Apportionment of Elms, Maryland
The apportionment of aerosol from Elms, Maryland, not only
comes out well but also provides an example the the self-correcting nature of
the apportionment process. We illustrate this property by showing three parallel
strands of apportionment and how they all end up in the same place.
The sequences of apportionments go like this:
| Elms, Maryland, 17 elements | |||
| Step 0 | Nothing chosen | ||
| Step 2 | Sea and crust (NACC) chosen, fit 6.57 | ||
| Step 3 | Add Allen, fit 1.87 | Add Wye, fit 1.01 | Add Sweden, fit 2.11 |
| Step 4 | Add Wye, fit 0.60 | Add Pr. Geo., fit 0.52 | Add Allen, fit 1.16 |
| Step 5 | Add Pr. George, fit 0.30 | Add Allen, fit 0.30 | Add Wye, fit 0.57 |
| Step 6 | Add Pr. Geo, del. Sweden, fit 0.30 | ||
The three strands differ in fundamental ways: the first
begins with a coal flyash because a large contribution from this type-source is
indicated in step 0; the second begins with the best place-signature (Wye); the
third begins with the second-best place-signature, Sweden, and pursues a
European solution. Note how the Europe solution eventually returns to the North
American solution as Sweden is deleted (negative coefficient) in the last step,
when Prince George is added.
The first strand is shown below, as illustrated in boldface
italic:
|
Elms, Maryland, 17 elements |
|||
| Step 0 | Nothing chosen | ||
| Step 2 | Sea and crust (NACC) chosen, fit 6.57 | ||
| Step 3 | Add Allen, fit 1.87 | Add Wye, fit 1.01 | Add Sweden, fit 2.11 |
| Step 4 | Add Wye, fit 0.60 | Add Pr. Geo., fit 0.52 | Add Allen, fit 1.16 |
| Step 5 | Add Pr. George, fit 0.30 | Add Allen, fit 0.30 | Add Wye, fit 0.57 |
| Step 6 | Add Pr. Geo, del. Sweden, fit 0.30 | ||
For the second and third strands, click here(2) and here(3), respectively.
The solution beginning with the Allen Steam Coal Plant
Step 0, shown below, points strongly to eastern North
America, and nearby Wye in particular. The second-highest place-signature is
found in Sweden. The various crusts and coal flyashes, on the far right, also
have high F-ratios.
Step 2 is after the sea and the best crust, NACC, have been chosen. Wye remains the highest F-ratio of North America. European locations have F-ratios about as high as North American sites. One type-signature, for Allen Steam Coal, is unusually strong. Thus there are three avenues of apportionments to investigate: a North American solution beginning with Wye, a North American solution beginning with Allen, and a European solution beginning with Sweden. The Allen thread is shown below.
Step 3 of this thread chooses Allen Steam Coal. North America now dominate Europe, with nearby Wye having the highest F-ratio.
Step 4 adds nearby Wye. The fit of 0.60 is already very good. Nearby Prince George now has the highest remaining F-ratio.
Step 5 chooses Prince George. The fit becomes so good (0.30) that the apportionment can stop. The final solution (for this thread) is Wye, Prince George, and Allen Steam Coal (in addition to crest and sea, of course).
