Basin and river profile morphometry: A new index with a high potential for relative dating of tectonic uplift

Geomorphometry may be a powerful tool to describe the characteristics of the landscape's response to tectonic signals, but the meaning of morphometric indices is often obscured by the interplay between the many variables controlling the geomorphological evolution. Moreover, although the so-called hypsometric integral refers to the basin scale, most indices are generally derived from the river long profiles and thus focus mainly on the short-term response of a drainage network to base level change, providing limited information in regions of older and/or moderate uplift. Here, using the Rhenish shield (western Europe), an area of moderate Quaternary uplift, as a test case, I attempt to build an index yielding a comprehensive view of the stage attained by the landscape's response and, indirectly, an evaluation of the timing of the triggering base level change. This index, called R₁, is a ratio of differences between the three integrals linked respectively to the classical basin's hypsometric curve, to the main river's long profile, and at the intermediate level, to a ‘drainage network's hypsometric curve’. While its ratio form minimizes the lithological effect on R₁, this index is strongly correlated with basin size (regional correlation coefficients are in the range 0.88–0.93), reflecting the way an erosion wave propagates from the outlet of a basin toward its headwaters. Therefore, it is not directly usable as a proxy for relative uplift age. However, one can show that the relation between R₁ and basin size is theoretically expected to change with time. Following uplift, the slope Sᵣ of the linear relation R₁=f(lnA) first increases rapidly but briefly, then it gradually diminishes over several million years. This is fully confirmed by the analysis of R₁ and Sᵣ in the study area. Once its initial increase is completed (assumedly in a few ten thousand years), Sᵣ appears to be a reliable indicator of relative uplift (or any other cause of base level lowering) age.