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In Part Six we looked at some of the different theories that confusingly go by the same name. The “Milankovitch” theories.

The essence of these many theories – even though the changes in “tilt” of the earth’s axis and the time of closest approach to the sun don’t change the total annual solar energy incident on the climate, the changing distribution of energy causes massive climate change over thousands of years.

One of the “classic” hypotheses is increases in July insolation at 65ºN cause the ice sheets to melt. Or conversely, reductions in July insolation at 65ºN cause the ice sheets to grow.

The hypotheses described can sound quite convincing. Well, one at a time can sound quite convincing – when all of the “Milankovitch theories” are all lined up alongside each other they start to sound more like hopeful ideas.

In this article we will start to consider what GCMs can do in falsifying these theories. For some basics on GCMs, take a look at Models On – and Off – the Catwalk.

Many readers of this blog have varying degrees of suspicion about GCMs. But as regular commenter DeWitt Payne often says, “all models are wrong, but some are useful“, that is, none are perfect, but some can shed light on the climate mechanisms we want to understand.

In fact, GCMs are essential to understand many climate mechanisms and essential to understand the interaction between different parts of the climate system.

Digression – Ice Sheets and Positive Feedback

For beginners, a quick digression into ice sheets and positive feedback. Melting and forming of ice & snow is undisputably a positive feedback within the climate system.

Snow reflects around 60-90% of incident solar radiation. Water reflects less than 10% and most ground surfaces reflect less than 25%.  If a region heats up sufficiently, ice and snow melt. Which means less solar radiation gets reflected, which means more radiation is absorbed, which means the region heats up some more. The effect “feeds itself”. It’s a positive feedback.

In the annual cycle it doesn’t lead to any kind of thermal runaway or a snowball earth because the solar radiation goes through a much bigger cycle.

Over much longer time periods it’s conceivable that (regional) melting of ice sheets leads to more (regional) solar radiation absorbed, causing more melting of ice sheets which leads to yet more melting. And the converse for growth of ice sheets. The reason it’s conceivable is because it’s just that same mechanism.

Digression over.

Why GCMs ?

The only alternative is to do the calculation in your head or on paper. Take a piece of paper, plot a graph of the incident radiation at all latitudes vs the time period we are interested in – say 150 kyrs ago through to 100 kyrs – now work out by year, decade or century, how much ice melts. Work out the new albedo for each region. Calculate the change in absorbed radiation. Calculate the regional temperature changes. Calculated the new heat transfer from low to high latitudes (lots of heat is exported from the equator to the poles via the atmosphere and the ocean) due to the latitudinal temperature gradient, the water vapor transported, and the rainfall and snowfall. Don’t forget to track ice melt at high latitudes and its impact on the Meridional Overturning Circulation (MOC) which drives a significant part of the heat transfer from the equator to poles. Step to the next year, decade or century and repeat.

How are those calculations coming along?

A GCM uses some fundamental physics equations like energy balance and mass balance. It uses a lot of parameterized equations to calculate things like heat transfer from the surface to the atmosphere dependent on the wind speed, cloud formation, momentum transfer from wind to ocean, etc. Whatever we have in a GCM is better than trying to do it on a sheet of paper (and in the end you will be using the same equations with much less spatial and time granularity).

If we are interested in the “classic” Milankovitch theory mentioned above we need to find out the impact of an increase of 50W/m² (over 10,000 years) in summer at 65ºN – see figure 1 in Ghosts of Climates Past – Part Five – Obliquity & Precession Changes.  What effect does the simultaneous spring reduction at 65ºN have. Do these two effects cancel each other out? Is the summer increase more significant than the spring reduction?

How quickly does the circulation lessen the impact? The equator-pole export of heat is driven by the temperature difference – as with all heat transfer. So if the northern polar region is heating up due to ice melting, the ocean and atmospheric circulation will change and less heat will be driven to the poles. What effect does this have?

How quickly does an ice sheet melt and form? Can the increases and reductions in solar radiation absorbed explain the massive ice sheet growth and shrinking?

If the positive feedback is so strong how does an ice age terminate and how does it restart 10,000 years later?

We can only assess all of these with a general circulation model.

There is a problem though. A typical GCM run is a few decades or a century. We need a 10,000 – 50,000 year run with a GCM. So we need 500x the computing power – or we have to reduce the complexity of the model.

Alternatively we can run a model to equilibrium at a particular time in history to see what effect the historical parameters had on the changes we are interested in.

Early Work

Many readers of this blog are frequently mystified by my choosing “old work” to illuminate a topic. Why not pick the most up to date research?

Because the older papers usually explain the problem more clearly and give more detail on the approach to the problem.

The latest papers are written for researchers in the field and assume most of the preceding knowledge – that everyone in that field already has. A good example is the Myhre et al (1998) paper on the “logarithmic formula” for radiative forcing with increasing CO2, cited by the IPCC TAR in 2001. This paper has mystified so many bloggers. I have read many blog articles where the blog authors and commenters throw up their metaphorical hands at the lack of justification for the contents of this paper. However, it is not mystifying if you are familiar with the physics of radiative transfer and the papers from the 70′s through the 90′s calculating radiative imbalance as a result of more “greenhouse” gases.

It’s all about the context.

We’ll take a walk through a few decades of GCMs..

We’ll start with Rind, Peteet & Kukla (1989). They review the classic thinking on the problem:

Kukla et al. [1981] described how the orbital configurations seemed to match up with gross climate variations for the last 150 millennia or so. As a result of these and other geological studies, the consensus exists that orbital variations are responsible for initiating glacial and interglacial climatic regimes. The most obvious difference between these two regimes, the existence of subpolar continental ice sheets, appears related to solar insolation at northern hemisphere high latitudes in summer. For example, solar insolation at these latitudes in August and September was reduced, compared with today’s values, around 116,000 years before the present (116 kyr B.P.), during the time when ice growth apparently began, and it was increased around 10 kyr B.P. during a time of rapid ice sheet retreat [e.g., Berger, 1978] (Figure 1).

And the question of whether basic physics can link the supposed cause and effect:

Are the solar radiation variations themselves sufficient to produce or destroy the continental ice sheets?

The July solar radiation incident at 50ºN and 60ºN over the past 170 kyr is shown in Figure 1, along with August and September values at 50ºN (as shown by the example for July, values at the various latitudes of concern for ice age initiation all have similar insolation fluctuations). The peak variations are of the order of 10%, which if translated with an equal percentage into surface air temperature changes would be of the order of 30ºC. This would certainly be sufficient to allow snow to remain throughout the summer in extreme northern portions of North America, where July surface temperatures today are only about 10ºC above freezing.

However, the direct translation ignores all of the other features which influence surface air temperature during summer, such as cloud cover and albedo variations, long wave radiation, surface flux effects, and advection.

[Emphasis added].

Various energy balance climate models have been used to assess how much cooling would be associated with changed orbital parameters. As the initiation of ice growth will alter the surface albedo and provide feedback to the climate change, the models also have to include crude estimates of how ice cover will change with climate. With the proper tuning of parameters, some of which is justified on observational grounds, the models can be made to simulate the gross glacial/interglacial climate changes.

However, these models do not calculate from first principles all the various influences on surface air temperature noted above, nor do they contain a hydrologic cycle which would allow snow cover to be generated or increase. The actual processes associated with allowing snow cover to remain through the summer will involve complex hydrologic and thermal influences, for which simple models can only provide gross approximations.

They comment then on the practical problems of using GCMs for 10 kyr runs that we noted above. The problem is worked around by using prescribed values for certain parameters and by using a coarse grid – 8° x 10° and 9 vertical layers.

