RivEX is capable of converting a river network into a measured network (PolylineM FeatureClass) using the build measured network tool. Your river network must conform to the RivEX  input specifications.

Build Measured Network tool

Such datasets when labelled with route ID's can be used for linear referencing.  You can display point and line data measured along your network.  If you are unfamiliar with linear referencing please refer to the on-line ESRI help for an overview.

Converting to a measured network and plotting events

Converting a network to a measured network to allow events to be plotted

Your data must have a valid coordinate system, this sets the data frame's units as this is needed when converting to different measurement units for the output.