Ice Ages - Geothermal energy is the driver

Abstract Ice and other cores show that Ice Ages had periods initially of 40k years, later becoming 100k. Explanations have involved very small changes in sunlight from the Earth's orbit every 41k years, and even smaller changes in 90 - 120k. It is not seen how these produce such large Polar changes, especially with the switch to the much smaller 90 - 120k year periods. It is known that geothermal heat melts the ice at the bottom of deep ice sheets. Calculations show that this heat is sufficient to melt the bulk of water released in an Ice Age Cycle, and its escape is the driver for the Polar Caps' rapid retreat.

1. Introduction

Ice Ages had c 40k year periods 2m years ago, becoming c 100k 1m years ago (Ref 1). Snowfall causes the Polar Caps to spread outwards, reflecting more of the Sun's heat and lowering global temperatures. Geothermal energy melts the Polar Caps from the bottom up. This current geothermal energy flow is enough to melt the bulk of the ice released in the 100k year period. Global temperature rises for 10k years, while the Polar Caps retreat increasingly fast and suddenly stop (Ref 2). These are shown to be caused by under ice melt fronts meeting the Polar Caps' edges, draining out rapidly, speeding up outflows of ice, so Caps thin, fracture, and break up at their edges. Less Polar sunlight is reflected from smaller Caps - increasing global temperatures. Recent findings that there had been liquid water under the Central S Polar Cap but since frozen onto the bottom of the ice sheet (Ref 3) provides values for the blanketing thickness of ice needed for bottom of ice melting, and illustrates the processes when the thinning of the ice breaches this blanketing thickness. So the outflow of ice is reduced to a minimum - and snowfall over the Pole must re-build the S Polar Cap's height before outflow pushes the S Polar Cap outwards again.

A recent review of the Ice Ages leaves doubt on the processes involved (Ref 4). For 150 years explanations sought from slight changes in the Earth's orbit, one with period of 41k years, and far smaller ones with 95k and 125k years. While these periods are seen in Ice Age cores it is not understood why there is a switch to the far weaker longer periods. The Polar Caps near halve their area, and reduce their thickness, which are not understood from the very small sunlight changes. Nor is the saw-tooth waveform of the temperature changes understood, with rapid rises and slow falls in temperature. The abrupt changes from rise to fall and then rise again suggests Catastrophes are involved.

Air carbon dioxide content follows temperature. This is explained as water being able to dissolve less at higher temperatures, so it boils off from the oceans. Maximum temperature in this cycle seems to have been 8 - 12k years ago, with the S Pole being a little earlier (Ref 5).

We live on a molten ball of iron at 5k° K. Radiation from the earth's surface to space enables us to inhabit a cool spot. Radiation also occurs from the atmosphere by rotational spectra from gas molecules, with conduction and convection from the surface - causing temperatures to fall with height to 15km. Minimum is 200° K at 100km height. Thereafter the sun's atmosphere starts to take over. The flow of heat from the Earth's interior is c 1/10 watt per sq m near the Earth's surface.

The S Polar Cap has ice commonly 4 - 8km thick (Ref 6). Winter snow is always more than any summer melt which is effectively zero. This accumulation moves outwards as a glacier at a few m a year at the surface, eventually breaking off at the edges of the Cap, often melting at lower latitudes. The oldest ice is less than 1 million years. Water lakes are found at the rock - ice interface. The blanketing effect of the thick ice causes the rock surface to warm up and melt the ice. This causes glaciers at this interface to move at several km a year.

The build-up of snow increases a Cap's height from the minimum of the last cycle, causing the Cap to expand outwards, lowering temperatures by both more sunlight reflected and increased height. Eventually the edge of the Cap reaches a milder latitude where natural melting matches the outflow of ice - an Equilibrium. Meanwhile under ice lakes have grown apace due to the blanketing of the thickening ice.

The Panel shows that the Earth's geothermal heat over the extent of the N Polar Cap can melt the water released in the last Ice Age from the Cap in 78k years.

2. Catastrophe One

Catastrophe 1 occurs as the minimum temperature and maximum advance of the Caps are approached, the bulk of the water to be released in that cycle is melted under the Caps. The main place where this melt will come to the surface is the edge of the Caps. It will be the last place the melt front will reach, aided by the Caps becoming stationary at Equilibrium. Once started, the melt water will leak out rapidly, as the melt front reaches various places round the Caps' edges.

Under-ice flows of water away from the Poles will speed up the under ice glaciers from a few Km pa seen today. When a significant volume of water has leaked out subsidence will occur, fracturing the ice. Water under pressure may come up through them, flowing along the surface, speeding up the surface outflow of ice as well. These increased ice movements away from the poles will thin the Caps, reducing their thickness and height. Fracturing of the ice will increase ice burgs breaking off at the edges to melt at lower latitudes. The Polar Caps are in retreat, reflective snow removed, temperatures rise, causing the Equilibrium to move nearer the Poles - aiding more melt fronts to meet the Caps' edges. It is understandable that the rate of retreat accelerates as in Ref 2.

