Once Again, Skeptics do the Math that Warmists Won't Do....

[Toddsterpatriot]

No, he didn't. 1.0138 is not 1.38%. It could be 101.38%, but that's not the same thing either and doesn't take you from 5W to 7W. He just fucked up the math.

By 2, an increase in mean surface temperature of 1C is a 292/291 change in the absolute temperature. By 3, that requires a (292/291)^4 increase in the total power, or a 1.38% increase in the total power. By 1, that requires 7 watts per square meter, continually operating.

Which part did he fuck up?

 

[mamooth]

The part about the backradiation increasing by almost as much.

The basics, in other words. He sort of forgot the atmosphere sends backradiation down.

 

[Toddsterpatriot]

The part about the backradiation increasing by almost as much.

The basics, in other words. He sort of forgot the atmosphere sends backradiation down.

I just reposted his original questions and his answers below. This should be clearer than the original post, which just had his answers. Any formatting errors are mine.

It looks like Answer 5 sort of covers backradiation.
Let me know if you agree or see anything else that you think looks wrong.
Thanks!


What is the current power at the earth's surface, as an average?

1. Power at the earth's surface is about 500 watts per square meter, by NASA estimates from a detailed power budget.

What average temperature does it presently maintain?

2. That power suffices to maintain an average temperature of 291 degrees kelvin (18C).

What physical law governs the relationship between power and temperature?

3. The Stefan Boltzmann radiation law governs the relationship between power and temperature, and specifies that the power emitted by a radiating black body is proportional to the fourth power of the absolute temperature (degrees kelvin).
Exactly how much power is required to raise the surface temperature by 1 degree C? Show your reasoning.

4. By 2, an increase in mean surface temperature of 1C is a 292/291 change in the absolute temperature. By 3, that requires a (292/291)^4 increase in the total power, or a 1.38% increase in the total power. By 1, that requires 7 watts per square meter, continually operating.

What is the power estimated to be supplied by CO2 greenhouse currently?

5. The power presently provided by direct CO2 greenhouse is 1.6 watts per square meter, by IPCC's own estimates.

What mathematical function describes the relationship between a given gas concentration and the greenhouse power it can supply, and why?

6. The mathematical relationship between CO2 concentration and greenhouse power is a logarithmic function of the atmospheric concentration. This happens because the specific wavelengths intercepted by CO2 get saturated as that concentration rises, so the first bit has the largest effect, subsequent additions have less, and so on.
What is an upper bound for the power that would be supplied by doubling the atmospheric CO2 concentration?


7. An upper bound for the power supplied directly by doubling CO2 concentration is log 2 times the effect of the present concentration, by 6. By 5, that effect is 1.6 watts per square meter so the bound on the direct effect is 0.693 x 1.6 = 1.11 additional watts per square meter. Notice, this is less than 1/6th the figure calculated above as necessary to raise mean surface temperature by 1C.

If that much power is supplied to the top of a water column 3 km deep at a starting temperature of 15C, what are the dynamics of the temperature at the top of the column? At the bottom of the column? (Bounds are acceptable).


8. If 1.1 watts if new power are supplied at the top of a water column 3 km deep, the temperature of the column will begin to rise, as 1.1 joules per second (definition of watt) enter the water as heat. The heat capacity of water is 4180 joules per kilogram per degree kelvin. The mass of water is 1000 kilograms per cubic meter. A 3 km deep column has a mass (under each surface meter) of 3 million kg and a heat capacity of 1.254x10^10 joules per degree. If the column were well mixed, it would take 9,543 years for the temperature to rise one degree, ignoring for a moment the restoring force of the higher temperature. Just the top 100 meters of the water column have a heat capacity one thirtieth part of that, implying an instantaneous rate of increase in temperature of one part in 318th of one degree per year.

For what length of time will the dynamics continue before approximating a steady state?

9. By the reasoning above, 1.1 watts on a 500 base are a change in the total power of 1.1/500, and in the equilibrium temperature of (501.1/500)^.25 or 0.00055 of the initial absolute temperature, or 0.16 degree. The temperature cannot rise more than that at the top of the column, because as soon as the top of the column gas warmed that much, its surface is reradiating as much additional power as the new forcing supplied, putting it back into equilibrium. This will take approximately 100 years for the top 100 meters, ignoring for now the slower diffusion of heat to lower layers of the water column. That 100 comes from the 318 years per degree figure above, averaged with zero at the end of the period, and a total temperature change if 0.16 degree.

