Synopsis of the CO2 problem

On what I believe is a private discussion site I was asked a number of questions about the climate problem. I'm copying my answers here (with some minor corrections of typos and for context) as they may be found helpful for others... or at least as a reminder to myself of what I know.

Q. 1 "I look forward to any insight you can provide into the real verifiable evidence of the human footprint."

A. 1
I'm not quite sure what you mean by "verifiable evidence". You acknowledge climate seems to be changing. There are two distinct pieces of knowledge that go into "blaming" it on us humans, each of which has been substantiated from multiple observations and physical understanding. These are:

(1) Humans have caused atmospheric CO2 levels to increase considerably over the past century. This youtube video shows the wide range of observations of that increase in considerable detail, also showing how it compares with past changes:
http://www.youtube.com/watch?v=H2mZyCblxS4
(each dot is a separate measurement location somewhere around the world - shown in the map). Skeptical science has a post comparing human CO2 with natural sources here: http://www.skepticalscience.com/human-co2-smaller-than-natural-emissions...
Also this post shows the human signature in atmospheric CO2 can be measured via isotope ratios: http://www.skepticalscience.com/Are-humans-too-insignificant-to-affect-g...
and we know it's not coming from the ocean thanks in part to measurements of a decrease in oxygen levels: http://www.skepticalscience.com/co2-coming-from-ocean.htm
(etc. - there are many more pieces of evidence that may answer more specific questions - measuring how much fossil fuels we burn for example).

(2) Higher CO2 levels cause a planetary energy imbalance leading to warming, with about 3 degrees C (to within a factor of 2) as the result of doubling CO2 levels after things have come back into balance. Lines of evidence in support of this half of the argument are:
* physical theory - the Schwarzchild equations, radiative transfer calculations, plus some understanding of expected feedback effects, in particular water vapor

* observations of changes in Earth's emission of radiation to space - see the discussion here for instance: http://www.skepticalscience.com/empirical-evidence-for-co2-enhanced-gree...

* analysis of past climate change - through the ice ages and earlier - Richard Alley's talk here discusses CO2 levels as Earth's "biggest control knob": http://www.agu.org/meetings/fm09/lectures/lecture_videos/A23A.shtml

* This review paper from Knutti and Hegerl summarizes the various sources of our understanding on the subject: http://www.iac.ethz.ch/people/knuttir/papers/knutti08natgeo.pdf
- of course the IPCC did much the same in 2007 with their report then.

Q. 2 How do you arrive at the 33 c in the first place based on 100% radiative effect?

A. 2
One (theoretical) method is a calculation done using the Schwarzchild equations for radiative transfer from the surface to the tropopause, taking into account the convective stability limit on temperature gradients. To be more specific, the inputs to that calculation are the existing composition of the atmosphere (ppm of different greenhouse gases at different altitudes, altitudes and fraction of clouds which also contribute to the radiative greenhouse effect, etc.), the quantity of energy we receive per unit time from the Sun, and the specific detailed properties of wavelength-dependent absorption of the various greenhouse gases, which themselves depend on pressure of the surrounding atmosphere. The full calculation even for a one-dimensional analysis of the problem is complex, requiring integration across potentially millions of absorption lines in the spectrum. David Archer has posted an online module that lets you run this radiative transfer calculation yourself if you want to try - see here: http://geoflop.uchicago.edu/forecast/docs/Projects/modtran_form.html

Not only that, you can't just do the calculation once, that just gives you the outgoing radiation to space for a given temperature profile. To get to radiative balance with incoming sunlight the calculation needs to be iterated to self-consistency to get the prediction for surface temperature. The result will include a prediction for the height of the tropopause and of the average radiating layer; the surface temperature will be warmer than the average radiating layer according to the lapse rate - i.e. if the average radiating layer is at 5 km and the lapse rate is 6.6 K/km then the surface temperature 33 K warmer than the no-greenhouse-effect state (where the average radiating layer is at 0 km altitude).

These theoretical considerations are supported by a multitude of observational data, as I documented earlier. Plus, we know the actual average surface temperature of the Earth is about 288 K, 33 K warmer than the 255 K of average radiation to space, so we know the number is true from observations of temperature (and outgoing and incoming radiation) as well. Which was the main point of my little article on arXiv here: http://arxiv.org/abs/0802.4324

Q. 3 How does the radiative greenhouse effect work in YOUR view?

A. 3
Briefly, it's the Schwarzchild equations. More specifically, the atmosphere absorbs a significant fraction (but not all) of outgoing thermal radiation from the surface. If the atmosphere was at the same temperature as the surface, then the same fraction absorbed would be re-emitted back to the surface (this is almost true in reality - if you've run into Misklolczi you'll have heard of this one) and only the small net fraction in the "window" would actually leave the surface. With the atmosphere at the same temperature there would be no energy loss by convection and conduction either, so most of the continued input of energy from the Sun would be retained at the surface and it would warm up.

That warming (caused directly by the atmosphere's infrared absorption - i.e. greenhouse effect) introduces a gradient in temperature between surface and atmosphere. Just as with a house warmer or colder than the outdoors, the temperature gradient causes heat to start leaving the surface by convection, latent heat, and conduction. It also causes the emission of the surface in the "window" to increase, and it ensures that the atmosphere's re-emission to the surface is slightly less than what the atmosphere absorbs (one place where Miskolczi goes wrong). All those factors mean that more energy is leaving the surface than was before. If that "more energy" is still less than what's coming in from the Sun, the surface will continue to warm up.

If the temperature gradient resulting from this warming gets too large (bigger than the adiabatic lapse rate), the atmosphere sees a convective instability, and heat flow by convection suddenly gets much larger. This has the general effect of keeping that temperature gradient very close to the lapse rate throughout the lower atmosphere (tropopshere), as long as the greenhouse effect causes enough warming to sustain it.

Once the surface has warmed up enough - and the lower troposphere has also warmed sufficiently to sustain that lapse rate up to the average radiating level and beyond - the planet reaches a condition of radiative balance, where the outgoing radiation matches what we receive from the Sun. Warming is complete at that point, as long as the various input parameters (atmospheric composition, solar input) remain steady.

And that's the Greenhouse Effect - the atmosphere's absorption of infrared radiation causes the surface to warm. Really quite basic physics, though the calculations on all but the simplest models can't be done by hand.