Thursday, 6 August 2020

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 say anything of the sort, 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 (weighted average albedo) = 18 million Joules.

Using James Hansen's leaky bucket analogy (a lousy physics analogy, but mathematically sound), that means that about 18 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, warmest at the hard surface, coldest at the tropopause, average about 255K. The specific heat capacity of air is 1,005 J/kg/K = 2.6 billion Joules of stored energy per m2 of surface.

[The Warmists call this "trapped" energy when referring to radiation. In the words of the song, "You can keep her lovin'... like you keep the sunshine in your hands..." Clue: you can't, you can't "store" or "trap" radiation. You could hold some warm air in your hands, but it wouldn't be a good song lyric.]

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 = 4.2 billion Joules.

The ocean is only two-thirds of the surface = 0.8 billion 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 billion Joules so that it doesn't feel left out.

That gives us a "stock" of energy of 3.5 billion Joules for every m2 and a daily gain/loss of 18 million.
That means a daily gain/loss of 0.5%.

The other way of guesstimating this would be to look at a vertical slice and compare day and night temperatures all the way up. The diurnal range at the ocean surface is about 5 degrees; in the desert it can be as much as 30 degrees, but the higher up you go, the smaller the diurnal range (which is why you can get temperature inversions overnight, the land cools down more than the air above it), if it's 2 or 3 degrees overall, that means a total cooling of about 1%.

Either way, that is such a small figure that it doesn't matter how far out we are and what assumptions we make, it's somewhere between 0.5% and 1%.

While the daily gain/loss is interesting in itself, it is a side-show, it tells us nothing about how the stock of energy is distributed within and between the atmosphere, the hard surface and the top bit of the ocean (let alone between the top bit and the ocean depths), or what forms that energy takes, how - or why - it converts from one form to another. That is all well-known and based on good old fashioned physics and long, hard number crunching.
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.


Dinero said...

So that prompts a question , if the air temperature comes from heating by the ground and the ocean and the ground and ocean are the same temperature at night why is the air temperature less at night.

Lola said...

Sensible chap, that pupil B. Becoming a carpenter. If he's any good he'll never be short of work. Come to think of it that other famous prophet, who lived about 2000 years ago, was also carpenter.

Mark Wadsworth said...

Din, everything cools down at night, and at different speeds.

L, ta.