Excuse my ignorance, but how do we know there is "missing heat"? I assume it is obtained from satellite measurement of outgoing radiation power, integrated over the Earth's surface, compared with measured total incoming radiation power from the Sun and the two don't match.

If there is a difference between the two that cannot be explained by instrumental error, then there is certainly a question to be answered.

The instruments will need to be pretty accurate - if the missing heat is reckoned to be around 1 W/m2, compared with average insolation of around 1.36 kW/m2, then the measurements will have to have been made with a precision of at least one part in 10,000. Presumably NASA know what are the precision of their measurements but it's worth checking that the measurements really do have such precision before spending time discussing the tiny difference between measured incoming and outgoing.

Green Sand (castings?) - well I probably don't know any more than you. But if the satellites are measuring the *total* outgoing they don't need to know the surface area so far as I can see. They will be well outside the atmosphere and (to a close approximation) orbiting in a sphere with the Earth inside it. Each orbit will trace out a line on the sphere. If their orbit is actually elliptical, this can be corrected numerically to give the effect of circular orbit.

What they need to do is measure the total radiation from the Earth coming out through the surface of the sphere. The actual surface area of the Earth should not affect things so far as I can see, as the total power will be measured in watts, not W/m2.

Does this make sense?

"as the total power will be measured in watts, not W/m2."

So why (and I sure don't know) is it expressed as W/m2 at the TOA, I think it is probably logical, it has been a long day for an old inquiring mind!
Jun 1, 2013 at 10:51 PM Green Sand

Good question. Beats me.

I'd surmise that W/m2 at the top of the atmosphere, which is a pretty vague concept, are translated into equivalent W/m2 at the Earth's surface. But even there, if you want to be precise, since the Earth is not flat (Everest) nor is spherical, you'd need to make some kind of adjustments.

I've got a couple of fat books on the physics of atmoshphere and climate, one by Murry Salby who was a consultant for NASA in calculating satellite radiation data. I'll see what the books say.

"Martin, I have searched for, and failed to find, such satellite measurements, integrated over time and space (@ TOA). If anybody has any references I would be grateful. (...)
Jun 2, 2013 at 10:13 AM Roger Longstaff "

Well, if they don't exist, that would be amazing.

But how you calibrate a satellite (and re-calibrate from time to time once it is in orbit) to produce measurements of LW infra red with a precision of 0.01 per cent or better is something outside anything I know about. Is such precision attainable? Maybe there is a NASA site that explains it all. Years back I worked for a firm that made IR sensors. Getting them to work at all was hard. Maybe things have changed.

I found a web page "Missing" Heat May Affect Future Climate Change

It says:

Either the satellite observations are incorrect, says Trenberth, or, more likely, large amounts of heat are penetrating to regions that are not adequately measured, such as the deepest parts of the oceans.

(...)

A percentage of the missing heat could be illusory, the result of imprecise measurements by satellites and surface sensors or incorrect processing of data from those sensors, the authors say.

My suggestion is to establish that there really is "missing heat", from measurements, before spending time figuring out where it has gone. There seems to me to be a strong smell of something or other here. There is no point in discussing where the heat has gone if the only evidence for it is from Hansen's imaginings.

In a search for information; I took a look at SkS:

Search For 'Missing Heat' Confirms More Global Warming 'In The Pipeline'

Increased concentrations of greenhouse gases, from the burning of fossil fuels, slows the loss of heat from Earth's atmosphere to space. This creates an imbalance between incoming solar energy and outgoing heat. The Earth will continue to warm until the balance is restored.

Because this planetary heat imbalance is tiny compared to the energy coming in from the sun, and the heat being radiated back out to space, it is too small to be measured directly by satellites. Earlier attempts to quantify this planetary heat imbalance were made in Hansen (2005) and Trenberth (2009) using earlier climate model-based estimates. Hansen (2005) had this planetary imbalance at 0.85 (±0.15) watts per square meter, and Trenberth 0.9 (±0.5) W/m2, in the earlier part of this century.

An apparent mismatch between the modeled estimate and the heat that could be accounted for on Earth, led to well-known climate scientist, Kevin Trenberth to lament that it was a travesty. (...)

So it's not a physical measurement, it's Trenberth not being able to get the modelled figures to add up. Inventing ways for the energy from incoming light to find its way into the deep ocean has a ring of desperation to it. It does not strike me as a thing to expend brain-seconds on.