Site Dependence of Fluvial Incision Rate Scaling With Timescale

Global measurements of incision rate typically show a negative scaling with the timescale over which they were averaged, a phenomenon referred to as the “Sadler effect.” This time dependency is thought to result from hiatus periods between incision phases, which leads to a power law scaling of incision rate with timescale. Alternatively, the “Sadler effect” has been argued to be a consequence of the mobility of the modern river bed, where the timescale dependency of incision rates arises from a bias due to the choice of the reference system. In this case, incision rates should be independent of the timescale, provided that the correct reference system is chosen. It is unclear which model best explains the “Sadler effect,” and, if a timescale dependency exists, which mathematical formulation can be used to describe it. Here, we present a compilation of 581 bedrock incision rates from 34 studies, averaged over timescales ranging from single floods to millions of years. We constrain the functional relationship between incision rate and timescale and show that time-independent incision rate is inconsistent with the global data. Using a power law dependence, a single constant power is inconsistent with the distribution of observed exponents. Therefore, the scaling exponent is site dependent. Consequently, incision rates measured over contrasting timescales cannot be meaningfully compared between different field sites without properly considering the “Sadler effect.” We explore the controls on the variable exponents and propose an empirical equation to correct observed incision rates for their timescale dependency.