The various GCMs runs are typical of the approach to using GCMs to “figure stuff out” – try different runs with different things changed to see what variations have the most impact and what variations, if any, result in the most realistic answers:

Rind et al 1989-1

We have thus used the Goddard Institute for Space Studies (GISS) GCM for a series of experiments in which orbital parameters, atmospheric composition, and sea surface temperatures are changed. We examine how the various influences affect snow cover and low-elevation ice sheets in regions of the northern hemisphere where ice existed at the Last Glacial Maximum (LGM). As we show, the GCM is generally incapable of simulating the beginnings of ice sheet growth, or of maintaining low-elevation ice sheets, regardless of the orbital parameters or sea surface temperatures used.

[Emphasis added].

And the result:

The experiments indicate there is a wide discrepancy between the model’s response to Milankovitch perturbations and the geophysical evidence of ice sheet initiation. As the model failed to grow or sustain low-altitude ice during the time of high-latitude maximum solar radiation reduction (120-110 kyrB.P.), it is unlikely it could have done so at any other time within the last several hundred thousand years.

If the model results are correct, it indicates that the growth of ice occurred in an extremely ablative environment, and thus demanded some complicated strategy, or else some other climate forcing occurred in addition to the orbital variation influence (and CO2 reduction), which would imply we do not really understand the cause of the ice ages and the Milankovitch connection. If the model is not nearly sensitive enough to climate forcing, it could have implications for projections of future climate change.

[Emphasis added].

The basic model experiment on the ability of Milankovitch variations by themselves to generate ice sheets in a GCM, experiment 2, shows that in the GISS GCM even exaggerated summer radiation deficits are not sufficient. If widespread ice sheets at 10-m elevation are inserted, CO2 reduced by 70ppm, sea ice increases to full ice age conditions, and sea surface temperatures reduced to CLIMAP 18 kyr BP estimates or below, the model is just barely able keep these ice sheets from melting in restricted regions. How likely are these results to represent the actual state of affairs?

That was 1989 GCM’s.

Phillipps & Held (1994) had basically the same problem. This is the famous Isaac Held, who has written extensively on climate dynamics, water vapor feedback, GCMs and runs an excellent blog that is well-worth reading.

While paleoclimatic records provide considerable evidence in support of the astronomical, or Milankovitch, theory of the ice ages (Hays et al. 1976), the mechanisms by which the orbital changes influence the climate are still poorly understood..

..For this study we utilize the atmosphere-mixed layer ocean model.. In examining this model’s sensitivity to different orbital parameter combinations, we have compared three numerical experiments.

They describe the comparison models:

Our starting point was to choose the two experiments that are likely to generate the largest differences in climate, given the range of the parameter variations computed to have occurred over the past few hundred thousand years. The eccentricity is set equal to 0.04 in both cases. This is considerably larger than the present value of 0.016 but comparable to that which existed from ~90 to 150k BP.

In the first experiment, the perihelion is located at NH summer solstice and the obliquity is set at the high value of 24°.

In the second case, perihelion is at NH winter solstice and the obliquity equals 22°.

The perihelion and obliquity are both favorable for warm northern summers in the first case, and for cool northern summers in the second. These experiments are referred to as WS and CS respectively.

We then performed another calculation to determine how much of the difference between these two integrations is due to the perihelion shift and how much to the change in obliquity. This third model has perihelion at summer solstice, but a low value (22°) of the obliquity. The eccentricity is still set at 0.04. This experiment is referred to as WS22.

Sadly:

We find that the favorable orbital configuration is far from being able to maintain snow cover throughout the summer anywhere in North America..

..Despite the large temperature changes on land the CS experiment does not generate any new regions of permanent snow cover over the NH. All snow cover melts away completely in the summer. Thus, the model as presently constituted is unable to initiate the growth of ice sheets from orbital perturbations alone. This is consistent with the results of Rind with a GCM (Rind et al. 1989)..

In the next article we will look at more favorable results in the 2000′s.

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 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 - 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

Can Milankovitch Orbital Variations Initiate the Growth of Ice Sheets in a General Circulation Model?, Rind, Peteet & Kukla, JGR (1989) – behind a paywall, email me if you want to read it, scienceofdoom – you know what goes here – gmail.com

Response to Orbital Perturbations in an Atmospheric Model Coupled to a Slab Ocean, Phillipps & Held, Journal of Climate (1994) – free paper

New estimates of radiative forcing due to well-mixed greenhouse gases, Myhre et al, GRL (1998)

It is common to find blogs and articles from what we might call the “consensus climate science” corner that we know what caused the ice ages.

The cause being changes in solar insolation at higher latitudes via the orbital changes described in Part Four and Five. These go under the banner of the “Milankovitch theory”.

While that same perspective is present in climate science papers, the case is presented more clearly. Or perhaps I could say, it’s made clear that the case is far from clear. It’s very very muddy.

Here are Smith & Gregory (2012):

It is generally accepted that the timing of glacials is linked to variations in solar insolation that result from the Earth’s orbit around the sun (Hays et al. 1976; Huybers and Wunsch 2005). These solar radiative anomalies must have been amplified by feedback processes within the climate system, including changes in atmospheric greenhouse gas (GHG) concentrations (Archer et al. 2000) and ice-sheet growth (Clark et al. 1999), and whilst hypotheses abound as to the details of these feedbacks, none is without its detractors and we cannot yet claim to know how the Earth system produced the climate we see recorded in numerous proxy records.

[Emphasis added].

Still, there are always outliers in every field and one paper doesn’t demonstrate a consensus on anything. So let’s take a walk through the mud..

Wintertime NH High Latitude Insolation

Kukla (1972):

The link between the Milankovitch mechanism and climate remains unclear. Summer half-year insolation curves for 65°N are usually offered on the assumption that the incoming radiation could directly control the retreat or advance of glaciers, thus controlling the global climate.

The validity of this assumption was questioned long ago by Croll (1875) and Ball (1891). Modern satellite measurements fully justify Croll’s concept of climate formation, with ocean currents playing the basic role in distributing heat and moisture to continents. The simplistic model of Koppen and Wegener must be definitely abandoned..

..The principal cold periods are found, within the accuracy limits of radiometric dating, to be precisely parallelled by intervals of decreasing winter insolation income for Northern Hemisphere (glacial insolation regime) and vice versa. Gross climatic changes originate in winters on the continents of the Northern Hemisphere.

Just for interest for history buffs, he also comments:

Two facts are highly probable: (1) in A. D. 2100 the globe will be cooler than today (Bray 1970), and (2) Man-made warming will hardly be noticeable on global scale at that time.

Self-Oscillations of the Climate System

Broecker & Denton (1990):

Although we are convinced that the Earth’s climate responds to orbital cycles in some fashion, we reject the view of a direct linkage between seasonality and ice-sheet size with consequent changes to climate of distant regions. Such a linkage cannot explain synchronous climate changes of similar severity in both polar hemispheres. Also, it cannot account for the rapidity of the transition from full glacial toward full interglacial conditions. If global climates are driven by changes in seasonality, then another linkage must exist.

We propose that Quaternary glacial cycles were dominated by abrupt reorganizations of the ocean-atmosphere system driven by orbitally induced changes in fresh water transports which impact salt structure in the sea. These reorganizations mark switches between stable modes of operation of the ocean-atmosphere system. Although we think that glacial cycles were driven by orbital change, we see no basis for rejecting the possibility that the mode changes are part of a self-sustained internal oscillation that would operate even in the absence of changes in the Earth’s orbital parameters. If so, as pointed out by Saltzman et al. (1984), orbital cycles can merely modulate and pace a self-oscillating climate system..

