A unified framework for evaluating step-pool spacing

Step-pool structures are natural features common in steep streams and often used in channel restoration projects. Proposed mechanisms for how step-pools form, however, make contrasting step spacing predictions, which hinders specific restoration targets from being established. In order to clarify how regular or random step-pool spacing should be, we create a generalized framework that allows comparison across mechanisms and applies to field, flume, and model observations. By comparing observed measures of spacing variability to reference values, we define a spectrum for step-pool spacing and observe limits on the maximum regularity or randomness natural sequences achieve. Within these limits, step-pools occupy a continuum rather than dividing into distinct random or regular clusters, although few mechanisms result in sequences with regularity comparable to antidunes. For the few cases where step-pool spacing exceeds the bounds of the continuum, external factors seem to prevent full equilibration. These exceptions mean that, in addition to enabling comparison across diverse settings, our framework makes testable predictions about the trajectory of step-evolution in disturbed streams.