Understanding the controls on rates of bedrock erosion is a crucial question in geomorphology. The ability of streams to downcut through bedrock ultimately sets the rate of lowering of a landscape. Time rate of change of river-bed elevation (dz/dt) is given by a competition between uplift and incision (Howard et al., 1994):

dz/dt = U(x,t) - kA^mSⁿ

where U is the rock uplift rate, A is upstream drainage area (a proxy for discharge), S is river bed gradient (dz/dx), k is a dimensional coefficient, and m and n are constants. The values k, m and n and their relation to lithology, climate, and tectonic setting need to be better constrained before channel profiles may be used to derive reliable estimates of the spatial pattern of rock uplift (U). We use 24 small coastal drainage basins (4.8 to 21 km²) in the King Range, northern California to constrain the bedrock erosion rate equation, by fitting modeled profiles to measured stream longitudinal profiles. The King Range is chosen as the study area for three reasons. First, uplift rates are variable and well-constrained, ranging from less than 1 mm/yr to greater than 4 mm/yr (Merritts and Vincent, 1989; Merritts and Bull, 1989). Second, channel gradients correlate well with local uplift rate. Third, lithology and climate are both generally constant spatially.

We extract trunk stream channel profiles for each drainage basin from 30 m USGS DEMs and topographic maps. Channel slope versus drainage area plots indicate that the drainages are in equilibrium with current uplift conditions and point to a concavity index (m/n) of 1/2. Derivations of equation 1 predict m/n to equal 1/2, consistent with field data in the King Range and elsewhere (e.g., Howard, et al, 1994). Therefore, the concavity index is well constrained. However, the value for n is not known, and it exerts strong control on both equilibrium profile slope and catchment response timescale. Using the known uplift rate for each drainage basin, k is constrained for different values of n. This calculation reveals that k varies with U. This result underscores the importance of factors such as channel width and presence or absence of alluvial cover, which are likely affected by uplift rate, in setting the value of k. Merritts and Bull (1989) show that the most rapidly uplifting part of the King Range, rising at 4 mm/yr, has only been this active for the past 96,000 years, prior to which the uplift rate was 0.5 mm/yr. Preliminary modeling efforts using these constraints and associated values of k, reveal that the current channel profiles in the high-uplift core of the range could only be achieved with values of n greater than or equal to 1. With n less than 1, channel response time is too long.

AAPG Search and Discovery Article #90937©1998 AAPG Annual Convention and Exhibition, Salt Lake City, Utah