..Existing data from the Earth’s glacier system thus imply that the last termination began simultaneously and abruptly in both polar hemispheres, despite the fact that summer insolation signals were out of phase at the latitude of the key glacial records..

..Although variations in the Earth’s orbital geometry are very likely the cause of glacial cycles (Hays et al., 1976; Imbrie et al., 1984), the nature of the link between seasonal insolation and global climate remains a major unanswered question..

[Emphasis added].

Strictly speaking this is a “not quite Milankovitch” theory (and there are other flavors of this theory not covered in this article). I put forward this paper because Wallace S. Broecker is a very influential climate scientist on this topic and the subject of the thermohaline circulation (THC) in past climate, has written many papers, and generally appears to stick with a “Milankovitch” flavor to his theories.

Temperature Gradient between Low & High Latitude

George Kukla, Clement, Cane, Gavin & Zebiak  (2002):

Although the link between insolation and climate is commonly thought to be in the high northern latitudes in summer, our results show that the start of the last glaciation in marine isotope stage (MIS) 5d was associated with a change of insolation during the transitional seasons in the low latitudes.

A simplified coupled ocean-atmosphere model shows that changes in the seasonal cycle of insolation could have altered El Nino Southern Oscillation (ENSO) variability so that there were almost twice as many warm ENSO events in the early glacial than in the last interglacial. This indicates that ice buildup in the cooled high latitudes could have been accelerated by a warmed tropical Pacific..

..Since the early 1900s, the link between insolation and climate has been seen in the high latitudes of the Northern Hemisphere where summer insolation varies significantly.

Insolation at the top of the atmosphere (TOA) during the summer solstice at 65°N is commonly taken to represent the solar forcing of changing global climate. This is at odds with the results of Berger et al. (1981), who correlated the varying monthly TOA insolation at different latitudes of both hemispheres with the marine oxygen isotope record of Hays et al. (1976). The highest positive correlation (p ≤ 0.01) was found not for June but for September, and not in the high latitudes but in the three latitudinal bands representing the tropics (25°N, 5°N, and 15°S)..

..At first glance the implications of our results appear to be counterintuitive, indicating that the early buildup of glacier ice was associated not with the cooling, but with a relative warming of tropical oceans. Recent analogs suggest that it might even have been accompanied by a temporary increase of globally averaged annual mean temperature. If correct, the main trigger of glaciations would not be the expansion of snow fields in subpolar belts, but rather the increase in temperature gradient between the low and the high latitudes.

[Emphasis added].

A Puzzle

George Kukla et al (2002) – written along with a cast of eminents like Shackleton, Imbrie, Broecker:

At the end of the last interglacial period, over 100,000 yr ago, the Earth’s environments, similar to those of today, switched into a profoundly colder glacial mode. Glaciers grew, sea level dropped, and deserts expanded. The same transition occurred many times earlier, linked to periodic shifts of the Earth’s orbit around the Sun. The mechanism of this change, the most important puzzle of climatology, remains unsolved.

[Emphasis added].

Gradient in Insolation from Low to High Latitudes

Maureen Raymo & Kerim Nisancioglu (2003):

Based mainly on climate proxy records of the last 0.5 Ma, a general scientific consensus has emerged that variations in summer insolation at high northern latitudes are the dominant influence on climate over tens of thousands of years. The logic behind nearly a century’s worth of thought on this topic is that times of reduced summer insolation could allow some snow and ice to persist from year to year, lasting through the ‘‘meltback’’ season. A slight increase in accumulation from year to year, enhanced by a positive snow-albedo feedback, would eventually lead to full glacial conditions. At the same time, the cool summers are proposed to be accompanied by mild winters which, through the temperature-moisture feedback, would lead to enhanced winter accumulation of snow. Both effects, reduced spring-to-fall snowmelt and greater winter accumulation, seem to provide a logical and physically sound explanation for the waxing and waning of the ice sheets as high-latitude insolation changes.

Then they point out the problems with this hypothesis and move onto their theory:

We propose that the gradient in insolation between high and low latitudes may, through its influence on the poleward flux of moisture which fuels ice sheet growth, play the dominant role in controlling climate from ~3 to 1 million years ago..

And conclude with an important comment:

..Building a model which can reproduce the first-order features of the Earth’s Ice Age history over the Plio-Pleistocene would be an important step forward in the understanding of the dynamic processes that drive global climate change.

In a later article we will look at the results of GCMs in starting and ending ice ages.

Summertime NH High Latitude Insolation

Roe (2006):

The Milankovitch hypothesis is widely held to be one of the cornerstones of climate science. Surprisingly, the hypothesis remains not clearly defined despite an extensive body of research on the link between global ice volume and insolation changes arising from variations in the Earth’s orbit. In this paper, a specific hypothesis is formulated. Basic physical arguments are used to show that, rather than focusing on the absolute global ice volume, it is much more informative to consider the time rate of change of global ice volume.

This simple and dynamically-logical change in perspective is used to show that the available records support a direct, zero-lag, antiphased relationship between the rate of change of global ice volume and summertime insolation in the northern high latitudes.

[Emphasis added]

And with very nice curve fits of his hypothesis.

Length of Southern Hemisphere Summer

Huybers & Denton (2008):

We conclude that the duration of Southern Hemisphere summer is more likely to control Antarctic climate than the intensity of Northern Hemisphere summer with which it (often misleadingly) covaries. In our view, near interhemispheric climate symmetry at the obliquity and precession timescales arises from a northern response to local summer intensity and a southern response to local summer duration.

And with very nice curve fits of their hypothesis.

Warming in Antarctic Changes Atmospheric CO2

Wolff et al (2009):

The change from a glacial to an interglacial climate is paced by variations in Earth’s orbit.

However, the detailed sequence of events that leads to a glacial termination remains controversial. It is particularly unclear whether the northern or southern hemisphere leads the termination. Here we present a hypothesis for the beginning and continuation of glacial terminations, which relies on the observation that the initial stages of terminations are indistinguishable from the warming stage of events in Antarctica known as Antarctic Isotopic Maxima, which occur frequently during glacial periods. Such warmings in Antarctica generally begin to reverse with the onset of a warm Dansgaard–Oeschger event in the northern hemisphere.

However, in the early stages of a termination, Antarctic warming is not followed by any abrupt warming in the north.

We propose that the lack of an Antarctic climate reversal enables southern warming and the associated atmospheric carbon dioxide rise to reach a point at which full deglaciation becomes inevitable. In our view, glacial terminations, in common with other warmings that do not lead to termination, are led from the southern hemisphere, but only specific conditions in the northern hemisphere enable the climate state to complete its shift to interglacial conditions.

[Emphasis added]

A Puzzle

In a paper on radiative forcing during glacial periods and attempts to calculate climate sensitivity, Köhler et al (2010) state:

Natural climate variations during the Pleistocene are still not fully understood. Neither do we know how much the Earth’s annual mean surface temperature changed in detail, nor which processes were responsible for how much of these temperature variations.

Another Perspective

Final comments from the always fascinating Carl Wunsch:

The long-standing question of how the slight Milankovitch forcing could possibly force such an enormous glacial–interglacial change is then answered by concluding that it does not do so..

..The appeal of explaining the glacial/interglacial cycles by way of the Milankovitch forcing is clear: it is a deterministic story..

