Under wing lighting considerations
Generally it is a good idea to shoot flying birds when there is sunshine since the light allows fast shutter speeds. This often results in harsh shadows on the bellies and under wings. Using a fast lens and bright overcast can reduce the under body darkening, but not all of us have fast telephoto lenses.
This picture is potentially decent, but the shadows are not acceptable and no amount of on-board DRO or levels changes (to the dark sections) will save this shot. Just too dark. There are ways around this.
The undersides of birds that are coming in to land on water will sometimes be lighted by light reflected off the water. The top image below shows an untouched image as shot (except resized) and you can see the lighting under the wing is not too bad--the shadows being eliminated by the light coming up from the water.
The images below are also untouched. How is that possible? The answer is reflection from snow and white sand. Around here February and March (lots of geese are back) can be a great time for flight shots if there is snow on the ground .. it is a marvelous mirror.
White beach sand is also good. This is a frigatebird flying a few meters over a white sand beach. There is decent under body detail and there are no manips of light levels.
Late in the day (or early morning) bird shots are possible if they can be captured with their wings up in the air and well exposed to light. You can take a LOT of pictures to get one or two that are "right." You can get wings and bellies well lighted in mid day ... Sometimes. If you are lucky, birds will flare away and as they turn the entire underside can be exposed to sunlight. This works best in spring and fall when the sun is lower on the horizon. Questions?
I prepared this quite fast....probably will edit later.