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# Blog - Week 317

Okay, I'm done procrastinating: it's time to talk about glacial cycles and Milankovich cycles! I'm starting a new blog entry:

Blog - Week 317

I haven't written much yet. It seems I need to start by reviewing a bit of the Earth's climate history — because surely it's important that the current round of glacial cycles is a new phenomenon, geologically speaking. So, I'll go through the Cenozoic and show lots of graphs of temperature data, raise a bunch of well-known questions, but not try to discuss people's answers. In later weeks we can get into more detail.

I say "we" because Tim has started writing something about stochastic resonance. If he wants, that could become part of This Week's Finds, when we reach the more mathematical aspects of glacial cycles. I like the idea of jointly written This Week's Finds.

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1.

I spent most of the day writing

Blog - Week 317

and it's close to done. I need to add some more colorful details near the end; it gets a bit boring there. And I need to include some more references. I want easy-to-read, not very technical references on the Cenozoic climate and ice ages. Does anyone know some good ones I haven't included?

Comment Source:I spent most of the day writing [[Blog - Week 317]] and it's close to done. I need to add some more colorful details near the end; it gets a bit boring there. And I need to include some more references. I want _easy-to-read, not very technical_ references on the Cenozoic climate and ice ages. Does anyone know some good ones I haven't included?
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My dates for the last few glacial periods could be wrong... it seems nobody agrees on these, and if you look at the graphs you'll see why. This is just a note to myself to check this out.

Comment Source:My dates for the last few glacial periods could be wrong... it seems nobody agrees on these, and if you look at the graphs you'll see why. This is just a note to myself to check this out.
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edited July 2011

I'm sorry, I don't know good easy (or difficult) references.

For me clicking on the link shows the same picture, but then from wikipedia. Perhaps you could you also add a link to sth like delta 18 oxygen and add that benthic means sea floor (if I'm correct)? [Note added: I see you've explained it later in the post]

Later we should delve into more technical details.

Is this an apology in advance that we won't, or do you mean "later we will"?

Later, the agricultural revolution

So, you could say we coevolved with grasses!

hmm, perhaps the "early farmers" coevolved with edible grasses... but that's certainly not in the Miocene, as you certainly know. [Ok, you later specify that you speak about apes and early humans, but the preceding paragraph makes your comment confusing, I think]

More important, you write:

The amount of oxygen-18 in these deposits is used as temperature proxy: the more of it there is, the colder we think it was.

but just to keep you on your toes, here up means warm, or at least more oxygen-18.

there were ice sheets down to the Great Lakes and the mouth of the Rhine, and covering the British Isles.

are you sure about this? The mouth of the Rhine is in South Holland, so it would be much further south than I thought

see this map, the Würm should equal the Weichsel period (North-European name), or the red line. The yellow is the Riss.

Btw, and completely unrelated to your blog post, the caption on the picture

65 Million years of climate change

seems really strange to me. Why not 65 Million years of Earth's climate (or is it so counterintuitive that climate could change that it has be added explicitly?)

Comment Source:I'm sorry, I don't know good easy (or difficult) references. For me clicking on the link shows the same picture, but then from wikipedia. Perhaps you could you also add a link to sth like [delta 18 oxygen](http://en.wikipedia.org/wiki/%CE%9418O) and add that benthic means sea floor (if I'm correct)? [Note added: I see you've explained it later in the post] > Later we should delve into more technical details. Is this an apology in advance that we won't, or do you mean "later we will"? > Later, the agricultural revolution > So, you could say we coevolved with grasses! hmm, perhaps the "early farmers" coevolved with edible grasses... but that's certainly not in the Miocene, as you certainly know. [Ok, you later specify that you speak about apes and early humans, but the preceding paragraph makes your comment confusing, I think] **More important**, you write: > The amount of oxygen-18 in these deposits is used as temperature proxy: the more of it there is, the colder we think it was. > but just to keep you on your toes, here up means warm, or at least more oxygen-18. isn't this contradictory? > there were ice sheets down to the Great Lakes and the mouth of the Rhine, and covering the British Isles. are you sure about this? The mouth of the Rhine is in South Holland, so it would be much further south than I thought see this [map](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/EisrandlagenNorddeutschland.png/450px-EisrandlagenNorddeutschland.png), the Würm should equal the Weichsel period (North-European name), or the red line. The yellow is the Riss. Btw, and completely unrelated to your blog post, the caption on the picture > 65 Million years of climate change seems really strange to me. Why not 65 Million years of Earth's climate (or is it so counterintuitive that climate could change that it has be added explicitly?)
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edited July 2011

