence for global cooling and subsequent eustatic drawdown." -- glaciers forming?
Milankovitch Modulation of 13C(org) and Fish Communities in the Tropical Great Lakes of the Triassic-Jurassic Pangean Rift System (http://www.cosis.net/abstracts/EGU04/07738/EGU04-A-07738.pdf) - 250-175 Mya - no details on the cycles themselves, but a report on evidence of changes in lake depth. These lakes would have been much like the lakes of the East African Rift Valley, where similar continent splitting is now occurring.
Intensification of Milankovitch Cycles Associated with the Triassic-Jurassic Super-Greenhouse (http://www.ldeo.columbia.edu/~polsen/nbcp/EGU_05-A-10827.pdf) - about a million years of enhanced cyclicity starting a little bit before the Triassic-Jurassic boundary.
Milankovitch fluctuations on supercontinents (http://www.agu.org/pubs/crossref/1992/92GL00561.shtml) describes some climate simulations of orbit-driven climate fluctuations for a simulated Pangaea. Summer warming could vary as much as 14 - 16 C in midlatitudes to poles; summer temperatures at 65-degree paleolatitudes could get up to 25 C (77 F).
Astronomical calibration of the Jurassic time-scale from cyclostratigraphy in British mudrock formations (http://www.journals.royalsoc.ac.uk/content/m1ht0mr9lpxq4h54/) - 205-190-183 Mya (latest Triassic - Sinemurian - Pliensbachian), 156-146 Mya (Kimmeridgian - Tithonian) -- evidence of the cycles again, with shifts from obliquity initially being dominant to eccentricity/periapsis-precession being dominant in the Pliensbachian and obliquity becoming dominant again later on. This is in agreement with Hinnov and Park, who had worked with sediments from elesewhere.
Long-period Milankovitch cycles from the Late Triassic and Early Jurassic of eastern North America and their implications for the calibration of the Early Mesozoic time-scale and the long-term behaviour of the planets (http://www.journals.royalsoc.ac.uk/content/fy2dwfc0kynbkdrh/)
During the Late Triassic and Early Jurassic the Newark rift basin of the northeastern US accumulated in excess 5 km of continental, mostly lacustrine strata that show a profound cyclicity previously interpreted as caused by the astronomical forcing of tropical climate. The Newark record is known virtually in its entirety as a result of scientific and other coring and provides what is arguably one of the longest records of climate cyclicity available. Two proxies of water depth and hence climate in this record are a classification of sedimentary structures (depth ranks) and sediment colour. The depth rank and colour depth series display a full range of climatic precession related cycles. Here, we tune the depth rank and colour records to the 404 ka astronomical cycle and use this tuned record to explore the existence and origin of very long-period climate. We find highly significant periods of climatic precession modulation at periods of ca.1.75 Ma, 1 Ma and 700 ka in not only the depth rank and colour records, but also in the sedimentation rate curve derived from the tuning process. We then use the colour and depth rank time-series to construct an astronomically tuned time-scale for the Late Triassic. While the Newark higher-frequency eccentricity cycles that modulate precession are indistinguishable from today, the 1.75 Ma cycle is significantly different from predictions based on the present day fundamental frequencies of the planets (i.e. 2.5 Ma) and provides the first geological evidence of the chaotic behaviour of the inner planets, otherwise known only from numerical calculations.

