The longitudinal profiles of bedrock channels are a major component of the relief structure of mountainous drainage basins and therefore limit the elevation of peaks and ridges. Further, bedrock channels communicate tectonic and climatic signals across the landscape, thus dictating, to first order, the dynamic response of mountainous landscapes to external forcings. We review and explore the stream-power erosion model in an effort to (1) elucidate its consequences in terms of large-scale topographic (fluvial) relief and its sensitivity to tectonic and climatic forcing, (2) derive a relationship for system response time to tectonic perturbations, (3) determine the sensitivity of model behavior to various model parameters, and (4) integrate the above to suggest useful guidelines for further study of bedrock channel systems and for future refinement of the streampower erosion law. Dimensional analysis reveals that the dynamic behavior of the stream-power erosion model is governed by a single nondimensional group that we term the uplift-erosion number, greatly reducing the number of variables that need to be considered in the sensitivity analysis. The degree of nonlinearity in the relationship between stream incision rate and channel gradient (slope exponent n) emerges as a fundamental unknown. The physics of the active erosion processes directly influence this nonlinearity, which is shown to dictate the relationship between the uplift-erosion number, the equilibrium stream channel gradient, and the total fluvial relief of mountain ranges. Similarly, the predicted response time to changes in rock uplift rate is shown to depend on climate, rock strength, and the magnitude of tectonic perturbation, with the slope exponent n controlling the degree of dependence on these various factors. For typical drainage basin geometries the response time is relatively insensitive to the size of the system. Work on the physics of bedrock erosion processes, their sensitivity to extreme floods, their transient responses to sudden changes in climate or uplift rate, and the scaling of local rock erosion studies to reach-scale modeling studies are most sorely needed.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JB900120

Dynamics of the stream‐power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs

The Al-in-hornblende barometer, which correlates Altot content of magmatic hornblende linearly with crystallization pressure of intrusion (Hammarstrom and Zen 1986), has been calibrated experimentally under water-saturated conditions at pressures of 2.5–13 kbar and temperatures of 700–655°C. Equilibration of the assemblage hornlende-biotite-plagioclase-orthoclasequartz-sphene-Fe-Ti-oxide-melt-vapor from a natural tonalite 15–20° above its wet solidus results in hornblende compositions which can be fit by the equation: P(±0.6 kbar) = −3.01 + 4.76 Al
 hbl
 tot
 
r
2=0.99, where Altot is the total Al content of hornblende in atoms per formula unit (apfu). Altot increase with pressure can be ascribed mainly to a tschermak-exchange (
 
$$t\vec k,{\text{ Mg}}_{{\text{ - 1 }}} {\text{Al}}^{{\text{VI}}} {\text{Si}}_{{\text{ - 1}}} {\text{ Al}}^{{\text{IV}}}$$

 ) accompanied by minor plagioclase-substitution (
 
$$\vec pl,{\text{ Ca}}_{{\text{ - 1 }}} {\text{Na}}^{{\text{M(4)}}} {\text{ Al}}_{{\text{ - 1}}}^{{\text{IV}}} {\text{ Si}}$$

 ). This experimental calibration agrees well with empirical field calibrations, wherein pressures are estimated by contact-aureole barometry, confirming that contact-aureole pressures and pressures calculated by the Al-in-hornblende barometer are essentially identical. This calibration is also consistent with the previous experimental calibration by Johnson and Rutherford (1989b) which was accomplished at higher temperatures, stabilizing the required buffer assemblage by use of mixed H2O-CO2 fluids. The latter calibration yields higher Altot content in hornblendes at corresponding pressures, this can be ascribed to increased edenite-exchange (
 
$$\vec ed,{\text{ }}\square _{{\text{ }} - {\text{ }}1}^{ A} {\text{ Na}}^{\text{A}} {\text{Si }}_{ - {\text{ }}1} {\text{Al}}^{{\text{IV}}}$$

 ) at elevated temperatures. The comparison of both experimental calibrations shows the important influence of the fluid composition, which affects the solidus temperature, on equilibration of hornblende in the buffering phase assemblage.

Amphibole composition in tonalite as a function of pressure: an experimental calibration of the Al-in-hornblende barometer

Post-collisional strongly peraluminous granites

Expression of active tectonics in erosional landscapes

Improved formulation of bedrock erosion laws requires knowledge of the actual processes operative at the bed. We present qualitative field evidence from a wide range of settings that the relative efficacy of the various processes of fluvial erosion (e.g., plucking, abrasion, cavitation, solution) is a strong function of substrate lithology, and that joint spacing, fractures, and bedding planes exert the most direct control. The relative importance of the various processes and the nature of the interplay between them are inferred from detailed observations of the morphology of erosional forms on channel bed and banks, and their spatial distributions. We find that plucking dominates wherever rocks are well jointed on a submeter scale. Hydraulic wedging of small clasts into cracks, bashing and abrasion by bedload, and chemical and physical weathering all contribute to the loosening and removal of joint blocks. In more massive rocks, abrasion by suspended sand appears to be rate limiting in the systems studied here. Concentration of erosion on downstream sides of obstacles and tight coupling between fluid-flow patterns and fine-scale morphology of erosion forms testify to the importance of abrasion by suspended-load, rather than bedload, particles. Mechanical analyses indicate that erosion by suspended-load abrasion is considerably more nonlinear in shear stress than erosion by plucking. In addition, a new analysis indicates that cavitation is more likely to occur in natural systems than previously argued. Cavitation must be considered a viable process in many actively incising bedrock channels and may contribute to the fluting and potholing of massive, unjointed rocks that is otherwise attributed to suspended-load abrasion. Direct field evidence of cavitation erosion is, however, lacking. In terms of the well-known shear-stress (or stream-power) erosion law, erosion by plucking is consistent with a slope exponent ( n ) of ∼2/3 to 1, whereas erosion by suspended-load abrasion is more consistent with a slope exponent of ∼5/3. Given that substrate lithology appears to dictate the dominant erosion process, this finding has important implications for long-term landscape evolution and the models used to study it.

