Topography and isotherms revisited: the influence of laterally migrating drainage divides

Drainage divides of mountain ranges will shift laterally during asymmetric erosion of the range. Such asymmetric erosion may occur due to differential precipitation on different sides of a range, or because of different topographic gradients, for example at passive margins. Here, a semi-analytical solution is presented that can be used to evaluate the shape of isotherms underneath an asymmetrically eroding, randomly shaped topography. It is shown that, because of this asymmetric erosion, cooling curves of rocks from the slowly denuding side of the range (in shift direction of divide) are characterized by a decrease in cooling rate with decreasing temperature, while cooling curves of rocks from the rapidly denuding side (in lee of the shift direction) are characterized by increasing cooling rate with decreasing temperature. Moreover, in rapidly denuding terrains, cooling through the 110°C and 75°C isotherms (approximating the retention temperatures of the apatite fission track and (U–Th)/He systems, respectively) may occur on the slowly denuding side of a range at twice the age of samples from the rapidly denuding side. In general, differences in cooling curves and cooling ages below 110°C should be recognizable in terrains where the erosion and lateral migration rates are of the order of 2 mm per year or more. In view of the recent developments of low temperature geochronological methods, our model provides an important tool to estimate the rate of lateral migration of drainage divides in regions where this is not constrained by the geomorphological record.