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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. 

Meandering rivers experience fluctuations in width whenever riverbanks migrate in different directions or at different rates, which can be observed after individual floods. However, meandering rivers maintain approximately constant widths over decadal timescales. This implies some timescale below which width fluctuates as banks migrate independently, and above which width is maintained by a bank‐coupling process. This coupling is thought to occur either as point bar deposition events induce cutbank erosion (bar‐push), or as cutbank erosion events induce point bar deposition (bank‐pull). This coupling, however, has been challenging to observe in natural rivers due to limited event‐scale field data. We present results from a 4.5‐year campaign with 22 drone‐based lidar surveys of a single point bar and cutbank (∼0.35 km²in area) on the White River near Worthington, Indiana, USA. The middle point bar experienced net erosion (5,400 m³), but net aggradation (17,100 m³) between 2019 and 2022 when including perennially submerged regions. This aggradation was less than the 35,700 m³of cutbank erosion over the same period. Combined, we have observed widening (1.58 m/yr bend‐averaged; 3.08 m/yr near apex) over the study period as point bar deposition has not kept up with cutbank erosion. Finally, we suggest that the difference between bar‐push and bank‐pull as width‐maintenance mechanisms may not be resolvable by observing bend widening or narrowing alone without an advancement of current theory, such as determining a long‐term equilibrium width and measuring deviations relative thereto.