Manabe (and a lot of other people!) really figured out the control dials on climate back in the 1970s The basic science on carbon dioxide and climate was settled by 1979, and ExxonMobil's scientists agreed internally, as recent revelations demonstrate (1). Everything since has mostly been fine-tuning and improved resolution due to computational technology advances. There has been a huge political effort to discredit this science ever since, by the fossil fuel industry and affiliated interests, since they have huge finacial interests in maintaining the current energy supply system - so, the science got politicized.

Let's take a look at the general concept though, from Manabe et al.'s 1975 paper (2):

> "The atmospheric part of the model incorporates the primitive equations of motion in a spherical coordinate system. The numerical problems associated with the treatment of mountains are minimized by using the “sigma” coordinate system in which pressure, normalized by surface pressure, is the vertical coordinate. For vertical finite differencing, nine levels are chosen so as to represent the planetary boundary layer and the stratosphere as well as the troposphere. For horizontal finite differencing, the regular latitude-longitude grid is used. To prevent linear computational instability in the time integration, Fourier filtering is applied in the longitudinal direction to all prognostic variables in higher latitudes such that the effective grid size of the model is approximately 500 km everywhere."

So, let's note that this general approach is applicable to planets like Mars and Venus as well as Earth. There is no ocean on those planets, however, but the atmospheric radiative-convection model approach is identical. Mars has something like 1% of Earth's surface pressure, Venus has 90X that pressure, but the same approach works. It's even applied to the gas giants. Note that 9 layers in the model is quite simple relative to modern models.

> "For the computation of radiative transfer, the distribution of water vapor, which is determined by the prognostic system of water vapor, is used. However, the distributions of carbon dioxide, ozone and cloudiness are prescribed as a function of latitude and height and assumed to be constant with time. The temperature of the ground surface is determined such that it satisfies the condition of heat balance."

Here's another key point - water vapor is modeled as a feedback, CO2 is modeled as a forcing. About 2/3 of radiative forcing in the atmosphere is due to water vapor, but that water vapor increases due to CO2 forcing (which has greatest effect higher in the atmosphere, closing windows that would allow IR to escape to space). This was verified by the Pinatubo explosion incidentally, in which predictions about water vapor feedback were highly accurate (3).

> "The prognostic system of water vapor includes the contribution of three-dimensional advection of water vapor and condensation in case of supersaturation. To simulate moist convection, a highly idealized procedure of moist convective adjustment is introduced. The prediction of soil moisture and snow depth is based upon the budget of water, snow and heat. Snow cover and sea ice are assumed to have much larger albedos than soil surface or open sea, and have a very significant effect upon the heat balance of the surface of the model."

So, that's the albedo effect, and as the poles melt albedo drops and you get more warming. You also get polewards heat transfer. Thus these scientists predicted warming at poles would be much faster than warming at equator, and that's been proven as well. Cloud feedbacks introduce a certain degree of variability, but definitely don't change the overall conclusions (see MIT's Richard Lindzen for that worn-out fossil-hyped argument if you like).

Now, I'll stop here but note that Manabe's other great contribution was linking the atmospheric model to the rather more difficult ocean circulation model. This allowed quantification of the lag effect, i.e. ocean warming absorbs a great % of the atmospheric forcing but warmer oceans warm the atmosphere and so on.

Incidentally, none of this would be at all controversial if human civilization had exhausted global fossil fuel reserves by 1980 and renewable adoption had been forced by necessity.

It's rather interesting though - science was once completely accepted by industry, but then scientific advances began undermining business profits - the discovery of industrial carcinogens, the discovery of fossil-fueled global warming, etc. really changed the dynamic and accurate science became as much of a threat to established interests as it was a boon.

[edit sources]:
1. https://www.climatefiles.com/exxonmobil/1978-exxon-memo-on-g...

2. https://journals.ametsoc.org/view/journals/phoc/5/1/1520-048...

3. https://www.science.org/doi/pdf/10.1126/science.296.5568.727