Are we heating the Earth too much - with heat?

As readers will know, I have been thinking about the hullabaloo about CO2 and global warming and I quickly concluded that CO2 is no threat [2], won't do any significant warming (which would be good anyway [3]), and is in fact 100% good for the planet. But someone said to me, if CO2 is no danger, that doesn't mean that humans are not causing a danger in some other way. Of course I agreed with this, because there are lots of things humans are doing wrongly and thereby causing terrible damage to our world (and the CO2 storm in a teacup is distracting us all from fixing those real problems).

My friend then went on, however, to propose that the danger was still global warming and that the mechanism was, instead of CO2 greenhouse warming, the mere fact that human technology gives off heat. All the power used by all the machines and transport and so on eventually ends up as waste heat. Maybe that is in itself enough to cause us serious warming trouble? So I did some calculations.

According to the laws of thermodynamics, the process of doing useful work must necessarily lose some of the energy from the fuel in the form of waste heat; and that heat, well, heats. In other words, because of the huge extra amount of useful work we do, we create excess heat that would not have been here otherwise, and that heat has to either be dissipated somehow, or else raise the temperature.

The factors that have caused the ice ages, as we saw, are primarily small changes in insolation (heating) by the Sun. The changes can happen because the Sun’s energy output changes or because of cyclic changes in the Earth’s orbit and inclination, etc., changing the amount of heat that actually arrives on the surface. Changes in the Earth’s orbit are believed to be the triggers for the onset of ice ages, and the changes in heating caused by those changes are thought to be quite small compared to the total power output of the Sun. This might lead us to suspect that human-caused changes in the amount of heat at the surface might indeed have a significant effect on the climate.

To answer this question, we need to compare the amount of variation due to the Sun with the amount of heat emitted by industrial civilisation. if the latter is ‘in the same ballpark’ as the former, then human civilisation might be holding off the onset of a new ice age.

Although there is much dispute about the exact mechanism that causes the onset of ice ages, much of it doesn’t concern us right now because one basic fact is clear: somehow or other, the responsibility lies with changes in the amount of heat received from the Sun.

One theory is that the cause is Northern Hemisphere summer cooling. At our current stage in geological history, the North Pole is surrounded by land masses, which are snowed under every winter. If the summers became just a bit colder, then some of that winter snow would remain on the ground throughout summer, and would then turn to ice. The ice will reflect sunlight much better than green plants or dirt or even liquid water, so the cooling will accelerate and the next summer will be even colder and leave even more ice lying around. And so the planet falls into an ice age. Retained heat in the oceans slows down the changes and ‘smooths over’ short-term effects, but once the process starts, the killing ice eventually reclaims its deathly kingdom.

Dr David Archibald suggests [4] that a key measure of this process is the amount of insolation at 65° north latitude. The power of the Sun at 65°N is about 476 Watts per square metre. That means that at midday in mid-summer at, say, Reykjavik (at 64°N, almost the only significant city anywhere close to 65°N), the Sun has about the power of five old-style incandescent light bulbs. When summer sun at this latitude is sufficient to melt the winter snowfall, all is well. Other factors in this calculation are the length of summer (because, for example, a longer, but slightly cooler summer might melt more ice than a shorter warmer one) and how high in the sky the Sun is in mid summer. And the higher it is in summer, the deeper and colder the long winter ‘night’ will be. The factors are complex and researchers disagree as to how exactly they should be combined in order to make good predictions, but some combination of these factors decides whether we bask in life-giving warmth or flee the deadly cold. We cannot hope to make predictions from the kind of short overview we are doing here, but we can get an idea of the magnitudes involved.

How much radiant energy the Sun has in the past or will in the future shine upon the Earth at this latitude can be reliably calculated from basic physical and astronomical properties of the way the Earth orbits the Sun and how that orbit changes with time. This is not an uncertain thing like the forecasts of climate models; it is not exactly easy to calculate, but it depends only upon the extremely well verified equations of Newtonian physics (or, if you prefer a few thousands of a percent more accuracy, relativity). If we didn’t know how to do these calculations, we could never have landed men on the Moon or flown discovery missions past Saturn and on to Uranus and Neptune. Yes, we do know how to make these calculations and we know it very reliably.

When the calculations are done, we find that at the depth of the last ice age, around 22,000 years ago, the Sun’s power (again at 65°N) was around 463Wm^-2. On the other hand, at the height of our own interglacial, the Holocene, which occurred about 11,000 years ago (yes, we have been on the downward slope ever since—though you would never guess it from the hairy scary stories about warming in the media) the summer insolation at 65°N was about 527Wm^-2. In other words, we have:

From these figures, we may make the following inferences:

• The difference between peak warmth and deepest cold was around 55Wm^-2;

• The current value, being only 13Wm^-2 above the value at the depth of the ice age, is almost all the way back to ‘cold conditions’; it may be that only stored ocean heat is keeping us out of an ice age (for now).

Moving on, how do these power figures compare with human energy output (mainly by burning fossil fuels)?

Human energy usage in 2006 was 491 exajoules. This translates to an average power usage of 15.56 terawatts each second (divide by the number of seconds in a year). To compare this with the Sun’s power as discussed above, we need to average this over the entire planet. The Earth’s surface area is 510 million sq. km., which gives 30,500 W per sq. km, or 0.03Wm^-2. One final adjustment is needed to allow us to do the comparison: the Sun’s insolation given above was as received at noon, whereas this figure is an average over the whole planet. Since the planet’s area is four times the areas of a circle of the same radius, we must multiply by four, giving about 0.12Wm^-2 as our final figure for comparison.

The human energy output of about 0.12Wm^-2 is clearly overpowered by even the smallest of the numbers we have looked at so far. The 13Wm^-2 difference between ice age conditions and today is at least a hundred times larger than human energy output. We might delay a killer ice age slightly, but our heating of the planet is nowhere near large enough to save us.