torsdag 22 juli 2010

Radiative Budget: In or Out?

Here is another argument indicating the non-physical nature of backradiation connecting to Global warming alarmists in full retreat as skeptics attack greenhouse theory. 

Do you carry a careful book of your expenditures or outflow of money? Is it accurate? Do you know how much you spend? 

Myself, like most people, don't: To keep track of the flow of money through your pocket, it suffices to know your income, and that you somehow spend whatever comes in (modulo savings).

Does Nature carry a book of expenditures or of incomes? We shall see that this question relates to our discussion of backradiation. 

Let's consider the radiation budget of an Earth at temperature TE with an income F from the Sun in interaction with an opaque Atmosphere at temperature TA absorbing radiation from the Earth and radiating to outer Emptyspace. Let's collect incomes:
  • F = Earth income
  • TE^4 - TA^4 = Atmosphere income assuming TE is bigger than TA
  • TA^4 = Emptyspace income
where we use a (normalized) Stefan-Boltzmann's Law (with Emptyspace temperature = 0). 

Can we now formulate balance equations from income and savings accounts, without invoking 
expenditure in the form of outgoing radiation? It is then natural to view Emptyspace as a savings account from which F is borrowed and payed back: We then have
  • TA^4 = F (Emptyspace receives T_A from Atmosphere to pay loan F)
  • TE^4 - TA^4 = F (Atmosphere receives TE^4 - TA^4 via the Earth, as a loan F from Emptyspace) 
Altogether, we get TE^4 = 2F and TA^4 = F. Simple? Yes, but this is the basic equations of 
climate science based on Stefan-Boltzmann's Law. Knowing F you conclude that TA = 255 K and thus TE = 303 K. 

If we now in an alternative approach include expenditure, we may get the following relations:
  • TE^4 = Atmosphere income from the Earth
  • 0.5 TE^4 = TA^4 = F Atmosphere expenditure radiation to Emptyspace
  • 0.5 TE^4 = Atmosphere expenditure backradiation to the Earth
with the same solution TE^4 = 2F and TA^4 = F.

We see that the difference lies in the account of the Atmosphere income from the Earth: 
The real income is TE^4 - TA^4 as in the first case, while in the second case there is a fictitious gross income of TE^4 which is compensated by the backradiation expenditure 0.5TE^4. 

The second case is like first getting the gross income and then paying back the tax to get the real net income = gross income - tax. The first case is like getting the real net income directly
into your pocket without having to worry about paying the tax (and maybe forgetting it). 

Which principle do you think Nature prefers?  Net income, or gross income with 
a request to pay tax? Is there a tax authority in Nature?

My basic idea is that it may be easier for a (selfish) system component to account for incoming data because it has a direct effect on the component itself, while the component may care less about outgoing data since it affects other components. You care about what you eat but less about what you deliver.

A similar situation is described in Many-Minds Relativity, where a moving observer receiving a light signal assumes it approaches with a certain constant speed (the speed of light), while the observer does not worry about the speed of a signal leaving the observer, which is possible because it is not needed.

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