I wrote:

Later we should delve into more technical details.

Frederik wrote:

Is this an apology in advance that we won't, or do you mean "later we will"?

I meant just what I said! I could be more explicit, and say:

In future This Week's Finds, I should talk about this. But I don't know if I will - and whenever I promise to write about something, it becomes a chore, and I start procrastinating... so I certainly won't -promise_ that I will.

But that seems a bit too long and self-centered.

hmm, perhaps the "early farmers" coevolved with edible grasses... but that's certainly not in the Miocene, as you certainly know.

The beginning of the coevolution happened in the Miocene when grasslands made it useful for apes to become bipedal and walk around. Later grasses led to agriculture, and then agriculture led to genetically modified grasses, and also the burning of forests to create more grasslands. I thought I said that, but I'll try to make it a bit clearer.

Yikes! Sorry - up means cold in this graph:

By the way, this graph is by Barry Saltzman, famous for the 'Saltzman model' of glacial cycles, which we've discussed a bit here.

No, I read it somewhere but it could be wrong. Thanks, I'll check.

Btw, and completely unrelated to your blog post, the caption on the picture

65 Million years of climate change

seems really strange to me. Why not 65 Million years of Earth's climate (or is it so counterintuitive that climate could change that it has be added explicitly?)

I would call that a slight poetic touch, added because these graphs are for the public rather than scientists.

Comment Source:I wrote: > Later we should delve into more technical details. Frederik wrote: > Is this an apology in advance that we won't, or do you mean "later we will"? I meant just what I said! I could be more explicit, and say: > In future _This Week's Finds_, I should talk about this. But I don't know if I will - and whenever I _promise_ to write about something, it becomes a chore, and I start procrastinating... so I certainly won't -promise_ that I will. But that seems a bit too long and self-centered. <img src = "http://math.ucr.edu/home/baez/emoticons/tongue2.gif" alt = ""/> > hmm, perhaps the "early farmers" coevolved with edible grasses... but that's certainly not in the Miocene, as you certainly know. The beginning of the coevolution happened in the Miocene when grasslands made it useful for apes to become bipedal and walk around. Later grasses led to agriculture, and then agriculture led to genetically modified grasses, and also the burning of forests to create more grasslands. I thought I said that, but I'll try to make it a bit clearer. > isn't this contradictory? Yikes! Sorry - up means _cold_ in this graph: <img src = "http://math.ucr.edu/home/baez/temperature/6Myr.jpg" alt = ""/> By the way, this graph is by Barry Saltzman, famous for the 'Saltzman model' of glacial cycles, which we've discussed a bit here. > are you sure about this? No, I read it somewhere but it could be wrong. Thanks, I'll check. > Btw, and completely unrelated to your blog post, the caption on the picture > > 65 Million years of climate change > seems really strange to me. Why not 65 Million years of Earth's climate (or is it so counterintuitive that climate could change that it has be added explicitly?) I would call that a slight poetic touch, added because these graphs are for the public rather than scientists.
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edited July 2011

Btw, just because of a comment on the Forum I was reminded again of your blog post:

But grasslands, as opposed to thicker forests and jungles, are characteristic of cooler climates.

C4 plants arose around 25 to 32 million years ago[8] during the Oligocene (precisely when is difficult to determine) and did not become ecologically significant until around 6 to 7 million years ago, in the Miocene Period.[8] C4 metabolism originated when grasses migrated from the shady forest undercanopy to more open environments,[9] where the high sunlight gave it an advantage over the C3 pathway.[10] Drought was not necessary for its innovation; rather, the increased resistance to water stress was a by-product of the pathway and allowed C4 plants to more readily colonise arid environments.[10]

Forty-six percent of grasses are C4 and together account for 61% of C4 species.

