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Abstract Earth's terrestrial surfaces commonly exhibit topographic roughness at the scale of meters to tens of meters. 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‐hydro‐geomorphic 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. 

Windthrow, or the uprooting of trees by extreme wind gusts, is a natural forest disturbance that creates microhabitats, turns over soil, alters hydrology, and removes carbon from the above-ground carbon stock. Long recurrence intervals between extreme wind events, however, make direct observations of windthrow rare, challenging our understanding of this important disturbance process. To overcome this difficulty, we present an approach that uses the geomorphic record of hillslope topographic roughness as a proxy for the occurrence of windthrow. The approach produces a probability function of the number of annual windthrow events for a maximum wind speed, allowing us to explore how windthrow or tree strengths may change due to shifting wind climates. Slight changes to extreme wind speeds may drive comparatively large changes in windthrow production rates or force trees to respond and change the distribution. We also highlight that topographic roughness has the potential to serve as an important archive of extreme wind speeds.