/pdf/river-incision-into-bedrock-mechanics-and-relative-efficacy-19jhsk73gg.pdf

River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion and cavitation

The direct and secondary effects of rapidly changing climate caused large rivers draining the Atlantic passive margin to incise quickly into bedrock beginning about 35,000 years ago. Measured in samples from bedrock fluvial terraces, 10-beryllium shows that both the Susquehanna and Potomac Rivers incised 10- to 20-meter-deep gorges along steep, convex lower reaches during the last glacial cycle. This short-lived pulse of unusually rapid down-cutting ended by 13,000 to 14,000 years ago. The timing and rate of downcutting are similar on the glaciated Susquehanna and unglaciated Potomac Rivers, indicating that regional changes, not simply glacial meltwater, initiated incision.

/pdf/rapid-late-pleistocene-incision-of-atlantic-passive-margin-3w79e8jptg.pdf

Rapid Late Pleistocene Incision of Atlantic Passive-Margin River Gorges

One-dimensional modelling of the thermal history of a sialic crust thickened by multiple overstack thrusting of upper crustal material shows that anatexis is likely. Both the uplift rate and the length of the incubation period between end of tectonism and start of uplift are important controls on the amount and temperature of the melt. Heat of fusion does not significantly affect the long-term thermal structure of the crust if the melt is not extracted because only a small fraction of conductive heat is converted to latent heat, though short-term thermal effects of latent heat can be locally important.Model results show that commonly <15% of mantle heat flux is converted to latent heat; even during peak melting in the most productive models, less than half of incremental mantle flux is converted. The results have obvious implications on the acceptability of proposed heat sources for crustal anatexis. Fusion could retard crustal temperature rise by nearly 100°C, but the system would recover except for situations of very rapid uplift. Understanding of the thermal evolution of a burial-uplift system requires knowledge not only of the timing of anatexis but of the pooling and movement of the magma, as well as the duration and nature of the incubation period; we are poorly equipped to measure these events. The model predicts that the characteristic time for anatexis in a thickened sialic crust is several tens of millions of years, comparable to the time lapse between orogenies; in making geological interpretations of magmatism, this time lag must be considered.

Thermal modelling of stepwise anatexis in a thrust-thickened sialic crust

Potholes preserved along abandoned sections of bedrock-bounded rivers should provide significant paleohydraulic data if the conditions for pothole formation are understood. In a prototype study, we recognize two kinds of potholes along the paleo-Potomac River near Great Falls, Virginia. Vertical potholes, drilled into the strath floor, are circular in plan and are interpreted to form at sites of small stream depths and high flow velocity. Lateral potholes, noncircular with overhanging roofs, are found on flanks of rock obstacles. They are interpreted to be eroded by sediment-laden vertical flow near the air-water interface. The vortices circulate water in the horizontal plane, and begin to form near the free surface in flow separation zones downstream of the obstacles. The geometry of flow separation zones and thus the location of the lateral potholes are scaled by flow Reynolds number. Therefore, lateral potholes could be used to reconstruct paleoflow depths and velocities if parts of the channel bed adjacent to the flow obstruction are preserved.

Possible hydraulic significance of two kinds of potholes: Examples from the paleo-Potomac River

Discussion of Blundy and Holland's (1990) “Calcic amphibole equilibria and a new amphibole-plagioclase geothermometer”

It should be possible to infer the thermal state of the source terrane for granitic bodies, provided we have independent means to establish the chemical nature of this terrane. The chemical nature of the granitic rocks, including their degree of hydration, implies the solidus temperature. The concentration of the heat-producing radioactive elements in the granite (K, U, and Th) probably provides an upper estimate of their concentration in the source rock, which is an important thermal parameter. The depth and ambient temperature of the country rock into which the granite magma intruded provide useful boundary conditions for the thermal regime at the crustal level of anatexis

E-an Zen

Papers

Rapid Late Pleistocene Incision of Atlantic Passive-Margin River Gorges

Thermal modelling of stepwise anatexis in a thrust-thickened sialic crust

Possible hydraulic significance of two kinds of potholes: Examples from the paleo-Potomac River

Discussion of Blundy and Holland's (1990) “Calcic amphibole equilibria and a new amphibole-plagioclase geothermometer”

Using granite to image the thermal state of the source terrane