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Archive for February, 2014

In Thirteen – Terminator II we had a cursory look at the different “proxies” for temperature and ice volume/sea level. And we’ve considered some issues around dating of proxies.

There are two main proxies we have used so far to take a look back into the ice ages:

  • δ18O in deep ocean cores in the shells of foraminifera – to measure ice volume
  • δ18O in the ice in ice cores (Greenland and Antarctica) – to measure temperature

Now we want to take a closer look at the proxies themselves. It’s a necessary subject if we want to understand ice ages, because the proxies don’t actually measure what they might be assumed to measure. This is a separate issue from the dating: of ice; of gas trapped in ice; and of sediments in deep ocean cores.

If we take samples of ocean water, H2O, and measure the proportion of the oxygen isotopes, we find (Ferronsky & Polyakov 2012):

  • 16O – 99.757 %
  • 17O –   0.038%
  • 18O –   0.205%

There is another significant water isotope, Deuterium – aka, “heavy hydrogen” – where the water molecule is HDO, also written as 1H2HO – instead of H2O.

The processes that affect ratios of HDO are similar to the processes that affect the ratios of H218O, and consequently either isotope ratio can provide a temperature proxy for ice cores. A value of δD equates, very roughly, to 10x a value of δ18O, so mentally you can use this ratio to convert from δ18O to δD (see note 1).

In Note 2 I’ve included some comments on the Dole effect, which is the relationship between the ocean isotopic composition and the atmospheric oxygen isotopic composition. It isn’t directly relevant to the discussion of proxies here, because the ocean is the massive reservoir of 18O and the amount in the atmosphere is very small in comparison (1/1000). However, it might be of interest to some readers and we will return to the atmospheric value later when looking at dating of Antarctic ice cores.

Terminology and Definitions

The isotope ratio, δ18O, of ocean water = 2.005 ‰, that is, 0.205 %. This is turned into a reference, known as Vienna Standard Mean Ocean Water. So with respect to VSMOW, δ18O, of ocean water = 0. It’s just a definition. The change is shown as δ, the Greek symbol for delta, very commonly used in maths and physics to mean “change”.

The values of isotopes are usually expressed in terms of changes from the norm, that is, from the absolute standard. And because the changes are quite small they are expressed as parts per thousand = per mil = ‰, instead of percent, %.

So as δ18O changes from 0 (ocean water) to -50‰ (typically the lowest value of ice in Antarctica), the proportion of 18O goes from 0.20% (2.0‰) to 0.19% (1.9‰).

If the terminology is confusing think of the above example as a 5% change. What is 5% of 20? Answer is 1; and 20 – 1 = 19. So the above example just says if we reduce the small amount, 2 parts per thousand of 18O by 5% we end up with 1.9 parts per thousand.

Here is a graph that links the values together:

From Hoef 2009

From Hoefs 2009

Figure 1

Fractionation, or Why Ice Sheets are So Light

We’ve seen this graph before – the δ18O (of ice) in Greenland (NGRIP) and Antarctica (EDML) ice sheets against time:

From EPICA 2006

From EPICA 2006

Figure 2

Note that the values of δ18O from Antarctica (EDML – top line) through the last 150 kyrs are from about -40 to -52 ‰. And the values from Greenland (NGRIP – black line in middle section) are from about -32 to -44 ‰.

There are some standard explanations around – like this link – but the I’m not sure the graphic alone quite explains it – unless you understand the subject already..

If we measure the 18O concentration of a body of water, then we measure the 18O concentration of the water vapor above it, we find that the water vapor value has 18O at about -10 ‰ compared with the body of water. We write this as δ18O = -10 ‰. That is, the water vapor is a little lighter, isotopically speaking, than the ocean water.

The processes (fractionation) that cause this are easy to reproduce in the lab:

  • during evaporation, the lighter isotopes evaporate preferentially
  • during precipitation, the heavier isotopes precipitate preferentially

(See note 3).

So let’s consider the journey of a parcel of water vapor evaporated somewhere near the equator. The water vapor is a little reduced in 18O (compared with the ocean) due to the evaporation process. As the parcel of air travels away from the equator it rises and cools and some of the water vapor condenses. The initial rain takes proportionately more 18O than is in the parcel – so the parcel of air gets depleted in 18O. It keeps moving away from the equator, the air gets progressively colder, it keeps raining out, and the further it goes the less the proportion of 18O remains in the parcel of air. By the time precipitation forms in polar regions the water or ice is very light isotopically, that is, δ18O is the most negative it can get.

As a very simplistic idea of water vapor transport, this explains why the ice sheets in Greenland and Antarctica have isotopic values that are very low in 18O. Let’s take a look at some data to see how well such a simplistic idea holds up..

The isotopic composition of precipitation:

From Gat 2010

From Gat 2010

Figure 3 – Click to Enlarge

We can see the broad result represented quite well – the further we are in the direction of the poles the lower the isotopic composition of precipitation.

