Posted by: ericgrimsrud | August 11, 2015

The Hansen paper viewed as a pie plate with ice cubes

In a recent post, I drew attention to the latest publication by James Hansen et al. (see it at ) which is sure to have a huge impact on our understanding of the most imminent effects of climate change resulting from greenhouse gas warming.  I believe that the issue addressed in this paper is so important to everyone – not just professional scientists – that I will try to provide here some additional assistance is understanding its contents via a simple analogy.

Ordinarily, we assume that increased  levels of warming will result in increased temperatures, right?  Isn’t that, after all, what “warming” is all about?  But not so, actually.  As more heat is deposited into the Earth by our out-of-control greenhouse effect, there is another means by which that excess heat is dissipated that does not result in increased temperatures. That mechanism is simply the melting of ice – by which huge amounts of energy is absorbed with no change in temperature.  And with the use of simple analogies associated with the melting of ice in a pie plate, we can better understand both the Hansen paper referred to above and why this means of heat dissipation is so very important to us – of more immediate importance, perhaps, than the temperature increases we usually focus on.

What the Hansen paper is all about can be better understood by doing the following “thought experiments” (which can also be done literally in one’s kitchen, if one wishes).  Imagine a simple pie plate about one foot in diameter with edges of about one inch in height.  Then add a bunch of standard (one inch) ice cubes to it and just enough water to cover the very bottom of the plate to a depth of only about 1/8 inch. Then place a thermometer in the middle of this ice-water mixture and a towel under the plate thereby providing a bit of heat insulation from the counter top.

Now position a standard clip-on lamp directly over the center of this ice-water mixture and begin recording the temperature indicated by the thermometer as the ice slowly and steadily melts and the depth of the water level increases.  What one will observe for the next many minutes as the ice melts is that the temperature of the water does not change at all.  Until almost all of the ice is gone, the water temperature will remain at the freezing point of water, which is +32 degrees F.  Only after that point when the ice is nearly gone, will the temperature then begin to increase beyond 32 degrees.  According to the laws of thermodynamics, this result is entirely expected – no surprises, so far.

Now let’s change the above experiment somewhat so that it more closely mimics our planet –  by placing two or three ice cubes only at the very top and the very bottom edges of the pie plate – thereby creating north and south “poles”.  (For those actually doing this experiment, two strings taped to the top and bottom of the plate will prevent these ice cubes from sliding away from their polar positions).  Again we also add enough water to fill the plate to a depth of about 1/8 inch.  With a thermometer again placed in the water at the center of the plate, we again suspend the lamp over the center of the pie plate and again start recording the temperature.  Now, if we do not stir the water at all, we will observe an increase in temperature with time, as would be expected, right? Since there is no stirring, the water in the center of the pan is now going to increase in temperature immediately upon application of extra heat from the lamp.  If one moves the thermometer to the water-ice mixture existing at the top or bottom of the plate, the temperature at those two locations would be 32 degrees F as in the first experiment, right?  Since the center of the plate is now farther from the poles, its temperature is less affected by the ice at the poles.

Next, let’s additionally improve our rough simulation of the Earth by introducing some stirring of the water, lightly at first and then progressively stronger. After all, we know that our oceans consist of numerous strong currents by which heat is being continuously transferred between all of its regions. As the degree of stirring is increased in our experiment, the temperature observed at the middle of the plate will then decrease, right?  If the degree of stirring is made sufficiently vigorous, the temperature at the center can be made to decrease downwards most of the way to that measured at the “poles”.

Lastly, repeat the experiment above using different levels of constant stirring and note the time required for the length of the ice cubes at the poles to decrease in size to approximately one-half their original size under each condition of stirring. One will certainly find that this measured “half-life” of the ice cubes deceases with increased stirring, right? This happens because increased stirring brings the total heat within the plate to its polar regions more rapidly, thereby causing the cubes to melt more quickly.