C4 plants have a competitive advantage over plants possessing the more common C3 carbon fixation pathway under conditions of drought, high temperatures, and nitrogen or CO2 limitation. When grown in the same environment, at 30°C, C3 grasses lose approximately 833 molecules of water per CO2 molecule that is fixed, whereas C4 grasses lose only 277 water molecules per CO2 molecule fixed. This increased water use efficiency of C4 grasses means that soil moisture is conserved, allowing them to grow for longer in arid environments.[7]

It's funny that cooler climates gave way to grasslands, and to the evolution of another carbon fixation pathway which turns out to be more efficient for higher temperatures too!

Comment Source:Btw, just because of a comment on the Forum I was reminded again of your blog post: > But grasslands, as opposed to thicker forests and jungles, are characteristic of cooler climates. On this page about [C4](http://en.wikipedia.org/wiki/C4_photosynthesis) is written: > C4 plants arose around 25 to 32 million years ago[8] during the Oligocene (precisely when is difficult to determine) and did not become ecologically significant until around 6 to 7 million years ago, in the Miocene Period.[8] C4 metabolism originated when grasses migrated from the shady forest undercanopy to more open environments,[9] where the high sunlight gave it an advantage over the C3 pathway.[10] Drought was not necessary for its innovation; rather, the increased resistance to water stress was a by-product of the pathway and allowed C4 plants to more readily colonise arid environments.[10] > Forty-six percent of grasses are C4 and together account for 61% of C4 species. > C4 plants have a competitive advantage over plants possessing the more common C3 carbon fixation pathway under conditions of drought, high temperatures, and nitrogen or CO2 limitation. When grown in the same environment, at 30°C, C3 grasses lose approximately 833 molecules of water per CO2 molecule that is fixed, whereas C4 grasses lose only 277 water molecules per CO2 molecule fixed. This increased water use efficiency of C4 grasses means that soil moisture is conserved, allowing them to grow for longer in arid environments.[7] It's funny that **cooler climates gave way to grasslands, and to** the evolution of **another carbon fixation pathway** which turns out to be **more efficient for higher temperatures** too!
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I meant just what I said!

I suppose I was confused because "should" and "must" can both be translated to the same word in Dutch (but sometimes they should be translated differently) so I misunderstood.

Comment Source:> I meant just what I said! I suppose I was confused because "should" and "must" can both be translated to the same word in Dutch (but sometimes they should be translated differently) so I misunderstood.
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edited July 2011

I see. Sorry if I sometimes obnoxiously act like everyone in the world knows English perfectly. I thought that in German 'sollen' and 'müssen' mean something pretty similar to the English 'should' (moral obligation) and 'must' (necessity). So I would have guessed Dutch also worked the same way. But I guess not! What are the relevant Dutch words?

Comment Source:I see. Sorry if I sometimes obnoxiously act like everyone in the world knows English perfectly. I thought that in German 'sollen' and 'm&uuml;ssen' mean something pretty similar to the English 'should' (moral obligation) and 'must' (necessity). So I would have guessed Dutch also worked the same way. But I guess not! What are the relevant Dutch words?
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Hmm, maybe I don't understand Dutch appropriately, but as far as I know there is only one "moeten".

The verb "zullen" exists but that's almost always used like "will" in English (or "werden" in German). (btw, there is also "willen" in Dutch which is "want" or "möchten")

But sometimes I would choose to translate "should" as "zou moeten" (would should)

It happens that people dare to say "moeten" when they mean "zou moeten" ;) so I suppose that's what I was thinking here, but that misinterpretation is purely in my head (in Dutch), and not in your writings in English...