In contrast, when we look at local results in some detail we don’t see such a tidy picture. Here are some results from Rindsberger et al (1990) from central and northern Israel:

From Rindsberger et al 1990

From Rindsberger et al 1990

Figure 4

From Rindsberger et al 1990

From Rindsberger et al 1990

Figure 5

The authors comment:

It is quite surprising that the seasonally averaged isotopic composition of precipitation converges to a rather well-defined value, in spite of the large differences in the δ value of the individual precipitation events which show a range of 12‰ in δ18O.. At Bet-Dagan.. from which we have a long history.. the amount weighted annual average is δ18O = 5.07 ‰ ± 0.62 ‰ for the 19 year period of 1965-86. Indeed the scatter of ± 0.6‰ in the 19-year long series is to a significant degree the result of a 4-year period with lower δ values, namely the years 1971-75 when the averaged values were δ18O = 5.7 ‰ ± 0.2 ‰. That period was one of worldwide climate anomalies. Evidently the synoptic pattern associated with the precipitation events controls both the mean isotopic values of the precipitation and its variability.

The seminal 1964 paper by Willi Dansgaard is well worth a read for a good overview of the subject:

As pointed out.. one cannot use the composition of the individual rain as a direct measure of the condensation temperature. Nevertheless, it has been possible to show a simple linear correlation between the annual mean values of the surface temperature and the δ18O content in high latitude, non-continental precipitation. The main reason is that the scattering of the individual precipitation compositions, caused by the influence of numerous meteorological parameters, is smoothed out when comparing average compositions at various locations over a sufficiently long period of time (a whole number of years).

The somewhat revised and extended correlation is shown in fig. 3..

From Dansgaard 1964

From Dansgaard 1964

Figure 6

So we appear to have a nice tidy picture when looking at annual means, a little bit like the (article) figure 3 from Gat’s 2010 textbook.

Before “muddying the waters” a little, let’s have a quick look at ocean values.

Ocean δ18O

We can see that the ocean, as we might expect, is much more homogenous, especially the deep ocean. Note that these results are δD (think, about 10x the value of δ18O):

From Ferronsky & Polyakov (2012)

From Ferronsky & Polyakov (2012)

Figure 7 – Click to enlarge

And some surface water values of δD (and also salinity), where we see a lot more variation, again as might expect:

From Ferronsky & Polyakov 2012

From Ferronsky & Polyakov 2012

Figure 8

If we do a quick back of the envelope calculation, using the fact that the sea level change between the last glacial maximum (LGM) and the current interglacial was about 120m, the average ocean depth is 3680m we expect a glacial-interglacial change in the ocean of about 1.5 ‰.

This is why the foraminifera near the bottom of the ocean, capturing 18O from the ocean, are recording ice volume, whereas the ice cores are recording atmospheric temperatures.

Note as well that during the glacial, with more ice locked up in ice sheets, the value of ocean δ18O will be higher. So colder atmospheric temperatures relate to lower values of δ18O in precipitation, but – due to the increase in ice, depleted in 18O – higher values of ocean δ18O.

Muddying the Waters

Hoefs 2009, gives a good summary of the different factors in isotopic precipitation:

The first detailed evaluation of the equilibrium and nonequilibrium factors that determine the isotopic composition of precipitation was published by Dansgaard (1964). He demonstrated that the observed geographic distribution in isotope composition is related to a number of environmental parameters that characterize a given sampling site, such as latitude, altitude, distance to the coast, amount of precipitation, and surface air temperature.

Out of these, two factors are of special significance: temperature and the amount of precipitation. The best temperature correlation is observed in continental regions nearer to the poles, whereas the correlation with amount of rainfall is most pronounced in tropical regions as shown in Fig. 3.15.

The apparent link between local surface air temperature and the isotope composition of precipitation is of special interest mainly because of the potential importance of stable isotopes as palaeoclimatic indicators. The amount effect is ascribed to gradual saturation of air below the cloud, which diminishes any shift to higher δ18O-values caused by evaporation during precipitation.

[Emphasis added]

From Hoefs 2009

From Hoefs 2009

Figure 9

The points that Hoefs make indicate some of the problems relating to using δ18O as the temperature proxy. We have competing influences that depend on the source and journey of the air parcel responsible for the precipitation. What if circulation changes?

For readers who have followed the past discussions here on water vapor (e.g., see Clouds & Water Vapor – Part Two) this is a similar kind of story. With water vapor, there is a very clear relationship between ocean temperature and absolute humidity, so long as we consider the boundary layer. But what happens when the air rises high above that – then the amount of water vapor at any location in the atmosphere is dependent on the past journey of air, and as a result the amount of water vapor in the atmosphere depends on large scale circulation and large scale circulation changes.

The same question arises with isotopes and precipitation.

The ubiquitous Jean Jouzel and his colleagues (including Willi Dansgaard) from their 1997 paper:

In Greenland there are significant differences between temperature records from the East coast and the West coast which are still evident in 30 yr smoothed records. The isotopic records from the interior of Greenland do not appear to follow consistently the temperature variations recorded at either the east coast or the west coast..

