I am not sure if this is what the earlier poster meant, but if it was a transient release rather than an ongoing discharge, the entire distribution curve you ar

I am not sure if this is what the earlier poster meant, but if it was a transient release rather than an ongoing discharge, the entire distribution curve you are referring to would be moving downstream. You have to work a flow model backwards to try to interpret where the pulse originated. It is a bit like trying to trace floating debris in the ocean backwards using models of currents and surface wave action. Because the velocity of flow varies throughout the cross section of the stream, this gradient will also get smeared out into a less distinct pulse as it flows downstream. If the contamination is not totally soluble, then this would get even more complicated as sedimentation would more likely occur in slower moving areas.