Comment Source:Hmm, maybe I don't understand Dutch appropriately, but as far as I know there is only one "moeten". The verb "zullen" exists but that's almost always used like "will" in English (or "werden" in German). (btw, there is also "willen" in Dutch which is "want" or "möchten") But sometimes I would choose to translate "should" as "zou moeten" (*would should*) It happens that people dare to say "moeten" when they mean "zou moeten" ;) so I suppose that's what I was thinking here, but that misinterpretation is purely in my head (in Dutch), and not in your writings in English...
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Seems Dutch and German aren't that similar?

This must/need/may (not) stuff was the only difficulty I had with english "grammar" during shool. I may memorize it one day (having learnt it 100s times again), but it keeps leaking out of my poor brain. Right now it's not there.

Comment Source:Seems Dutch and German aren't that similar? This must/need/may (not) stuff was the only difficulty I had with english "grammar" during shool. I may memorize it one day (having learnt it 100s times again), but it keeps leaking out of my poor brain. Right now it's not there.
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edited July 2011

Just had a quick glance (sitting at work). The picture "65 Million years of climate change" reminds me of a great 8min lecture of Hansen.

Comment Source:Just had a quick glance (sitting at work). The picture "65 Million years of climate change" reminds me of a [great 8min lecture of Hansen](http://climatecrocks.com/2011/01/03/the-8-minute-epoch-65-million-years-with-james-hansen/).
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11.

You might want to link more directly the review article on the Cenozoic that your first figure is derived from, instead of just linking to the Wikipedia figure. It's not non-technical, but it's not very technical either - a reasonable entry point into the scientific research.

Comment Source:You might want to link more directly <a href="http://www.sciencemag.org/content/292/5517/686">the review article</a> on the Cenozoic that your first figure is derived from, instead of just linking to the Wikipedia figure. It's not non-technical, but it's not very technical either - a reasonable entry point into the scientific research.
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The book "Ice, Mud, and Blood" is another pop-sci type book on glacial periods.

Comment Source:The book "Ice, Mud, and Blood" is another pop-sci type book on glacial periods.
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Thanks for the suggestions! There should be some nice overview textbook on Cenozoic climate, no?

I need to add some more juicy details, like how thick the ice was at the Last Glacial Maximum, and a bit about what it was like when it melted... I have some of these packed away in my diary.

Comment Source:Thanks for the suggestions! There should be some nice overview textbook on Cenozoic climate, no? I need to add some more juicy details, like how thick the ice was at the Last Glacial Maximum, and a bit about what it was like when it melted... I have some of these packed away in my diary.
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Okay, I put the article on the blog here:

This Week's Finds (Week 317)

As compared with what Nathan and Frederik saw, the actual blog article has 3 extra pictures illustrating continental drift and ice sheets, a bit more about human life during the last glacial period, and a couple more references.

Comment Source:Okay, I put the article on the blog here: [This Week's Finds (Week 317)](http://johncarlosbaez.wordpress.com/2011/07/22/this-weeks-finds-week-317/) As compared with what Nathan and Frederik saw, the actual blog article has 3 extra pictures illustrating continental drift and ice sheets, a bit more about human life during the last glacial period, and a couple more references.
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edited July 2011

I raised a question on the blog, which might be something for us to work on:

If you read about this graph, you'll see quite elaborate data processing was used to produce it: they took sediment samples from 57 different locations and correlated them assuming the fluctuations were synchronized with the Milankovitch cycles in the Earth's orbit!

We need to do something like this because sediments are deposited at different rates at different locations and times. But clearly it's a tricky business: if you're not careful, you can fool yourself into seeing patterns that aren't there! It would be nice to investigate the procedure that was done, and see how convincing it seems. It could be a fun nontrivial exercise in data analysis.

Maybe someone can tell me what's known about this puzzle. Suppose you have a bunch of wiggly graphs

$$x_i = f_i(t_i)$$ and you want the wiggles to become highly correlated when you reparametrize the time coordinates $t_i$, but you don't want to allow yourself to reparametrize the time coordinates 'too much', since that's cheating. What's a good algorithm for doing this? You're trying to maximize some sort of correlation while imposing a penalty for reparametrizing the time coordinates in too wiggly a way.

