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 to try to build my own simple atmospheric simulation models. Regular readers will have noticed my periodic occasional unsuccessful attempts (for instance here). The trouble is that I simply don’t know enough about atmospheric physics to do it.
But I keep going back to have another try. And over the past month or so I’ve been thinking not so much about the atmosphere (which I don’t know how to model) but the Earth beneath the atmosphere (which is much easier to model, because it’s all conductive heat flow of a kind with which I was very familiar in my university days).
And I was thinking about ice ages. We’re currently living in a warm interglacial period, at the end of an ice age which lasted about 100,000 years. Our current interglacial has only lasted for 12,000 years, during which time us humans have emerged from a Stone Age into a Bronze Age and an Iron Age. And since the last interglacial, 100,000 years ago, only lasted for 10 – 15,000 years before the ice returned, many people believe that our own interglacial is due to come to an end sometime soon. Others think that it could last for another 30,000 years or more. And of course Global Warming alarmists are far more worried about global warming than global cooling. But it’s always seemed to me that we should be much more worried in the long term about the return of an ice age than any temporary warming that may be happening.
And a few weeks ago I had an idea about how the Earth might alternate between ice ages and interglacials. It was a very simple idea, and one that anyone will be able to understand. Here it is:
During an ice age, when the Earth is covered in ice which may be 3 – 4 km deep, the ice acts as a layer of insulation on the surface of the Earth. And because the Earth has a hot core, from which heat is flowing out through the surface, the effect of this layer of insulation is to warm the rock underlying the ice sheets. And so the temperature of the underlying rock gradually rises. And it keeps on rising, and begins to melt the ice at the very bottom of the ice sheet. And eventually the hot rock under the ice completely melts all the ice. And when the hot rock meets the atmosphere, it warms the atmosphere, and begins to itself cool down. Eventually (and in fact quite rapidly) the rock cools back down to its original temperature. And then the snow and ice falling on it stops melting, and remains freezing, and a new layer of ice starts growing. In this manner the cycle repeats itself, again and again and again.
Very simple. Almost too simple. Think of the ice as a garment that the Earth dons and gets warmer, and then takes off and gets colder.
But would it work? I set out to build a heat flow simulation model of it. To simplify things, I constructed a little 50 km radius asteroid made of granite at 5000ºK (somewhere around the temperature of the core of the Earth), and allowed the heat stored in it to radiate away into space from its hot surface. Over several million years, the surface of the asteroid gradually fell until it was near the temperature where ice melts, 273ºK (0ºC).
And then I started to drop a steady rain of lumps of ice onto its surface.
Initially the ice melted very quickly. But as the asteroid continued to cool, it took longer and longer for the ice to melt. And finally, after it had cooled down enough, the asteroid remained covered in a steadily deepening layer of ice, which was melting at its base where it was in contact with the still-warm asteroid below, while further layers of ice were being added at the top.
But the really interesting thing was what happened during the period when the asteroid was neither too hot (and quickly melted the ice falling on it) nor too cold (and didn’t melt the ice at all). For during this period I found that the ice would build up for a while, and then melt away completely. And during the times when it was covered in ice, the surface of the asteroid would warm up, and during the periods when there was no ice the surface of the asteroid would cool down. Here’s a plot of the almost thermostatic cycling of the asteroid rock surface temperature (T1 red) and the outer radiating surface temperature (Ts white), and ice thickness (ice green). 40 years ago I was looking at oscilloscopes showing exactly these sorts of growth and decay curves every day.
In this manner I watched a succession of ice ages alternating with interglacial periods. And as the asteroid cooled, the ice ages got longer and longer, and the interglacials shorter and shorter, until finally the ice age never ended.
And this, more or less, is what has also been happening on the surface of the Earth for the past several million years. There have been a succession of ice ages, with the duration of the ice ages gradually getting longer and longer. Currently they seem to last about 100,000 years, but before that they lasted about 40,000 years, and before that they were even shorter. So maybe the exact same thing is happening with the Earth as happened with my asteroid.
