You and of course scienceofdoom have done the calculations yourself and you are to be commended for that. Also, you are correct that the vast majority of blog readers, not just WUWT, haven’t done the calculations and most never will. I can’t worry about that. I can only do the best I can to understand reality. Don’t be offended that I don’t assume that your version of things is reality. I hope you don’t think that makess me 3x hopeless. Since I’m not going to take the 3.7 W/m2 forcing for doubling CO2 on faith, I choose the other alternative to spend more time reading posts here.

I am reluctant to draw conclusions based on these calculation methods alone. I’ll give some examples. You stated that “every complication raised at WUWT has been dealt with in the Schwarzschild equation.” Even I know that is hyperbole. Does the Schwarzschild equation deal with convection or advection?

Another example, DeWitt noted above that HITRAN data has been calculated from theory as well as measured in the lab and in the field. Yet the physicist, Roy Clark, using the same techniques concludes that “it is impossible for a 100 ppm increase in atmospheric CO2 concentration to cause global warming.” http://venturaphotonics.com/GlobalWarming.html “The atmospheric absorption bands consist of a large number of overlapping lines due to transitions between specific rotation-vibration states of the IR molecules involved. The individual lines are quite narrow with line widths of a few tenths of a wavenumber. The line profiles are Lorentzian and the line widths decrease with altitude as the pressure decreases. This means that the upward and downward LWIR fluxes are not equivalent [Rothman, 2005]. Any atmospheric energy transfer analysis must explicitly consider these linewidth effects and any approximations made to simplify the lineshape calculations have to be properly validated using high resolution results. These linewidth effects invalidate all of the flux equilibrium assumptions used in radiative forcing calculations.”

The last example of my skepticism of calculation and model-based conclusions about the degree of warming due to increasing CO2 comes from the plethora of opinions on the sensitiviy of CO2 ranging from less than zero to more than 4 deg C.

]]>The great country of NZ is blessed with renewables. Plus the All Blacks.

Imagine if you will a country with almost no hydro, that has signalled the desire within a few decades to transform from conventional coal, gas & nuclear to renewables. How does the pricing mechanism work?

Put it another way – if the pricing signal indicates the profit potential of more capacity how many years between the start of frequent power outages and the arrival new capacity?

I’m not sure how pricing mechanisms work for occasional outages. I’m sure smart operators see the opportunity. But the regulatory risk is also quite high, possibly deterring smart operators – politicians might change the rules, politicians might “over tax” the “*greedy capitalists who made all that money last quarter from the energy bills of poor hard working [Americans/British/Germans/Australians/etc]*“. New politicians might win elections on such a ticket, replacing politicians who had let the market produce new supply..

A few countries have gone for something quite different – massively inflated consumer feed-in prices for solar energy. This is more like a transfer of wealth from “the taxpayer” to “the reasonably affluent classes that can afford the investment”.

]]>Thanks – it’s an interesting site. There’s some good data on California wind power variability.

]]>The key elements are no subsidies, open access to market, price signals and access to market price data.

You can see live pricing http://www.electricityinfo.co.nz/comitFta/ftapage.main and more about market on good old wikipedia.https://en.wikipedia.org/wiki/New_Zealand_electricity_market#Wholesale_Spot_Market

Implementing things like carbon tax or carbon trading feed into market as higher costs for would be FF generators.

]]>The bottom axis is wavenumber in cm^{-1} so the scale corresponds to 14.99 – 15.02 μm. The side axis is arbitrary units.

You can see that for a 2K increase in temperature the change is almost invisible. For a 20K increase it is more noticeable. Again, the higher temperature has the stronger emission at the very center of the line. The area under the curve – the line strength – is the same.

The increase at the peak for the 20K change is 3%, for the 2K change it is 0.3%

]]>You asked about the temperature dependence of the emissivity of CO2.

The “line strength” of an absorption line (which is also an emission line) doesn’t change with temperature.

But the line width does. What does this mean?

It’s explained in some detail in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Nine.

