From regular to random: a unifying framework for step-pool spacing

Abstract. Steep streams frequently display a distinctive step-pool structure where water crests over a near-vertical drop and plunges into a deeper depression in a repeated pattern. Because they naturally moderate the flow of water and sediment in hazardous mountain catchments, step-pools are often installed in stream management and restoration projects. However, emulating step-pool sequences is hindered by debate on whether natural step-pools are themselves regularly or randomly spaced. Here we show that the spacing of step-pool sequences spans a continuum between regularity and randomness driven by multiple formation mechanisms. Analyzing a compilation of natural, experimental, and numerically simulated step-pools, we found that natural variability and inherent limits on minimum spacing prevent fully regular or random sequences. While certain mechanisms result in comparatively regular or random spacing, no single mechanism dominates step-pool development. Our results resolve longstanding tension between a plethora of proposed formation mechanisms that yield contrasting predictions. Furthermore, the emergent limits on spacing variability provide testable predictions about the adjustment of sequence spacing following river disturbance that may eventually be used to define concrete targets for stream restoration and hazard management.