This behavior may reflect the alternating modes of the North Atlantic Oscillation..

They [simple models] are, however, limited to the study of idealized clouds and cannot account for the complexity of large convective systems, such as those occurring in tropical and equatorial regions. Despite such limitations, simple isotopic models are appropriate to explain the main characteristics of dD and d18O in precipitation, at least in middle and high latitudes where the precipitation is not predominantly produced by large convective systems.

Indeed, their ability to correctly simulate the present-day temperature-isotope relationships in those regions has been the main justification of the standard practice of using the present day spatial slope to interpret the isotopic data in terms of records of past temperature changes.

Notice that, at least for Antarctica, data and simple models agree only with respect to the temperature of formation of the precipitation, estimated by the temperature just above the inversion layer, and not with respect to the surface temperature, which owing to a strong inversion is much lower..

Thus one can easily see that using the spatial slope as a surrogate of the temporal slope strictly holds true only if the characteristics of the source have remained constant through time.

[Emphases added]

If all the precipitation occurs during warm summer months, for example, the “annual δ18O” will naturally reflect a temperature warmer than Ts [annual mean]..

If major changes in seasonality occur between climates, such as a shift from summer-dominated to winter- dominated precipitation, the impact on the isotope signal could be large..it is the temperature during the precipitation events that is imprinted in the isotopic signal.

Second, the formation of an inversion layer of cold air up to several hundred meters thick over polar ice sheets makes the temperature of formation of precipitation warmer than the temperature at the surface of the ice sheet. Inversion forms under a clear sky.. but even in winter it is destroyed rapidly if thick cloud moves over a site..

As a consequence of precipitation intermittancy and of the existence of an inversion layer, the isotope record is only a discrete and biased sampling of the surface temperature and even of the temperature at the atmospheric level where the precipitation forms. Current interpretation of paleodata implicitly assumes that this bias is not affected by climate change itself.

Now onto the oceans, surely much simpler, given the massive well-mixed reservoir of 18O?

Mix & Ruddiman (1984):

The oxygen-isotopic composition of calcite is dependent on both the temperature and the isotopic composition of the water in which it is precipitated

..Because he [Shackleton] analyzed benthonic, instead of planktonic, species he could assume minimal temperature change (limited by the freezing point of deep-ocean water). Using this constraint, he inferred that most of the oxygen-isotope signal in foraminifera must be caused by changes in the isotopic composition of seawater related to changing ice volume, that temperature changes are a secondary effect, and that the isotopic composition of mean glacier ice must have been about -30 ‰.

This estimate has generally been accepted, although other estimates of the isotopic composition have been made by Craig (-17‰); Eriksson (-25‰), Weyl (-40‰) and Dansgaard & Tauber (≤30‰)

..Although Shackleton’s interpretation of the benthonic isotope record as an ice-volume/sea- level proxy is widely quoted, there is considerable disagreement between ice-volume and sea- level estimates based on δ18O and those based on direct indicators of local sea level. A change in δ18O of 1.6‰ at δ(ice) = – 35‰ suggests a sea-level change of 165 m.

..In addition, the effect of deep-ocean temperature changes on benthonic isotope records is not well constrained. Benthonic δ18O curves with amplitudes up to 2.2 ‰ exist (Shackleton, 1977; Duplessy et al., 1980; Ruddiman and McIntyre, 1981) which seem to require both large ice- volume and temperature effects for their explanation.

Many other heavyweights in the field have explained similar problems.

We will return to both of these questions in the next article.

Conclusion

Understanding the basics of isotopic changes in water and water vapor is essential to understand the main proxies for past temperatures and past ice volumes. Previously we have looked at problems relating to dating of the proxies, in this article we have looked at the proxies themselves.

There is good evidence that current values of isotopes in precipitation and ocean values give us a consistent picture that we can largely understand. The question about the past is more problematic.

I started looking seriously at proxies as a means to perhaps understand the discrepancies for key dates of ice age terminations between radiometric dating and ocean cores (see Thirteen – Terminator II). Sometimes the more you know, the less you understand..

Articles in the Series

Part One – An introduction

Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz

Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory

Part Four – Understanding Orbits, Seasons and Stuff – how the wobbles and movements of the earth’s orbit affect incoming solar radiation

Part Five – Obliquity & Precession Changes – and in a bit more detail

Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name

Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago

Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers

Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover

Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs

Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs

Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age

Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2

Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland

Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II

Fourteen – Concepts & HD Data – getting a conceptual feel for the impacts of obliquity and precession, and some ice age datasets in high resolution

Fifteen – Roe vs Huybers – reviewing In Defence of Milankovitch, by Gerard Roe

Sixteen – Roe vs Huybers II – comparing the results if we take the Huybers dataset and tie the last termination to the date implied by various radiometric dating

Eighteen – “Probably Nonlinearity” of Unknown Origin – what is believed and what is put forward as evidence for the theory that ice age terminations were caused by orbital changes

