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24 10,000 ;; ,,; ~ ;:; >- ~ llJOO " ;; So az wa wu uw X~ w ~ ~w a~ a~ WW ~W ~~ ~u 0- W~ ~ wu " ~ ~ '" 100 u ~ 5 a a ~ 10 I PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS ,," Hudson ~urve for stations in TaO!; arld$antl Fe Counties defined as "Area 2" 100 DRAINAGE AREA, IN SQUARE MILES llJOO 10,000 Fm1:1llE 21.-Relation of mean annual tlood discharge (equaled or exceeded in 2.3 years) to drainage area. Kllmber beside point is serial number in appendix. of the two lines should be alike, and indeed, they are similar. The intercepts should not be cxpected to be exactly the same bccause the discharge determined from flood-frequency data was chosen to represent a frequency of 2.3 years. Tbe frequency of that dis- charge which corresponds to full channel width is un- known and necd not be identical to the discharge ha~ing a 2.3-year recurrence. It should be recognized that cach of the graphical relations presented has considerable scatter owing to the nature of the measurement.s and the inherent variability of these factors in the field. It should not be inferred that a relation such as that presented be- tween discharge and stream order is considered precise. Rather we are concerned with explaining a methodology by which generalized relations can be obtained, and with demonstrating the nature of the interrelations between a variety of hydraulic and physiographic factors. In summary, it has becn shown that the ephemeral streams in N e\\T 1:fexico are characterized by a uniform do\vnstream increase of width, depth, and velocity with stream order, and also with drainage-basin size. Increasing size of drainage basins is accompanied by a do\vnstream increase in discharge. Furthermore, the interrelations among all of these factors, both hydraulic and physiographic, may be expressed in simple terms, either as exponential or power functions. The method of combining the hydraulic variables with factors measured on a map or obtained in the field from a dry stream bed allows a sincple means of obtaining inter- relations which cannot be measured directly. SOME RELATIONS OF HYDRAULIC AND PHYSIO_ GRAPHIC FACTORS TO THE LONGITUDINAL PROFILE CHANNEL ROUGHNESS AND PARTICLE SIZE The longitudinal profile of a river is ordinarily drawn as a graph showing elevation as a function of horizontal distance from the headwaters. Hack (1955) showed that if slope were substituted for elevation as the ordi- nate, the gradual downstream decrease in streaIll gradi-