The dynamic reference frame of rivers and apparent transience in incision rates

Incision rates derived from river terraces are commonly used to infer rock uplift rates; however, an apparent dependence of incision rate on measured time interval may confound directly relating incision to uplift. The time-dependent incision rates are a Sadler effect that have been argued to result from a stochastic distribution of hiatal intervals in river incision, potentially reducing the utility of incision records for interpreting unsteadiness in tectonic processes. Here we show that time-dependent incision rates can arise from a simple systematic bias in the distance measurement used to calculate incision rate, and thus stochastic causes are not required. We present a conceptual model that describes the dynamic history of streambed elevation over cycles of terrace formation, illustrating that measured incision rate is time dependent because the stream channel reference frame is not fixed with respect to the geoid. Because it is challenging to reconstruct the full elevation history for a river channel, most researchers use the modern streambed elevation as a reference datum, but we demonstrate that doing so imposes a bias that manifests as an apparent dependence of rate on measured time interval. Fortunately, correction of this bias is straightforward, and allows river incision data to be used in studies of tectonic or climatic unsteadiness.