This type of problem must show up in various contexts.

It would be nice to align the data without assuming correlation to Milankovitch cycles and then see how much correlation there actually is to the Milankovitch cycles. Maybe someone else has already done that.

Comment Source:I raised a question on the blog, which might be something for us to work on: <img width="600" src="http://math.ucr.edu/home/baez/temperature/5Myr.png" alt="" /> If you [read about this graph](http://www.globalwarmingart.com/wiki/File:Five_Myr_Climate_Change_Rev_png), you'll see quite elaborate data processing was used to produce it: they took sediment samples from 57 different locations and correlated them _assuming_ the fluctuations were synchronized with the Milankovitch cycles in the Earth's orbit! We _need_ to do something like this because sediments are deposited at different rates at different locations and times. But clearly it's a tricky business: if you're not careful, you can fool yourself into seeing patterns that aren't there! It would be nice to investigate the procedure that was done, and see how convincing it seems. It could be a fun nontrivial exercise in data analysis. Maybe someone can tell me what's known about this puzzle. Suppose you have a bunch of wiggly graphs $$x_i = f_i(t_i)$$ and you want the wiggles to become highly correlated when you reparametrize the time coordinates $t_i$, but you don't want to allow yourself to reparametrize the time coordinates 'too much', since that's cheating. What's a good algorithm for doing this? You're trying to maximize some sort of correlation while imposing a penalty for reparametrizing the time coordinates in too wiggly a way. This type of problem must show up in various contexts. It would be nice to align the data _without_ assuming correlation to Milankovitch cycles and then see how much correlation there actually is to the Milankovitch cycles. Maybe someone else has already done that.
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This type of problem must show up in various contexts.

Indeed it does. Dynamic time warping is used in several contexts. A similar problem occurs when aligning DNA sequences, where insertions and deletions as well as point mutations have occurred.

Comment Source:> This type of problem must show up in various contexts. Indeed it does. [Dynamic time warping](http://en.wikipedia.org/wiki/Dynamic_time_warping) is used in several contexts. A similar problem occurs when [aligning DNA sequences](http://en.wikipedia.org/wiki/Sequence_alignment), where insertions and deletions as well as point mutations have occurred.
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Dynamic time warping! Sounds like something out of Star Trek!

Thanks - it's amazing what horizons knowing the right buzzword can open up.

Comment Source:Dynamic time warping! Sounds like something out of Star Trek! Thanks - it's amazing what horizons knowing the right buzzword can open up.
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John wrote:

It would be nice to investigate the procedure that was done, and see how convincing it seems.

Is the data available?

Graham wrote:

Indeed it does. Dynamic time warping is used in several contexts.

I'm a little bit confused about this, don't speech recognition algorithms use hidden Markov models? How is "dynamic time warping" related to this? Wouldn't the correct mathematical buzzword be "hidden Markov model" where time is part of the hidden random process?

Since I had difficulties to find literature about unevenly spaced time series, I'd actually be rather surprised if mathematicians had published a lot about the situation where the time of observation itself is an unkown increasing function.

Comment Source:John wrote: <blockquote> <p> It would be nice to investigate the procedure that was done, and see how convincing it seems. </p> </blockquote> Is the data available? Graham wrote: <blockquote> <p> Indeed it does. Dynamic time warping is used in several contexts. </p> </blockquote> I'm a little bit confused about this, don't speech recognition algorithms use hidden Markov models? How is "dynamic time warping" related to this? Wouldn't the correct mathematical buzzword be "hidden Markov model" where time is part of the hidden random process? Since I had difficulties to find literature about <a href="http://mathoverflow.net/questions/48913/uneven-spaced-time-series">unevenly spaced time series</a>, I'd actually be rather surprised if mathematicians had published a lot about the situation where the time of observation itself is an unkown increasing function.
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When I do statistics with unevenly spaced time series, I use methods from spatial statistics / geostatistics, where you define a continuous covariance function and evaluate it at the set of discrete locations (times) where (when) your data are observed. For example, for an evenly spaced discrete time series you can use a traditional AR(1) process, but for an irregular time series you can instead use an exponential covariance function.