Milankovitch climatic signals in Lower Triassic (Olenekian) peritidal carbonate successions, Nanpanjiang Basin, South China (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V6R-4B0WMFG-1&_user=10&_coverDate=12%2F05%2F2003&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=9f6fbf132f8a7bc28e5f69aa75faa4d8) - 250-245 Mya
The Full Spectrum of Milankovitch Precession-Related Periodicities in Triassic Age Lacustrine Strata of Eastern North America: from 10 k.y. to 3.5 m.y. (http://www.cosis.net/abstracts/EGU04/07733/EGU04-A-07733.pdf)
The pioneering work of Van Houten in the 1960’s (1) first established the Milankovitch character of lake level fluctuations in the tropics of central Pangea and laid the foundation for quantitative analysis of core and outcrops in the 1990’s (2,3). Based on our multitaper spectral analysis, moving window Fourier analysis, and wavelet analysis, as well as new independent constraints on accumulation rates, giant rift lakes in the region from about 3◦ to 10◦ N latitude fluctuated to the classic Milankovitch periods of precession-related forcing of approximately 20, 96, 128, and 404 ky, as well as longer period cycles of 1.75 and 3.5 M.y. The latter correspond to periods of g4-g3 of eccentricity related precessional forcing and the secular resonance, theta (2(g4-g3) - (s4-s3)), of combined precessional and obliquity related forcing, but differ from the modern values because of chaotic drift in the orbital behavior Earth and Mars (3). We attribute the forcing of lake depth largely to modulation of the strength of tropical con- vergence and hence the Monsoon system. The coal-bearing Late Triassic rifts located from 0◦ to 3◦ N latitude show similar frequency patterns, except with a strong ten- dency towards a doubling of the climatic precessional frequency (4,5,6). The strength of the expression of the long-period cycles of 1.75 and 3.5 M.y. is much larger than expected by direct insolation forcing and has a strong effect on the long term accumulation rate in these rift basins suggesting that they may be amplified by a greenhouse gas feedback such as weathering-related CO2 fluctuations.
Climate-induced fluctuations in sea level during non-glacial times (http://www.nature.com/nature/journal/v361/n6414/abs/361710a0.html) - noting that the cyclicities are present even with no significant continental glaciation, like in the Late Triassic. "We argue here that, in times of limited ice volume, periodic climate-induced changes in lake and groundwater storage have the potential to produce small fluctuations in sea level." In effect, lakes would grow and shrink as the climate changes.
Shallow marine record of orbitally forced cyclicity in a Late Triassic carbonate platform, Hungary (http://jsedres.sepmonline.org/cgi/content/abstract/67/4/661) - 228-200 Mya - not very well preserved.
Unraveling the Origin of Carbonate Platform Cyclothems in the Upper Triassic Dürrenstein Formation (Dolomites, Italy) (http://jsedres.sepmonline.org/cgi/content/abstract/73/5/774) - 237-220 Mya (Ladinian - Early Carnian) - "The recovery of Milankovitch periodicities allows reconstruction of a high-resolution timescale that is in good agreement with published durations of the Carnian based on radiometric ages."
A Triassic Geochronology Controversy: Milankovitch Versus Zircon Radioisotope Time Calibration of the Latemar Platform Cycles (http://aapg.confex.com/aapg/sl2003/techprogram/paper_78974.htm) - 245-228 Mya (Anisian-Ladinian) - "Evidence for strong Milankovitch forcing of the cyclic succession indicates a depositional duration for the Latemar Limestone of 10-12 million years, whereas U/Pb-dated zircons from volcaniclastics in coeval basinal Buchenstein beds indicate only 2-4 million years."
Biostratigraphic and radiometric age data question the Milankovitch characteristics of the Latemar cycles (Southern Alps, Italy) (http://geology.geoscienceworld.org/cgi/content/abstract/24/4/371)
Middle Triassic orbital signature recorded in the shallow-marine Latemar carbonate buildup (Dolomites, Italy) (http://geology.geoscienceworld.org/cgi/content/abstract/29/12/1123) - "The Latemar signature thus constitutes the oldest pristine Milankovitch signature yet observed in the geologic record. Its fidelity rivals that of the Pliocene-Pleistocene record originally used to confirm the theory of orbitally forced climates. This evidence deepens a widely noted disagreement between radiometric and cyclostratigraphic time scales for the Latemar buildup. The Latemar cycles indicate that orbitally forced sea-level oscillations were operative in the ice-free Middle Triassic hothouse world."
High frequency glacio-eustatic sealevel oscillations with Milankovitch characteristics recorded in Middle Triassic platform carbonates in northern Italy (http://ajsonline.org/cgi/content/abstract/287/9/853) - 245-228 Mya - evidence of Ice Ages modulated by Milankovitch cycles.


