The longitudinal river, valley and regional profiles were plotted for the Red River. Plotting was done in such a way that specific geographic points and hydraulic parameters on one of the profiles could be correlated with the corresponding geographic points on the others.

Strong interrelationships were found for the Red River between river sinuosity and valley slope. A smooth longitudinal river profile was maintained, in spite of irregularities in the valley or regional slope, by changes in sinuosity. A channel pattern alternation between braided and non-braided was found to be associated with changes in water surface slope. A new function was developed, herein called the meander function, which was found to be correlated with channel pattern and slope.

Although this paper is confined to the Red River the techniques used can be applied to any river.