3. Catastrophe Two

Catastrophe 2 is when most of the melt water has leaked out. This can be expected to be sudden in a particular location, resulting in the abrupt halt of the retreat, as seen in Ref 2. This will be repeated round the Caps. Most of the forces fracturing the ice, encouraging its movement away from the Poles and thinning it come to an end. Temperature rise comes to an end. Ground that has been buried under ice for a long time has been warmed up by tens of degrees by the blanketing to a considerable depth can now cool by radiation to its natural temperature, contributing to a fall in global temperature. Such a fall has been seen since the abrupt halt of the retreat (from 1 above).

One would not expect the advance of the Caps to occur at maximum temperature. The record has been, after the sudden halt near maximum temperature, for a slow retreat of the Caps for the past 8.5k years (Ref 2). Snowfall at the Poles continues throughout, but at maximum temperature the Cap's thickness and height will be much reduced. Outflow of ice will be a function of the Cap's height, and this must be built up again before a combination of temperature and outflow starts another advance of the Caps.

Antarctica's high interior glacier has formally liquid water frozen onto the bottom of the regular ice sheet (Ref 3). The glacier flow moves ground melt water to sites where the blanketing thickness of ice is insufficient and this water freezes. This area has blanketing ice of 2,400 – 3000m, and indicates today the threshold of blanketing ice needed for the ice to melt at the rock surface in the central Polar region. Here is another mechanism contributing to Catastrophe 2 – when the thinning of the ice (within Catastrophe 1) breaches this blanketing threshold. Then new melt ceases, melt which has not leaked out will start to freeze, more sites will have no water interface, and the glacier bottom flow will slow from kms to meters pa.

4. Solar orbit modulation

If two oscillating systems happen to have similar periods they commonly can latch onto each other. Refs 1 & 4 indicate evidence that Ice Age periods have latched onto several weak orbital effects on sunlight. But it is not these weak sunlight changes that are driving the Ice Ages. Ref 4 gives theories that at the end of the cooling period somehow the edges of the Polar Caps become very sensitive to changes in sunlight. Catastrophe 1 indicates that indeed they do. At Equilibrium the Cap's edges are waiting for the under ice melt front to catch up. Blanketing here will be small, so geothermal energy may have little effect - it may take a chance fluctuation to break the rock/ice seal. A slight orbital rise in sunlight will push the above Equilibrium towards the Pole - and break the ice seal in many places, and start the leak-out in earnest.

The Ice Age period is controlled by the time it takes for the snow to re-build the height of the Poles, for the edges of the Caps to move from the previous minimum to Equilibrium, to build up sufficient blanketing thickness at relevant latitudes for the bottom of the ice to melt and the Earth's internal heat flow to melt the ice released in that cycle, and for the melt front to reach Equilibrium. If the cycle starts with much smaller Polar Caps or from scratch, the period may be different or none at all for some time. If the Earth's internal heat flow was greater in the past, blanketing requirements were then less, and the period shorter. This may be the explanation for 41K year period (Ref 1), which was held until the natural Ice Age period got too far removed from it, and the weaker longer orbital periods took over. Refs 7 suggest that the current geothermal heat flow is larger than the replacement from radioactive decay within the earth. It follows that the Earth's internal temperature will have been higher in the past, so the heat flow was higher, and the Ice Age period shorter than now.

5. Discussion

The Phases of key variables over the Ice Cycle are given in Figs 1 – 4 for discussion, starting with the Temperature Change over the current 100k year cycle as the key fact. The captions suggest key issues. The Ice Height is the key driver for the Speed of Outflow of Ice, which in turn determines the Advance of the Ice, with leak-out causing the Retreat.

Fig 5 gives a simple model of the Blanketing Thickness of Ice needed for under-ice melting. From the boundary conditions mentioned in the caption, once Blanketing has occurred at the Pole it is likely that Blanketing will occur out to near the edge of the Cap, subject to local terrain.

From the Fig 4 Advance & Retreat of the Ice, where the vertical scale is assumed to be linear with latitude, a simple integration is given to see how much of the under ice melting contributes to the 120m sea level rise discussed in the Panel. For the N Cap it is assumed it starts at 80° N latitude. The integration will take 10k year intervals from 40 K years to 100k years. The Panel indicates geothermal energy will melt under ice to raise sea level by 120m in 78k years for a 50° latitude Cap. For 10k years sea will rise by 15.4m. For larger angle of latitude l the sea level rise per 10k years will be reduced by (1 – sin l)/(1 – sin 50).