Looking more broadly, it looks like we may also get a Milankovitch chronology for the entire Mesozoic, extending the cyclicities' useful reach to the Permo-Triassic boundary (250 mya). Furthermore, this may provide constraints on the Earth's spin-axis precession rate, which can be calibrated with the help of the periods of the other cycles. And those periods can be cross-compared to help provide constraints on how much the planets' major axes have changed.

But the successes in recovering the cycles indicate that the Earth's spin-axis precession rate has not changed much since the Permo-Triassic boundary, which implies that the Earth's obliquity has not changed very much over that time. That precession rate is proportional to the cosine of the obliquity, which is now 0.917. Zero obliquity would produce 1 and an obliquity of 33.4 would produce 0.835.

This contention could possibly be tested with climate modeling of Milankovitch-cycle effects; what obliquities produce not only reasonable approximations of the observed climates but also reasonable approximations of the observed climate cyclicities? This can also be used to derive constraints on the eccentricity and inclination amplitudes, which can then be compared to their present-day values. Has dynamical chaos changed those amplitudes significantly?

And even in the absence of detailed climate modeling, one could find the relative amplitudes of the various modes and find out how they have changed over time.


Numbers from Hinnov and Park's paper (periods in kyr):

Present-day with precession 50.417262 arcsec/yr (period 25.706 kyr)
Middle Jurassic (170 Mya) with precession 53.80204918 arcsec/yr (period 24.089 kyr)
My numbers and those quoted earlier

Eccentricity cycles:
#2 - 18.98 - 72.54 - 18.07 - 72.33
#4 - 22.43 - 176.0 - 21.16 - 174.1
#6 - 23.72 - 307.1 - 22.33 - 305.9
Inclination cycles:
#1 - 53.62 - 49.38 - 47.18 - 49.22
#2 - 41 - 68.91 - 37.11 - 68.65
#3 - 39.73 - 72.82 - 35.99 - 72.84
#5 - 28.9 - 232.6 - 26.89 - 231.2

Molinie and Ogg:
Present
Possible early Permian (270 Mya)
Eccentricity
#2 - 19 - 17.6
#4,6 - 23 - 21
Inclination
#2 - 41 - 35
Inferred precession period: 23.2 kyr
Earth orbit eccentricity varies from 0.0005 to 0.0607 (presently 0.0167)

My periods vs. Laskar's periods in Milankovitch Theory and Climate (http://www.ldeo.columbia.edu/~polsen/nbcp/cmintro.html); I've included Laskar's notation for the modes here:
Eccentricity
#1 - 58 -
#2 - 72 - g4 - 72.34
#3 - 75 - g3 - 74.63
#4 - 180 - g2 - 173.8
#5 - 240 - g1 - 231.6
#6 - 350 - g5 - 305.0
#7 - 480 -
#8 - 2000 -
Inclination
#1 - 50 - s6
#2 - 69 - s3 - 68.75
#3 - 73 - s4 - 73.02
#4 - 200 -
#5 - 250 - s1
#6 - 440 -
#7 - 1900 -

[lpetrich]

And now into the Paleozoic.

