How canyons evolve by incision into bedrock: Rainbow Canyon, Death Valley National Park, United States

Abstract

Incising rivers may be confined by low-slope, erodible hillslopes or steep, resistant sidewalls. In the latter case, the system forms a canyon. We present a morphodynamic model that includes the essential elements of a canyon incising into a plateau, including 1) abrasion-driven channel incision, 2) migration of a canyon-head knickpoint, 3) sediment feed from an alluvial channel upstream of the knickpoint, and 4) production of sediment by sidewall collapse. We calculate incision in terms of collision of clasts with the bed. We calculate knickpoint migration using a moving-boundary formulation that allows a slope discontinuity where the channel head meets an alluvial plateau feeder channel. Rather than modeling sidewall collapse events, we model long-term behavior using a constant sidewall slope as the channel incises. Our morphodynamic model specifically applies to canyon, rather than river-hillslope evolution. We implement it for Rainbow Canyon, CA. Salient results are as follows: 1) Sediment supply from collapsing canyon sidewalls can be substantially larger than that supplied from the feeder channel on the plateau. 2) For any given quasi-equilibrium canyon bedrock slope, two conjugate slopes are possible for the alluvial channel upstream, with the lower of the two corresponding to a substantially lower knickpoint migration rate and higher preservation potential. 3) Knickpoint migration occurs at a substantially faster time scale than regrading of the bedrock channel itself, underlying the significance of disequilibrium processes. Although implemented for constant climactic conditions, the model warrants extension to long-term climate variation.

Keywords: bedrock; canyon; incision; knickpoint; uplift.

Fig. 1.

Configuration. (A) Schematic plan view shown a tableland, knickpoint, canyon walls, and canyon bed. (B) Schematic cross-sectional view showing the beds of the feeder channel and canyon, with partial alluvial cover. (C) Annotated plan view image © 2020 Google Earth showing Panamint Valley, Rainbow Canyon (section B‒C), and the Santa Rosa Wash (section A‒B). The head of the canyon is denoted as B, upstream of which is Santa Rosa Wash. The upstream and downstream ends of the study reach are denoted as A and C. (D) View of Rainbow Canyon looking downstream from Father Crowley Outlook, with Panamint Valley in the distance.

Fig. 2.

Schematization of sidewall configuration and morphodynamics of tableland canyons. (A) Parameters associated with canyon cross-section. The orange color denotes failed material. (B) Illustration of connection between sidewall failure and channel bedrock morphodynamics as the canyon evolves. Symbols are defined in the text.

Fig. 3.

(A) Plot of steady-state downstream bedrock-alluvial slope S_d,bed versus upstream alluvial slope S_u,all. The minimum value of bedrock-alluvial slope at S_d,bed = 0.03 for S_u,all = 0.021. The left branch of the curve corresponds to cases like Rainbow Canyon, where the bedrock slope is substantially higher than the alluvial slope. The minimum value of S_d,bed (0.03) is at S_u,all = 0.021. (B) Illustration of the conjugate high alluvial slope (0.0898) and low alluvial slope (0.0156), which provides a sediment feed rate (0.0230 and 0.00134 m²/s, respectively) allowing the bedrock reach with slope 0.094 to be in balance with an uplift rate of 3 mm/y.

Fig. 4.

Results of modeling of canyon evolution. (A) Canyon evolution with S_u,all = 0.0156 and (B) canyon evolution with S_u,all = 0.0898. These are conjugate alluvial slopes, both of which result in an equilibrium canyon bedrock slope S_d,bed = 0.094. The left-hand case has an alluvial slope in agreement with the present-day Santa Rosa Wash. In both cases, the equilibrium bedrock slope is maintained as the knickpoint migrates upstream.

Fig. 5.

Results of calculations with fraction of sidewall material that contributes to bed material load f_b = 0, 0.25, 0.5, 0.75, and 1. All calculations use the same input parameters as those of Fig. 4A, i.e., Santa Rosa Wash. (A) Canyon long profiles, showing an autogenic knickpoint where slope suddenly decreases for each case f_b > 0. (B) Downstream variation in volume sediment transport rate/width q_a. (C) Downstream variation in cover fraction p. (D) Downstream variation in canyon top width B_T.

Fig. 6.

Three-dimensional views of predicted morphology of Rainbow Canyon at (A) t = 0 y, (B) t = 72,000 y, (C) t = 96,000 y, and (D) t = 120,000 y. The calculations are for f_b = 0.75.