To analyze the development of erosional topography the writer studied geomorphic processes and landforms in a small badlands area at Perth Amboy, New Jersey. The badlands developed on a clay-sand fill and were morphologically similar to badlands and areas of high relief in semiarid and arid regions. A fifth-order drainage system was selected for detailed study.
Composition of this drainage network conforms to Horton's laws. Within an area of homogeneous lithology and simple structure the drainage network develops in direct relation to a fixed value for the minimum area required for channel maintenance. Observed relationships between channel length, drainage-basin area, and stream-order number are dependent on this constant of channel maintenance which is in turn dependent on relative relief, lithology, and climate of any area.
Other characteristics of the drainage network and topography such as texture, maximum slope angles, stream gradients, drainage-basin shape, annual sediment loss per unit area, infiltration rate, drainage pattern, and even the morphologic evolution of the area appear related to relative relief expressed as a relief ratio, the height of the drainage basin divided by the length. Within one topographic unit or between areas of dissimilar but homogeneous lithology the relief ratio is a valuable means of comparing geomorphic characteristics.
Hypsometric curves are available for a series of 11 second-order drainage basins ranging in stage of development from initial to mature. Relief ratio and stream gradients attain a constant value when approximately 25 per cent of the mass of the basin has been eroded. Basin shape becomes essentially constant at 40 per cent of mass removed in accord with Strahler's hypothesis of time-independent forms of the steady state.
Comparison of the drainage pattern as mapped in 1948 with that of 1952 reveals a systematic change in angles of junction and a shift of the entire drainage pattern accompanying changes in the ratio between ground and channel slope.
Field observations and experimental studies suggest that badland slopes may retreat in parallel planes and that the rate of erosion on a slope is a function of the slope angle. The retreat of slopes may not conform to accepted concepts of runoff action as a function of depth and distance downslope. Runoff occurs as surge and subdivided flow which may be closely analogous to surficial creep.
Rills follow a definite cycle of destruction and reappearance throughout the year under the action of runoff and frost heaving.
At Perth Amboy, slopes are initiated by channel degradation and maintained by runoff and by creep induced through frost heaving. Runoff or creep may form convex divides, and both parallel and declining slope retreat are important in the evolution of stream-carved topography.
Hypsometric curves reveal that the point of maximum erosion within a drainage basin migrates upchannel and that the mass-distribution curve of any basin has a similar evolution to that of the longitudinal stream profile.
Comparative studies in badland areas of South Dakota and Arizona confirm conclusions drawn at Perth Amboy and show the importance of infiltration of runoff on topographic development and of subsurface flow in slope retreat and miniature pediment formation.