Nineteen – Ice Sheet Models I – looking at the state of ice sheet models

References

Isotopes of the Earth’s Hydrosphere, VI Ferronsky & VA Polyakov, Springer (2012)

Isotope Hydrology – A Study of the Water Cycle, Joel R Gat, Imperial College Press (2010)

Stable Isotope Geochemistry, Jochen Hoefs, Springer (2009)

Patterns of the isotopic composition of precipitation in time and space: data from the Israeli storm water collection program, M Rindsberger, Sh Jaffe, Sh Rahamim and JR Gat, Tellus (1990) – free paper

Stable isotopes in precipitation, Willi Dansgaard, Tellus (1964) – free paper

Validity of the temperature reconstruction from water isotopes in ice cores, J Jouzel, RB Alley, KM Cuffey, W Dansgaard, P Grootes, G Hoffmann, SJ Johnsen, RD Koster, D Peel, CA Shuman, M Stievenard, M Stuiver, J White, Journal of Geophysical Research (1997) – free paper

Oxygen Isotope Analyses and Pleistocene Ice Volumes, Mix & Ruddiman, Quaternary Research (1984)  – free paper

– and on the Dole effect, only covered in Note 2:

The Dole effect and its variations during the last 130,000 years as measured in the Vostok ice core, Michael Bender, Todd Sowers, Laurent Labeyrie, Global Biogeochemical Cycles (1994) – free paper

A model of the Earth’s Dole effect, Georg Hoffmann, Matthias Cuntz, Christine Weber, Philippe Ciais, Pierre Friedlingstein, Martin Heimann, Jean Jouzel, Jörg Kaduk, Ernst Maier-Reimer, Ulrike Seibt & Katharina Six, Global Biogeochemical Cycles (2004) – free paper

The isotopic composition of atmospheric oxygen Boaz Luz & Eugeni Barkan, Global Biogeochemical Cycles (2011) – free paper

Notes

Note 1: There is a relationship between δ18O and δD which is linked to the difference in vapor pressures between H2O and HDO in one case and H216O and H218O in the other case.

δD = 8 δ18O + 10 – known as the Global Meteoric Water Line.

The equation is more of a guide and real values vary sufficiently that I’m not really clear about its value. There are lengthy discussions of it and the variations from it in Ferronsky & Polyakov.

Note 2: The Dole effect

When we measure atmospheric oxygen, we find that the δ18O = 23.5 ‰ with respect to the oceans (VSMOW) – this is the Dole effect

So, oxygen in the atmosphere has a greater proportion of 18O than the ocean

Why?

How do the atmosphere and ocean exchange oxygen? In essence, photosynthesis turns sunlight + water (H2O) + carbon dioxide (CO2) –> sugar + oxygen (O2).

Respiration turns sugar + oxygen –> water + carbon dioxide + energy

The isotopic composition of the water in photosynthesis affects the resulting isotopic composition in the atmospheric oxygen.

The reason the Dole effect exists is well understood, but the reason why the value comes out at 23.5‰ is still under investigation. This is because the result is the global aggregate of lots of different processes. So we might understand the individual processes quite well, but that doesn’t mean the global value can be calculated accurately.

It is also the case that δ18O of atmospheric O2 has varied in the past – as revealed first of all in the Vostok ice core from Antarctica.

Michael Bender and his colleagues had a go at calculating the value from first principles in 1994. As they explain (see below), although it might seem as though their result is quite close to the actual number it is not a very successful result at all. Basically due to the essential process you start at 20‰ and should get to 23.5‰, but they o to 20.8‰.

Bender et al 1994:

The δ18O of O2.. reflects the global responses of the land and marine biospheres to climate change, albeit in a complex manner.. The magnitude of the Dole effect mainly reflects the isotopic composition of O2 produced by marine and terrestrial photosynthesis, as well as the extent to while the heavy isotope is discriminated against during respiration..

..Over the time period of interest here, photosynthesis and respiration are the most important reactions producing and consuming O2. The isotopic composition of O2 in air must therefore be understood in terms of isotope fractionation associated with these reactions.

The δ18O of O2 produced by photosynthesis is similar to that of the source water. The δ18O of O2 produced by marine plants is thus 0‰. The δ18O of O2 produced on the continents has been estimated to lie between +4 and +8‰. These elevated δ18O values are the result of elevated leaf water δ18O values resulting from evapotranspiration.

..The calculated value for the Dole effect is then the productivity-weighted values of the terrestrial and marine Dole effects minus the stratospheric diminution: +20.8‰. This value is considerably less than observed (23.5‰). The difference between the expected value and the observed value reflects errors in our estimates and, conceivably, unrecognized processes.

Then they assess the Vostok record, where the main question is less about why the Dole effect varies apparently with precession (period of about 20 kyrs), than why the variation is so small. After all, if marine and terrestrial biosphere changes are significant from interglacial to glacial then surely those changes would reflect more strongly in the Dole effect:

Why has the Dole effect been so constant? Answering this question is impossible at the present time, but we can probably recognize the key influences..

