# Pupil B Recants, Or Maybe Not.

Pupil B's homework was ripped to shreds by a warmist and a lukewarmist.
Highlight: "[Having calculated the effective temperature of the cloud-free hard surface on the basis of incoming solar radiation] would he now say the following for night time hard surface? Hard surface is easy, 0 W /m2 = 0 K.?
Pupil B is not a total idiot and would never have assumed this, but can't resist rising to the bait one last time.
-----------------------------
Total incoming solar radiation in 12 hours on the day side for each m2 (to keep the numbers manageable) = 685 W/m2 x 3,600 seconds per hour x 12 hours = 30 million Joules (1 Watt = 1 Joule per second).
Less 40% reflected by clouds, hard surface and ocean, less another 10% for infra red emitted from surface* = 15 million.
* Clearly the hard surface and oceans emit infra red which can punch straight through the air. If you are outside on a cool night and low level cloud drifts overhead, it gets reflected and warms you up a bit. 10% is an estimate.
Using James Hansen's leaky bucket analogy (a lousy physics analogy, but mathematically sound), that means that about 15 million Joules must be radiated away again in 12 hours on the night side.
------------------------------
OK, that's the daily +/- flow. What's the average "stock" of energy per m2?
1. There are 10,000 kilos of air for each m2 of surface, at about 288K. The specific heat capacity of air is 1,005 J/kg/K = 3 trillion.
2. Ball park, it's the top 1m of the ocean surface which exchanges heat with the air every day (warms up or cools down) and is roughly the same temperature (cooler by day, warmer at night).
That's 1,000 kg of water at 288 K, specific heat capacity of water 4,200/J/kg/K = 1.2 trillion Joules.
The ocean is only two-thirds of the surface = 0.8 trillion Joules.
3. Hard surface is tricky, it's only the top 25cm or something which warms or cools every day, its specific heat capacity is much lower than water, and it's only one-third of the surface, let's just call it a token 0.1 trillion Joules.
That gives us a "stock" of energy of 3.9 trillion Joules for every m2 and a daily gain/loss of 15 million.
--------------------------------
That means a daily gain/loss of 0.4%. That is such a small figure that it doesn't matter how far out we are, whatever assumptions you make, it's less than 1%.
While the daily gain/loss is interesting in itself, it is a side-show, it tells us nothing about energy is distributed within the atmosphere, the hard surface and the top bit of the ocean. That is well-known and based on good old fashioned physics.
------------------------------
But Pupil B knows it is far too late for recanting, has written off the Physics GCSE and signed up for an NVQ in carpentry at the new school instead and so doesn't really care.