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 totectonic signals, but the meaning of morphometric indices is often obscured by the interplay between themany variables controlling the geomorphological evolution. Moreover, although the so-called hypsometricintegral refers to the basin scale, most indices are generally derived from the river long profiles and thus focusmainly on the short-term response of a drainage network to base level change, providing limited informationin regions of older and/or moderate uplift. Here, using the Rhenish shield (western Europe), an area ofmoderate Quaternary uplift, as a test case, I attempt to build an index yielding a comprehensive view of thestage attained by the landscape's response and, indirectly, an evaluation of the timing of the triggering baselevel change. This index, called R1, is a ratio of differences between the three integrals linked respectively tothe 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 indexis strongly correlated with basin size (regional correlation coefficients are in the range 0.88–0.93), reflectingthe way an erosion wave propagates from the outlet of a basin toward its headwaters. Therefore, it is notdirectly usable as a proxy for relative uplift age. However, one can show that the relation between R1 and basinsize 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 fullyconfirmed by the analysis of R1 and Sr in the study area. Once its initial increase is completed (assumedly in afew ten thousand years), Sr appears to be a reliable indicator of relative uplift (or any other cause of base levellowering) age.