Here’s an extract, showing the pressure dependence:

Pressure varies by a factor of 5 in the troposphere, whereas temperature varies by a factor of 1.5. If you go from the surface to the tropopause in the tropics, the line width will be 16% of the value at the surface. Most of this is due to pressure.

The effect of increasing temperature on line width is relatively quite small. If we are considering how changing emissivity in a warmer world will “offset” the warming from more GHGs – going from 300K to 302K will reduce the line width by 0.3%. A reduced line width **increases** the emissivity in the line center and reduces the emissivity further away from the line center.

I’ll plot some examples shortly.

]]>Unfortunately, the people creating your doubts never show you how to properly calculate the reduction in flux using correct physics. And the people who do know how to do the calculation – for some reason – don’t want to specify that they are actually using the Schwarzschild equation. They say they are doing “radiative transfer calculations” and omit saying “using the Schwarzschild equation. I think they skip doing so because this equation doesn’t provide any intuitive feeling for what is going on and the process is complicated.

dI = n*o*B(λ,T)*ds – n*o*I*ds

dI is the net change in radiation intensity (I) from both emission and absorption moving a short distance ds along a path through the atmosphere. It varies with wavelength and technically should be written as dI(λ) or dI subscript λ. It needs to be integrated over all wavelengths before it becomes a change in power flux (dW measured in W/m2).

The first term is the emission term – how many photons are added by a GHG moving an incremental distance ds on the path from the surface to space or space to the surface. The second term is the absorption term – how many photons are absorbed by a GHG moving an incremental distance ds on the path from the surface to space or space to the surface. When dI is numerically integrated from space to the surface over all wavelengths, about 333 W/m2 of DLR is the result. When dI is numerically integrated from the surface (emitting 390 W/m2) to space over all wavelengths 150 W/m2 is LOST. And if CO2 is doubled, an additional 3.5 W/m2 is lost.

n is the amount of GHG per unit volume, which varies with altitude and technically should be written n(z).

The cross-section, o, tells us how strongly a GHG interacts with radiation of a given wavelength – how effectively that GHG both absorbs and emits per molecule. The cross-section varies with wavelength and modestly with temperature and pressure. Technically I should write o(λ,T,P). Since T and P vary with altitude, we could even say o(λ,T(z),P(z)).

The Planck function, B(λ,T), takes into account the fraction of molecules in the excited state at any given temperature arising from the Boltzmann distribution for an energy difference of E = hv = hc/λ, some geometric factors, and some quantum mechanics. When dI = 0, absorption = emission and the intensity of the radiation (I) = B(λ,T) – blackbody intensity.

The absorption term, n*o*I*ds might be more familiar to you. Laboratory spectrophotometers use very hot lamps to produce radiation so intense that emission from a sample can be neglected. Since n and o don’t change along the path in the laboratory and emission is insignificant, integration along a path of length r gives Beer’s Law: I/I_0 = exp(-n*o*r). The cross-section o is called the absorption coefficient in chemistry.)

Every complication raised at WUWT and elsewhere has been dealt in the Schwarzschild equation. However, WUWT is usually trying to deal with these complications in the context of a crude model that reduces all of the interactions between the atmosphere and radiation to an EMISSIVITY term and a single temperature Ts = 288 degK. Hopeless, hopeless, hopeless.

The alternative is mastering the Schwarzschild eqn – which is so complicated that even those who understand the process don’t want explain what they are really doing. (SOD’s green and blue graph above was constructed by numerically integrating the Schwarzschild equation for an atmosphere with two different concentrations of CO2.) This required writing a program to use a database with absorption cross-sections (o(λ,T,P)) for all GHGs (tens of thousands of individual lines) and specifying how T, P, density, water vapor vary with altitude. You can use the online MODTRAN calculator or Spectrocalc to do the work for you, but that requires trusting the developers of this software. Getting most WUWT readers (and maybe you?) to understand this process is also hopeless, hopeless, hopeless. The only alternative is to take a 3.7 W/m2 forcing for 2XCO2 on faith as “settled science” (heresy!) or spend much more time reading SOD’s posts.

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