Tempo of the end-Permian event: High-resolution cyclostratigraphy at the Permian-Triassic boundary (http://geology.geoscienceworld.org/cgi/content/abstract/28/7/643) - 251 Mya - evidence of cycles with lengths 20, 40, 100, and 400 kyr; the Milankovitch values.
Shallow-Marine Sedimentary Rhythms from the Onshore Canning Basin, Western Australia: A Mid-Permian Record of Glacio-Eustacy (http://www.searchanddiscovery.net/documents/abstracts/2005annual_calgary/abstracts/welch.htm) - 284-275 Mya (Artiniskian) - evidence of Milankovitch cycles suggests that ice ages persisted until then.
Sequential architecture and cyclicity in Permian desert deposits, Brodick Beds, Arran, Scotland (http://cat.inist.fr/?aModele=afficheN&cpsidt=2404543) - the relative lengths of the sediment-deposition cycles fits the Milankovitch ones quite well, despite the lack of absolute time calibration.
U-Pb dates of Paleosols; constraints on late Paleozoic cycle durations and boundary ages (http://geology.geoscienceworld.org/cgi/content/abstract/26/5/403) - 299 Mya (Carboniferous-Permian boundary)
Rhythmic Upper Paleozoic Strata of Euramerica: Equatorial Indicators of Gondwanan Glaciation? (http://gsa.confex.com/gsa/2005AM/finalprogram/abstract_94138.htm) - 416-299 Mya (Devonian - Carboniferous) - possible evidence of Milankovitch modulation of Ice Ages; there is evidence of the familiar cyclicities.
Onset of late palaeozoic glacio-eustasy and the evolving climates of low latitude areas: A synthesis of current understanding (http://findarticles.com/p/articles/mi_qa3721/is_200107/ai_n8980125) - Late-Paleozoic Ice Ages started rather abruptly around 330 Mya (late Asbian), and then came and went with a fairly regular periodicity much like Pleistocene Ice Ages. This glaciation lowered the sea level and had other climate effects, which could be seen at the low latitudes that Britain was then at. However, the authors could not get good numbers for the amounts of those periods.
On the periodicity and magnitude of Late Carboniferous glacio-eustatie sea-level changes (http://www.ingentaconnect.com/content/geol/jgs/1992/00000149/00000003/14930303;jsessionid=1najil948y0a5.alice) - 318-299 Mya - evidence of various periods, but with discrepancies that may be due to calibration problems.
Milankovitch cycles and Carboniferous climate (http://adsabs.harvard.edu/abs/1993GeoRL..20.1175C)
Cyclical Permo-Carboniferous sea level fluctuations have long been linked to glacial-interglacial fluctuations on Gondwanaland. Similar to the Pleistocene, such fluctuations may in turn have been driven by variations in orbital isolation forcing. Herein we report results from climate model simulations that examine the effect of Milankovitch insolation variations on the climate of the Gondwanan supercontinent. Utilizing maximum summer insolation values typical of interglacials, we simulate completely snow-free conditions, with summer temperatures at the South Pole >20°C. Modifying orbital configuration to minimum summer insolation receipt results in a large area of below freezing temperatures. Comparison of model-generated summer snow cover for the latter run with reconstructions of glacial ice extent indicates a good first-order agreement. These calculations support the cyclothem model and suggest that the entire glacial-interglacial couplet for the Carboniferous can be simulated with a minimum number of adjustable parameters.
Middle Carboniferous Milankovitch Cyclicity: MSEC Data from Three Middle Carboniferous Sections Including the GSSP at Arrow Canyon, Nevada, and from the Lower Pennsylvanian Pinkerton Formation, Colorado (http://gsa.confex.com/gsa/2002AM/finalprogram/abstract_46205.htm) - 320 Mya

Milankovitch Cyclicity in the Ohio and Sunbury Shales: Astronomical Calibration of the Late Devonian-Early Carboniferous Timescale (http://gsa.confex.com/gsa/2006AM/finalprogram/abstract_113078.htm) - 375-345 Mya (Famennian - Tournasian) - evidence for the 20-kyr precession and 100-kyr eccentricity cycles.
The Upper Devonian orbital cyclostratigraphy and numerical dating conodont zones from Guangxi,South China (http://scholar.ilib.cn/Abstract.aspx?A=zgkx-ed200501004)
Orbital cyclostratigraphy of the Devonian Frasnian–Famennian transition in South China (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V6R-42SPWP3-3&_user=10&_coverDate=04%2F15%2F2001&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ac310441bc42a9e2ae6ff6f72887f648) - 375 Mya - periods are 400, 100, 33.3, and 16.7 kyr; these results are consistent with an estimate of the Earth's spin-precession period in the Devonian calculated from its rotation rate and the Moon's distance at that time.
Edward Cotter's home page (http://www.facstaff.bucknell.edu/cotter/) - he cites evidence of sea-level cyclicities in several places during the Upper Devonian, suggesting that they are a global effect possibly caused by Milankovitch cycles.
Orbital forcing of a hierarchy of carbonate allocycles: Devonian Cedar Valley Group, Iowa (http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=6860124) - 398-385 Mya (Middle Devonian)
Calibrating the Devonian Time Scale: A synthesis of U-Pb ID-TIMS ages and conodont stratigraphy (http://www.earth-time.org/Kaufmann_2006_CalibratingDe.pdf) - discusses a serious problem in testing hypotheses of Milankovitch cyclicity: finding time references for observed cycles. The Devonian's beginning has been estimated at 420 - 400 Mya, while its end has been estimated at 360 - 350 Mya over the last three decades, with subdivisions having similar variations.