You can handle regression with locations (times) that have measurement errors using errors-in-variables regression methods, but that's not quite the problem here where the time of observation has some unknown functional form related to orbital cycles.

Comment Source:When I do statistics with unevenly spaced time series, I use methods from spatial statistics / geostatistics, where you define a continuous covariance function and evaluate it at the set of discrete locations (times) where (when) your data are observed. For example, for an evenly spaced discrete time series you can use a traditional AR(1) process, but for an irregular time series you can instead use an exponential covariance function. You can handle regression with locations (times) that have measurement errors using errors-in-variables regression methods, but that's not quite the problem here where the time of observation has some unknown functional form related to orbital cycles.
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edited July 2011

I'm a little bit confused about this, don't speech recognition algorithms use hidden Markov models? How is "dynamic time warping" related to this? Wouldn't the correct mathematical buzzword be "hidden Markov model" where time is part of the hidden random process?

One of the common problems you want to avoid when using "machine learning style" mathematical models is having combinations of parameters that never naturally occur being valid in the model. So my limited understanding is that in speech the changes in speed are almost independent of anything else about speech -- such as the combinations of phonemes, etc -- it generally makes sense to have a separate mechanism for dealing with time warping and the issues the HMM deals with: if you put them both in one big model it'd generally be less constrained, and thus generally perform worse. (You can have Markov models that incorporate time in various ways, but they tend to be ones where the time interacts with other variables in the kind of way that they do at each timestep.)

Graham can probably explain how it works more technically in his areas.

Comment Source:Tim asked > I'm a little bit confused about this, don't speech recognition algorithms use hidden Markov models? How is "dynamic time warping" related to this? Wouldn't the correct mathematical buzzword be "hidden Markov model" where time is part of the hidden random process? One of the common problems you want to avoid when using "machine learning style" mathematical models is having combinations of parameters that never naturally occur being valid in the model. So _my limited understanding_ is that in speech the changes in speed are almost independent of anything else about speech -- such as the combinations of phonemes, etc -- it generally makes sense to have a separate mechanism for dealing with time warping and the issues the HMM deals with: if you put them both in one big model it'd generally be less constrained, and thus generally perform worse. (You can have Markov models that incorporate time in various ways, but they tend to be ones where the time interacts with other variables in the kind of way that they do at each timestep.) Graham can probably explain how it works more technically in his areas.
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edited July 2011

John wrote:

If you read about this graph, you'll see quite elaborate data processing was used to produce it: they took sediment samples from 57 different locations and correlated them assuming the fluctuations were synchronized with the Milankovitch cycles in the Earth's orbit!

We need to do something like this because sediments are deposited at different rates at different locations and times. But clearly it's a tricky business: if you're not careful, you can fool yourself into seeing patterns that aren't there! It would be nice to investigate the procedure that was done, and see how convincing it seems. It could be a fun nontrivial exercise in data analysis.

Tim wrote:

Is the data available?

I don't know yet. There must be some such data available. You can read the paper behind this graph... maybe it says something about where the data is... I haven't had time to check yet:

Comment Source:John wrote: > <img width="600" src="http://math.ucr.edu/home/baez/temperature/5Myr.png" alt="" /> >If you read about this graph, you'll see quite elaborate data processing was used to produce it: they took sediment samples from 57 different locations and correlated them assuming the fluctuations were synchronized with the Milankovitch cycles in the Earth's orbit! > We need to do something like this because sediments are deposited at different rates at different locations and times. But clearly it's a tricky business: if you're not careful, you can fool yourself into seeing patterns that aren't there! It would be nice to investigate the procedure that was done, and see how convincing it seems. It could be a fun nontrivial exercise in data analysis. Tim wrote: > Is the data available? I don't know yet. There must be _some_ such data available. You can read the paper behind this graph... maybe it says something about where the data is... I haven't had time to check yet: * Lorraine E. Lisiecki and Maureen E. Raymo, [A Pliocene-Pleistocene stack of 57 globally distributed benthic $\delta^{18}$O records](http://www.naturals.ukpc.net/TimAndTim/Hansen/LisieckiRaymo_preprint.pdf), <i><a href = "http://www.agu.org/pubs/crossref/2005/2004PA001071.shtml">Paleoceanography</a></i> <b>20</b> (2005) PA1003, 17 pp.
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edited July 2011

At Lisiecki's website there is data and software. However, the data seems to be the processed data that was used to produce the above graph (together with some other stuff), not the 'raw' data.

