The response of erosional systems to climate cyclic variations

Abstract:

The stream power law commonly used to parameterize bedrock incision by mountain channels predicts that rainfall directly controls the rate of erosion and thus landform evolution. We have shown that cyclic variations in rainfall may induce a measurable response from erosional systems that is delayed by a time lag that depends on the forcing period. Here we will generalize this result using a simple landscape evolution model over a wide range of forcing periods to infer the potential erosional response of active tectonic systems to rainfall variability. In particular, we will show that each orogenic system is characterized by a response time scale that can be defined from its height and mean rock uplift rate. When the climate forcing period is much shorter than the response time of the orogenic system, the erosional response is amplified by a factor m, the area exponent in the stream power law, and in phase with the forcing signal (the time lag is nil). To the contrary, when the climate forcing period is longer than the response time of the orogen, the erosional signal is nil. This is what we show in the accompanying diagram where the time lag, θ, (normalized by the forcing period, P) and the gain, G, (relative amplitude of the erosional response normalized by the relative amplitude of the climate forcing) are plotted as a function of the climate forcing period normalized by the response time scale (τ). The time lags are the results of erosional waves propagating upstream at a rate that is independent of channel length, insuring that all rivers in a mountain belt respond in phase with each other and therefore constructively contribute to the overall sedimentary flux. Our work demonstrates that before interrogating the geological record to find evidence for climate control on erosional systems and, a fortiori, on tectonic systems, one needs to carefully consider the period (or the rate) at which the climate has changed. One must also consider that, when that response is measurable, there might exist an important time lag between the climate signal and the erosional response. We will also show how climate variability affects the sediment transport capacity of rivers and the effect this has on the relationship between climate and erosion in active mountain belts.