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.