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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.
We present a new algorithm for solving the common problem of flow trapped in closed depressions within digital elevation models, as encountered in many applications relying on flow routing. Unlike other approaches (e.g., the Priority-Flood depression filling algorithm), this solution is based on the explicit computation of the flow paths both within and across the depressions through the construction of a graph connecting together all adjacent drainage basins. Although this represents many operations, a linear time complexity can be reached for the whole computation, making it very efficient. Compared to the most optimized solutions proposed so far, we show that this algorithm of flow path enforcement yields the best performance when used in landscape evolution models. In addition to its efficiency, our proposed method also has the advantage of letting the user choose among different strategies of flow path enforcement within the depressions (i.e., filling vs. carving). Furthermore, the computed graph of basins is a generic structure that has the potential to be reused for solving other problems as well, such as the simulation of erosion. This sequential algorithm may be helpful for those who need to, e.g., process digital elevation models of moderate size on single computers or run batches of simulations as part of an inference study.
Long-term river evolution depends partly on crustal deformation, which shapes the topography crossed by rivers. On glacial timescales, ice-sheet growth and decay can produce crustal vertical motion of ∼10 mm/yr resulting from the solid Earth's adjustment to variations in ice and water loads, comparable to tectonically-driven rates in the most rapidly uplifting mountains on Earth. This process of glacial isostatic adjustment (GIA) can influence river courses and drainage basins substantially, particularly near former ice margins. We explore the extent to which GIA influenced the evolution of rivers along the United States east coast during the last glacial cycle. We compute gravitationally self-consistent GIA responses that incorporate recent constraints on the Laurentide Ice Sheet history through the last glacial build-up phase, and we connect the predicted variations in topography to abrupt changes in river dynamics recorded in the Hudson, Delaware, Susquehanna, and Potomac Rivers from 40 ka to present. To the extent that increases in sediment transport capacity imply increases in river incision rate, the GIA-driven changes in slope and drainage area are consistent with episodes of erosion and sedimentation observed in the Hudson, Delaware, and Potomac Rivers, but inconsistent with the observed accelerated river incision in the Susquehanna River at 30-14 ka. These analyses add to a growing body of evidence showing that GIA strongly influences river evolution over millennial timescales.
The marine sedimentary record contains unique information about the history of erosion, uplift and climate of the adjacent continent. Inverting this record has been the purpose of many numerical studies. However, limited attention has been given to linking continental erosion to marine sediment transport and deposition in large-scale surface process evolution models. Here we present a new numerical method for marine sediment transport and deposition that is directly coupled to a landscape evolution algorithm solving for the continental fluvial and hillslope erosion equations using implicit and O(N) algorithms. The new method takes into account the sorting of grain sizes (e.g., silt and sand) in the marine domain using a non-linear multiple grain-size diffusion equation and assumes that the sediment flux exported from the continental domain is proportional to the bathymetric slope. Specific transport coefficients and compaction factors are assumed for the two different grain sizes to simulate the stratigraphic architecture. The resulting set of equations is solved using an efficient (O(N) and implicit) algorithm. It can thus be used to invert stratigraphic geometries using a Bayesian approach that requires a large number of simulations. This new method is used to invert the sedimentary geometry of a natural example, the Ogooue Delta (Gabon), over the last similar to 5 Myr. The objective is to unravel the set of erosional histories of the adjacent continental domain compatible with the observed geometry of the offshore delta. For this, we use a Bayesian inversion scheme in which the misfit function is constructed by comparing four geometrical parameters between the natural and the simulated delta: the volume of sediments stored in the delta, the surface slope, the initial and the final shelf lengths. We find that the best-fit values of the transport coefficients for silt in the marine domain are in the range of 300 - 500 m(2)/yr, in agreement with previous studies on offshore diffusion. We also show that, in order to fit the sedimentary geometry, erosion rate on the continental domain must have increased by a factor of 6 to 8 since 5.3 Ma. (C) 2019 Elsevier B.V. All rights reserved.
The processes that control long term landscape evolution in continental interiors and, in particular, along passive margins such as in southern Africa, are still the subject of much debate (e.g. Braun, 2018). Although today the Namibian margin is characterized by an arid climate, it has experienced climatic fluctuations during the Cenozoic and, yet, to date no study has documented the potential role of climate on its erosion history. In western Namibia, the Brandberg Massif, an erosional remnant or inselberg, provides a good opportunity to document the Cenozoic denudation history of the margin using the relationship between rock cooling or exhumation ages and their elevation. Here we provide new apatite (UThSm)/He dates on the Brandberg Inselberg that range from 151 +/- 12 to 30 +/- 2 Ma. Combined with existing apatite fission track data, they yield new constraints on the denudation history of the margin. These data document two main cooling phases since continental break-up 130 Myr ago, a rapid one (similar to 10 degrees C/Myr) following break-up and a slower one (similar to 12 degrees C/Myr) between 65 and 35 Ma. We interpret them respectively to be related to escarpment erosion following rifting and continental break-up and as a phase of enhanced denudation during the Early Eocene Climatic Optimum. We propose that during the Early Eocene Climatic Optimum chemical weathering was important and contributed significantly to the denudation of the Namibian margin and the formation of a pediplain around the Brandberg and enhanced valley incision within the massif. Additionally, aridification of the region since 35 Ma has resulted in negligible denudation rates since that time. (C) 2019 Elsevier B.V. All rights reserved.