The relation between overland-flow erosion and gradient on debris-covered semiarid hillslopes in Walnut Gulch Experimental Watershed, Arizona, is investigated by conducting three sets of field experiments under simulated rainfall on two different substrates. Each set of experiments yields a convex-upward sediment yield-gradient relation with a vertex at about 12°. The key to understanding this relation is the relation between runoff and gradient. On slopes less than 12° runoff appears to increase very slowly with gradient, and so sediment yield increases with gradient mainly in response to the increase in the downslope component of gravity. On slopes steeper than 12°, runoff decreases rapidly as gradient increases. This decrease in runoff outweighs the increase in the down-slope component of gravity as gradient increases and causes sediment yield to decrease.

In all three sets of experiments, runoff is controlled by either stone cover or stone size, and stone size increases with gradient. Inasmuch as stone cover and stone size are indicators of mantle stoniness, these findings suggest that curvilinear relations between runoff and gradient and, hence, convex-upward relations between sediment yield and gradient occur only on hillslopes with coarse weathering mantles in which stoniness increases with gradient. Different combinations of substrate and climate may produce such hillslopes. They are especially likely to develop in arid and semiarid climates, but they may also form in alpine, periglacial, and humid ones where substrates are favorable. Hillslopes on which mass movement processes are the dominant denudational agents will not have convex-upward relations.

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