But the other interesting thing is that my asteroid had no atmosphere above its surface (because I don’t know how to model atmospheres). And it had no sunlight falling on it either. It was just a bare rock radiating heat into space. Yet despite that, there was still a long succession of ice ages with interglacials between them. The ice ages on my little asteroid happened completely independently of any atmosphere or sun. And so maybe terrestrial ice ages are independent of sun and atmosphere as well? Or very nearly completely independent.
But the oddest thing of all is that I have never heard of this particular theory of ice ages. It simply doesn’t seem to exist in the literature at all. Wikipedia’s Ice age has no mention of anything like it. It gives:
6 Causes of ice ages
6.1 Changes in Earth’s atmosphere
6.1.1 Human-induced changes
6.2 Position of the continents
6.3 Fluctuations in ocean currents
6.4 Uplift of the Tibetan plateau and surrounding mountain areas above the snowline
6.5 Variations in Earth’s orbit (Milankovitch cycles)
6.6 Variations in the Sun’s energy output
6.7 Volcanism
It seems that climate scientists haven’t been considering heat flow from inside the Earth at all. Or rather, they’ve been dismissing it as unimportant, as I found one academic doing:
Although there is nothing wrong with the statement that the Earth is truly very hot at its center (actually as hot as the surface of the sun) the notion that it is a significant source of heat at the surface is easily dismissed with a little critical thinking. If the inner heat were really the dominant factor, then surely the day-night cycle would not be what it is, nor would you expect such variation in climates over seasons and latitudes. How can the south pole be covered with thousands of meters of ice with all this heat supposedly bubbling up from the surface? Why would a little lower angle of sunlight cause the average temperature to drop from +20°C in the summer to -20°C in the winter?
The fact of the matter is, solid rock is an extremely good insulator and the heat from the mantle propagates up very slowly and diminishes very quickly (at about 20°C/km) to almost nothing by the time it is at the surface. At the surface, the earth is releasing less than one-tenth of one Watt/m2. If you could somehow capture all of the energy coming up from the earth’s core into the foundation of an average-sized home, you might have enough to power one 15W light bulb! Not a lot of of juice when you compare it to the sun, which provides on average some 342W/m2 of energy to the earth’s surface.
Well, he’s quite right that the present heat flow from inside the Earth is only about 0.1 watts/square metre. But this heat flow isn’t a constant, and we’re looking at the heat flow 12,000 years after the beginning of our present interglacial, when we should have expected to see hot rocks cooling, and heat flow diminishing.
Anyway, I’m now planning to scale up my asteroid to the size of the Earth, and add some sort of simple atmosphere on its surface (no idea how), and some sunshine as well, and see what happens then. Maybe I’ll find that the ice is melted by all the sun and CO2 and stuff in the atmosphere above. But at the moment I think it’s going to carry on being the Earth beneath the ice that will melt the ice, as it warms and cools.
Frank Davis 
Fascinating!
Thanks for sharing…
Reblogged this on Tallbloke's Talkshop and commented:
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Some blue-ice thinking from Frank Davis. We like open, out of the box discussions about the cause of ice agaes at the talkshop. This is as good a starter for 10 as any.
Great!
Frank ==> Very pragmatic — thus intriguing. The internal heat of the planet is not insignificant and is, indeed, and endless [almost] source of energy — for the climate and for Mankind, once we figure out how to safely tap it.
Look forward to your more comlete model.
My results need to be replicated by someone else. So I’m hoping that someone else is intrigued enough to build their own dynamic heat flow model. And as I said in the post, I don’t know how to model and atmosphere. So my model of the Earth is likely to be a pretty bad one.
Don’t worry, there aren’t too many good ones ;-)
Very interesting and well done Frank.
Sadly your very first reply here (my results need to be replicated by someone) is anathema to our global warming practitioners.
It has and never will happen in case their doomsday predictions are disproved.
Ummm, your model results in a’snowball Earth’; not, the Northern hemisphere glaciation that has occurred.
