A Theory Of Ice Ages

Posted: February 14, 2018 by tallbloke in solar system dynamics

Some blue-ice thinking from Frank Davis. We like open, out of the box discussions about the cause of ice ages at the talkshop. This is as good a starter for 10 as any.

Frank Davis

Forty years ago I was in university working on energy conservation in buildings. I worked with an electronic analogue simulation model in which thermal resistance was represented by electrical resistance, temperature by voltage, heat flow by current. My job was to control the model with one of the new microcomputers that had become available. I spent a lot of my time with a soldering iron and wires and Veroboards, getting DACs and ADCs and other bits of electronics working.

Eventually the money ran out, and I left the university, and became a freelance software engineer, working on all sorts of stuff unrelated to energy conservation.

But I never forgot what I’d learned during that time. And so I’ve always been interested in Anthropogenic Global Warming, because it’s essentially all about heat flow, although in the Earth’s atmosphere rather than in the walls and rooms of buildings. And it’s prompted me…

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  1. Frank Davis says:

    Thanks for reblogging my post, Roger.

  2. The Badger says:

    Frank – very useful work and original thinking.

    However before moving on with the atmosphere bit, which may well be complicated, I think the bare planet with ice age cycles can be explored further. The model does need to be scaled up to Earth sizes.

    What assumptions are you making about the Earth’s core?
    Are any of these testable?

    What assumptions are you making about the source of heat in the Earth’s core?
    Are any of these testable?

    How old is the Earth in your model?
    Can the assumed age be reconciled with the theories of heat being generated via radioactive decay bearing in mind known half-lifes of known isotopes.

    Are you familiar with the hypothesis of Loschmidt regarding heat gradients in gases (atmosphere) and solids (Earth all the way to the core)?

    Can you engineer a model where there is a continuous top up of heat energy back into the core from a hypothetical/mysterious external source. This could represent radioactive decay and/or heat from the sun via the gravity induced gradient.

    It would be fun to play around with these ideas based upon a reality sized rock, top up to core input of some % of known solar input and both with and without some radioactive input which is decaying.

    You would have a daily input of a pseudo sine wave via a diode (day/night), a continuous input for radioactivity but with a very long timescale exponential decay.

    I speculate you might end up with something much closer to actual condition than 100K. Maybe then the atmosphere effect can be added. It may be possible to crudely split the atmosphere into the insulating effect (another resistor) and the gravity induced concentration (current inject into a node).

  3. ren says:

    The atmosphere without water vapor is not able to maintain heat at medium latitudes. When the amount of water vapor decreases during the periods of La Niña, the temperature of the atmosphere decreases.

  4. ren says:

    Let’s see how the temperature of the sea surface drops.

  5. donald penman says:

    I have recently thought that the increase of snow ice cover in the Northern hemisphere which survives the summer into the next winter could be reflecting the energy balance of the Earth. It is not caused by a gradual increase in albedo as thought but is just there. If the Earth is gaining more energy than it loses then there could be a gap between all snow cover melting on land in the Northern Hemisphere and forming again the next winter but if Earth is losing more energy then it is gaining then there could be an increase of snow cover remaining into the next winter which then increases the albedo effect. The size of the gap between snow cover ending in summer and snow cover starting again in winter would give an indication of how much the Earth is warming and the amount of snow cover remaining at the end of summer into the next winter would give an indication of how much the Earth is cooling.

  6. JB says:

    As I read the experiment, the first assumption is the core energy output remains constant.
    Over multiple ages?
    An infinitely constant heat source?
    The source of the energy keeping the core hot?

  7. Richard111 says:

    A question for ren.

    If there were NO radiative gases in the atmosphere how would the atmosphere cool?

  8. ren says:

    Solar activity is very important. During high solar activity, the energy of the upper winds in the atmosphere increases. This affects not only the change of circulation, but also increases the effect of evaporation on the oceans. It’s like blowing on hot tea.

