Erosional response of an actively uplifting mountain belt to cyclic rainfall variations

We present an approximate analytical solution to the stream power equation describing the erosion of bedrock in an actively uplifting mountain range subject to periodic variations in precipitation rate. It predicts a time lag between the climate forcing and the erosional response of the system that increases with the forcing period. The predicted variations in the sedimentary flux coming out of the mountain are also scaled with respect to the imposed rainfall variations in a direct proportion to the discharge exponent, m, in the stream power law expression. These findings are confirmed by 1-D and 2-D numerical solutions. We also show that the response of a river channel is independent of its length and thus the size of its catchment area, implying that all actively eroding streams in a mountain belt will constructively contribute to the integrated signal in the sedimentary record. We show that rainfall variability at Milankovitch periods should affect the erosional response of fast uplifting mountain belts such as the Himalayas, Taiwan or the South Island, New Zealand, and predict 1000 to 10 000-year offsets between forcing and response. We suggest that this theoretical prediction could be used to independently constrain the value of the poorly defined stream power law exponents, and provide an example of how this could be done, using geochemical proxy signals from an ODP borehole in the Bengal Fan.