Short communication: Forward and inverse analytic models relating river long profile to tectonic uplift history, assuming a nonlinear slope–erosion dependency

Abstract

The long profile of rivers is shaped by the tectonic history that acted on the landscape. Faster uplift produces steeper channel segments, and knickpoints form in response to changes in the tectonic uplift rates. However, when the fluvial incision depends non-linearly on the river slope, as commonly expressed with a slope exponent of n≠1, the links between tectonic uplift rates and channel profile are complicated by channel dynamics that consume and form river segments. These non-linear dynamics hinder formal attempts to associate the form of channel profiles with the tectonic uplift history. Here, we derive an analytic model that explores a subset of the emergent non-linear dynamics relating to consuming channel segments and merging knickpoints. We find a criterion for knickpoint preservation and merging, and we develop a forward analytic model that resolves knickpoints and long profile evolution before and after knickpoint merging. We further develop a linear inverse scheme to infer tectonic uplift history from river profiles when all knickpoints are preserved. Application of the inverse scheme is demonstrated over the main trunks of the Dadu River basin that drains portions of the east Tibetan Plateau. The model infers two significant changes in the relative uplift rate history since the late Miocene that are compatible with low-temperature thermochronology. The analytic derivation and associated models provide a new framework to explore the links between tectonic uplift history and river profile evolution when the erosion rate and local slopes are non-linearly related.