On the inference of denudation rates from cooling ages of minerals

The inference of denudation rates from the temperature–time histories of rocks is not straightforward, because the geothermal gradient evolves with time, as denudation advects heat towards the land surface. We show that the curvature in the temperature–time path recorded by an exhumed rock is strongly dependent upon denudation rate, and upon the temperature of the rock before denudation began, but only weakly dependent upon the initial geothermal gradient, the original depth of burial of the rock, or the duration of the denudation. For the case in which denudation rate is constant, a systematic search of parameter space yields robust estimates of denudation rate, and of the initial temperature. If there is prior knowledge of the initial geothermal gradient, the original depth of burial of the rock, or the duration of the denudation, this may be used further to limit the acceptable ranges of the other two parameters. Application of this procedure to two geological examples suggests that denudation rates in the Nanga Parbat massif are lower and less variable than previously suggested, and that the inference, drawn from accelerated cooling rates, of accelerating denudation in the Andes is incorrect.