Site Dependence of Fluvial Incision Rate Scaling With Timescale

Abstract

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.Plain Language Summary: The rate at which rivers cut into their own bed (incision) typically decreases with the age of past river surfaces used to infer it. This phenomenon, previously described for numerous geological processes, has been traditionally attributed to be a result of an unsteady incision process over the time of investigation. Alternatively, it has been argued that it is a consequence of a measurement bias that can occur when the modern river bed is used as a reference point. To test which of these contrasting hypotheses is valid, we designed specific tests for the competing models, yielding statistical criteria that can be used against actual data. We compiled data on river incision from 34 papers and compared them to the tests. A bias due to the choice of the modern river bed as reference point cannot explain the observations. Instead, we find a site‐specific dependence of incision on timescale. Thus, when comparing incision rates measured at different sites, time dependency needs to be corrected for. Using the field data, we offer a simple empirical equation that can be utilized for such a correction.Key Points: Fluvial bedrock incision rates decrease with the timescale over which they are averaged. Among the examined models, a power law model with a site‐dependent exponent is consistent with 26 previously published field data sets. An empirical equation is proposed to remove the Sadler effect and make incision rates measured at different timescales comparable.Israel Science Foundation (ISF) http://dx.doi.org/10.13039/501100003977Ben Gurion University of the Negev http://dx.doi.org/10.13039/501100014833National Cooperative for the Disposal of Radioactive Waste (NAGRA