So that’s it.  Very simple experiments with results that are in line with common sense, right?  But  what do these simple experiments tell us about what the Earth is likely to do in response to our extra greenhouse gas heating?  It tells us several very important things, as related below.

First, there are, indeed, two different mechanisms by which the extra heat provided by greenhouse gases is dissipated.  One is via temperature increase and the other is via the melting of ice. In addition, these experiments show us that the loss of ice can occur with either no or little change in temperature (as in the first experiment and in a later one with ice “poles” and vigorous stirring).

Secondly, these experiments tell us that the rate of ice loss at the poles of our over- heated world will depend on the degree of “stirring” or heat transfer provided by our oceans.  That is, the speed and efficiency of heat exchange between our mid latitude oceans and our polar glaciers will be determined by ocean currents and ocean-glacial interfaces – factors that we are just beginning to understand as related in the Hansen paper.

Thirdly, one of the most detrimental and immediate consequences of global warming is expected to be an increases in our sea levels and the simple experiments related above suggest that large increases in sea levels can occur with relatively little changes in the Earth’s average temperatures. This is especially true  if the “stirring” or heat transfer between the poles and the lower latitudes via our oceans is relatively efficient.  Just how efficient that transfer of heat is constitutes an extremely important question about which too little has been known up to the present.

In any case, the simple thought experiments described here allow one to better understand the purpose and goal of the paper by Hansen et al.  Its goal is to understand and determine the speed by which the extra heat of our planet is transferred to the polar regions, where most of the world’s ice is.  And what they discovered is that the rate of heat transfer will be increasing much more rapidly during the coming decades than was previously expected. As a result, their prediction is that sea levels will rise by about 10 feet by the year 2100 if our “business-as-usual” rate of fossil-fuel consumption continues – instead of less than 3 feet as was previously thought.  In order to prevent that outcome, Hansen et al. conclude that atmospheric CO2 levels would have to be reduced from its present level of 400 ppm back down to about 350 ppm. Given that our background CO2 levels are currently increasing at a rate of about 3 ppm per year and that atmospheric CO2 is removed very, very slowly by natural processes, a return to 350 ppm constitutes is an exceedingly formidable task that is doable only if extreme measures are immediately undertaken .

The main reason we have not previously been aware of these exceedingly dire predictions is that we  have not sufficiently understood the details of the “mixing” processes illustrated by the simple experiments provided above – as they play out on our planet. The Hansen paper is therefore particularly important because it attempts to understand  those processes and, in doing so, finds that these heat transfer factors are, indeed, determining ones  with respect to the changes in our sea levels that are expected to occur during the current century.  And  in case you missed the point previously, an increase in the sea level of 3 meters by the end of this century would render many of our coastal cities, including New York, London and Shanghai, uninhabitable!

Finally, thanks to Heart Climate Scientists for the following relevant cartoon.

2015 Toon 32

And Hansen et al .predict that the rate of glacial melting and fresh water production will be increasing exponentially with business-as-usual practices throughout the current century!  Yes, there does appear to be some very good reasons for becoming VERY ALARMED and for undertaking extreme and immediate actions, does there not?  The only question is are human beings going to be up to this task or will they simply continue to enjoy the fossil-fuel-fired party while it lasts?  That is the BIG QUESTION of our era – and, unfortunately, is still one that is masked by so many other issues of far less immediate importance.


  1. Very well done Eric, We have to get people from all over this world, especially the GOP to realize that CW is an absolute fact.
    The Republicans are doing the same thing as they did the beginning of WWII. Roosevelt had to perform all sorts of maneuvers with the Republicans to help the UK in its war with Hitler’s Germany; the US provided 50 naval destroyers to the UK. This was accomplished under the Lend-Lease Act which actually was a gift but Roosevelt had to trick the GOP that the US would get these 50 back at a later date..

    • spot on Arlo; great and SIMPLE experiment that even GOP can grasp! That said, I left the GOP because the are NOT the party of SCIENCE anymore and leaders believe the Earth only 6,000 years old while we have carbon-dating SCIENCE to prove otherwise.

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