‘Snowball Earth’ has rarely occurred and, to my knowledge, South Africa or South America have never had massive glaciation.
Maybe oceans have something to do with that?
Well, since the Earth is gradually cooling down, I wouldn’t be too surprised if we end up with a snowball Earth.
But anyway, my model was just of an asteroid, with no atmosphere or sun. I have yet to try to model an Earth with both of those. And I may never be able to do so, because I simply don’t know how to model an atmosphere.
Both the sun and the atmosphere are going to have a huge influence on your results.
Since you don’t know how to model an atmosphere, could you not, as an interim measure, represent the atmosphere simply as a layer of insulation? How you would calculate the degree of insulation I have no idea, not being of a scientific bent, but there must be some way of estimating a figure. And the sun would just be a heat source following a predictable path.
My asteroid has a very cold surface. It hovers around 100 degrees K. The Earth’s atmosphere, down at the bottom, at least, is more like 273 degrees K. So there’ll be a smaller heat flow. And the solar heat gain from the Sun is pushing it higher. So it will have a big effect.
Yes, I could model the atmosphere as another layer of insulation, because that’s effectively what it is. But most of the heat exchanges in the atmosphere are radiative rather than conductive, and that’s where I usually end up going round and round in circles. It’s all nice and simple below the Earth’s surface, and completely crazy above it (to me at least).
There is evidence of glaciers in Australia, particularly in Tasmania where the age is relatively recent (eg Hartz Mountain not far from Hobart and Cradle Mt). There are three glaciers existing in New Zealand ( I have walked on the Franz Joseph glacier on the west of the south island and seen the one on Mt Cook) and evidence of many more. There are existing glaciers in South America. I am sure there is evidence of past glaciers in South Africa. There are of course glaciers in Antarctica.
Frank, I am not surprised that climate scientists won’t look at this because of two reasons.
1) it goes against their ‘CO2 is bad’ mantra.
2) it is the correct use of models and can be validated, something their climate models will never be able to do.
I could add a third reason, you have looked at it as an engineering problem while they look at it as an ideological problem and engineering wins every time in the real world.
I suspect that there may be a much simpler reason why climate scientists may not have seen this (if indeed they haven’t seen it , and if indeed I have), and it is that they mostly think in terms of equilibrium steady states. Take the article by the academic that I quoted in my post: the author regarded the Earth as being in a steady state, steadily losing a completely inconsequential 0.1 W/m^2 from its surface. And what’s to worry about with 0.1 W/m^2? It’s next to nothing.
But back in my university days I was using a dynamic heat flow model in which you could watch walls and rooms warming up and cooling down. And a slightly different picture emerges when you do things that way. And you really have to look at the Earth’s dynamic behaviour if you’re going to see anything other than an equilibrium steady state 0.1 W/m^2 the whole time.
It’s like someone looking at a flat calm sea one day, and supposing that it’s always going to be a flat calm sea, and always has been.
Yes, maybe they’re ideologues as well. They certainly seem to be. Maybe ideologues are all steady state thinkers?
Interesting but why are we in an geological** Ice Age? We have had geological Ice Ages before, pre-Cambrian, end Ordovician, end Carboniferous and a short sharp one in the Early Triassic, although the last followed a massive volcanic flow in Siberia. Also the sun is a variable star and might vary as much as 4% in its output – based on astronomers observations of other mainline stars output.
Your model could explain the varying length of ice ages in the last million years, indeed might be extendible further back for a few million years, and certainly appears better than the Milankovitch cycles idea so popular with academics.
If rock is an slowly warming insulator then the atmosphere is a faster warming insulator with heat input from the sun, but also from volcanic heat from the interior. There have been massive lava flows in the past – the Siberian and Deccan traps etc. although the claim is that they are initiated by asteroid impact – and the atmosphere surely distributed the heat outflow perhaps warming the surface rock a little. On top of that there are the oceans which are warmed by the sunn and by subterranean heat. There are thousands of hot vents in the Pacific alone. The more I look at it the more complicated it becomes.