If so, we can't use it to study the processing method. However, we could do wavelet transforms on this data - as others have already done, but without (if I recall correctly from our earlier discussion here) explaining what algorithm they used. That might be fairly easy and fun, no?

Here's a word about one piece of software at Lisiecki's website, the 'Match' program:

This software package uses dynamic programming to find the optimal alignment of two paleoclimate signals using penalty functions to constrain accumulation rates. The Match program is written in C++ and requires a command line interface to run. It should run on any Unix-style operating system, in Cygwin under Windows, and on Macs running MacOS 10 and should be easily portable to any platform with a C++ compiler. The matching algorithm is fairly memory and computation intensive, especially as the number of matching intervals increases. A graphical user interface for the Match program is available and runs in Matlab version 6 and 7. However, the Match program can be operated using only text files for configuration.

Comment Source:At [Lisiecki's website](http://lorraine-lisiecki.com/) there is data and software. However, the data seems to be the _processed_ data that was used to produce the above graph (together with some other stuff), not the 'raw' data. If so, we can't use it to study the processing method. However, we _could_ do wavelet transforms on this data - as others have already done, but without (if I recall correctly from our earlier discussion here) explaining what algorithm they used. That might be fairly easy and fun, no? Here's a word about one piece of software at Lisiecki's website, the 'Match' program: > This software package uses dynamic programming to find the optimal alignment of two paleoclimate signals using penalty functions to constrain accumulation rates. The Match program is written in C++ and requires a command line interface to run. It should run on any Unix-style operating system, in Cygwin under Windows, and on Macs running MacOS 10 and should be easily portable to any platform with a C++ compiler. The matching algorithm is fairly memory and computation intensive, especially as the number of matching intervals increases. A graphical user interface for the Match program is available and runs in Matlab version 6 and 7. However, the Match program can be operated using only text files for configuration.
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23.

Looking at their Match paper and its citations, it looks like they are indeed using a dynamic time warping algorithm.

Comment Source:Looking at their Match paper and its citations, it looks like they are indeed using a dynamic time warping algorithm.
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I wonder if people know a disciplined way to measure the goodness of fit between two curves (like $\delta^{18}$O and insolation as determined by Milankovitch cycles) when you need to use dynamic time warping to fit one curve to the other. This could be a fun statistical problem for certain people...

Comment Source:I wonder if people know a disciplined way to measure the goodness of fit between two curves (like $\delta^{18}$O and insolation as determined by Milankovitch cycles) when you need to use dynamic time warping to fit one curve to the other. This could be a fun statistical problem for certain people...
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edited July 2011

There are concrete criteria in

• L. R. Rabiner and B. Juang: "Fundamentals of speech recognition."

mentioned in the Wikipedia aricle. I haven't found the time to read it, but it has chapters that explain the assumptions for measures of goodness of fits, which are approriate for speech recognition. Question is: does this carry over to geophysical time series, too?

Comment Source:There are concrete criteria in * L. R. Rabiner and B. Juang: "Fundamentals of speech recognition." mentioned in the Wikipedia aricle. I haven't found the time to read it, but it has chapters that explain the assumptions for measures of goodness of fits, which are approriate for speech recognition. Question is: does this carry over to geophysical time series, too?
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I am sure there is some kind of goodness of fit measure, because the algorithm uses dynamic programming, which is designed to optimize some "goodness of fit" function.