They conclude:

Our ability to explain the magnitude of the contemporary Dole effect is a measure of our understanding of the global cycles of oxygen and water. A variety of recent studies have improved our understanding of many of the principles governing oxygen isotope fractionation during photosynthesis and respiration.. However, our attempt to quantitively account for the Dole effect in terms of these principles was not very successful.. The agreement is considerably worse than it might appear given the fact that respiratory isotope fractionation alone must account for ~20‰ of the stationary enrichment of the 18O of O2 compared with seawater..

..[On the Vostok record] Our results show that variation in the Dole effect have been relatively small during most of the last glacial-interglacial cycle. These small changes are not consistent with large glacial increases in global oceanic productivity.

[Emphasis added]

Georg Hoffmann and his colleagues had another bash 10 years later and did a fair bit better:

The Earth’s Dole effect describes the isotopic 18O/16O-enrichment of atmospheric oxygen with respect to ocean water, amounting under today’s conditions to 23.5‰. We have developed a model of the Earth’s Dole effect by combining the results of three- dimensional models of the oceanic and terrestrial carbon and oxygen cycles with results of atmospheric general circulation models (AGCMs) with built-in water isotope diagnostics.

We obtain a range from 22.4‰ to 23.3‰ for the isotopic enrichment of atmospheric oxygen. We estimate a stronger contribution to the global Dole effect by the terrestrial relative to the marine biosphere in contrast to previous studies. This is primarily caused by a modeled high leaf water enrichment of 5–6‰. Leaf water enrichment rises by ~1‰ to 6–7‰ when we use it to fit the observed 23.5‰ of the global Dole effect.

Very recently Luz & Barkan (2011), backed up by lots of new experimental work produced a slightly closer estimate with some revisions of the Hoffman et al results:

Based on the new information on the biogeochemical mechanisms involved in the global oxygen cycle, as well as new and more precise experimental data on oxygen isotopic fractionation in various processes obtained over the last 15 years, we have reevaluated the components of the Dole effect.Our new observations on marine oxygen isotope effects, as well as, new findings on photosynthetic fractionation by marine organisms lead to the important conclusion that the marine, terrestrial and the global Dole effects are of similar magnitudes.

This result allows answering a long‐standing unresolved question on why the magnitude of the Dole effect of the last glacial maximum is so similar to the present value despite enormous environmental differences between the two periods. The answer is simple: if DEmar [marine Dole effect] and DEterr [terrestrial Dole effect] are similar, there is no reason to expect considerable variations in the magnitude of the Dole effect as the result of variations in the ratio terrestrial to marine O2 production.

Finally, the widely accepted view that the magnitude of the Dole effect is controlled by the ratio of land‐to‐sea productivity must be changed. Instead of the land‐sea control, past variations in the Dole effect are more likely the result of changes in low‐latitude hydrology and, perhaps, in structure of marine phytoplankton communities.

[Emphasis added]

Note 3:

Jochen Hoefs (2009):

Under equilibrium conditions at 25ºC, the fractionation factors for evaporating water are 1.0092 for 18O and 1.074 for D. However under natural conditions, the actual isotopic composition of water is more negative than the predicted equilibrium values due to kinetic effects.

The discussion of kinetic effects gets a little involved and I don’t think is really necessary to understand – the values of isotopic fractionation during evaporation and condensation are well understood. The confounding factors around what the proxies really measure relate to the journey (i.e. temperature history) and mixing of the various air parcels as well as the temperature of air relating to the precipitation event – is the surface temperature, the inversion temperature, both?

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In the last article – Fifteen – Roe vs Huybers – we had a look at the 2006 paper by Gerard Roe, In defense of Milankovitch.

We compared the rate of change of ice volume – as measured in the Huybers 2007 dataset – with summer insolation at 65ºN. The results were interesting, the results correlated very well for the first 200 kyrs, then drifted out of phase. As a result the (Pearson) correlation over 500 kyrs was very low, but quite decent for the first 200 kyrs.

Without any further data we might assume that the results demonstrated that the dataset without “orbital tuning” – and a lack of objective radiometric dating – was drifting away from reality as time went on, and an “orbitally tuned” dataset was the best approach. We would definitely expect that older dates have more uncertainty, as errors accumulate when we use any kind of model for time vs depth.

However, in an earlier article we looked at more objective dates for Termination II (and also in the comments, at some earlier terminations). These dates were obtained via radiometric dating from a variety of locations and methods.

So I wondered:

What happens if we take a dataset like Huybers 2007 and “remap” it using agemarkers?

This is basically how most of the ice core datasets are constructed, although the methods are more sophisticated (see note 1).

For my rough and ready approach I simply provided a set of termination dates (halfway point of ice volume from peak glacial to peak interglacial) from both Huybers and from Winograd et al 1992. Then I remapped the timebase for the existing Huybers proxy data between each set of agemarkers.

