Hi Ken,
I'm busy with another TIGHAR project, but I just happened to check in and saw your question.
The "donut" was computed by the ICEPAC propagation model, using the dorsal antenna gain pattern computed by 4NEC2. The SNR at the Itasca was computed versus Electra distance in 20-mile increments along the LOP, from 20 miles to 340 miles.
At short distances, the antenna gain is sharply reduced due to the radiation pattern. You can visualize the pattern by cutting an apple in half at its "equator", and letting the distance from the the apple's original center point (which is now in the "equator" plane) to the skin represent the gain. The dimple where the stem attached to the apple is a good illustration of the antenna's performance at high takeoff angles. When the Electra was close to Itasca, the SNR was low enough to preclude clear reception. As the distance increased, the SNR increased, until the distance reached the point where the SNR fell off again due to propagation loss. Hence the notion of "donut"
It's possible that there was direct path propagation at short distances, due to excitation of the airframe, but ICEPAC only calculates path loss for an ionospheric path. However, at 1,000 feet altitude (where Earhart said she was flying then), the horizon distance is about 38 miles. So outside about 40 miles, there wouldn't be any direct path, and skywave would govern.
Anyway, it's a safe bet that Earhart wasn't within the horizon of Itasca, since the ship would have been visible against the horizon at that distance -- contrary to the common assumption that the visibility of Howland was the controlling factor. There also seems to be a common assumption that Howland was obscured by the sun. The only plausible reason for Earhart to be at 1,000 is that there was a cloud deck obscuring the surface from 8,000 feet. Going down to 1,000 feet put her in the clear, with the cloud deck between her and the sun. but also limited her search horizon. The Itasca -- even hull down on the horizon -- would be visible against the cloud deck background. Moreover, Itasca reported making smoke, which would blow along the surface with the wind [coming from about east], and which would be visible as a dark mark on the surface. I have serious doubts about the feasibility of laying down black smoke for very long, since doing so carried a non-trivial risk of damaging the ship's boiler(s). But even without the smoke, Earhart and/or Noonan [who had extensive seagoing experience and would know about sighting ships on the horizon] could have seen the Itasca if they were within the visual horizon.
So the donut is our best guess of where the Electra could have been when Itasca was hearing Earhart.
Bob
Bob