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Critical wedge theory provides a direct link between the form of an orogen, the rate of orogen evolution, and the accretionary and erosional fluxes that promote orogen growth and decay, respectively. We explore several fundamental characteristics of an eroding critical orogen: (1) the sensitivity of steady-state orogen size to tectonic and climatic forcing, (2) the response time of a critical orogen to perturbations in forcing, and (3) the behavior of surface topography and the rock uplift field in a system in which they are not prescribed. To do this, we develop a numerical model that couples a two-dimensional, planform surface erosion model with a two-dimensional, plane-strain finite element model of deformation. We first present a base model in which a critical orogen evolves to a steady-state under boundary conditions similar to those of analog sandbox experiments. We find that mean topography and tectonic uplift reach steady states, whereas planform topography remains dynamic throughout the simulation. From a suite of simulations, we determine the steady-state scaling relationship between orogen size and tectonic and climatic forcing and find good agreement with predictions from one-dimensional models. In addition, we examine the response of the steady-state orogen to climatic and tectonic perturbation with four simulations in which changes in tectonic and climatic conditions lead to either growth or contraction of the orogen to a new steady state. We show that the response time to perturbation agrees well with predictions from a one-dimensional semi-analytical model. We find that the transient evolution of erosion rate and erosional flux is potentially useful for distinguishing between tectonic and climatic forcing mechanisms.

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