It’s probably easier to show the before and after comparison, rather than explain the method further. Note the low point between 100 and 150 kyrs BP. This corresponds to less ice, it is the interglacial:

Huybers-icevolume-last-270kyrs-remapped

Figure 1

The method is basically a linear remapping. I’m sure there are better ways, but I don’t expect they would have a material impact on the outcome.

One point that’s important (with my very simple method) is the oldest agemarker we consider can cause an inconsistency (as there is nothing to constrain the dates between the last agemarker and the end date), which is why the first set below uses 270 kyrs.

T- III is dated by Winograd 1992 at 253 kyrs. So I picked a date shortly after that.

Here is the comparison of rate of change of ice volume with insolation, with the same conventions as in the last article. We can see that everything is nicely anti-correlated:

Roe-comparison-last-270kyrs-remappedHuybers-499px

Figure 2 – Click to Expand

For comparison, the result (in the last article) from 0-200 kyrs BP without remapping the proxy dataset. We can see that everything is nicely correlated:

Roe-comparison-last-200kyrs

Figure 3 – Click to Expand

For the remapped data: correlation  = -0.30. This is as negatively correlated to the insolation value as LR04 (an “orbitally-tuned” dataset) is positively correlated.

For interest I did the same exercise with a 0 – 200kyr BP timebase. This means everything from 140 kyrs – 200 yrs was not constrained by a revised T-III date. The result: correlation = 0. The interpretation is simple – the older data is not pulled out of alignment due to a later objective T-III date, so there is a better match of insolation with rate of change of ice volume for this older data.

Conclusion

Is there a conclusion? It’s surely staring us in the face so is left as an exercise for the interested student.

I have a headache.

Articles in the Series

Part One – An introduction

Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz

Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory

Part Four – Understanding Orbits, Seasons and Stuff – how the wobbles and movements of the earth’s orbit affect incoming solar radiation

Part Five – Obliquity & Precession Changes – and in a bit more detail

Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name

Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago

Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers

Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover

Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs

Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs

Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age

Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2

Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland

Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II

Fourteen – Concepts & HD Data – getting a conceptual feel for the impacts of obliquity and precession, and some ice age datasets in high resolution

Fifteen – Roe vs Huybers – reviewing In Defence of Milankovitch, by Gerard Roe

Seventeen – Proxies under Water I – explaining the isotopic proxies and what they actually measure

Eighteen – “Probably Nonlinearity” of Unknown Origin – what is believed and what is put forward as evidence for the theory that ice age terminations were caused by orbital changes

Nineteen – Ice Sheet Models I – looking at the state of ice sheet models

References

In defense of Milankovitch, Gerard Roe, Geophysical Research Letters (2006) – free paper

Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression, Peter Huybers, Quaternary Science Reviews (2007) – free paper

Datasets for Huybers 2007 are here:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/contributions_by_author/huybers2006/
and
http://www.people.fas.harvard.edu/~phuybers/Progression/

Continuous 500,000-Year Climate Record from Vein Calcite in Devils Hole, Nevada, Winograd, Coplen, Landwehr, Riggs, Ludwig, Szabo, Kolesar & Revesz, Science (1992) – paywall, but might be available with a free Science registration

Insolation data calculated from Jonathan Levine’s MATLAB program

Notes

Note 1:

Here is an extract from Parennin et al 2007, The EDC3 chronology for the EPICA Dome C ice core:

In this article, we present EDC3, the new 800 kyr age scale of the EPICA Dome C ice core, which is generated using a combination of various age markers and a glaciological model. It is constructed in three steps.

First, an age scale is created by applying an ice flow model at Dome C. Independent age markers are used to control several poorly known parameters of this model (such as the conditions at the base of the glacier), through an inverse method.

Second, the age scale is synchronised onto the new Greenlandic GICC05 age scale over three time periods: the last 6 kyr, the last deglaciation, and the Laschamp event (around 41 kyr BP).

Third, the age scale is corrected in the bottom ∼500 m (corresponding to the time period 400–800 kyr BP), where the model is unable to capture the complex ice flow pattern..

From Parennin et al 2007

From Parennin et al 2007

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A few people have asked about the fascinating 2006 paper by Gerard Roe, In defense of Milankovitch.

Roe’s paper appears to show an excellent match between the rate of change of ice volume and insolation at 65°N in June. I’ve been puzzled by the paper for a while, because if this value of insolation does successfully predict changes in ice volume then case closed. Except we struggle to match glacial terminations with insolation (see earlier posts like Part Thirteen, Twelve, Eleven – End of the Last Ice age).

And we should also expect to find a 100 kyr period in the 65°N insolation spectrum. But we don’t.

To be fair to Roe, he does state:

The Milankovitch hypothesis as formulated here does not explain the large rapid deglaciations that occurred at the end of some of the ice age cycles

[Emphasis added].

