It is what it is- and the GOD of Physics will have it no other way!
Posted by Jeff Id on December 5, 2009
Warning, global warming believer, read at your own risk.
I’m writing this post to make a point to all the new readers here why I’m not a denier yet am a skeptic. I’m an aeronautical engineer who works as an optical engineer but mostly business owner in my day job. Therefore the following equations are very familiar to me. I’ve received permission from Lucia at the Blackboard to repost this here . My opinion is that people who deny the possibaility of greenhouse climate change do not understand the basic proof – and it IS an absolute proof of the warming effect of greenhouse gasses.
My opinion is that people who deny have the basic understanding that the science is politicized, corrupted and exaggerated for a hidden agenda. Something revealed quite clearly in the ClimateGate emails and subsequent events. What they don’t understand is that the argument against global warming goes too far and is completely unnecessary.
I’ll try to keep all of this simple but it might get a bit tricky for non-scientific folks. My hope though is to convince some of those who are ‘deniers’ that the warming effect exists and that the proper ‘and far stronger’ argument lies elsewhere. First the basic physics have been around for hundreds of years. These physics actually have a consensus because unlike treerings, hockeysticks, and climate models these equations have been validated by experiment.
Before we step into the math. There is a known effect which in optics is referred to as a Planck blackbody radiator. A blackbody is a perfect radiation emitter whereas the light energy coming off it can be calculated from its temperature. A greybody is an imperfect yet similar version of a blackbody. Physicists are pretty simple sometimes.
What it means is that if you have an object at a known temperature you can predict the color spectrum (wavelength) and total brightness emitted by it. Every object not at an absolute zero temperature emits electromagnetic energy – everything! It’s so well known and understood that the spectrum for light bulbs is even referred to as color temperature. I don’t want to go too far into this but you can buy (evil) white color incandescent lights with a blueish cool white 6500Kelvin filament or a yellow-red 3000Kelvin filament – the kelvin rating is called “color temperature”. The color is created by the temp – bluer is shorter wavelength redder is longer. As hot objects such as bulb filaments (turned off) cool they continue to produce longer and longer wavelengths until the outgoing energy balances the incoming energy. The same is true for the earth.
Greenhouse theory is that gasses are more transparent to incoming high frequency visible light (Sun 6500Kelvin) and less transparent to outgoing infrared from a cold body (Earth’s surface 288 Kelvin).
The following math was done by Lucia at the blackboard. I went searching by google for the best description and it was amazing to find it at one of the few blogs linked at the right. All of the detail I was looking for laid right out in front of us like 6 pages deep into my google search.
The purpose of the math below is to look at incoming energy and determine how hot the earth should be from incoming energy alone. If the math is too much skip through it to the result.
Derivation of formula to calculate the effective radiating temperature, Te
If the earth’s temperature is assumed at steady state, then the net rate of energy from the sun, accounting for reflection, must balance the energy emitted from the earth. In terms of variables show in the figure to the left, conservation of energy requires:
Ps – α Ps = Pe or
Where Ps is the rate of energy intercepted by the earth, α is the fraction of the energy reflected by clouds, ice or anything reflective on the earth’s surface represented as α Ps. And Pe is the amount of energy emitted by the earth.
The solar constant, S, describe the energy flux from the sun at the earth’s distance from the sun, and from the perspective of the sun, the earth is seen as as a disk with radius R. So, the rate at which the sun’s energy intercepted by the earth is:
Ps= π R2 S .
Assuming the earth is a black body, the full spherical shell of the earth emits as a black body in all directions and obeys the Stefan-Boltzmann law:
Pe= σ (4 π R2) Te4
where σ is the Stefan-Boltzmann constant and is equal to 5.67 x 10-8 Watts m-2 K-4, and temperature Te must be expressed in Kelvins.
Rearranging and canceling, we obtain
Te4 = (1-α) S / (4 σ)
Calculation of Te
To determine the effective radiating temperature, Teneed values for everything on the right hand side of (4). We make the following selections:
- The Stefan-Boltzman constant, σ= 5.67 x 10-8 Watts m-2 K-4.
- The albedo of the earth is estimated to be α=0.30. This is the commonly used value for the earth; it is a function of the amount of cloud cover, and ice cover. So, it could change if the earth warms or cools.
- The yearly average measured value of the solar constant is S= 1368 W m-2 (See NASA.)
Substituting into (4) results in and effective radiating temperature of Te = 255 K = -18 C = -1 F.
This is the temperature predicted by this very simple baseline model. Since the surface we stand on is not an ice covered snowball, it is obvious that this is not the average temperature at the surface where we all live and breath.
Measurement indicate the average temperature near the surface of the earth’s crust and over the oceans is closer to Ts≅ 288K (15C, 59F)
So, the difference between the effective radiating temperature and the temperature near the earth surface is
So as Lucia has shown the earth is warmer than Planck and Stefan Boltzmann would calculate from solar enery alone. This is the simple proof that without greenhouse gasses we would have 33C less warming than we do right now. It is proven unless you want to deny your lightbulbs.
This ends the simple, inarguable, absolute proof that some level of global warming is true. If you are technical and disagree, the next section may satisfy your argument.
Update: I need to mention that the blackbody assumption isn’t perfect, after rereading the post it should be made more clear. There are also assumptions about absorption rate of incoming energy. Therefore 33 isn’t an abs0lute which I think more technical readers get but the point is that there is some effect caused by NATURAL GHG.