For the N Cap, the advance at the last Ice Age Maximum in N America can be taken to make up for the Atlantic Ocean, while the 50 degree N Latitude runs mainly over or near land where ice can be expected to form. Then from Advance & Retreat of Ice for:
40 – 50K years – average 45k years – Ice to ~ 73° N but little Blanketing.
50 – 60k years - Ice to ~ 68° N, but little Blanketing.
60 – 70k years - Ice to ~ 60° N, Blanketing likely to occur from Height of Ice,
Sea level rise 15.4m x 0.57 = 8.8m.
70 – 80k years - Ice to ~ 53° N, Sea level rise 15.4m x 0.86 = 13.2m.
80 – 100k years – Ice to ~ 50° N, Sea level rise 2 x 15.4m = 30.8m.
0 – 10k years - Blanketing may fail, take 15.4m x 0.25 = 3.9m.
Sum sea level rise from under ice melting for N Cap = 56.7m.

For the S Cap likely to be Blanketing for 40 to 100k years for a Cap of 75° S
latitude. Sea level rise = 6 x 15.4 x 0.146 = 13.5m.
For 0 - 10k years, assume half the interval 0.5 x 15.4 x .146 = 1.1m.
Sum Sea level rise for S Cap 14.6m

Sum of likely under ice melting from the Caps is 71.3m, leaving around 49m melting by other means.

6. New glaciation form

From Fig 5, where a Pole has sufficient Blanketing Thickness of Ice for most of the Ice Age Cycle, under Ice lakes will form, with a depths (from the Panel) of about 1/3 the distance from the rock to the Blanketing Surface. The shape of this Ice – Melt Surface will be a similar bell shape as the Blanketing and Ice Surfaces.

If readers imaging this third, Ice – Melt Surface, put into Fig 5, then where we have a section from the Pole without mountain ranges blocking the Melt Lakes, we have a very different form of glaciation at Equilibrium. With the only places where the Ice is in contact with the ground being near Equilibrium, and with the figures for speed of outflow given in (1) above, remembering this is near Maximum Height and Outflow of Ice, we can expect the edges of the Caps to be pushed rapidly well beyond Equilibrium (as defined in 1 above), to a New Equilibrium where the natural melting is considerably higher in the warmer latitude.

This New Equilibrium will be unstable, for it is maintained so far from the Pole by the reduction in Ice Height (Fig 2), and after being reached will shortly start to retreat. This may be the retreat described by Holmes (Ref 2), and this mechanism may be the main reason why the Caps go so far from the Poles. During the period to reaching the New Equilibrium, more sunlight is reflected from the Caps and the Earth’s temperature accordingly fall.

Once the unstable New Equilibrium starts to retreat, these processes are reversed, global temperatures rise, together with the Caps retreating over their rapid advance, we can expect leak-out to start if it has not already or to be increased, washing ice to lower latitudes. Leak out may also start in a big way before New Equilibrium – hastening its retreat.

Surveying parts of the world where this condition may have occurred at the last Ice Age Maximum we have the plains of N America, where the Caps got to 40° latitude. Parts of Antarctica may also have complied, with the Cap pushed outwards over the sea.

7. Conclusion - Climate Change

Only 26% of Britons believe the notion that burning fuels causes significant atmospheric temperature rise. There have been dozens of Ice Ages running like clockwork. So we must assume the ice sheets 3 miles thick are likely to come down again to London, over all of Canada and to Indiana. - unless something is done to melt the Caps. The 74% of these populations are more likely to think if there is anything in these Climate Change theories we should go all out to triple the carbon dioxide atmospheric content – to match previous ice-free worlds (Ref 8). Fig 4 enables a more informed debate of how long we have got to achieve this - for once the ice sheets start to roll outwards again we may be powerless to stop them. Indeed a little known fact is that the Winter extent of the S Polar Cap has been growing since records began in 1979. On 15 September 2014 it broke previous records in this period (Ref 10). Are we already too late?

Acknowledgement

Assistance from P C S Laurie, (Dorset Roman Occupation Group; A L Systems, p.c.s.laurie.58@cantab.net) who produced the calculation of ice melting time in the Panel. Richard Whaley

REFERENCES
This is the online version of a shorter article published in North East Hants Historical & Archaeological Society e News No. 10, Winter 2014 - 5 www.nehhas.org.uk/ices.htm
1. A Roberts, R Grün, Nature 466 8 July 2010, p189
2. A Holmes, Principles of Physical Geology, Thomas Nelson & Son 1944 - 60, p239
3. R Bell, Science 331, 25 March 2011, p1592; Nature 471, 10 March 2011, p138
4. S Battersby, Great melt down, New Scientist 22 May 2010, p32
5. Nature 470, 10 Feb 2011, p181 & 251
6. BBC Radio 4, In our time, 24 June 2010, British Broadcasting Corporation
7. http://en.wikipedia.org/wiki/Geothermal_energy Resources. H Pollack, S Harter, J Johson, Rev Geophys 30 (3), p267, 1993. J Mackay, Sustainable energy without hot air, UIT Cambridge 2009, p97
8. BBC Radio 4, In our time, 14 Feburary 2013, British Broadcasting Corporation
9. R Fairbanks, Nature 342, p637, 1989. R Kopp, Nature 483 29 March 2012. P Deschaps et al, Nature 483 29 March 2012 p554
10 Antarctica extent of Winter Sea Ice, New Scientist 20 September 2014, p6

