Apportionment of Jungfraujoch
As noted earlier in the text, the apportionment of Jungfraujoch is a failure, at least on the surface. The steps are shown in the table, with links for quick viewing.
| Jungfraujoch, 20 elements | ||
| Japan/Korea branch | European branch | |
| Step 0 | ||
| Step 2 | ||
| Step 3 | Japan added, fit 1.17 | Plynlimon added, fit 1.76 |
| Step 4 | Niigata added, fit 0.92 | Belgium added, fit 1.46 |
| Step 5 | DCref added, fit 0.65 | DCref added, fit 0.73 |
Its step 0, before any signatures are chosen, points equivalently to a variety of widely separated places, including North America, parts of Europe and Russia, China, Japan, and several type-sources.
Step 2, after selecting sea and Far East Crust, shows that Japanese signatures strongly dominate. Japanese sources are obviously not the right ones for Jungfraujoch, however, because the Swiss Alps are nearly halfway around the world from Japan. But to be fair, we must begin with Japan and see how the solution looks.
Step 3 adds the best Japanese signature, the average of all the Japanese cities. Nearly everything else collapses.
Step 4 adds Niigata, the best of the remaining signatures. This brings the fit to a decent 0.92.
Step 5 adds the type-signature DCref, from a refuse incinerator in Washington, D.C. This improves the numerical fit to 0.65 without adding much sense or believability to it. It also marks the end of this strand.
In a nonblind attempt to see whether closer signatures could produce a fit equivalent to Japan's, a solution was begun with Plynlimon, the best-fitting of the European signatures. Its entry, after crust and sea, is shown as the new step 3 below.
The new step 4 added Belgium, the best of the remaining European signatures.
The new step 5 adds the next-best F-ratio, which is DCref again. (The very high samples just left of Plynlimon is not in contention because its coefficient is negative.) That improves the overall fit to a decent 0.73, nearly as good as the 0.65 for the Japanese signatures. The moral here is that the most obvious sources may not be the only ones to give a good fit, and may not represent the correct solution. The real solution may be one that is a combination hidden from view and developed only by two or three probing steps. As we further develop this tracer system, we hope to be able to find algorithms for discovering these hidden solutions.
Two solutions were found for the Jungfraujoch aerosol, an obvious one that failed (Japan) and a hidden one that seemed to succeed (as defined by a good fit made from reasonable signatures).