The influence of surface topography on the form of steady-state isotherms during erosion-driven denudation is investigated. This is of particular interest to the interpretation of low-temperature geochronological data, for example fission track data, because this rests generally on the untested assumption that isotherms are not perturbed by topography and, therefore, that the data can be interpreted with one-dimensional models. In order to calculate isotherms and investigate the potential errors introduced by this assumption we use an approximate analytical solution of the diffusion-advection equation in two dimensions. It is shown that, for realistic geothermal gradients and a topography amplitude of H = 3 km and wavelength of w = 20 km, the 100-degrees-C isotherm may be perturbed to an amplitude of < 400 vertical metres if the denudation rate is < 500 m/Ma, but may have an amplitude of 1500 m or more if the denudation rate is > 1000 m/Ma. The effect increases for larger H and smaller w. For the interpretation of denudation histories derived from fission tracks, these relationships imply that the denudation rate of a terrain may be substantially overestimated, if it is only inferred from the slope of data points in a plot of sample elevation versus fission track age and if the sampling profile is not exactly vertical. A simple relationship is discussed that can be used to estimate the real denudation rate from the apparent denudation rate in an elevation-age plot.
