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We present an approximate analytical solution to the stream power equationdescribing the erosion of bedrock in an actively uplifting mountain rangesubject to periodic variations in precipitation rate. It predicts a time lagbetween the climate forcing and the erosional response of the system thatincreases with the forcing period. The predicted variations in thesedimentary flux coming out of the mountain are also scaled with respect tothe imposed rainfall variations in a direct proportion to the dischargeexponent, <i>m</i>, in the stream power law expression. These findings areconfirmed by 1-D and 2-D numerical solutions. We also show that the response ofa river channel is independent of its length and thus the size of itscatchment area, implying that all actively eroding streams in a mountain beltwill constructively contribute to the integrated signal in the sedimentaryrecord. We show that rainfall variability at Milankovitch periods shouldaffect the erosional response of fast uplifting mountain belts such as theHimalayas, Taiwan or the South Island, New Zealand, and predict 1000 to 10 000-yearoffsets between forcing and response. We suggest that this theoreticalprediction could be used to independently constrain the value of the poorlydefined stream power law exponents, and provide an example of how this couldbe done, using geochemical proxy signals from an ODP borehole in the Bengal Fan

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