  9. ren says:

    The adiabatic atmosphere
    Of course, we know that the atmosphere is not isothermal. In fact, air temperature falls quite noticeably with increasing altitude. In ski resorts, you are told to expect the temperature to drop by about 1 degree per 100 meters you go upwards. Many people cannot understand why the atmosphere gets colder the higher up you go. They reason that as higher altitudes are closer to the Sun they ought to be hotter. In fact, the explanation is quite simple. It depends on three important properties of air. The first important property is that air is transparent to most, but by no means all, of the electromagnetic spectrum. In particular, most infrared radiation, which carries heat energy, passes straight through the lower atmosphere and heats the ground. In other words, the lower atmosphere is heated from below, not from above. The second important property of air is that it is constantly in motion. In fact, the lower 20 kilometers of the atmosphere (the so called troposphere) are fairly thoroughly mixed. You might think that this would imply that the atmosphere is isothermal. However, this is not the case because of the final important properly of air: i.e., it is a very poor conductor of heat. This, of course, is why woolly sweaters work: they trap a layer of air close to the body, and because air is such a poor conductor of heat you stay warm.

  10. ren says:

    On all planets whose atmosphere has a enough large mass, the temperature in the troposphere drops linearly to a pressure level of about 0.1 bar.

  11. ren says:

    Interestingly, in the atmosphere of Venus, at a pressure level of 1000 hPa, the temperature is similar to the temperature of the Earth’s surface (despite the difference in the force of gravity and distance from the Sun).

  12. Richard111 says:

    Thanks ren, (I think), battling with your link to figure out where the energy went and how the upper air cools.

  13. oldbrew says:

    Hot rocks…

    Geothermal energy can be used as a means for generating electricity, by using the heat of the surrounding layers of rock underground to heat water and then routing the steam from this process through a turbine connected to a generator.

    On the other hand, drill bits have to be cooled not only because of the friction created by the process of drilling itself but also because of the heat of the surrounding rock at great depth. [bold added]


    Geothermal gradient is the rate of increasing temperature with respect to increasing depth in the Earth’s interior. Away from tectonic plate boundaries, it is about 25–30 °C/km (28–34 °F/mi) of depth near the surface in most of the world. – Wikipedia

  14. ren says:

    Again, very heavy snowfall in the Swiss Alps.

  15. ren says:

    This year snowfalls in the northern hemisphere are record-breaking.

  16. dscott says:

    Regarding the reference to the temperature sensitivity to latitude, one should consider that the ratio of the volume to surface area increases as the sphere diameter increases, i.e. as the volume increases due to increasing diameter, the volume per surface area increases. Stated in the reverse, an increasing volume has a decreasing surface area ratio.

    What is your assumption on the surface temperature as the diameter increases? One would assume that the increasing distance for a larger sphere from the center point would allow a more gradual temperature drop to the surface. This in turn changes the rate of black body radiation from the sphere to space as opposed to radiative heating from the sun to the sphere’s surface.

    Finally, what in your opinion creates the oscillating effect since the tendency of cooling or heating is to come to a steady state value that is equal to its surroundings? Are you proposing a resonance between different cycles of say, seasonal/orbital point, rotation, and lunar orbit due to tidal heating?

  17. Roger Clague says:

    oldbrew says:
    February 15, 2018 at 9:32 am


    From the graph shown the temperature gradients are

    Bottom of upper mantle 1900K/660km = 2.9K/km
    Bottom of lower mantle 3000K/2900km = 10.3K/km
    Bottom of outer core 5000K/5150km = 9.7K/km
    inner core 7000K/6370km = 10.9K/km

    Not 25 -30C/km as is claimed in the text.

    Looks closer to atmosphere lapse rate of 6K/km

    Thus supporting gravity as cause of temperature gradient above and below surface.

  18. oldbrew says:

    it is about 25–30 °C/km (28–34 °F/mi) of depth

    That doesn’t look right either :/
    ~Same F per mile as C per km?

  19. oldbrew says:

    You might think that this would imply that the atmosphere is isothermal. However, this is not the case because of the final important property of air: i.e., it is a very poor conductor of heat.

    Bzzt! Venus is 95% ‘radiative’ CO2 but it still isn’t isothermal.
    7.72/ 1.176 (V/E solar input ratio) = ~6.56 = Earth lapse rate.

  20. Frank Davis says:

    An afterthought I had last night about the Younger Dryas.

  21. Frank Davis says:

    @the Badger

    Lots of questions!