To be critical, it doesn’t seem like anyone is disputing that ice sheets wax and wane with at least some attachment to 40k (obliquity) and 20k (precession) cycles so what exactly does the paper demonstrate that is new? The missing bit of the puzzle is why ice ages start and end.

On the plus side, Roe points out:

Surprisingly, the [Milankovitch] hypothesis remains not clearly defined..

Which is the same point I made in Ghosts of Climates Past – Part Six – “Hypotheses Abound”.

One of the reasons I’ve spent quite a bit of time collecting and understanding datasets – see Part Fourteen – Concepts & HD Data – was for this kind of problem. Roe’s figure 2 spans half a page but covers 800,000 years. With the thick lines used I can’t actually tell if there is a match, and being poor at real statistics I want to see the data rather than just accept a correlation.

There’s not much point comparing SPECMAP (or LR04) with insolation because both of these datasets are “tuned” to summer 65°N insolation. If we find success then we accept that the producers of the dataset were competent in their objective. If we find lack of success we have to write to them with bad news. No one wants to do that.

Fortunately we have an interesting dataset from Peter Huybers (2007). This is an update of HW04 (Huybers & Wunsch 2004) which created a proxy for global ice volume from deep ocean cores without “orbital tuning”. It’s based on an autocorrelated sedimentation model, requiring that key turning points from many different cores all occur at the same time, and a key dateable event at around 800,000 years ago that shows up in most cores.

Some readers are wondering:

Why not use the ice cores you have been writing about?

Good question. The oxygen isotope (δ18O), or deuterium isotope (δD), in the ice is more a measure of local temperature than anything else (and it’s complicated). So Greenland and Antarctic ice cores provide lots of useful data, but not global ice volume. For that, we need to capture the δ18O stored in deep ocean sediments. The δ18O in deep ocean cores, to a first order, appears to be a measure of the amount of water locked up in global ice sheets. However, we have no easy way to objectively date the ocean cores, so some assumptions are needed.

Fortunately, Roe compared his theory with two datasets, the famous SPECMAP (warning, orbital tuning was used in the creation of this dataset) and HW04:

Roe2006-fig2-499px

Figure 1

I downloaded the updated Huybers 2007 dataset. It is in 1 kyr intervals. I have calculated the insolation at all latitudes and all days for the last 500 kyrs using Jonathan Levine’s MATLAB program. This is also in 1 kyrs intervals. I used the values at 65N and June 21st (day 172 – thanks Climateer, for helping me with the basics of calendar days!).

I calculated change in ice volume in a very simple way – (value at time t+1 – value at time t) divided by time change. I scaled the resulting dataset to the same range as the insolation anomalies – so that they plot nicely. And I plotted insolation anomaly = mean(insolation) – insolation:

Roe-comparison-499px

Figure 2 – Click to Expand

The two sets of data look very similar over the last 500 kyrs. I assume that some minor changes, e.g., at about 370 kyrs, are due to dataset updates. Note that insolation anomaly is effectively inverted to help match trends by eye – high insolation should lead to negative change in ice volume and vice-versa.

For reference, here is my calculation on its own (click to get the large version):

dHuybers2007dt-vs-Insolation-65N-499px

Figure 3 – Click to Expand

I did a Pearson correlation between the two datasets and obtained 0.08. That is, very little correlation. This just tells us what we can see from looking at the graph – the two key values are in phase to begin with then move out of phase and back into phase by the end.

Correlation between 0-100 kyrs:   0.66 (great)
Correlation between 101-200 kyrs:  0.51 (great)
Correlation between 201-300 kyrs:  -0.72 (wrong direction)
Correlation between 301-400 kyrs  -0.27 (wrong direction)
Correlation between 401-500 kyrs:  0.18 (wavering)

I also did a Spearman rank correlation (correlates the rank of the two datasets to make it resistance to outliers) = 0.09, and just because I could, a Kendall correlation as well = 0.07.

I’m a bit of a statistics amateur so comparing datasets except by looking is not my forte. Perhaps a rookie mistake somewhere.

Then I checked lag correlations. The physical reasoning is that deep ocean concentration of 18O will take a few thousand years at least to respond to ice volume changes, simply due to the slow circulation of the major ocean currents. The results show there is a better correlation with a lag of 35,000 years, but there is no physical reason for this, it is probably just a better fit to a dataset with an apparent slow phase drift across the period of record. At a meaningful large ocean current lag of a few thousand years the correlation is worse (anti-correlated):

Roe-comparison-lag-correlation

Figure 4

On the plus side, the first 200 kyrs look quite impressive, including terminations:

Roe-comparison-last-100kyrs

Figure 5

Roe-comparison-last-200kyrs

Figure 6

This has got me wondering.

What do we notice from the data for the first 200 kyrs (figure 6)? Well, the last two terminations (check out the last few posts) are easily identified because the rate of change of ice volume in proportion to insolation is about four times its value when no termination takes place.