Correlation of hierarchal Upper Silurian stacking patterns generated by Milankovitch orbital forcing (http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=5640091) - 423-416 Mya
Eccentricity and precession forced cyclicity in the Upper Silurian Williamsport Sandstone Member of the Wills Creek Formation (http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=5805740)
Paleoceanography of the Michigan Basin in Silurian Time as Revealed from Stable Isotopic Analysis of Brachiopods (http://gsa.confex.com/gsa/2004AM/finalprogram/abstract_80017.htm) - 428-423 Mya (Middle Silurian)
Milankovitch-band cyclicity in bedded halite deposits contemporaneous with Late Ordovician-Early Silurian glaciation, Canning Basin, Western Australia (http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V61-4729HS0-1V&_user=10&_coverDate=04%2F30%2F1991&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=14c9d18aae89b2ae36bb4233bed74efa) - 461-428 Mya - evidence of periodicities in salt deposits from that time. Calibrating using the eccentricity period of 100 kya, the resulting periods agree rather well with estimates derived from the estimated spin-precession rate for that time:
31.3 +/- 3.0 -- 30.5
19.6 +/- 1.1 -- 19.3
17.4 +/- 1.1 -- 16.4
This calculation also assumed an obliquity value close to the present-day obliquity, and the estimated deposition rate is close to estimates of other such deposits' deposition rates.
A High Resolution Late Ordovician - Early Silurian Composite Carbon Isotope Profile from Western Laurentia (http://gsa.confex.com/gsa/2006AM/finalprogram/abstract_110364.htm) - has cyclicity which might be Milankovitch.
Calibrating the Late Ordovician glaciation and mass extinction by the eccentricity cycles of Earth's orbit (http://geology.geoscienceworld.org/cgi/content/abstract/28/11/967)
Paleomagnetism and Cyclostratigraphy of the Middle Ordovician Krivolutsky Suite, Krivaya Luka Section, Southern Siberian Platform: Record of Non-Synchronous NRM-Components or a Non-Axial Geomagnetic Field? (http://www.springerlink.com/content/q825m8l17x7x8k26/) - 472-461 Mya - evidence of Milankovitch cycles with the appropriate periods.


A deficiency in the literature so far is the lack of addressing of relative amplitudes of the various oscillations. This is a possible result of the nonlinearities and the dynamical chaos of the planets' orbits. As mentioned earlier, their Lyapunov time is about 5 to 10 Myr; since the Ordovician-Silurian boundary is at 444 Myr, about 40 to 80 Lyapunov times have elapsed since then.

But it may be possible to test whether such changes are likely to happen by doing long intergrations with slight changes in initial conditions, and then checking on what amplitudes the modes have.

Nevertheless, eccentricity modes #2, #4, and #6 (g4, g2, g5) and inclination modes #2 and #3 (s3, s4) continue to be the most prominent ones, and the eccentricity modes especially offer the ability to check on relative amplitudes.

And the success in extrapolating the Earth's spin-precession period suggests that the Earth's obliquity has not changed much over that time. This is consistent with evidence from climate zones; referring back to the OP, it suggests that for most of the Phanerozoic, the Earth has had hurricanes in roughly the patterns that it has them today, though the hurricane spawning grounds had been affected by the drifting of the continents.

