Uplift histories of Africa and Australia from linear inverse modeling of drainage inventories

Abstract

We describe and apply a linear inverse model which calculates spatial and temporal patterns of uplift rate by minimizing the misfit between inventories of observed and predicted longitudinal river profiles. Our approach builds upon a more general, nonlinear, optimization model, which suggests that shapes of river profiles are dominantly controlled by upstream advection of kinematic waves of incision produced by spatial and temporal changes in regional uplift rate. Here we use the method of characteristics to solve a version of this problem. A damped, nonnegative, least squares approach is developed that permits river profiles to be inverted as a function of uplift rate. An important benefit of a linearized treatment is low computational cost. We have tested our algorithm by inverting 957 river profiles from both Africa and Australia. For each continent, the drainage network was constructed from a digital elevation model. The fidelity of river profiles extracted from this network was carefully checked using satellite imagery. River profiles were inverted many times to systematically investigate the trade-off between model misfit and smoothness. Spatial and temporal patterns of both uplift rate and cumulative uplift were calibrated using independent geologic and geophysical observations. Uplift patterns suggest that the topography of Africa and Australia grew in Cenozoic times. Inverse modeling of large inventories of river profiles demonstrates that drainage networks contain coherent signals that record the regional growth of elevation.

Numerical modelling of landscape and sediment flux response to precipitation rate change

“…However, recent numerical studies, such as Rudge et al (2015), have expanded this model to cover continent-scale landscapes. It is clearly plausible to suppose that erosion is primarily due to flowing water, so the assumption of geologically instantaneous transport may well be valid for mass that is transported as suspended load within the water column.…”

“…Using a version of Eq. (11) to invert river profiles for uplift histories, it is argued by some authors that n is close to unity (Rudge et al, 2015). However, certain river profiles may arguably be indicative of n > 1 (Lague, 2014).…”

“…However, there is reasonable debate as to the value of the slope exponent n in the stream power model (e.g. Lague, 2014;Croissant and Braun, 2014;Rudge et al, 2015) and likewise within the transport model it is plausible that the slope exponent γ > 1. The response time for the stream power model for various values of n has been explored within Baldwin et al (2003).…”

“…Pritchard et al, 2009). Studies of continent-scale inversion have found that the best fit value of k for the stream power model increases by 2 orders of magnitude to fit river profiles in Africa relative to Australia (Rudge et al, 2015). Such a large change in k would result in a highly significant difference in response time from continent to continent, which in itself would imply that tectonic and climatic signals are preserved in landscapes and sediment archives over vastly different time periods (see Demoulin et al, 2017).…”

The CAIRN method: automated, reproducible calculation of catchment-averaged denudation rates from cosmogenic nuclide concentrations

“…Simulating nuclide concentrations in settings where denudation rates vary in space and time is possible (Mudd, 2016), but computationally intensive and one must have some confidence that one can accurately reconstruct the temporal evolution of denudation rates. Although recent progress has been made in deriving time series of denudation rates from current topography (e.g., Whittaker et al, 2008;Pritchard et al, 2009;Hurst et al, 2013;Goren et al, 2014;Fox et al, 2014;Croissant and Braun, 2014;Rudge et al, 2015), these methods still suffer from the fact that we lack devices for time travel and struggle to test such reconstructions.…”