..Evidence that Milankovitch forcing ‘‘controls’’ the records, in particular the 100 ka glacial/ interglacial, is very thin and somewhat implausible, given that most of the high frequency variability lies elsewhere. These results are not a proof of stochastic control of the Pleistocene glaciations, nor that deterministic elements are not in part a factor. But the stochastic behavior hypothesis should not be set aside arbitrarily—as it has at least as strong a foundation as does that of orbital control. There is a common view in the paleoclimate community that describing a system as ‘‘stochastic’’ is equivalent to ‘‘unexplainable’’.

Nothing could be further from the truth (e.g., Gardiner, 1985): stochastic processes have a rich physics and kinematics which can be described and understood, and even predicted.

Conclusion

This is not an exhaustive list of hypotheses because I have definitely missed some (Wunsch, in another paper, notes there are at least 30 theories).

It’s also possible I have misinterpreted the key point of at least one of the hypotheses above (apologies to any authors of papers if so). Attempting to understand the ice ages, and attempting to survey the ideas of climate science on the ice ages are both daunting tasks.

What should be clear from this small foray into the subject is that there is no “Milankovitch theory”.

There are many theories with a common premise – solar insolation changes via orbital changes “explain” the start and end of ice ages – but then each with a contradictory theory of how this change is effected.

Therefore, a maximum of one of these theories is correct.

And my current perspective – and an obvious one from reading over 50 papers on the causes of the ice ages – is the number of confusingly-named “Milankovitch theories” that are correct is zero.

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 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 - 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

Hopefully in the order they appeared in the article:

The last glacial cycle: transient simulations with an AOGCM, Robin Smith & Jonathan Gregory, Climate Dynamics (2012)

Insolation and Glacials, George Kukla (1972)

The role of ocean-atmosphere reorganizations in glacial cycles, Wallace Broecker & George Denton, Quaternary Science Reviews (1990)

Last Interglacial and Early Glacial ENSO, George Kukla, Clement, Cane, Gavin & Zebiak (2002)

Last Interglacial Climates, George Kukla et al, Quaternary Research (2002)

The 41 kyr world: Milankovitch’s other unsolved mystery, Maureen Raymo & Kerim Nisancioglu, Paleoceanography (2003)

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

Antarctic temperature at orbital timescales controlled by local summer duration, Huybers & Denton, Nature Geoscience (2008)

Glacial terminations as southern warmings without northern control, E. W. Wolff, H. Fischer & R. Röthlisberger, Nature Geoscience (2009)

What caused Earth’s temperature variations during the last 800,000 years? Data-based evidence on radiative forcing and constraints on climate sensitivity, Peter Köhler, Bintanja, Fischer, Joos,  Knutti, Lohmann, & Masson-Delmotte, Quaternary Science Reviews (2010)

Quantitative estimate of the Milankovitch-forced contribution to observed Quaternary climate change, Carl Wunsch, Quaternary Science Reviews (2004)

In Part Four we  started looking at the changes in solar insolation due to the different orbital effects.

Eccentricity itself has a negligible effect on solar insolation. Obliquity and precession change the (geographic and temporal) distribution of solar radiation, but not the annual amount.

Here is the annual variation for each season at 65ºN:

TOA-time-65N-500kyr-by-quarter

Figure 1

There is less variation by year than the value on any given day (compare fig 5 & 6) in Part Four.

Here is the corresponding graph for 55ºN:

TOA-time-55N-500kyr-by-quarter

Figure 2

Of course, higher solar radiation in one part of the year due to tilt, or obliquity, means less solar radiation in the “opposite” part of the year.

In the graphs above we see that at the peak of the Eemian inter-glacial, JJA (June-July-August) radiation is a minimum, MAM (March-April-May) is on the upswing towards its peak, SON is on a downswing past its peak and of course, DJF is very low and not changing much because there isn’t much sun at high latitudes during the winter.

So what about the annual variation? Let’s zoom in on the period around the Eemian inter-glacial. The top graph shows the daily average insolation for four different years, and the bottom graph shows the annual average by year:

TOA-time-120k-150kyrs-65'N-by-day-and-annual

Figure 3

And for reference the annual variation over the last 500 kyrs:

TOA-time-500ky-65N-annual-variation

Figure 4

And the same data for 55ºN:

TOA-time-120k-150kyrs-55'N-by-day-and-annual

Figure 5

TOA-time-500ky-55N-annual-variation

Figure 6

As we would expect, the peaks and troughs occur at the same times for 55ºN and 65ºN.

What is different between the two latitudes is the change in annual insolation with time at a given latitude. The 65ºN insolation varies by 7 W/m² over the last 500 kyrs, while the 55ºN figure is not quite 3 W/m². By comparison 45ºN varies by less than 1 W/m².

Around the 30 kyrs centered on the Eemian inter-glacial, the variation is:

  • 65ºN – 5.5 W/m²
  • 55ºN – 2.2 W/m²
  • 45ºN – 0.3 W/m²

And if we take the steepest part of the increase from 145  kyr – 135 kyr, we get a per century value of:

  • 65ºN – 40 mW/m² per century
  • 55ºN – 25 mW/m² per century
  • 45ºN – 2 mW/m² per century
  • (and in the southern hemisphere there were similar reductions in insolation over this period)

Now by comparison, due to increases in atmospheric CO2 and other “greenhouse” gases, the “radiative forcing” prior to any feedbacks (i.e., all other things remaining the same) is about 1.7 W/m² over 130 years, or 1.3 W/m² per century.

Now this has been applied globally of course, but in any case recent changes have been 30 – 50 times the rate of increase of high latitude radiative change during one of the key transitions in our past climate.

These values and comparisons aren’t aimed at promoting or attacking any theory, they are just intended to get some understanding of the values in question.

Of course, annual changes are smaller than seasonal changes. So let’s look back at the seasonal values around 120 kyrs – 150 kyrs:

TOA-time-120k-150kyrs-65'N-by-season

Figure 7

And let’s make it easier to understand the changes by looking at the anomaly plot (signal minus the mean for each season):

TOA-detrended-time-120k-150kyrs-65'N-by-season

Figure 8

We have quite large changes (comparatively) in each season. For example, the March-April-May figure increases by 60 W/m² from 143 kyrs ago to 130 kyrs ago, which is almost 0.5 W/m² per century, on a par with recent radiative forcing changes due to GHGs.

The problem with just looking at MAM – and is the reason why I started plotting all these results – is if the increase in MAM insolation caused more rapid ice melt at the end of winter, then didn’t the similarly large reduction in SON (autumn) insolation cause more ice to be there ready for spring? Each year has all the seasons so the whole year has to be considered..

And if there is such a clear argument for one season being some kind of dominant force compared with another season (some strong non-linearity), why isn’t there a consensus on what it is (along with some evidence)?

Huybers & Wunsch (2005) noted:

Taking these two [Milankovitch and chaos] perspectives together, there are currently more than 30 different models of the seven late Pleistocene glacial cycles.

Lastly, for interest, here is a typical spectral power plot of the TOA solar insolation (normalized). This one happens to have each season as a separate curve, but there isn’t much difference between each period so the plots pretty much overlay each other. The 3 vertical magenta lines represent (from left to right) the frequencies of 41 kyrs, 23 kyrs and 19 kyrs:

TOA-Spectral-power-last500ky-by-season-65N

Figure 7

In some later articles we will look at the spectral characteristics of the ice age record so knowing the spectral characteristics of orbital effects on insolation is important.

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 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

References

Obliquity pacing of the late Pleistocene glacial terminations, Peter Huybers & Carl Wunsch, Nature (2005)

All graphs produced thanks to the Matlab code supplied by Jonathan Levine.

In Part Three we had a very brief look at the orbital factors that affect solar insolation.

Here we will look at these factors in more detail. We start with the current situation.

