"Dunno muj thrmodynamix but I no wut I like!"Global average energy budget of the Earth

As a follow up to Alan Siddons's refutation of the quaint nineteenth century notion of 'radiative equilibrium' - a theory now as thoroughly passe as Pythagoras's quaint idea that the Earth is spherical* - Jennifer Marohasy has posted this '

proof' from Bill Kininmonth that greenhouse gasses actually cool the earth.

Kininmonth's argument starts with the diagram above and this howler:

At the surface there is a net accumulation of radiation energy because the incoming solar radiation (168 units) exceeds the net loss of longwave radiation (66 units).

The units that Kininmonth is talking about here are Watts per square meter. As commenters on Siddons's post

*Chez Marohasy* pointed out, the

Watt is a measure of power, not energy. A 100 Watt lightbulb converts one hundred

*joules* of energy to light and waste heat every second. What's measured in Watts per square meter is either heat flux density or irradiance - that is, the number of joules that pass through a square meter of an object's surface in one second.

So, in the diagram, we have 168

*joules per second* reaching each square metre of the Earth's surface in an average year. To find out how much energy that is, we'd need two more pieces of information: the total surface area of the Earth, and the number of seconds in a year. That would produce a very large and intimidating figure, but the calculation is otherwise irrelevant. Let's look instead on what would happen if there really was a net accumulation of 'radiation energy' at the Earth's surface.

The joule, the unit we use to measure energy, is named after

James Prescott Joule who came up with another of those quaint nineteenth century ideas that still plague modern science - the idea that heat and mechanical work are equivalent. He also had the gall to claim that he had proved it experimentally. It's in part thanks to Joule that modern physicists treat energy as just energy rather than radiation energy, heat energy, electrical energy etc. Energy is energy, however you get it.

If every square meter of the surface of the earth actually were accumulating 102 joules of energy every second, its temperature would rise. It's as simple as that. Let's look at what would happen to the temperature of a cubic meter of water, accumulating 102 joules of energy each second over an average day.

Ignoring

leap seconds, each day has:

24 * 60 * 60 = 86400 seconds

So our cubic meter of water will accumulate:

86400 * 102 = 8 812 800 joules of energy

4.2 joules of energy will raise the temperature of 1

*millitre* of water by 1 degree Celsius; there are 1 million millitres in a cubic metre. So the temperature of the water will increase by approximately:

8.8 million/(4.2 * 1 million) = 2.1 degrees Celsius

In less than 50 days it will reach boiling temperature. Imagine that happening over every square metre of the Earth's ocean surfaces. Thanks to heat transfer from the surface waters it would take longer for the water to reach boiling point but they'd still get very hot.

Where Kininmonth has gone so hilariously wrong is that he has overlooked two heat flows out of the Earth's surface that account for the 102 'units' of 'radiation energy' that he thinks are accumulating there. They are the heat losses due to thermals - 24 W/m

2, and evaporation and transpiration (evapotranspiration) - 78 W/m

2. That's a total of 24 + 78 = 102, leaving no energy accumulation at the earth's surface and nothing that has to be explained away by asserting that greenhouse gases actually cool the atmosphere.

* Since this 'scientific' theory is so thoroughly past its use by date, nominations are now open for a replacement theory of the shape of the Earth. This is my first preference:

Update: Dr Marohasy is now hinting that her most recent blog posts have been exercises in

Socratic Irony. I wonder who she thinks has been fooling whom.