In my next post I'll continue on to the Cambrian and beyond.

[KeithJM]

Haven't posted in this thread before, but just wanted to thank you for this. I think I've spent about 2-3 days worth of time reading and pondering all the information and papers you've given.

[lpetrich]

I've found this interesting paper:
Climate friction and the Earth's obliquity (http://www.blackwell-synergy.com/doi/abs/10.1046/j.1365-246X.2003.02021.x) by B. Levrard and J. Laskar - they analyzed the effect of the Earth's polar continental regions sagging underneath glaciers and bouncing back when those glaciers melt, and concluded that the resulting "climate friction" cannot have changed the Earth's obliquity more than 3 or 4 degrees over the last 800 million years. They analyzed three big ice-age periods:
Late Pliocene - Pleistocene (0.3 Mya)
Permo-Carboniferous (260-340 Mya)
Late Proterozoic (Cryogenian):
Varanger: 570-620 Mya
Sturtian: 700-750 Mya

And some more Milankovitch cyclicity:
Shallowing-Upward Cycles in the Lower Paleozoic Shallow-Marine Carbonates of Malyi Karatau, Kazakhstan (http://www.maik.ru/cgi-bin/search.pl?type=abstract&name=litmin&number=2&year=97&page=97) - - a possible connection mentioned. This place and its cycles are also mentioned in a paper tidle here (http://wwwalt.uni-wuerzburg.de/palaeontologie/Stuff/casu3.htm): "Bazykin, D. A. & Hinnov, L. A. 1996. Milankovitch forcing of Cambrian cyclic shallow marine carbonates of Malyi Karatau Range, Kazakhstan Republic; preliminary results of advanced time series analysis. - In: American Association of Petroleum Geologists 1996 annual convention. Annual Meeting Abstracts, 5: 12."
Spectral Analysis of Late Cambrian Cyclic Carbonates and Astronomical Forcing (http://gsa.confex.com/gsa/2002RM/finalprogram/abstract_34036.htm) - 504-488 Mya - no identifications made, however.

It is difficult for me to find anything before the Cambrian, so this is as far as my searching will go.

Dr. Linda Hinnov has some interesting pages (http://www.jhu.edu/~lhinnov1) on Milankovitch-cycle stratigraphy, or cyclostratrigraphy as it is now sometimes called.

She tries to explain the the Earth's orbital parameters (http://www.jhu.edu/~lhinnov1/hinnovresearch/earthsorbitalparameters.htm), noting that the Earth's orbit plane does precess -- something missing from a lot of nontechnical presentations of Milankovitch cycles. However, I think that the trajectories of the Earth's eccentricity vector and orbit north pole over time would be visually interesting, but She also has some nice graphs of the various cyclicities, including a sliding-window frequency analysis of them. It is easy to see the various Milankovitch frequencies in it.

In Astronomical Time for Earth History (http://www.jhu.edu/~lhinnov1/hinnovresearch/astronomical.htm), she explains that the International Commission on Stratigraphy (ICS) is now using Milankovitch cycles to provide time references. The Orbital Coverage (http://www.jhu.edu/~eps/chronoscyclostrat/aimandscope/orbitalcoverage.html) page shows how much of the geological timescale is covered by Milankovitch-calibrated stratigraphy.

In the Cenozoic, the Neogene (23.03 Mya to present) now has complete Milankovitch-cycle linkage, while the Paleogene (65.5 - 23.03 Mya) is getting there.

But only about 50% of the Mesozoic has Milankovitch linkage, and the Paleozoic has even less.

But geologists are working on trying to extending the Milankovich-linkage timescale into the Paleogene, and perhaps even into the Creataceous. As they do so, they will face the challenge of coping with the effects of chaos, which will make it difficult to simply integrate back from the present. It may be necessary to work out corrections for the oscillations' phases from geological data, and perhaps also corrections for their amplitudes.