Seasonal Distribution of Incoming Solar Radiation

The earth is tilted on its axis (relative to the plane of orbit) so that in July the north pole “faces” the sun, while in January the south pole “faces” the sun.

Here are the TOA graphs for average incident solar radiation at different latitudes by month:

From Vardavas & Taylor (2007)

From Vardavas & Taylor (2007)

Figure 1

And now the average values first by latitude for the year, then by month for northern hemisphere, southern hemisphere and the globe:

TOA-solar-total-by-month-and-latitude-present

Figure 2

We can see that the southern hemisphere has a higher peak value – this is because the earth is closest to the sun (perihelion) on January 3rd, during the southern hemisphere summer.

This is also reflected in the global value which varies between 330 W/m² at aphelion (furthest away from the sun) to 352 W/m² at perihelion.

Eccentricity

There is a good introduction to planetary orbits in Wikipedia. I was saved from the tedium of having to work out how to implement an elliptical orbit vs time by the Matlab code kindly supplied by Jonathan Levine. He also supplied the solution to the much more difficult problem of insolation vs latitude at any day in the Quaternary period, which we will look at later.

Here is the the TOA solar insolation by day of the year, as a function of the eccentricity of the orbit:

Daily-Change-TOA-Solar-vs-Eccentricity-2

Figure 3 – Updated

The earth’s orbit currently has an eccentricity of 0.0167. This means that the maximum variation in solar radiation is 6.9%.

Perihelion is 147.1 million km, while aphelion is 152.1 million km. The amount of solar radiation we receive is “the inverse square law”, which means if you move twice as far away, the solar radiation reduces by a factor of four. So to calculate the difference between the min and max you simply calculate: (152.1/147.1)² = 1.069 or a change of 6.9%.

Over the past million or more years the earth’s orbit has changed its eccentricity, from a low close to zero, to a maximum of about 0.055. The period of each cycle is about 100,000 years.

Here is my calculation of change in total annual TOA solar radiation with eccentricity:

Annual-%Change-TOA-Solar-vs-Eccentricity

Figure 4

Looking at figure 1 of Imbrie & Imbrie (1980), just to get a rule of thumb, eccentricity changed from 0.05 to 0.02 over a 50,000 year period (about 220k years ago to 170k years ago). This means that the annual solar insolation dropped by 0.1% over 50,000 years or 3 mW/m² per century. (This value is an over-estimate because it is the peak value with sun overhead, if instead we take the summer months at high latitude the change becomes  0.8 mW/m² per century)

It’s a staggering drop, and no wonder the strong 100,000 year cycle in climate history matching the Milankovitch eccentricity cycles is such a difficult theory to put together.

Obliquity & Precession

To understand those basics of these changes take a look at the Milankovitch article. Neither of these two effects, precession and obliquity, changes the total annual TOA incident solar radiation. They just change its distribution.

Here is the last 250,000 years of solar radiation on July 1st – for a few different latitudes:

TOA-Solar-July1-Latitude-vs0-250k-499px

Figure 5 – Click for a larger image

Notice that the equatorial insolation is of course lower than the mid-summer polar insolation.

Here is the same plot but for October 1st. Now the equatorial value is higher:

TOA-Solar-Oct1-Latitude-vs0-250k-499px

Figure 6 - Click for a larger image

Let’s take a look at the values for 65ºN, often implicated in ice age studies, but this time for the beginning of each month of the year (so the legend is now 1 = January 1st, 2 = Feb 1st, etc):

TOA-Solar-65N-bymonth-vs0-250k-lb-499px

Figure 7 - Click for a larger image

And just for interest I marked one date for the last inter-glacial – the Eemian inter-glacial as it is known.

Come up with a theory:

  • peak insolation at 65ºN
  • fastest rate of change
  • minimum insolation
  • average of summer months
  • average of winter half year
  • average autumn 3 months

Then pick from the graph and let’s start cooking.. Having trouble? Pick a different latitude. Southern Hemisphere – no problem, also welcome.

As we will see, there are a lot of theories, all of which call themselves “Milankovitch” but each one is apparently incompatible with other similarly-named “Milankovitch” theories.

At least we have a tool, kindly supplied by Jonathan Levine, which allows us to compute any value. So if any readers have an output request, just ask.

One word of caution for budding theorists of ice ages (hopefully we have many already) from Kukla et al (2002):

..The marine isotope record is commonly tuned to astronomic chronology, represented by June insolation at the top of the atmosphere at 60′ or 65′ north latitude. This was deemed justified because the frequency of the Pleistocene gross global climate states matches the frequency of orbital variations..

..The mechanism of the climate response to insolation remains unclear and the role of insolation in the high latitudes as opposed to that in the low latitudes is still debated..

..In either case, the link between global climates and orbital variations appears to be complicated and not directly controlled by June insolation at latitude 65′N. We strongly discourage dating local climate proxies by unsubstantiated links to astronomic variations..

[Emphasis added].

I’m a novice with the historical records and how they have been constructed, but I understand that SPECMAP is tuned to a Milankovitch theory, i.e., the dates of peak glacials and peak inter-glacials are set by astronomical values.

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 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

References

Last Interglacial Climates, Kukla et al, Quaternary Research (2002)

Modeling the Climatic Response to Orbital Variations, John Imbrie & John Z. Imbrie, Science (1980)

In Part Two we looked at one paper by Lorenz from 1968 where he put forward the theory that climate might be “intransitive”. In common parlance we could write this as “climate might be chaotic” (even though there is a slight but important difference between the two definitions).

In this article we will have a bit of a look at the history of the history of climate – that is, a couple of old papers about ice ages.

These papers are quite dated and lots of new information has since come to light, and of course thousands of papers have since been written about the ice ages. So why a couple of old papers? It helps to create some context around the problem. These are “oft-cited”, or seminal, papers, and understanding ice ages is so complex that it is probably easiest to set out an older view as some kind of perspective.

At the very least, it helps get my thinking into order. Whenever I try to understand a climate problem I usually end up trying to understand some of the earlier oft-cited papers because most later papers rely on that context without necessarily repeating it.

Variations in the Earth’s Orbit: Pacemaker of the Ice Ages by JD Hays, J Imbrie, NJ Shackleton (1976) is referenced by many more recent papers that I’ve read – and, according to Google Scholar, cited by 2,656 other papers – that’s a lot in climate science.

For more than a century the cause of fluctuations in the Pleistocene ice sheets has remained an intriguing and unsolved scientific mystery. Interest in this problem has generated a number of possible explanations.

One group of theories invokes factors external to the climate system, including variations in the output of the sun, or the amount of solar energy reaching the earth caused by changing concentrations of interstellar dust; the seasonal and latitudinal distribution of incoming radiation caused by changes in the earth’s orbital geometry; the volcanic dust content of the atmosphere; and the earth’s magnetic field. Other theories are based on internal elements of the system believed to have response times sufficiently long to yield fluctuations in the range 10,000 to 1,000,000 years.

Such features include the growth and decay of ice sheets, the surging of the Antarctic ice sheet; the ice cover of the Arctic Ocean; the distribution of carbon dioxide between atmosphere and ocean; and the deep circulation of the ocean.

Additionally, it has been argued that as an almost intransitive system, climate could alternate between different states on an appropriate time scale without the intervention of any external stimulus or internal time constant.

This last idea is referenced as Lorenz 1968, the paper we reviewed in Part Two.

The authors note that previous work has provided evidence of orbital changes being involved in climate change, and make an interesting comment that we will see has not changed in the intervening 38 years:

The first [problem] is the uncertainty in identifying which aspects of the radiation budget are critical to climate change. Depending on the latitude and season considered most significant, grossly different climate records can be predicted from the same astronomical data..