 

Panel for Melting Time

 

The North Ice Cap covered the Earth from the Pole to about 50° latitude at Ice Age Maximum.  Assume the heat flow from the Earth’s core is everywhere 0.1 watt per sq m (Ref 7),   the proportion of the Earth’s surface covered by the North Ice Cap is
2πr2(1- Sin50°) (1)
With the Earth’s surface area 4πr2   = 5 1014  sq m, (2) 
so the Ice Cap covers 5.85 1013  sq m, (3)   
so the sum of the under ice heat flow from the core is 5.85 1012  w. (4)    
The oceans cover 3.61 1014 sq m, (5) 
the last Ice Age reduced sea level by 120 m (Ref 9), (6) 
so the volume of water released in the Warm Age was 4.32 1016  Cu m (7)
which weighs 4.32 1019 Kg. (8) 
Latent Heat of freezing water is 334 KJ per Kg, (9) 
so heat required to melt this much ice is 4.32 1019 x 334 KJ = 1.44 1025   J. (10) 
Time for the heat from the Earth’s core under N Ice Cap to melt this much ice is 1.44 1025  /  5.85  1012  secs = 78K years. (11)

 

Overall caption for Figs 1 – 4: The phases of the various parameters involved in the Ice Age Cycle are presented for discussion. Ice Age Maximum is at Year 0, Ice Age Minimum is at Year 10K, and the next Ice Age Maximum is at Year100K.

Fig 1 The Ice Age Temperature Change is the prime fact coming from ice and other cores. The change is 10 to 12 degrees C. The Temperature rise is fast over 10K years, and slowly falls over 90K years. There is a lot of noise or random Temperature fluctuations, but the basic form of saw tooth wave is given in the Temperature Change graph (Ref 6 of e-news article).

Fig 2 Ice Height. The leak out of under ice melt from Year 0 speeds up the outflow of ice considerably which must result in reduction of polar ice thickness and height, until Year 10K, when the ice will be near minimum height. With Temperature at its maximum but slowly falling it will be well above its average for 10 – 20K years. Further slow thawing and reduction in extent and height of polar ice may occur. Eventually the excessive heat in Earth’s crust in polar regions caused by the former blanketing will radiate away, lowering Temperature, and causing polar caps to start rising in height from increased snow. This will continue until maximum height is reached around Year 100K.

Fig 3 Outflow of Ice - Speed. Out flow of polar ice will rise considerably by leak out from Year 0, and increase as more leak out sites occur – until leak out ends around Year 10K, when speed of outflow will become near minimum. Thereafter outflow will be a function of the Height of Ice, especially around the S Pole - until the next leak out starts around Year 100K.

Fig 4 Advance / Retreat of Ice. From Year 0 leak out will cause Retreat of the Polar Ice, aided by more of the sun’s light being absorbed by the smaller Polar Caps increasing Temperature, until leak out ends around Year 10K. Thereafter the Advance of the Caps will be a function of the Speed of Outflow of Ice, which will eventually push the edges of the Caps outwards, then aided by more sunlight being reflected and lowering Temperature. Advance of the Caps will start to level off as Equilibrium is approached around year 100K.

Fig 5 Ice Age Blanketing Question: how much of the poles are covered by sufficient Blanketing Thickness for under-ice lakes to form. At present in the S Polar region 3 to 4Km of ice needed. This Blanketing Thickness will be a function of surface temperature T which is also a function of latitude and height. The shape of the ice as it goes from Pole to Cap’s edges will be approximately bell shaped as in the Diagram below. Where T = 0, generally near the Cap’s edges, Blanketing Thickness will = 0. If the ice thickness at the Pole exceeds the Blanketing Thickness (as at present for S Pole at Ice Age Minimum) the general form of the Blanketing Surface will be as in the Diagram. As the ice is advancing outwards the Blanketing Surface may lag behind the Cap’s edges slightly. At Ice Age Maximum a Temperature fluctuation may often be necessary to insure leak-out occurs over a significant part of the Caps – a part played by 41K year orbital. Though at Equilibrium T at Cap’s edges will generally be over 0 degrees on average. Conclusion: once the Pole has Blanketing Thickness, then to a first approximation most of the Cap will do so.

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