**geological Ice Age roughly 35 million years, when there is a permanent ice sheet at one or both poles.
why are we in an geological** Ice Age?
Good question. And I’ve puzzled over it myself. The Mesozoic era, a bit over 65 million years ago, was a very warm era. But the Cenozoic era that followed it, and in which we live, seems to have just been getting colder and colder. Why?
And could my theory explain ice ages many millions of years ago? I haven’t tried to apply it to such long periods of time, but what’s happening on my asteroid is that there are periods of low heat flow from it during glaciations, and high heat flows during interglacials. So there’s a sort of slow chugging heat loss rather than a steady heat loss. And maybe exact same thing could happen at 100 million year intervals rather than the 10,000 year intervals on my asteroid. It may be that a very long and deep ice age (e.g. Permian) resulted in higher heat flow from the Earth over the next few million years, not just the next few thousand years. There could be cycles overlaid on cycles. After all the diurnal and annual cyclicity of the Earth’s atmosphere is also being overlaid on any other cycles there might be.
But I’m just guessing. You’d have to build dynamic heat flow models to study it. And you might also need a computer that’s a bit more powerful than my PC.
You forgot to add into your qualifers the factors, non circularl orbit, non circular sun, and eight maybe nine planets, but, otherwise a good logic experiment.
For a geologist’s view please read my post:
Do geologists build dynamic heat flow models? Because if they don’t, I think they ought to.
Frank Davis, nice job! In the end, the whole thing is a thermodynamics problem anyway – heat sources, heat sinks, resistances, and good old entropy. Zeller and Nikolov along with Scafetta have all gone a long way to explaining some the heat sources and variability. Take a look at their papers I think you may find them helpful in adding more flows in your model.
Hallo Frank
Are you by chance the Frank I have/had a discussion with in the Ideal Gases thread on WUWT?
About you’re Ice Age ideas, imo you’re on the right track.
Will be back later.
Probably not. I’m not that big on ideal gases, and can’t imagine arguing about them.
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Frank,
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?
Frank; nice job of modeling, You have given us a good demonstration of logical science from a practical viewpoint. Your little asteroid is a good proxy for continental surface. The deep soil temperature here is 54F and gets warmer as you go deeper. Even in Alaska where it is is covered with permafrost it is over 100F a thousand feet down.
The Great Ice Mountains were built from the top down and melted from the bottom up. As a person that spent many years in frigid areas I can attest to this. The key to the melt off from the land is from below. Now add the key to the increase in snow fall is from below in the deep Oceans, where rising energy Increase surface temperatures cause increased evaporation and heavier winter snows as the atmosphere cools over the land.
Water’s large “change of state” energy demands, causes build up of energy bulk before the change happens. High conductivity in it means the bulk approaches the change, in mass, so a lot changes when the threshold is reached.
As to atmospheric energy flows, the lowest 30,000feet is mostly conductive, so it could be modeled as insulation. The Real Green House gases Oxygen&Nitrogen are insulators.
The refrigeration effect of the water, working fluid, is the main transfer mechanism for energy from the surface to the higher atmosphere where it is radiated into space.
You are correct, the key to Ice age cycling is from below. Lots of moving parts here but your point is the place to start in a real understanding of climate change. At least from an engineers point og view…pg
The biggest problem with this hypothesis is that eras of glaciation only make up a small portion of Earth’s history. If bottom up warming of land areas is the mechanism for glacial cycling why was there no glaciation during most of geologic time?
My rock surface temperature graph isn’t a sawtooth. But the ice depth one is a ctually quite near a sawtooth. Remember that I don’t have an atmosphere on my asteroid.
Interesting. The naysayers about “global” ice ages seem to forget that the majority of the Northern Hemisphere is land whereas the majority of the Suthern Hemisphere is ocean. Heat flow through solids is very different to heat flow through water.
The problem is that the temperature graph shown isn’t anywhere near as sawtooth as the temperatures derived from ice cores.
