Upon having some astronomical phenomena explained to him, Alfonso X, King of Castile and Leon (1252–84) exclaimed,

River engineers and geomorphologists might well have a similar opinion especially when it is recognized how variable a river can be through time and from reach to reach. However, when Leopold and Maddock published US Geological Survey Professional Paper 252 it was a landmark occasion. Geologists and geomorphologists suddenly became aware of order in rivers, although engineers with their regime equations had anticipated these hydraulic geometry relations. The hydraulic geometry relations of width, depth, and velocity were immediately of value in prediction of river characteristics. However, some of us neglected to recognize how variable the relations were and how significant was the scatter about the regression lines. This should have warned us that, yes, in a general sense channel width increased downstream as the 0.5 power of discharge, but a prediction of what the width was around the next bend could be in gross error, and, therefore recognizing this variability could be of considerable practical significance.

River characteristics vary sometimes little and sometimes greatly. Reaches are singular because of the numerous variables acting that prevent a single variable, discharge, from dominating river morphology and behavior. The question to be answered is why is one reach of a river connected to a different type of reach? That is, why can reaches be so different?