Milankovitch followed Koppen and Wegener’s view that the distribution of summer insolation at 65°N should be critical to the growth and decay of ice sheets.. Kukla pointed out weaknesses.. and suggested that the critical time may be Sep and Oct in both hemispheres.. As a result, dates estimated for the last interglacial on the basis of these curves have ranged from 80,000 to 180,000 years ago.

The other problem at that time was the lack of quality data on the dating of various glacials and interglacials:

The second and more critical problem in testing the orbital theory has been the uncertainty of geological chronology. Until recently, the inaccuracy of dating methods limited the interval over which a meaningful test could be made to the last 150,000 years.

This paper then draws on some newer, better quality data for the last few hundred thousand years of temperature history. By the way, Hays was (and is) a Professor of Geology, Imbrie was (and is) a Professor of Oceanography and Shackleton was at the time in Quarternary Research, later a professor in the field.

Brief Introduction to Orbital Parameters that Might Be Important

Now, something we will look at in a later article, probably Part Four, is exactly what changes in solar insolation are caused by changes in the earth’s orbital geometry. But as an introduction to that question, there are three parameters that vary and are linked to climate change:

  1. Eccentricity, e, (how close is the earth’s orbit to a circle) – currently 0.0167
  2. Obliquity, ε, (the tilt of the earth’s axis) – currently 23.439°
  3. Precession, ω, (how close is the earth to the sun in June or December) – currently the earth is closest to the sun on January 3rd

The first, eccentricity, is the only one that changes the total amount of solar insolation received at top of atmosphere in a given year. Note that a constant solar insolation at the top of atmosphere can be a varying solar absorbed radiation if more or less of that solar radiation happens to be reflected off, say, ice sheets, due to, say, obliquity.

The second, obliquity, or tilt, affects the difference between summer and winter TOA insolation. So it affects seasons and, specifically, the strength of seasons.

The third, precession, affects the amount of radiation received at different times of the year (moderated by item 1, eccentricity). So if the earth’s orbit was a perfect circle this parameter would disappear. When the earth is closest to the sun in June/July the Northern Hemisphere summer is stronger and the SH summer is weaker, and vice versa for winters.

So eccentricity affects total TOA insolation, while obliquity and precession change its distribution in season and latitude. However, variations in solar insolation at TOA depend on e² and so the total variation in TOA radiation has, over a very long period, only been only 0.1%.

This variation is very small and yet the strongest “orbital signal” in the ice age record is that of eccentricity. A problem, that even for the proponents of this theory, has not yet been solved.

Last Interglacial Climates, by a cast of many including George J. Kukla, Wallace S. Broecker, John Imbrie, Nicholas J. Shackleton:

At the end of the last interglacial period, over 100,000 yr ago, the Earth’s environments, similar to those of today, switched into a profoundly colder glacial mode. Glaciers grew, sea level dropped, and deserts expanded. The same transition occurred many times earlier, linked to periodic shifts of the Earth’s orbit around the Sun. The mechanism of this change, the most important puzzle of climatology, remains unsolved.

[Emphasis added].

History Cores

Our geological data comprise measurements of three climatically sensitive parameters in two deep-sea sediment cores. These cores were taken from an area where previous work shows that sediment is accumulating fast enough to preserve information at the frequencies of interest. Measurements of one variable, the per mil enrichment of oxygen 18 (δ18O), make it possible to correlate these records with others throughout the world, and to establish that the sediment studied accumulated without significant hiatuses and at rates which show no major fluctuations..

.. From several hundred cores studied stratigraphically by the CLIMAP project, we selected two whose location and properties make them ideal for testing the orbital hypothesis. Most important, they contain together a climatic record that is continuous, long enough to be statistically useful (450,000 years) and characterized by accumulation rates fast enough (>3 cm per 1,000 years) to resolve climatic fluctuations with periods well below 20,000 years.

The cores were located in the Southern Indian ocean. What is interesting about the cores is that 3 different mechanisms are captured from each location, including δ18O isotopes which should be a measure of ice sheets globally and temperature in the ocean at the location of the cores.

Hays, Imbrie & Shackleton (1976)

Hays, Imbrie & Shackleton (1976)

Figure 1

There is much discussion about the dating of the cores. In essence, other information allows a few transitions to be dated, while the working assumption is that within these transitions the sediment accumulation is at a constant rate.

Although uniform sedimentation is an ideal which is unlikely to prevail precisely anywhere, the fact that the characteristics of the oxygen isotope record are present throughout the cores suggests that there can be no substantial lacunae, while the striking resemblance to records from distant areas shows that there can be no gross distortion of accumulation rate.

Spectral Analysis

The key part of their analysis is a spectral analysis of the data, compared with a spectral analysis of the “astronomical forcing”.

The authors say:

.. we postulate a single, radiation-climate system which transforms orbital inputs into climatic outputs. We can therefore avoid the obligation of identifying the physical mechanism of climatic response and specify the behavior of the system only in general terms. The dynamics of our model are fixed by assuming that the system is a time-invariant, linear system – that is, that its behavior in the time domain can be described by a linear differential equation with constant coefficients. The response of such a system in the frequency domain is well known: frequencies in the output match those of the input, but their amplitudes are modulated at different frequencies according to a gain function. Therefore, whatever frequencies characterize the orbital signals, we will expect to find them emphasized in paleoclimatic spectra (except for frequencies so high they would be greatly attenuated by the time constants of response)..

My translation – let’s compare the orbital spectrum with the historical spectrum without trying to formulate a theory and see how the two spectra compare.

The orbital effects:

From Hays et al (1976)

From Hays et al (1976)

Figure 2

The historical data:

From Hays et al (1976)

From Hays et al (1976)

Figure 3

We have also calculated spectra for two time series recording variations in insolation [their fig 4 - our fig 2], one for 55°S and the other for 60°N. To the nearest 1,000 years, the three dominant cycles in these spectra (41,000, 23,000 and 19,000 years) correspond to those observed in the spectra for obliquity and precession.

This result, although expected, underscores two important points. First, insolation spectra are characterized by frequencies reflecting obliquity and precession, but not eccentricity.

Second, the relative importance of the insolation components due to obliquity and precession varies with latitude and season.

[Emphasis added]

In commenting on the historical spectra they say:

Nevertheless, five of the six spectra calculated are characterized by three discrete peaks, which occupy the same parts of the frequency range in each spectrum. Those correspond to periods from 87,000 to 119,000 years are labeled a; 37,000 to 47,000 years b; and 21,000 to 24,000 years c. This suggest that the b and c peaks represent a response to obliquity and precession variation, respectively.

Note that the major cycle shown in the frequency spectrum is the 100,000 peak.

There is a lot of discussion in their paper of the data analysis, please have a read of their paper to learn more. The detail probably isn’t so important for current understanding.

The authors conclude:

Over the frequency range 10,000 to 100,000 cycle per year, climatic variance of these records is concentrated in three discrete spectral peaks at periods of 23,000, 42,000, and approximately 100,000 years. These peaks correspond to the dominant periods of the earth’s solar orbit and contain respectively about 10, 25 and 50% of the climatic variance.

The 42,000-year climatic component has the same period as variations in the obliquity of the earth’s axis and retains a constant phase relationship with it.

The 23,000-year portion of the variance displays the same periods (about 23,000 and 19,000 years) as the quasi-periodic precession index.

The dominant 100,000 year climatic component has an average period close to, and is in phase with, orbital eccentricity. Unlike the correlations between climate and the higher frequency orbital variations (which can be explained on the assumption that the climate system responds linearly to orbital forcing) an explanation of the correlations between climate and eccentricity probably requires an assumption of non-linearity.