And now we get to the fancy stuff which if you have no science background may not make much sense so skip this section.
I’ve not read this step at any blogs. It’s a big internet so this must be done somewhere but an interesting argument has been made that the reason for the 33 C change is due to the emission altitude of the IR radiation from the gas.
Ya see, the outgoing surface radiation is captured by the gasses in the atmosphere. The energy is absorbed and re-emitted repeatedly until it finally makes its escape to space. The capture and re-emission is because the gasses are not transmissive at very long infrared wavelengths. To be clear, gasses like CO2, H20 and Methane love to let through visible sunlight while blocking long wave IR.
We therefore KNOW the average emission altitude of the warming is not ground level. As outgoing energy is captured and re-emitted (from an alien invaders perspective) the average altitude which outgoing energy emits from is well above ground. So one strong sounding and often repeated argument goes like this.
At least some of the warming is created by the pressure difference from ground to the true emission altitude. Therefore there isn’t 33C of warming from greenhouse gasses because the emission altitude is well above ground and there is an expected reduction of pressure and temperature with altitude in the atmosphere.
This point can be disproven with a simple thought experiment. Extremes in thought experiments can often provide answers we otherwise miss. I learned this trick (some pun intended) in school.
For this experiment, all we need to do is assume all gasses on earth have NO absorption of electromagnetic radiation on ANY wavelength. All sunlight comes in and all of it exits. We still have standard 14.7 PSI pressure on the earths surface so the pressure gradient still exists. The atmosphere has no effect on temperature whatsoever b/c the heat isn’t blocked or even slowed down from the earth. The emission altitude then becomes zero…..
According to the assumptions and math above, what would the earths surface temperature would be —– ????
Te = 255 K = -18 C = -1 F. – according to Planck, Boltzmann, Stefan, Michael Mann, Jeff and Lucia.
No warming gasses, no increase in emission altitude, no surface warming beyond Planck whatsoever.
Therefore the argument that 33C of additional warming is caused entirely and completely by ‘greenhouse gasses’ – is TRUE. It’s completely 100% right. Impossible to deny. –
— And there is simply no reason to deny it.
Finally, we come to the point where we can discuss rationally what that means.
- It means that global greenhouse gas warming is real
- It means that NATURAL greenhouse gasses are responsible for about 33C of earth warming
Where do we go from here?
That’s it. So if I’m such a believer, where is the disagreement? Where can WE Skeptics and now ex-denialists go? What doesn’t it mean?
Beyond these simple proven equations that AGW advocates like Michael Mann depend on for their continued paychecks, there is a LOT of exaggeration in climate science.
Additional simple equations can show 1.2 C of C02 warming for doubling of CO2. This is completely different than the above calculation I’ll show the math later but consider that the above 33C calculation uses known and tested physics. Endlessly verified in laboratories combined with measured surface temperatures. Now 33C does rely on a surface temperature measurement but this measurement isn’t the tenths of a degree measurements used to discuss trends of DOOOOOMMM(haha – couldn’ t resist) but rather 33 friggin’ degrees different from the expected temp. – this is not 2C of urban warming but rather proof of global warmth (not warming) caused by greenhouse gas!!
The 1.2 C from doubling of CO2 is far more complex because in this case it assumes no feedbacks from the atmosphere. No added clouds, aerosol changes or any other imagined feedback. Sounds weak but guess what, feedbacks are completely unknown and untested. This is the beginning of where the argument and discussion exists. In addition, doubling the CO2 is not terribly easy with your SUV.
Therefore one thing an honest thinker should put their focus on is the feedback mechanisms. The feedbacks of an increase in CO2 can result in more OR less warming than the baseline and there is a lot of evidence for less. Climate models ASSUME (and it is a complete assumtion) MORE warming than CO2 alone creates through cloud feedback by several times (four times!! -called positive feedback). There is simply no proof of accuracy. What’s more, these models fail in comparison to temp measures in that the measured warming is statistically significantly less than modeled. McIntyre and McKitrick have a paper being held up by ‘peer review’ on this very topic right now. I would love permission to write on that, but it will wait. In the meantime, Treesfortheforest (link on right) absolutely installed a new @#%^ in the now famous Ben Santer’s work again demonstrating the poor results of temperature trend modeling.
What if the feedback is actually negative? That would mean even less than 1.2 C of warming for an absolutely MASSIVE increase in Co2. Can you prove to me that it’s not!!! Can anyone.!! —Let me get this for you NO!! The CO2 zero feedback scenario is enough to buy us centuries of non-regulation because the IPCC relies on this completely unproven, untested and poorly measured cloud feedback.
More fodder for us skeptics is that the warming is unprecedented. This is completely undetermined by science, unsupported by historic evidence and current papers are horrible in quality. Nobody knows the real answer, and anyone with the skill to know, knows damn well that they don’t really know. hahaha. This is the field of “hide the decline” and “ten ways to hockeysticization”.
Finally, how bad is a bit of warming? Will it really melt the caps? Will it cause more storms? How is it that flooding the earth with water results in drought? These are even less determined avenues of climate science yet they get the same weight in political reports.
Is global warming from CO2 real? – Hell yes!
Is it measurably warmer due to CO2 — not sure.
Are claims of ice melt, fish shrinking, model projections, temperature measurements, paleo science, drought, increased storms and FLOODING!! exaggerated? – Yup!
Is it being done with intent. OH HELL YES.
We cannot choose physics, but we can choose reason.