Dynamic base level and deterministic climate forcing as a possible explanation for transience in bedrock river incision rates

Abstract:

Records of bedrock river incision are commonly used to infer rock uplift under the assumption that rates of these two processes match over the long term (>10⁵ yrs). A recent compilation of 14 bedrock river incision records, however, illustrates a dependence of rate on measured interval on time scales approaching 10⁷ yrs, a characteristic that we term the fluvial Sadler effect. The process(es) responsible for such a fluvial Sadler effect over long time scales is unknown, but it is argued to arise because hiatuses in fluvial incision follow a stochastic, heavy-tailed distribution. If correct, linking river incision and rock uplift becomes more complicated than previously thought. Motivated by pervasive evidence in support of non-stochastic, quasi-cyclic climate forcing as modulating rates of bedrock river incision, we explore the degree to which the fluvial Sadler effect may instead arise by such deterministic forcing. We demonstrate that river incision rate is inherently a time dependent measurement, because the reference frame from which it is calculated (the river profile) is dynamic and not fixed with respect to the geoid. Out of necessity, the modern river profile is often used to calculate river incision. Even when uplift is steady and uniform and incision is modulated by quasi-cyclic, deterministic forcing, the use of this static reference systematically biases calculations of river incision producing a dependence of rate on measured interval that is similar to expectations for a stochastic, heavy-tailed distribution. In such cases, the fluvial Sadler effect persists at all time scales, but is largely minimized at times greater than one period of the longest quasi-cyclic forcing. We conclude that bedrock river incision rate, when modulated by deterministic climatic forcing, provides a reliable proxy for rock uplift rate given integration across at least one glacial-interglacial cycle (>10⁵ yrs) and consideration of the correct local base level datum.