It is concluded that changes in the earth’s orbital geometry are the fundamental cause of the succession of Quarternary ice ages.

Things were looking good for explanations of the ice ages in 1975..

For those who want to understand more recent evaluation of the spectral analysis of temperature history vs orbital forcing, check out papers by Carl Wunsch from 2003, 2004 and 2005, e.g. The spectral description of climate change including the 100 ky energyClimate Dynamics (2003).

A Few Years Later

Here are a few comments from Imbrie & Imbrie (1980):

Since the work of Croll and Milankovitch, many investigations have been aimed at the central question of the astronomical theory of the ice ages:

Do changes in orbital geometry cause changes in climate that are geologically detectable?

On the one hand, climatologists have attacked the problem theoretically by adjusting the boundary conditions of energy-balance models, and then observing the magnitude of the calculated response. If these numerical experiments are viewed narrowly as a test of the astronomical theory, they are open to question because the models used contain untested parameterizations of important physical processes. Work with early models suggested that the climatic response to orbital changes was too small to account for the succession of Pleistocene ice ages. But experiments with a new generation of models suggest that orbital variations are sufficient to account for major changes in the size of Northern Hemisphere ice sheets..

..In 1968, Broecker et al. (34, 35) pointed out that the curve for summertime irradiation at 45°N was a much better match to the paleoclimatic records of the past 150,000 years than the curve for 65°N chosen by Milankovitch..

Current Status. This is not to say that all important questions have been answered. In fact, one purpose of this article is to contribute to the solution of one of the remaining major problems: the origin and history of the 100,000-year climatic cycle.

At least over the past 600,000 years, almost all climatic records are dominated by variance components in a narrow frequency band centered near a 100,000-year cycle. Yet a climatic response at these frequencies is not predicted by the Milankovitch version of the astronomical theory – or any other version that involves a linear response..

..Another problem is that most published climatic records that are more than 600,000 years old do not exhibit a strong 100,000-year cycle..

The goal of our modeling effort has been to simulate the climatic response to orbital variations over the past 500,000 years. The resulting model fails to simulate four important aspects of this record. It fails to produce sufficient 100k power; it produces too much 23k and 19k power; it produces too much 413k power; and it loses its match with the record around the time of the last 413k eccentricity minimum, when values of e [eccentricity] were low and the amplitude of the 100k eccentricity cycle was much reduced..

..The existence of an unstable fixed point makes tuning an extremely sensitive task. For example, Weertman notes that changing the value of one parameter by less than 1 percent of its physically allowed range made the difference between a glacial regime and an interglacial regime in one portion of an experimental run while leaving the rest virtually unchanged..

This would be a good example of Lorenz’s concept of an almost intransitive system (one whose characteristics over long but finite intervals of time depend strongly on initial conditions).

Once again the spectre of the Eminent Lorenz is raised. We will see in later articles that with much more sophisticated models it is not easy to create an ice-age, or to turn an ice-age into an inter-glacial.

Articles in the Series

Part One - An introduction

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

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

References

Variations in the Earth’s Orbit: Pacemaker of the Ice Ages, JD Hays, J Imbrie & NJ Shackleton, Science (1976)

Modeling the Climatic Response to Orbital Variations, John Imbrie & John Z. Imbrie, Science (1980)

Last Interglacial Climates, Kukla et al, Quaternary Research (2002)

A really long time ago I wrote Ghosts of Climates Past. I’ve read a lot of papers on the ice ages and inter-glacials but never got to the point of being able to write anything coherent.

This post is my attempt to get myself back into gear – after a long time being too busy to write any articles.

Here is what the famous Edward Lorenz said in his 1968 paper, Climatic Determinism – the opening paper at a symposium titled Causes of Climatic Change:

The often-accepted hypothesis that the physical laws governing the behavior of an atmosphere determine a unique climate is examined critically. It is noted that there are some physical systems (transitive systems) whose statistics taken over infinite time intervals are uniquely determined by the governing laws and the environmental conditions, and other systems (intransitive systems) where this is not the case.

There are also certain transitive systems (almost intransitive systems) whose statistics taken over very long but finite intervals differ considerably from one such interval to another. The possibility that long-term climatic changes may result from the almost-intransitivity of the atmosphere rather than from environmental changes is suggested.

The language might be obscure to many readers. But he makes it clear in the paper:

lorenz-1968-1

Here Lorenz describes transitive systems – that is,  starting conditions do not determine the future state of the climate. Instead, the physics and the “outside influences” or forcings (such as the solar radiation incident on the planet) determine the future climate.

lorenz-1968-2

Here Lorenz introduces the well-known concept of “chaotic systems” where different initial conditions result in different long term results. (Note that there can be chaotic systems where different initial conditions produce different time-series results but the same statistical results over a period of time – so the term intransitive is a more restrictive term, see the paper for more details).

lorenz-1968-3

lorenz-1968-4

lorenz-1968-5

Well, interesting stuff from the eminent Lorenz.

A later paper, Kagan, Maslova & Sept (1994), commented on (perhaps inspired by) Lorenz’s 1968 paper and produced some interesting results from quite a simple model:

Kagan et al 1994-2 Kagan et al 1994-1

That is, a few coupled systems, working together can produce profound shifts in the Earth’s climate with periods like 80,000 years.

In case anyone thinks it’s just obscure foreign journals that comment approvingly on Lorenz’s work, the well-published climate skeptic James Hansen had this to say:

The variation of the global-mean annual-mean surface air temperature during the 100-year control run is shown in Figure 1. The global mean temperature at the end of the run is very similar to that at the beginning, but there is substantial unforced variability on all time scales that can be examined, that is, up to decadal time scales. Note that an unforced change in global temperature of about 0.4°C (0.3°C, if the curve is smoothed with a 5-year running mean) occurred in one 20-year period (years 50-70). The standard deviation about the 100-year mean is 0.11°C. This unforced variability of global temperature in the model is only slightly smaller than the observed variability of global surface air temperature in the past century, as discussed in section 5. The conclusion that unforced (and unpredictable) climate variability may account for a large portion of climate change has been stressed by many researchers; for example, Lorenz [1968], Hasselmann [1976] and Robock [1978].

[Emphasis added].

And here is their Figure 1, the control run, from that paper:

Hansen et al 1998

In later articles we will look at some of the theories of Milankovitch cycles. Confusingly, many different theories, mostly inconsistent with each other, all go by the same name.

Articles in the Series

Part One - An introduction

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

References

Climatic Determinism, Edward Lorenz (1968)

Discontinuous auto-oscillations of the ocean thermohaline circulation and internal variability of the climate system, Kagan, Maslova & Sept (1994)

Global Climate Changes as Forecast by Goddard Institute for Space Studies Three-Dimensional Model, Hansen et al (1998)

In Wonderland, Radiative Forcing and the Rate of Inflation we looked at the definition of radiative forcing and a few concepts around it:

  • why the instantaneous forcing is different from the adjusted forcing
  • what adjusted forcing is and why it’s a more useful concept
  • why the definition of the tropopause affects the value
  • GCM results usually don’t use radiative forcing as an input

In this article we will look at some results using the Wonderland model.

Remember the Wonderland model is not the earth. But the same is also true of “real” GCMs with geographical boundaries that match the earth as we know it. They are not the earth either. All models have limitations. This is easy to understand in principle. It is challenging to understand in the specifics of where the limitations are, even for specialists – and especially for non-specialists.

What the Wonderland model provides is a coarse geography with earth-like layout of land and ocean, plus of course, physics that follows the basic equations. And using this model we can get a sense of how radiative forcing is related to temperature changes when the same value of radiative forcing is applied via different mechanisms.