Your model has the rate of change in the glacial/interglacial cycle inverted. The planet warmed rapidly and cooled slowly.
Ben Wouters says: February 15, 2018 at 10:45 am
As promised.
I like your ideas about the heat flows through Earths crust, and how they can be restricted, causing the temperature of the crust to increase. I’m convinced that here we’ll find the answer to why the GAT (Global Average Temperature) on Earth is >90K higher than on our moon. Obviously the atmosphere plays a role, but not a warming one.
I think I can explain things like the Faint Young Sun Paradox, why Earth has been going in and out of Ice ages, how glacials develop slowly and end quickly etc.
I need to discuss these ideas with someone who actually understands heat flows.
Hope you are willing to have a look.
Also posted on Tallblokes:
and
After posting I calculated the energy content of 1 million km^3 magma as enough to warm ALL ocean water 1K.
One thing I like to know the answer to is:
how long does it take for the oceanic crust ( say 10 km thick) to increase 1k in temperature when the flux of ~100 mW/m^2 is blocked by eg warmer deep ocean water.
From the Engineering Toolbox, the specific heat of granite is 790 J/Kg degree K. That means that it requires 790 Joules of heat to raise a kilogram of granite by 1 degree K
Granite has a density of 2650 kg/m3, So the mass of 1 square metre of granite 10000 metres high will be 2650 * 10000.kg. And the amount of heat required to raise it by 1 degree K will be 2650 * 10000 * 790 Joules.
A Watt is a heat flow of 1 Joule/second. So to find the time it takes for a heat flow of 100 watts to raise 10 km of granite by 1 degree K you must divide the heat required by 100.
So the answer to your question is:
It takes (2650 * 10000 * 790) / 100 seconds.
Ok. Thanks.
The geothermal flux is more like 100 mW/m^2. (0,1 W/m^2).
What I’m unsure about is:
the flux is ‘running’ since there is a temperature difference over the 10 km crust.
Assuming the ocean floor to be 273K, what is the temperature below the 10 km crust to maintain this flux, and can you just assume that the entire crust is evenly warmed by this flux? Shouldn’t thermal resistivity be taken into account?
How does increasing the temperature of the deep ocean water with eg 1K influence this process?
The conductive heat flow rate Q through a material with thermal conductivity k, and thickness d and area a and a temperature difference T1 – T2 across it Is given by
Q = k.A.(T1 – T2) / d Watts
i.e. it increases with increasing conductivity and area and temperature difference, and decreases with increasing depth.
The thermal conductivities of the main minerals of granite are in the range of 1.6 to 7.7 W/mK at room temperature (source)
If we take k to be 3.0 W/m degK, then area a is 1 squ metre and depth d is 10000 m And we know T2 is 273, and the heat flow rate is 100mW or 0.1 W
So the above equation becomes
0.1 = 3.0 ( T1 – 273 ) / 10000
and so T1 = ( 0.1 , 10000 / 3.0 ) + 273. And that’s the temperature at a depth of 10 km.
In an equilibrium state, there’ll be a constant decrease in the temperature of the 10 km of rock of T1/10000 degrees K / m
When the ocean water rises by 1 degree K, the above equation will need to have 273 replaced by 274 to find the heat flow rate.
However, when you start changing temperatures you get into a non-equilibrium condition, and that’s when it becomes important to be able to dynamically model it as a process in time.
And to do that you need to build up a set of layers of rock, and calculate the amount of heat that flows between the various layers at short intervals of time. So if you know the heat flow rate Q Watts from one layer to another, then you know that over a short period of time DT, there will be Q.DT Joules of heat gained (or lost), and knowing the specific heat of the the materials, you can then find by how much the temperature has risen (or fallen), and adjust it accordingly. And you do this repeatedly over many small intervals of time, watching the temperatures all gradually changing.
And that’s why you need a simulation model to carry out all these many calculations. And I use a simulation model with hundreds of layers of different materials,and using time steps of about a day in duration.
