Time-dependent effects of heat advection and topography on cooling histories during erosion

Both erosion and surface topography cause a time-dependent variation in isotherm geometry that can result in significant errors in estimating natural exhumation rates from geochronologic data. Analytical solutions and two-dimensional numerical modelling are used to investigate the magnitude of these inaccuracies for conditions appropriate to many rapidly exhumed mountain chains of rugged relief. It is readily demonstrated that uplift of the topographic surface has a negligible effect on the cooling history of an exhumed rock sample and cannot be quantified by current geochronologic methods. The topography itself perturbs the isotherms to a depth that depends on both the vertical and horizontal scale of the surface relief. Estimations employing different isotopic systems in the same sample with higher closure temperatures (> 200°C) are not generally influenced by topography. However, direct conversion of cooling rates to exhumation rates assuming a simple constant linear geotherm markedly underestimates peak rates, due to variation of the geothermal gradient in time and space and to the time lag between exhumation and cooling. Estimations based on the altitude variation in apatite fission-track ages are less prone to such inaccuracies in geothermal gradient but are affected by near-surface time-dependent variation in isotherm depth due to advection and topography. In tectonically active mountain belts, high exhumation rates are coupled with rugged topography, and exhumation rates may be markedly overestimated, by factors of 2 or more. Even at lower exhumation rates on the order of 1 mm/a, the shape of the cooling curve is modified by advection and topography. A convex-concave shape to the cooling curve does not necessarily imply a change of exhumation rate; it may also be attained by a more complicated geothermal gradient induced by topographic relief. Very fast cooling below 100°C, often interpreted as reflecting faster exhumation, can be more simply explained by the lateral cooling effect of topographic relief, with samples exhumed in valleys displaying a different near-surface cooling history to those on ridge crests.