Numerical modelling landscape and sediment flux response to precipitation rate change

Abstract

Abstract. Laboratory-scale experiments of erosion have demonstrated that landscapes have a natural (or intrinsic) response time to a change in precipitation rate. In the last few decades there has been a growth in the development of numerical models that attempt to capture landscape evolution over long time-scales. Recently, a sub-set of these numerical models have been used to invert river profiles for past tectonic conditions even during variable climatic conditions. However, there is still an 5 uncertainty over validity of the basic assumption of mass transport that are made in deriving these models. In this contribution we therefore return to a principle assumption of sediment transport within the mass balance for surface processes, and explore the sensitivity of the classic end-member landscape evolution models to change in precipitation rates. One end-member model takes the mathematical form of a kinetic wave equation and is known as the stream power model, where sediment is assumed to be transported immediately out of the model domain. The second end-member model takes the form of a diffusion equation, 10 and assumes that the sediment flux is a function of the water flux and slope. We find that both of these end-member models have a response time that has a proportionality to the precipitation rate that follows a negative power law. For the stream power model the exponent on the water flux term must be less than one, and for the sediment transport model the exponent must be greater than one in order to match the observed concavity of natural systems. This difference in exponent means that sediment transport model responds more rapidly to an increase in precipitation rates, on the order of 10 5 years for a landscape with 15 a scale of 10 5 m. In nature, landscape response times to a rapid environmental change have been estimated for events such as the Paleocene-Eocene thermal maximum (PETM). In the Spanish Pyrenees, a relatively rapid, 20 to 100 kyr, duration of deposition of gravel during the PETM is observed for a climatic shift that is thought to be towards increased precipitation rates. We suggest the rapid response observed is more easily explained through a diffusive sediment transport model, as (1) this model has a faster response time, consistent with the documented stratigraphic data, and (2) the assumption of instantaneous 20 transport is difficult to justify for the transport of large grain sizes as an alluvial bed-load.

Ecohydrology Controls the Geomorphic Response to Climate Change

“…For the wet‐to‐dry shift, the trajectory begins at B w , and landscape slope and erosion rate gradually increase, returning the landscape state to dry equilibrium (B d ) at a slower pace (red arrows). This behavior is consistent with previous modeling (Armitage et al, , ) and experimental landscape evolution results (Singh et al, ).…”

Continental‐Scale Landscape Evolution: A History of North American Topography

“…Nevertheless, there is a substantial body of work which demonstrates that at smaller scales these processes determine the efficacy of fluvial erosion and the geometry of river profiles (e.g. Armitage et al, 2018;Baynes et al, 2018;Forte & Whipple, 2018;Gallen, 2018). It is unclear how these complex, dynamic, threshold-dependent, and undoubtedly nonlinear, processes scale over geologic timescales.…”

Global Sensitivity Analysis of Parameter Uncertainty in Landscape Evolution Models

“…There are several past studies investigating how LEMs respond to process changes and model parameters, including changes in climate variability and precipitation resolution (Armitage et al, 2017;Coulthard and Skinner, 2016a;Ijjasz-Vasquez et al, 1992;Tucker and Bras, 2000), channel widths (Attal et al, 2008), vegetation (Collins, 2004;Istanbulluoglu and Bras, 2005), and variations in initial conditions (Hancock, 2006;Hancock et al, 2016;Ijjasz-Vasquez et al, 1992;Willgoose et al, 2013).…”

“…Yet few studies explicitly perform SA and most of the applications described above are exploring LEM sensitivity to processes, or changes in environmental conditions, and are more correctly referred to as exploratory tests (Larsen et al, 2014). On the other hand, investigations to ascertain the model's response to potential uncertainties (e.g from model parameterisation) can be deemed as true SA (eg, Armitage et al, 2017;Coulthard and Skinner, 2016a;Hancock et al, 2016).…”