    In brief, I’ve just assumed that the temperature at the centre of the Earth actually is what it is said to be – about 6000K give or take a thousand or two. And so that was the initial temperature I gave my asteroid. And I also gave it the physical characteristics of granite – density, conductivity, specific heat, etc. And I cooled radiatively to deep space, which I assumed to be at 0K, Absolute Zero, using the Stefan-Boltzmann radiation law. And then watched it cool over the next few million years using time steps of 10 years or so.

    As for the source of the heat in the Earth’s core, I have no hypothesis. However, a month or so back, I was looking at “dirty snowball” asteroids/comets with radioactive rock as the dirt. I got the radioactive rock to melt the ice, and precipitate to the centre of the asteroid to form a rock core, with a warm sea above it and ice above that. It was via that model that I ended up thinking about terrestrial ice ages, and adapted my asteroid model accordingly.

    I don’t have an age for the Earth.

    Not heard of Loschmidt.

    Yes, I could adapt my model to have a continuous supply of energy in the core. In fact, it’s already got radioactive granite rock that are doing that, but not at the core.

  22. oldbrew says:

    Radioactivity can’t make a planet spin. All bodies in the universe spin, maybe the universe itself too 😉


  23. Frank Davis says:

    @dscott (assuming his questions were addressed to me)

    I know that small bodies have larger surface area to volume ratio. It’s why they cool more quickly. But I was looking for an asteroid that was neither to big nor too small, and I plumped for 100 km diameter. I haven’t looked at what happens with different diameters.

    And my model is of a single square metre on its surface, and a set of layers all the way down to the centre, gradually diminishing in size, so it’s like a very long thin carrot.

    As for the “oscillating effect”, I presume you mean the oscillation between ice age and interglacial. The cause of this is the variation of insulation on the surface due to the ice. When there’s an insulating layer of ice, there’s a small heat flow, and the underlying rock temperature rises. When there’s no insulation, there’s a large heat flow, and the rock temperature falls.

    And my asteroid has no sun, no moon, no ratation, and no seasons.

  24. gregole says:

    Posted this on Frank’s blog:

    Found you through Tallbloke. Thanks Tallbloke!

    Interesting theory and I am underwhelmed by the refutation you posted; that a relatively thin layer of rock somehow perfectly insulates us from temperatures exceeding the surface of the sun. Really, Because it needs to be a perfect insulator to absolutely shield / insulate. Clearly it is not; in fact, it’s porous enough to permit volcanic eruption, so there is some heat-transfer from core to surface.

    The question is: how much? And I would venture that we do not know; and further that we are not actively seeking to understand said heat flow by measurement as far as I know. But I’m not an earth scientist (I’m a mechanical engineer) so I don’t keep up on this sort of thing except on blogs and by self-directed study.

    Another conjecture I have studied is that ENSO is caused by undersea ring-of fire volcanism. http://www.plateclimatology.com/further-proof-el-nios-are-fueled-by-deepsea-geological-heat-flow/
    Have you thought about this?

    And speaking of modeling heat-transfer from core to surface, and considering a building insulation problem by analogy, wouldn’t it be similar to a building with highly insulated walls, slightly less insulated windows, and cracks under doors? Think plate tectonics.

    This is why I am underwhelmed by the refutation(s) to earth core temperature to surface heat-transfer. Sure, at the center of a tectonic plate, insulation may approach infinity, but what about sub-sea plate-boundary cracks making direct contact to sea-water; itself a powerful heat conductor? “

  25. p.g.sharrow says:

    Frank; Good K.I.S.S. start to understanding the basics of the problem of Ice Age cycling.
    The Great Ice Mountains were built from the top down and melted from the bottom up. The large “Change of State” requirements of water and it’s fairly good energy conductivity means that changes happen in bulk after a period of buildup of energy…pg

  26. oldbrew says:

    Volcano suppression by ice cover

    Researchers have found that glacial erosion and melting ice caps both played a key role in driving the observed global increase in volcanic activity at the end of the last ice age.
    . . .
    A typical ice age lasting 100,000 years can be characterised into periods of advancing and retreating ice – the ice grows for 80,000 years, but it only takes 20,000 years for that ice to melt.

