Modeling the influence of rainfall gradients on discharge, bedrock erodibility, and river profile evolution, with application to the Big Island, Hawai'i

Abstract

Motivated by convex-concave bedrock river profiles developed across a climate gradient on the wetside of the Kohala Peninsula of the Big Island of Hawai'i, we numerically model how rainfall gradients may influence longitudinal fluvial incision patterns. First, we model transient profile adjustment with two tectonic boundary conditions: subsidence and uplift. In this generalized analysis, we assume that rainfall gradients only influence incision by modifying the relation between upstream drainage area and local discharge. Using a detachment-limited model, downstream increases in rainfall lead to profile convexities during transient adjustment in both tectonic settings, and this is the opposite of the predicted increase in profile concavity that would develop in a steady state uplifting profile. A transport-limited erosion model develops only concave channel profiles without clear signatures of the rainfall pattern. Second, we model the development of convex-concave transient profiles and incision patterns on Kohala using a detachment-limited model. If rainfall gradients only influence incision through the local discharge, reasonable rainfall gradients can only develop channel convexities that are much smaller than those observed. Instead, we hypothesize that local bedrock erodibility increases with the degree of rainfall-dependent chemical weathering. When local erodibility is assumed to scale with local rainfall rate, the model can produce convex-concave profiles similar to those observed in Kohala. Our results suggest that changes in local bedrock erodibility due to local climate-dependent weathering may be an important mechanism by which climate influences landscape form and rates of evolution. This hypothesis requires further testing in this study area and beyond.

Spatially Variable Increase in Rock Uplift in the Northern U.S. Cordillera Recorded in the Distribution of River Knickpoints and Incision Depths

“…Because the dimensions of k s depend on the value of θ, we use a reference concavity θ ref = 0.5 for m/n, consistent with other studies (Tucker & Whipple, 2002;Whittaker, 2012;Gasparini & Whipple, 2014;Han et al, 2014;. With this reference concavity, all profiles have a normalized steepness (k sn ) with units of meters (Figure 3).…”

Exploring landscape sensitivity to the Pacific Trade Wind Inversion on the subsiding island of Hawaii

“…Han et al . [] followed this work by modeling Kohala stream longitudinal profiles and reinforced the view that discharge changes due to precipitation gradients are only partly responsible for the convexo‐concave form of the profiles; increased erodibility of bedrock in high‐precipitation zones may also play an important role. Similarly, Ferrier et al .…”

Bedrock channels response to differential rock uplift in eastern Qilian Mountain along the northeastern margin of the Tibetan Plateau

“…These factors mainly include (1) nonlinearities in the incision process (Snyder et al, 2003b;Tucker and Bras, 2000;Whipple and Tucker, 1999), (2) dynamic adjustments in channel hydraulic geometry (Duvall et al, 2004; (Allen et al, 2013;Duvall et al, 2004;Goode and Wohl, 2010;Johnson and Whipple, 2010;Johnson et al, 2009;Lavé and Avouac, 2001;Moglen and Bras, 1995;Dietrich, 1998, 2001;Stock and Montgomery, 1999;Whipple and Tucker, 2002), and (4) gradient of precipitation (Craddock et al, 2007;Han et al, 2014;Roe et al, 2002Roe et al, , 2003Wu et al, 2006). Given various potential complexity mentioned above in model application, in order to evaluate to how and what degree channel longitudinal profiles respond to differential rock uplift in eastern Qilian Mountain, we should first calibrate key model parameters cautiously utilizing local survey data.…”

“…(2) seems to mainly depend on lithologic resistance, stream bed material, channel width, and discharge (climate controlled) (Han et al, 2014;Whipple, 2004). Stock and Montgomery (1999) suggest that K may scale over $4 orders of magnitude owing to variability in lithologic resistance and/or climate among field sites.…”