I noticed a recent paper by Huybers proposing a new test for the success of orbital tuning, and using it to claim that existing orbital tuning may have problems.

Comment Source:I am sure there is some kind of goodness of fit measure, because the algorithm uses dynamic programming, which is designed to optimize some "goodness of fit" function. I noticed <a href="http://www.people.fas.harvard.edu/~phuybers/Doc/amfm_paleoc2010.pdf">a recent paper by Huybers</a> proposing a new test for the success of orbital tuning, and using it to claim that existing orbital tuning may have problems.
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27.
edited July 2011

Thanks, Nathan! Huyber writes, in part:

Neeman [1993] demonstrated that eccentricity-like amplitude modulation tended to result from filtering noisy records that were tuned to precession. This can be understood as the direct result of the celestial-mechanical relationship between eccentricity and the frequency of climatic precession, and from the signal-processing relationship between frequency and amplitude modulation that arises when a signal is filtered. The large excursions in the frequency of climatic precession that accompany low eccentricity orbital configurations cause a systematic reduction in the energy passed through a filter. Filtered records containing frequency variations like those of climatic precession then have reduced amplitude during times of low eccentricity. Thus, contrary to earlier suggestions, the appearance of eccentricity-like amplitude modulation in paleoclimate records that have been tuned to precession and filtered is not diagnostic of skill in the tuned timescale. Once tuned to precession, records routinely display eccentricity-like amplitude modulation after filtering, regardless of the accuracy of the tuned timescale.

A small literature is emerging regarding the statistical implications of time errors and intentional time adjustments [e.g. Thomson and Robinson, 1996; Buck and Millard, 2004; Mudelsee et al., 2009; Haam and Huybers, 2010], but this area of research remains in its infancy. Caution is warranted in drawing conclusions from records whose timing has been intentionally adjusted, particularly when the possibility of circularity exists between assumptions built into a record’s chronology and the inferences derived from it. In the amplitude-modulation case considered here, it was possible to substitute purely random signals for the ODP 677 $\delta^{18}$O record and obtain similar results, thereby showing circularity,and analogous approaches for checking the sensitivity of results to orbital tuning should generally be possible. The failure of the amplitude-modulation test underscores both the need to understand how time adjustments influence the statistical properties of a record and the need to develop general tests for the accuracy of orbitally tuned records.

Comment Source:Thanks, Nathan! Huyber writes, in part: > Neeman [1993] demonstrated that eccentricity-like amplitude modulation tended to result from filtering noisy records that were tuned to precession. This can be understood as the direct result of the celestial-mechanical relationship between eccentricity and the frequency of climatic precession, and from the signal-processing relationship between frequency and amplitude modulation that arises when a signal is filtered. The large excursions in the frequency of climatic precession that accompany low eccentricity orbital configurations cause a systematic reduction in the energy passed through a filter. Filtered records containing frequency variations like those of climatic precession then have reduced amplitude during times of low eccentricity. Thus, contrary to earlier suggestions, the appearance of eccentricity-like amplitude modulation in paleoclimate records that have been tuned to precession and filtered is not diagnostic of skill in the tuned timescale. Once tuned to precession, records routinely display eccentricity-like amplitude modulation after filtering, regardless of the accuracy of the tuned timescale. > A small literature is emerging regarding the statistical implications of time errors and intentional time adjustments [e.g. Thomson and Robinson, 1996; Buck and Millard, 2004; Mudelsee et al., 2009; Haam and Huybers, 2010], but this area of research remains in its infancy. Caution is warranted in drawing conclusions from records whose timing has been intentionally adjusted, particularly when the possibility of circularity exists between assumptions built into a record’s chronology and the inferences derived from it. In the amplitude-modulation case considered here, it was possible to substitute purely random signals for the ODP 677 $\delta^{18}$O record and obtain similar results, thereby showing circularity,and analogous approaches for checking the sensitivity of results to orbital tuning should generally be possible. The failure of the amplitude-modulation test underscores both the need to understand how time adjustments influence the statistical properties of a record and the need to develop general tests for the accuracy of orbitally tuned records.