Any geometric element of the Earth’s solid surface at an angle from the horizontal. Slope profiles are generally surveyed along a straight line (on a map) from the divide, following a line of steepest descent, to the nearest point at their base. The four possible elements of a hillslope profile are: an upper convexity, a free face, a straight slope of almost constant gradient, and a basal concavity. Not all of these features are found in every slope profile, and some may be repeated more than once within a profile.

The amount of the hillside that is convex in profile is usually expressed as a proportion of the total slope length, and most slopes are mainly convex. This proportion of convexity results from the processes acting on the slope, and the effects of the river at the base of the slope; rapid undercutting results in steeper and more convex slopes. With aggrading streams, more of the slope profile will be concave.

Hillslopes evolve over time in response to the redistribution of their surface sediments, usually with some net removal of material to rivers or the ocean. Where there is a plentiful supply of material, and the removal processes can only move a limited amount for a short distance, the rate of transport is limited by the transporting capacity of the process, which is defined as the maximum amount of material that the process can carry. Hence transport-limited hillslopes, where the rate of erosion/deposition is related to the divergence of shear stress, power, or velocity; see Pelletier (2012) ESPL 37, 1, 37.