The image below shows what I'm after. Each river segment has two values, the first is the number of obstructions on that segment, the second in parenthesis is the sum of the down stream obstructions and the obstruction on that segment. This would be similar to assigning a reach code except its not just a sum of a series of 1s based on the number of down stream segments.
I assume this is a network analyst issue but wanted to see if anyone here has other ways of approaching the problem? Any and all help is appreciated.