I know that AM radio station signals fluctuate in quality with time of day because of changes in the ionosphere. How do these changes trend with time of day?
I'll give this one a shot.
The ionosphere is a region of the upper atmosphere, where the atoms and molecules are ionized by photons coming primarily from the sun, but also from cosmic rays. During the day, the ionosphere is said to be "charged" - there are loads of free electrons bumping into each other. This charged state of the ionosphere is what causes radio waves to lose strength - a phenomenon called ionospheric absorption. At night, due to the absence of ionizing sunlight, the ions recombine and this charge is drained due to absence of a source of ionizing radiation. A small part, however, remains due to cosmic rays.
A consequence of all this is that during the day, AM radio signals can't really travel by skywave, and so travel by groundwave, diffracting around the curve of the earth. Since the ground is not a perfect electrical conductor, ground waves lose strength as they follow the earth’s surface, although this loss of signal strength is low for lower frequencies. The conductivity of the surface affects propagation of groundwaves - that means if the groundwave is travelling over water, it will travel further for the same loss in signal strength.
However, after sunset, the the AM radio signals can bounce off the bottom of the ionosphere and head back towards the earth as if they were reflected by a mirror. These 'hops' are quite large. The surface of the earth and the ionosphere form a kind of waveguide in which the AM radio signals can travel. The range using skywave is often much larger than it is using groundwave, which is why AM radio stations can be heard much farther from their point of origin during the night than during the day. Since skywave propagation depends on the state of the ionosphere, it should be sensitive to ionospheric disturbances caused by solar flares or geomagnetic storms.