Are parameters akin to the factors of Raymond Cattell’s “factor analysis”?

I’m not sure, but I doubt it! (I’m not familiar with Raynold Cattell’s “factor analysis” but,mostly, the parameters in AOGCMs’ don’t come from factor analyses of anything.

a “functional form” mean something expressed like a typical formula I might see in a high school physics textbook (or college textbook if it were expressed with differentials)?

That’s a good analogy. The difference is that in your high school physics texts the authors focus on physical processes that are very well understood.

Incidentally, is Roy a verb in “predict that Roy a value”?

And the next natural question, when architects and engineers design a skyscraper. How often do they get the size of their air conditioning units wrong? Judging from news reports regarding the State of Illinois building in Chicago – It can happen.

Close passages of coronal mass ejections from the sun are signaled at the Earth’s surface by Forbush decreases in cosmic ray counts. We find that low clouds contain less liquid water following Forbush decreases (FDs), and for the most influential events the liquid water in the oceanic atmosphere can diminish by as much as 7%. Cloud water content as gauged by the Special Sensor Microwave/Imager (SSM/I) reaches a minimum around 7 days after the Forbush minimum in cosmic rays, and so does the fraction of low clouds seen by the Moderate Resolution Imaging Spectroradiometer (MODIS) and in the International Satellite Cloud Climate Project (ISCCP). Parallel observations by the aerosol robotic network AERONET reveal falls in the relative abundance of fine aerosol particles which, in normal circumstances, could have evolved into cloud condensation nuclei (CCN). Thus a link between the sun, cosmic rays, aerosols, and liquid-water clouds appears to exist on a global scale.

Svensmark, H., T. Bondo, and J. Svensmark (2009),
Cosmic ray decreases affect atmospheric aerosols and clouds,
Geophys. Res. Lett., doi:10.1029/2009GL038429, in press.
(accepted 17 June 2009)

1) Calculate a raw projection based on the last 12 months of data. *THIS IS NOT MY JUNE FORECAST*. For June, I have…
Hadley temp 0.385; slope 0.407
GISS temp 0.40; slope 0.602
UAH temp -0.087; slope 0.997
RSS temp 0.113; slope 0.922

2) Wait for RSS to come out, and make my June forecasts as follows…
delta = RSS(June) – 0.113
Hadley = 0.385 + delta * 0.407 / 0.922
GISS = 0.40 + delta * 0.602 / 0.922

I don’t bother with UAH monthly, because it seems all over the place. Anyhow, Roy publishes it on his blog at http://www.drroyspencer.com/category/blogarticle/ before updating the monthly temperature.

Note:

Aqua Mission
Aqua is a major international Earth Science satellite mission centered at NASA. Launched on May 4, 2002, the satellite has six different Earth-observing instruments on board and is named for the large amount of information being obtained about water in the Earth system from its stream of approximately 89 Gigabytes of data a day. The water variables being measured include almost all elements of the water cycle and involve water in its liquid, solid, and vapor forms. Additional variables being measured include radiative energy fluxes, aerosols, vegetation cover on the land, phytoplankton and dissolved organic matter in the oceans, and air, land, and water temperatures.

2.7 Terabytes of data per month should give you plenty to play with!

More importantly, showing the trends in H2O optical depth, the CO2 optical depth and the Total optical depth should clearly show the relative impacts and the amplification factor.

After his figure 19, see Miskolczi’s (2009) graphs:
“Trends in the NOAA 61 year series” where he shows annual data for Temperature, H2O column amount, and CO2 column amount.
Below that he shows:
“Trends in Flux Optical Depth”

As data is available, I am suggesting that it might be possible to calculate monthly “Flux Optical Depth”.
NOAA nominally provides monthly values for Air Temperature, and specific humidity. (Though it would take some digging to trace raw data to delivered parameters.) CO2 is available from Mauna Loa.
With those parameters, Miskolczi calculates the flux optical depth with his very high resolution HARTCODE.

(I don’t think this depends on the planetary greenhouse theory he developed. The moisture and CO2 lapse rate could be included for refinement.)

There are also new satellites providing current detailed H2O and CO2 with altitude and location. (Apparently the
Orbiting Carbon Observatory didn’t make it into orbit.)
It would be worth a megabuck grant and several PhD theses to evaluate those for a more accurate global flux optical depth.