The constant supply of a river is the bay, sea, etc. When that bay experiences high tide, there is more water in the bay. That water wants to go somewhere, so it proceeds downriver, and increase the water level in the river as well. The smaller and shallower the river, the greater tide it will experience. Eventually, the extra tidal water reaches a point a larger part of the river, where it has covered a certain area of river, and thus the extra water flow has less of an effect.
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