Topographic roughness is a popular yet ambiguous metric used in surface process research for many applications that indicates something about the variation of topography over specified measurement intervals. In soil- and sediment-mantled settings topographic roughness may be framed as a competition between roughening and smoothing processes. In many cases, roughening processes may be specific eco-geo-hydromorphic events like shrub deaths, tree uprooting, river avulsions, or impact craters. The smoothing processes are all geomorphic processes that operate at smaller scales and tend to drive a diffusive evolution of the surface. In this article, we present a generalized theory that explains topographic roughness as an emergent property of geomorphic systems (semi-arid plains, forests, alluvial fans, heavily bombarded surfaces) that are periodically shocked by an addition of roughness which subsequently decays due to the action of all small scale, creep-like processes. We demonstrate theory for the examples listed above, but also illustrate that there is a continuum of topographic forms that the roughening process may take on so that the theory is broadly applicable. Furthermore, we demonstrate how our theory applies to any geomorphic feature that can be described as a pit or mound, pit-mound couplet, or mound-pit-mound complex.