Good morning, Dan~
In my experience - based on those tidal waters around Long Island - the tides probably play the largest role in determining the movements of waterfowl. The "normal" daily tide ranges vary from about 2 feet to about 7 feet around the Island.
The natural relationship is between water depth and availability of food, both vegetable and animal. On a normal tide cycle, most waterfowl feed on the falling tide because the food is once again within reach after the flood tide. Of course, this is more important to puddle ducks - and Geese and Brant.
Time of day gains importance during the hunting season because of gunner pressure. Waterfowl often adopt a feeding schedule that allows them to loaf away from hunters and feed only during the darker hours. So, birds may leave feeding areas at first light and return only after quitting time.
Daily weather affects the patterns, especially with stressful conditions like cold and strong winds. Birds may alter their daily rituals because they need the energy to keep warm/survive.
Big flood tides - driven by wind and or the moon - can also "open up" great feeding areas, such as the High Marsh (salt hay meadows). When inundated, ducks flock here to get at the Salt Marsh Snails (Melampus) and other invertebrates that are normally on "dry" land.
When I lived on LI - before the interwebs - I kept a copy of the tide tables in my glove compartment - and planned my hunts around the falling tides, especially if they were in the afternoons. And, I soon learned that these tables are predictions - not guarantees. Strong winds can and do change the magnitude and time of tides.
This, of course, is just a very brief overview of a complex and fascinating topic.
All the best,
SJS