Controls on the strength of coupling among climate, erosion, and deformation in two-sided, frictional orogenic wedges at steady state

[1] Many important insights regarding the coupling among climate, erosion, and tectonics have come from numerical simulations using coupled tectonic and surface process models. However, analyses to date have left the strength of the coupling between climate and tectonics uncertain and many questions unanswered. We present an approximate analytical solution for two-sided orogenic wedges obeying a frictional rheology, and in a condition of flux steady state, that makes explicit the nature and sensitivity of the coupling between climate and deformation. We make the simplifying assumption that the wedge grows in a self-similar fashion consistent with Airy isostasy such that topographic taper is invariant with orogen width, tectonic influx rate, and climate. We illustrate first how and why the form of the erosion rule matters to orogen evolution and then derive a physically based orogen-scale erosion rule. We show that steady state orogen width, crest elevation, and crustal thickness are controlled by the ratio of accretionary flux to erosional efficiency to a power dictated by the erosion process. Remarkably, we show that for most combinations of parameters in the erosion law, rock uplift rate is more strongly controlled by erosional efficiency than it is by the accretionary flux. Further, assuming frontal accretion with no underplating, the spatial distribution of erosional efficiency dictates the relative rock uplift rates on the pro-wedge and retro-wedge and the time-averaged trajectories of rocks through the orogen. The restriction to invariant frictional properties is conservative in these respects; systems subject to positive feedback between erosion and rheology will exhibit even stronger coupling among climate, erosion, and deformation than shown here.