I think I may write a little heat flow simulation model in Basic or something to show exactly how it’s done.
Would be relevant to see how the release of 100 million km^3 magma into the oceans possibly blocks the geothermal flux through the crust.
Are you able to program computers?
If you are, I’ll be happy to write some code for you to see how, in principle, heat flow can be modelled.
I’d like to help out a bit, but I don’t want to get involved with your project. I have other things to do.
Something like this might be useful for you:
http://energy.concord.org/energy2d/
It seems to be a convection and conduction and radiation heat flow simulation model.
Even better might be https://www.simscale.com/ which seems to offer free cloud-based simulations of a variety of processes, including heat flow.
Frank Davis says: February 19, 2018 at 4:42 pm
It’s not really a project. I’ve just uncovered the reason for our GAT being >90K higher than that of the moon. This also means no GHE and no role for CO2 in the climate.
Regarding your ideas about ice ages this may be relevant:
https://en.wikipedia.org/wiki/Geothermal_gradient#Variations
especially the part about cold spots originating in the Pleistocene.
Ah! So you’re not trying to construct a heat flow model. I seem to have misunderstood you. Perhaps you might explain again.
Frank Davis says: February 22, 2018 at 11:42 am
No. I’m looking for an indication of how fast the small geothermal flux can change the temperature of the crust when the surface temperature changes. The cold spots I linked to indicate that after >10.000 years the effect of a glacial is still apparent.
These cold spots also mean that on a solar heated planet your idea for the surface becoming warmer under the ice doesn’t seem to work.
Imo it DOES work for our oceans.
On WUWT I had a few exchanges with W. Eschenbach, ao on this subject.
Search on my name for my posts (17 posts in this thread) to see the nonsense that is going around about geothermal.
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I read something a little like your idea 20-odd years ago. The basic premise was that to get that much land based ice/snow demanded a huge investment of energy in evaporating seawater. The hypothesis was that the Arctic ocean was ice free and that the gulf stream/ nad carried the waters, now keeping nw europe warmer than Vladivostok, into the arctic. So the Alps recieved more snow every winter than melted in summer, as did Norway, the colder it got the more that accelerated. Beringia was intact so the coastal mountains of west N. America were similar. Siberia’s western plain was an extension of the arctic and was connected to the Caspian by a river outflow. Greenland was ice free, apart from it’s mountains, and enjoyed a maritime climate more like an English springtime, but year round. The clash of Arctic waters and tropical waters took place much as they do now in the Labrrador sea, and points south. There was a single cell of atmospheric circulation,[N.H.] with local quirks, so the evaporation taking place here settled out in Quebec, more settled than melted until the ice sheet caused it’s own weather system. Eventually, as sea levels dropped, only Fram connected the arctic to the rest of the world ocean, some catastrophy caused the Arctic ocean to freeze over and the melt began.
If you check wiki for the deepest drill hole [Kola peninsular] they were surprised how warm it was, and how much water was present. I’ve no idea where to start with the math but the geothermal gradient from that depth would seem to suggest a rather sudden event created the permafrost, and entombed the mammoths.
Sounds a lot more complex than my theory. From Wikipedia:
The hole reached 12,262 m (40,230 ft) in 1989. In that year, the hole depth was expected to reach 13,500 m (44,300 ft) by the end of 1990 and 15,000 m (49,000 ft) by 1993.[6][7] However, because of higher-than-expected temperatures at this depth and location—180 °C (356 °F) instead of the expected 100 °C (212 °F)—drilling deeper was deemed unfeasible and the drilling was stopped in 1992.[5] With the projected further increase in temperature with increasing depth, drilling to 15,000 m (49,000 ft) would have meant working at a temperature of 300 °C (570 °F), at which the drill bit would no longer work.[
Not so different, if in your model the water disappears as vapour, cools at the top of the atmosphere and eventually falls as snow/hail, at -40deg. rapidly cooling the rocks again.
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You are one highly intelligent dude x
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