In the 1997 paper I think that Hansen, Sato & Ruedy did a decent job of explaining the limitations of radiative forcing, at least as far as the Wonderland climate model is able to assist us with that understanding. Remember as well that, in general, results we see from GCMs do not use radiative forcing. Instead they calculate from first principles – or parameterized first principles.

Doubling CO2

Now there’s a lot in this first figure, it can be a bit overwhelming. We’ll take it one step at a time. We double CO2 overnight – in Wonderland – and we see various results. The left half of the figure is all about flux while the right half is all about temperature:

From Hansen et al 1997

From Hansen et al 1997

Figure 1 – Green text added – Click to Expand

On the top line, the first two graphs are the net flux change, as a function of height and latitude. First left – instantaneous; second left – adjusted. These two cases were explained in the last article.

The second left is effectively the “radiative forcing”, and we can see that the above the tropopause (at about 200 mbar) the net flux change with height is constant. This is because the stratosphere has come into radiative balance. Refer to the last article for more explanation. On the right hand side, with all feedbacks from this one change in Wonderland, we can see the famous predicted “tropospheric hot spot” and the cooling of the stratosphere.

We see in the bottom two rows on the right the expected temperature change :

  • second row – change in temperature as a function of latitude and season (where temperature is averaged across all longitudes)
  • third row – change in temperature as a function of latitude and longitude (averaged annually)

It’s interesting to see the larger temperature increases predicted near the poles. I’m not sure I really understand the mechanisms driving that. Note that the radiative forcing is generally higher in the tropics and lower at the poles, yet the temperature change is the other way round.

Increasing Solar Radiation by 2%

Now let’s take a look at a comparison exercise, increasing solar radiation by 2%.

The responses to these comparable global forcings, 2xCO2 & +2% S0, are similar in a gross sense, as found by previous investigators. However, as we show in the sections below, the similarity of the responses is partly accidental, a cancellation of two contrary effects. We show in section 5 that the climate model (and presumably the real world) is much more sensitive to a forcing at high latitudes than to a forcing at low latitudes; this tends to cause a greater response for 2xCO2 (compare figures 4c & 4g); but the forcing is also more sensitive to a forcing that acts at the surface and lower troposphere than to a forcing which acts higher in the troposphere; this favors the solar forcing (compare figures 4a & 4e), partially offsetting the latitudinal sensitivity.

We saw figure 4 in the previous article, repeated again here for reference:

From Hansen et al (1997)

From Hansen et al (1997)

Figure 2

In case the above comment is not clear, absorbed solar radiation is more concentrated in the tropics and a minimum at the poles, whereas CO2 is evenly distributed (a “well-mixed greenhouse gas”). So a similar average radiative change will cause a more tropical effect for solar but a more even effect for CO2.

We can see that clearly in the comparable graphic for a solar increase of 2%:

From Hansen et al (1997)

From Hansen et al (1997)

Figure 3 - Green text added - Click to Expand

We see that the change in net flux is higher at the surface than the 2xCO2 case, and is much more concentrated in the tropics.

We also see the predicted tropospheric hot spot looking pretty similar to the 2xCO2 tropospheric hot spot (see note 1).

But unlike the cooler stratosphere of the 2xCO2 case, we see an unchanging stratosphere for this increase in solar irradiation.

These same points can also be seen in figure 2 above (figure 4 from Hansen et al).

Here is the table which compares radiative forcing (instantaneous and adjusted), no feedback temperature change, and full-GCM calculated temperature change for doubling CO2, increasing solar by 2% and reducing solar by 2%:

From Hansen et al 1997

From Hansen et al 1997

Figure 4 – Green text added – Click to Expand

The value R (far right of table) is the ratio of the predicted temperature change from a given forcing divided by the predicted temperature change from the 2% increase in solar radiation.

Now the paper also includes some ozone changes which are pretty interesting, but won’t be discussed here (unless we have questions from people who have read the paper of course).

“Ghost” Forcings

The authors then go on to consider what they call ghost forcings:

How does the climate response depend on the time and place at which a forcing is applied? The forcings considered above all have complex spatial and temporal variations. For example, the change of solar irradiance varies with time of day, season, latitude, and even longitude because of zonal variations in ground albedo and cloud cover. We would like a simpler test forcing.

We define a “ghost” forcing as an arbitrary heating added to the radiative source term in the energy equation.. The forcing, in effect, appears magically from outer space at an atmospheric level, latitude range, season and time of day. Usually we choose a ghost forcing with a global and annual mean of 4 W/m², making it comparable to the 2xCO2 and +2% S0 experiments.

In the following table we see the results of various experiments:

Hansen et al (1997)

Hansen et al (1997)

Figure 5 – Click to Expand

We note that the feedback factor for the ghost forcing varies with the altitude of the forcing by about a factor of two. We also note that a substantial surface temperature response is obtained even when the forcing is located entirely within the stratosphere. Analysis of these results requires that we first quantify the effect of cloud changes. However, the results can be understood qualitatively as follows.

Consider ΔTs in the case of fixed clouds. As the forcing is added to successively higher layers, there are two principal competing effects. First, as the heating moves higher, a larger fraction of the energy is radiated directly to space without warming the surface, causing ΔTs to decline as the altitude of the forcing increases. However, second, warming of a given level allows more water vapor to exist there, and at the higher levels water vapor is a particularly effective greenhouse gas. The net result is that ΔTs tends to decline with the altitude of the forcing, but it has a relative maximum near the tropopause.

When clouds are free to change the surface temperature change depends even more on the altitude of the forcing (figure 8). The principal mechanism is that heating of a given layer tends to decrease large-scale cloud cover within that layer. The dominant effect of decreased low-level clouds is a reduced planetary albedo, thus a warming, while the dominant effect of decreased high clouds is a reduced greenhouse effect, thus a cooling. However, the cloud cover, the cloud cover changes and the surface temperature sensitivity to changes may depend on characteristics of the forcing other than altitude, e.g. latitude, so quantitive evaluation requires detailed examination of the cloud changes (section 6).

Conclusion

Radiative forcing is a useful concept which gives a headline idea about the imbalance in climate equilibrium caused by something like a change in “greenhouse” gas concentration.

GCM calculations of temperature change over a few centuries do vary significantly with the exact nature of the forcing – primarily its vertical and geographical distribution. This means that a calculated radiative forcing of, say, 1 W/m² from two different mechanisms (e.g. ozone and CFCs) would (according to GCMs) not necessarily produce the same surface temperature change.

References

Radiative forcing and climate response, Hansen, Sato & Ruedy, Journal of Geophysical Research (1997) – free paper

Notes

Note 1: The reason for the predicted hot spot is more water vapor causes a lower lapse rate – which increases the temperature higher up in the troposphere relative to the surface. This change is concentrated in the tropics because the tropics are hotter and, therefore, have much more water vapor. The dry polar regions cannot get a lapse rate change from more water vapor because the effect is so small.

Any increase in surface temperature is predicted to cause this same change.

With limited research on my part, the idealized picture of the hotspot as shown above is not actually the real model results. The top graph is the “just CO2″ graph, and the bottom graph is the “CO2 + aerosols” – the second graph is obviously closer to the real case:

From Santer et al 1996

From Santer et al 1996

Many people have asked for my comment on the hot spot, but apart from putting forward an opinion I haven’t spent enough time researching this topic to understand it. From time to time I do dig in, but it seems that there are about 20 papers that need to be read to say something useful on the topic. Unfortunately many of them are heavy in stats and my interest wanes.

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