What mathematical form or shape will the temperature series describe in the meantime?

10. The temperature will describe a slowing curve, max rate at the start, falling smoothly to zero as the reradiation term rises with the temperature of the surface.

Does it reach a steady state, and if so at what value?


11. After that century long, 0.16 degree transient, it will still take millenia or the higher temperature at the top of the water column to reach thermal equilibrium with the deeper layers, which have 30 times the heat capacity, and will load with joules slower, as the hotter surface is already reradiating most of the new incoming power.
The very long run steady state is 0.16 degree hotter throughout the entire column, but will not be reached for thousands of years.

I didn't have to look up anything to give those answers. It is enough to know any physics and think through the problem for yourself.

The 3-5C warming prediction requires 21.1 to 35.5 watts per square meter of new, continually operating power. The larger figure is equivalent to moving the earth's orbit nearer to the sun by over 3 million miles. It is also 32 times the power anyone can expect directly from CO2 greenhouse from doubling its atmospheric concentration. To raise the surface temperature even 1 degree C by direct CO2 greenhouse would require a 31 fold increase in its atmospheric concentration, by the log formula. In reality those wavelengths would be saturated and opaque from below well before such an increase.

They don't have a power budget and cannot tell any of us who know the actual physics where they expect the other 20 to 35 watts per square meter of power to come from. They just wave their hands and say climate sensitivity. Every actual power source they have proposed has been checked, and they have random signs (as many negative as positive), and all are an order of magnitude too small to account for 3-5C warming.

Then the huge warming they predicted fails to appear, and they are surprised. People who asked where the power supposedly was to come from are not surprised.

Then all hide behind lawyer phrases, dodging the hopeless miss on the basic scale of the effect. Yes there is slight warming, in the record and in the reasoning. Yes the CO2 component of that warming is plausibly man made. But it is also less than a degree in direct effect. "Well, reasonable people can disagree about how much, the important thing is that it is happening etc". No. The important thing is the amount, which is nothing to worry about, on all empirical evidence and all actually scientific reasoning.

 

[IanC]

I couldnt be bothered to look at anyone's math but if I remember correctly an extra degree at OC adds about 5w, and every degree afterwards gains about 1/20 of a watt and every degree downwards loses 1/20 w. linear estimation but good enough for purpose. the poles warm up and cool down much easier than the equator does. 4w/C vs 6w/C.

and then there are the inefficiencies and alternate pathways. adding energy doesnt just raise temps, it changes evaporation, convection, etc, etc.

 

[Crick]

Ian, you said "take a look at this reasoning from one of the best numbers guys I've seen". But the fellow can't handle the basics. And that mistake was the basis for his entire contention.

He still has the math error. (292/291)^4 is NOT 1.38% Check it yourself. I'd also suggest you look up Stefan Boltzman cause it looks to me as if what he's looking for is ((292-291)/291)^4. Does it seem reasonable to you that it would take a 40% increase in power (5W to 7W) to get a 00.34% increase (291K to 292K) in temperature?

 

[Toddsterpatriot]

Ian, you said "take a look at this reasoning from one of the best numbers guys I've seen". But the fellow can't handle the basics. And that mistake was the basis for his entire contention.

He still has the math error. (292/291)^4 is NOT 1.38% Check it yourself. I'd also suggest you look up Stefan Boltzman cause it looks to me as if what he's looking for is ((292-291)/291)^4. Does it seem reasonable to you that it would take a 40% increase in power (5W to 7W) to get a 00.34% increase (291K to 292K) in temperature?

Ian, you said "take a look at this reasoning from one of the best numbers guys I've seen".

No, I said that.

He still has the math error. (292/291)^4 is NOT 1.38%

It is an increase of 1.38%.

that requires a (292/291)^4 increase in the total power, or a 1.38% increase in the total power.

Which is what he said.

Does it seem reasonable to you that it would take a 40% increase in power (5W to 7W) to get a 00.34% increase (291K to 292K) in temperature


Huh?

Power at the earth's surface is about 500 watts per square meter,

An additional 7W is an increase of 1.4%.

But the fellow can't handle the basics.

You might want to rethink your claim.

 

[IanC]

I would like to see the sideways radiation band at various altitudes. Do the CO2 bands remain high as CO2 theory demands or does it quickly fade after the first few tens of metres, or perhaps lie somewhere in between?

Blackbody radiation or specific molecular emission. They both come from the same available energy. Every CO2 photon that get recycled into BB radiation reduces the greenhouse effect. A natural negative feedback.