Forgetting about the small problem of the Southern Hemisphere lead in the last deglaciation (Part Eleven – End of the Last Ice age), there is something interesting going on here. Almost like a theory that is just missing one easily identified link, one piece of the jigsaw puzzle that just needs to be fitted in, and the new Nature paper is waiting..

Onto some details.. it seems that T-II, if marked by the various radiometric dating values we saw Part Thirteen – Terminator II, would cause the 100k-200k values to move out of phase (the big black dip at about 125 kyrs would move about 15 kyrs to the left). So my next objective (see Sixteen – Roe vs Huybers II) is to set an age marker for Termination II from the radiometric dating values and “slide” the Huybers 2007 dataset to this and the current T1 dating. Also, the ice core proxies recorded in deep ocean cores must lag real ice volume changes by some period like say 1 – 3 kyrs (see note 1). This helps the Roe hypothesis because the black curves move to the left.

Let’s see what happens with these changes.

And hopefully, sharp-eyed readers are going to identify opportunities for improvement in this article, as well as the missing piece of the puzzle that will lead to the coveted Nature paper..

Articles in the Series

Part One – An introduction

Part Two – Lorenz – one point of view from the exceptional E.N. Lorenz

Part Three – Hays, Imbrie & Shackleton – how everyone got onto the Milankovitch theory

Part Four – Understanding Orbits, Seasons and Stuff – how the wobbles and movements of the earth’s orbit affect incoming solar radiation

Part Five – Obliquity & Precession Changes – and in a bit more detail

Part Six – “Hypotheses Abound” – lots of different theories that confusingly go by the same name

Part Seven – GCM I – early work with climate models to try and get “perennial snow cover” at high latitudes to start an ice age around 116,000 years ago

Part Seven and a Half – Mindmap – my mind map at that time, with many of the papers I have been reviewing and categorizing plus key extracts from those papers

Part Eight – GCM II – more recent work from the “noughties” – GCM results plus EMIC (earth models of intermediate complexity) again trying to produce perennial snow cover

Part Nine – GCM III – very recent work from 2012, a full GCM, with reduced spatial resolution and speeding up external forcings by a factors of 10, modeling the last 120 kyrs

Part Ten – GCM IV – very recent work from 2012, a high resolution GCM called CCSM4, producing glacial inception at 115 kyrs

Pop Quiz: End of An Ice Age – a chance for people to test their ideas about whether solar insolation is the factor that ended the last ice age

Eleven – End of the Last Ice age – latest data showing relationship between Southern Hemisphere temperatures, global temperatures and CO2

Twelve – GCM V – Ice Age Termination – very recent work from He et al 2013, using a high resolution GCM (CCSM3) to analyze the end of the last ice age and the complex link between Antarctic and Greenland

Thirteen – Terminator II – looking at the date of Termination II, the end of the penultimate ice age – and implications for the cause of Termination II

Fourteen – Concepts & HD Data – getting a conceptual feel for the impacts of obliquity and precession, and some ice age datasets in high resolution

Sixteen – Roe vs Huybers II – remapping a deep ocean core dataset and updating the previous article

Seventeen – Proxies under Water I – explaining the isotopic proxies and what they actually measure

Eighteen – “Probably Nonlinearity” of Unknown Origin – what is believed and what is put forward as evidence for the theory that ice age terminations were caused by orbital changes

Nineteen – Ice Sheet Models I – looking at the state of ice sheet models

References

In defense of Milankovitch, Gerard Roe, Geophysical Research Letters (2006) – free paper

Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression, Peter Huybers, Quaternary Science Reviews (2007) – free paper

How long to oceanic tracer and proxy equilibrium?, C Wunsch & P Heimbach, Quaternary Science Reviews (2008) – free paper

Datasets for Huybers 2007 are here:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/contributions_by_author/huybers2006/
and
http://www.people.fas.harvard.edu/~phuybers/Progression/

Insolation data calculated from Jonathan Levine’s MATLAB program (just ask for this data in Excel or MATLAB format)

Notes

Note 1: See, for example, Wunsch & Heimbach 2008:

The various time scales for distribution of tracers and proxies in the global ocean are critical to the interpretation of data from deep- sea cores. To obtain some basic physical insight into their behavior, a global ocean circulation model, forced to least-square consistency with modern data, is used to find lower bounds for the time taken by surface-injected passive tracers to reach equilibrium. Depending upon the geographical scope of the injection, major gradients exist, laterally, between the abyssal North Atlantic and North Pacific, and vertically over much of the ocean, persisting for periods longer than 2000 years and with magnitudes bearing little or no relation to radiocarbon ages. The relative vigor of the North Atlantic convective process means that tracer events originating far from that location at the sea surface will tend to display abyssal signatures there first, possibly leading to misinterpretation of the event location. Ice volume (glacio-eustatic) corrections to deep-sea d18O values, involving fresh water addition or subtraction, regionally at the sea surface, cannot be assumed to be close to instantaneous in the global ocean, and must be determined quantitatively by modelling the flow and by including numerous more complex dynamical interactions.

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