    “There are several factors that contribute to climate warming and cooling trends, and many of them are related to the Earth’s orbital parameters,” said Sternai. “But we know that much faster warming that cooling can’t be caused solely by changes in the Earth’s orbit – it must be, at least to some extent, related to something within the Earth system itself. Erosion, by contributing to unload the Earth’s surface and enhance volcanic CO2 emissions, may be the missing factor required to explain such persistent climate asymmetry.” [bold added]


    Pietro Sternai et al. ‘Deglaciation and glacial erosion: a joint control on magma productivity by continental unloading.’ Geophysical Research Letters (2016). DOI: 10.1002/2015GL067285

  27. gallopingcamel says:

    “Bzzt! Venus is 95% ‘radiative’ CO2 but it still isn’t isothermal.”

    Yes! The fact that CO2 is the dominant component of the Venusian atmosphere explains why the stratospheric lapse rate is anomalous. Venus is the only body in the solar system that does not have a positive stratospheric lapse rate.

    Regardless of the composition a body’s atmosphere the tropopause is located wherever the atmospheric pressure is 0.1 to 0.2 bars. At higher pressures the lapse rate is always negative in what we call the troposphere. This is what is observed on all seven bodies in our solar system with dense atmospheres.

    Is there a theory or model that explains this? There is and it is based on heat transfer equations applied to mixed gases:

    Click to access Robinson2014_0.1bar_Tropopause.pdf

    This NatGeo letter contains enough detail to enable an amateur (e.g. this camel) to reproduce the Robinson & Catling model:

    I was stunned how well the R&C model worked in spite of its relative simplicity. It has only one “Down” radiative channel and two “Up” channels. You can run the model on your laptop so you don’t have to take my work for it.

    The idea that CO2 causes “Radiative Forcing” at the surface of a planet is total BS given that collision broadening ensures that tropospheres are essentially opaque to thermal radiation. Thus radiation works just like convection in the troposphere. The energy that is radiated into space comes from the TOA (Top Of the Atmosphere) that is at a lower temperature than anywhere in the troposphere.

  28. Richard111 says:

    Thank you GC, best comment so far.

  29. oldbrew says:

    GC – yes, the trace gas theorists ignore atmospheric pressure which aligns with temperature.

    In the lapse rate graphic above, Venus at 1 bar a.p. is about 340-350K
    Earth surface (1 bar) @ 288K * 1.176 (4th root of V:E solar irradiation ratio) = 338.7K

    Surely not a coincidence?

  30. […] quite a strong response from the climate (sceptic) community for my Theory Of Ice Ages. Tallbloke reblogged my post on his […]

  31. Frank Davis says:

    Anyone who wants to look at heat flow really needs to have a heat flow simulation model. If you can’t do it digitally, you can always do it electrically or hydraulically. I’ve sketched out how today on my blog.

  32. dscott says:

    Frank As for the “oscillating effect”, I presume you mean the oscillation between ice age and interglacial. The cause of this is the variation of insulation on the surface due to the ice. When there’s an insulating layer of ice, there’s a small heat flow, and the underlying rock temperature rises. When there’s no insulation, there’s a large heat flow, and the rock temperature falls.

    So what you are saying is assuming a steady heat source with no external influences, that a system has a natural tendency to oscillate on its own based upon a feedback in this case the boundary layer insulation value changing due to change of states?

  33. Frank Davis says:


    More than that, when the ice changes state to water, I remove the water, because I assume that water is likely to flow out from under the ice in a subglacial stream. So it’s not just that the ice changes state, but also that when it changes state it ceases to provide any insulation at all.

    Of course the water might not run away, but form a lake beneath the ice which would provide some insulation. And I can model this if I want to. But it seemed to me that given that most continents are convex rather than concave, one should expect that melt water would have a definite direction in which to flow.

  34. p.g.sharrow says:

    As in melting of glass, the liquid fluxes the solid and speeds the melt by improving conductivity…pg

  35. […] Soon I had a molten ball of granite, 5,000ºK at the centre, and about 273º K (melting point of ice) at its surface. And then I steadily rained down ice on its surface (to simulate snowfall), and watched what happened. And to my astonishment, what happened was that the ice would grow in depth for a bit, and then completely melt away, over and over again. I was seeing a repeat cycle of ice ages, almost as regular as clockwork. I wrote about in A Theory Of Ice Ages a week or two back. It got reblogged on the climate sceptical Tallbloke’s Talkshop. […]