They lay out the state-of-the-art of their model in detail, and it gives a good introduction to how they handle various parts of the climate system -- atmosphere (interactive or noninteractive), ocean, GHGs, aerosols, solar irradiance, volcanoes, etc -- and how the different pieces compare.
They end up with 6 different versions of their GISS E2 model, which are all the pairings of 3 different atmospheric models (distinguished by their treatment of atmospheric composition and the aerosol indirect effect) with 2 ocean models.
There are a lot of interesting results that show their model's strengths and weaknesses. Here, for example, are the results for their six versions for the surface air temperature for a historical reconstruction of the 1850-2012 period:
Here "R" and "H" represent their two different ocean models (the differences are subtle; see Section 2.2 of their paper), and "NINT," "TCAD," and "TCADI" are their atmospheric models, each with a different approach to determing atmospheric constituents (in short, whether some gases are specified or allowed to vary chemically, and how they handle the aerosol indirect effects).
That's a pretty good result for most permutations of their model, especially that which uses the "H" model of the ocean, and shows that they are "running hot" mostly only in the last decade or so, and begins to give a sense of why (based on the assumptions of the two different ocean models).
There are other interesting results, like a demonstration (yet again) that this period's climate cannot be explained by natural forcings alone, but can by including anthropogenic factors:
They have all kinds of other interesting results, like this for ocean heat content:
and this for polar sea ice:
so, perhaps not surprisingly, the Antarctic is tricky to capture; and finally, this table for observed and modeled atmospheric temperature trends from 1979 to 2005:
In a next paper (Nazarenko et al.), they use their model to project into the future:
The RCPs are the Representative Concentration Pathways that the IPCC is using now; Figure 2 in Nazarenko et al. give the GHG mixing ratios out to the year 2500 -- if someone put a gun to my head and made me pick just one RCP as most likely (and these days in America you never know), I'd probably go with RCP6.0 (the "6.0" means a radiative forcing of 6.0 W/m2 in the year 2100); it has an atmospheric CO2e level of about 725 ppm at the end of the century.
To the extent that this group's E2 model seems to work best with the "R" model of the ocean, RCP6.0 would imply a surface temperature about 2.0 to 2.5°C above the 1951-1980 baseline (call it 2.25°C). That's the global average; if you use the observed regional ratios from, say, the 34 years of the UAH results for the lower troposphere, it would mean an increase of
global surface: 2.25°C (4.1°F)
global land: 3.1°C (5.5°F)
northern hemisphere land: 3.8°C (6.9°F)
USA48: 4.0°C (7.1°F)
North Pole: 7.4°C (13.3°F)
Call it 1/3rd of an inverse ice age. In 150 years.
Anyway, these preprints, especially the first one, give a good little tutorial on what the models are trying to do, and how, and how well they can do it. There's lots to study there, and it answered some questions I've been carrying around.