Green Open-Access
A New Efficient Method to Solve the Stream Power Law Model Taking Into Account Sediment Deposition
(2019)
The stream power law model has been widely used to represent erosion by rivers but does not take into account the role played by sediment in modulating erosion and deposition rates. Davy and Lague (2009, ) provide an approach to address this issue, but it is computationally demanding because the local balance between erosion and deposition depends on sediment flux resulting from net upstream erosion. Here, we propose an efficient (i.e., O(N) and implicit) method to solve their equation. This means that, unlike other methods used to study the complete dynamics of fluvial systems (e.g., including the transition from detachment-limited to transport-limited behavior), our method is unconditionally stable even when large time steps are used. We demonstrate its applicability by performing a range of simulations based on a simple setup composed of an uplifting region adjacent to a stable foreland basin. As uplift and erosion progress, the mean elevations of the uplifting relief and the foreland increase, together with the average slope in the foreland. Sediments aggrade in the foreland and prograde to reach the base level where sediments are allowed to leave the system. We show how the topography of the uplifting relief and the stratigraphy of the foreland basin are controlled by the efficiency of river erosion and the efficiency of sediment transport by rivers. We observe the formation of a steady-state geometry in the uplifting region, and a dynamic steady state (i.e., autocyclic aggradation and incision) in the foreland, with aggradation and incision thicknesses up to tens of meters.
Many regions central to our understanding of tectonics and landscape evolution are active or ancient magmatic terranes, and robust interpretation of low-temperature thermochronologic ages in these settings requires careful attention to the drivers of rock heating and cooling, including magmatism. However, we currently lack a quantitative framework for evaluating the potential role of magmatic coolingthat is, post-magmatic thermal relaxationin shaping cooling age patterns in regions with a history of intrusive magmatism. Here we use analytical approximations and numerical models to characterize how low-temperature thermochronometers document cooling inside and around plutons in steadily exhuming environments. Our models predict that the thermal field a pluton intrudes into, specifically the ambient temperatures relative to the closure temperature of a given thermochronometer, is as important as the pluton size and temperature in controlling the pattern and extent of thermochronometer resetting in the country rocks around a pluton. We identify one advective and several conductive timescales that govern the relationship between the crystallization and cooling ages inside a pluton. In synthetic vertical age-elevation relationships (AERs), resetting next to plutons results in changes in AER slope that could be misinterpreted as past changes in exhumation rate if the history of magmatism is not accounted for. Finally, we find that large midcrustal plutons, such as those emplaced at similar to 10-15-km depth, can reset the low-temperature thermochronometers far above them in the upper crusta result with considerable consequences for thermochronology in arcs and regions with a history of magmatic activity that may not have a surface expression.
Due to the challenges in upscaling daily climatic forcing to geological time, physically realistic models describing how rainfall drives fluvial erosion are lacking. To bridge this gap between short-term hydrology and long-term geomorphology, we derive a theoretical framework for long-term fluvial erosion rates driven by realistic climate by integrating an established stochastic-mechanistic model of hydrology into a threshold-stochastic formulation of stream power. The hydrological theory provides equations for the daily streamflow probability distribution as a function of climatic boundary conditions. The new parameters introduced are rooted firmly in established climatic and hydrological theory. This allows us to account for how fluvial erosion rates respond to changes in rainfall intensity, frequency, evapotranspiration rates, and soil moisture dynamics in a way that is consistent with existing theories. We use this framework to demonstrate how hydroclimatic conditions and erosion threshold magnitude control the degree of nonlinearity between steepness index and erosion rate. We find that hydrological processes can have a significant influence on how erosive a particular climatic forcing will be. By accounting for the influence of hydrology on fluvial erosion, we conclude that climate is an important control on erosion rates and long-term landscape evolution.