In this presentation, I will demonstrate that the Sun drives climate, and use that demonstrated relationship to predict the Earth’s climate to 2030. It is a prediction that differs from most in the public domain. It is a prediction of imminent cooling.
-- Solar Cycle 24: Implications for the United States, Archibald, 2008
I contacted Archibald earlier this year as I attempted to reproduce a couple of the graphs in his 2008 Solar Cooling presentation. He responded promptly but wasn't able to provide me any help telling me that the computer he used for that presentation had crashed some time before and he had no alternate sources. Nor did he recall the methods used.
I began with Archibald's chart entitled 'A US Rural Data Set.' I note that 1) he used GISTEMP data and 2) listed the five stations he used by name and 3) that he smoothed the annual average
I know that the source of GISTEMP US data is USHCN, so I turned there for the station data. Strangely, all the USHCN data begins in 1895, but the first time tick on the chart is for 1893.
Archibald has chosen five widely distributed, rural stations as representative of the continental United States. It was easy to locate the Station IDs by name in the USHCN station inventory. The stations are mapped below.
093754 31.9881 -81.9522 61.0 GA GLENNVILLE 3NW
094170 33.2842 -83.4681 74.7 GA HAWKINSVILLE
098535 32.6875 -84.5197 195.1 GA TALBOTTON
161411 32.5133 -92.3478 54.9 LA CALHOUN RSCH STN
314055 35.0536 -83.1892 1170.4 NC HIGHLANDS

Archibald mentions that he smoothed annual averages, but does not recall the exact method. Examining several different smooths, the best fit I could find was a 3 year moving average, which fits well in recent decades, but diverges somewhat in middle decades while maintaining a similar variation throughout. I cut the station data at the year 2003, the last year shown on the original chart. This fit is shown below.

Having found a reasonable fit to the station data, I turn next to the "Projected Temperature Profile to 2030." The pre-2003 rural US data set has been further smoothed and, strangely, cooled by about 0.5C. This may be due to some sort of averaging with the solar smooth shown earlier in the presentation. Nevertheless, I found a lowess smooth (f=0.04) of the 3 year moving average creates a reasonable likeness of the 2030 projection chart. I have added the post-2003 data points and the continued lowess in red.

This is not a perfect reconstruction by any means. The data sets are not the same. The range appears to be different. The visual matching may be impaired by poor scaling in the background images. Nevertheless, it should be adequate for qualitative comparisons of future observations to the original temperature projection.

Combining the rural US data set we saw earlier and the projected temperature response to the length of Solar Cycle 23, this graph shows the expected decline to 2030. The temperature decline will be as steep as that of the 1970s cooling scare, but will go on for longer.
-- Solar Cycle 24: Implications for the United States, Archibald, 2008