Relationship of channel steepness to channel incision rate from a tilted and progressively exposed unconformity surface

We examine the relationship of channel steepness to incision rate from channels eroding into a previously tilted, planar, and progressively exhumed unconformity surface. Channel and unconformity slopes are measured from a suite of channels developed on erosionally resistant Paleozoic limestone exhumed by the removal of Cenozoic sediments from the Baybeiche Range bordering the Naryn basin in the western Tian Shan. The compiled data set, sampling 5 orders of magnitude of upstream drainage area (0.03 to 227 km2), is used to derive the exponent, n, relating channel steepness to channel incision rate and the ratio, K∕V , of the rate constant for channel incision of the resistant substrate, K , to the erosion rate, V , of the cover strata. We show that for a typical value of intrinsic concavity (slope-area exponent, ! = 0.5), erosion rates that are proportional to specific stream power (n = 1) satisfy the data set. However, valley width data suggest that the intrinsic concavity is higher (! = 0.8) and that the channel incision data can also be fit if erosion is proportional to basal shear stress (n = 2∕3). Our results do not support values of n significantly greater than one. Using 36Cl exposure age dating of the unconformity surface, we independently demonstrate that the Cenozoic cover strata have been progressively stripped downward from the unconformity surface at a vertical rate of 1 to 2 m/kyr. Using V = 1 m/kyr, we constrain the rate constant, K , to between 6 ± 1 and 9 ± 2 ×10−4 kyr−1 for incision of resistant limestone bedrock in this field setting.