A Simple Model for the Response Time of Landforms, its Use in Unravelling the Effect of Time-varying Climate and Tectonics on Landforms, and its Use in Assessing the Role in Landform Response to These Time-varying Inputs of Co-evolving Landscape Properties Such as Soils and Vegetation

Abstract:

Unravelling the geomorphic effect of time-varying inputs into landscape evolution involves understanding the impact of numerous exogenic inputs (e.g. climate, tectonics) with different timescales on processes (e.g. vegetation growth) and geomorphic variables (e.g. topography, soils) that themselves have varying response times. If the geomorphology has long response times relative to the rate of time variation of the inputs then the geomorphology will likely respond to the statistics of the inputs, but if timescales of inputs are comparable to the response times then the deterministic details of the time-varying inputs may be important leading to co-evolution. As a first step to unravelling these interactions this paper shows that landforms have a spectrum of response times. This will be shown using a simple analytic model of landform response times that has been validated against a landform evolution model. The analytic model shows that response time (1) varies within the catchment (thus generating a spectrum of response times), (2) the spatial distribution of the response rate (relative to the spatial mean) is easily predicted based on catchment elevation, (3) is a function of whether climate or tectonics is the time-varying exogenic input, and (4) is independent of whether erosion is transport- or detachment-limited and is a function only of the erosion rate (for catchments at or near the dynamic equilibrium with the mean of the exogenic input). The paper will show that the analytic response time model, while simple in conception, is also a potentially powerful tool for understanding the importance of the response times of other, potentially co-evolving, components of the landscape (e.g. soils and vegetation) in determining the trajectory of landscape evolution. A simple example of a hillslope with time-varying soils evolution (using a calibrated pedogenesis model) will be shown. This example will demonstrate how this analytic model can be used in both modelling and field studies to simplify the interpretation and modelling of the interacting components of landscape evolution.