Dimitri Lague

Links between erosion, runoff variability and seismicity in the Taiwan orogen

The erosion of mountain belts controls their topographic and structural evolution and is the main source of sediment delivered to the oceans. Mountain erosion rates have been estimated from current relief and precipitation, but a more complete evaluation of the controls on erosion rates requires detailed measurements across a range of timescales. Here we report erosion rates in the Taiwan mountains estimated from modern river sediment loads, Holocene river incision and thermochronometry on a million-year scale. Estimated erosion rates within the actively deforming mountains are high (3–6 mm yr-1) on all timescales, but the pattern of erosion has changed over time in response to the migration of localized tectonic deformation. Modern, decadal-scale erosion rates correlate with historical seismicity and storm-driven runoff variability. The highest erosion rates are found where rapid deformation, high storm frequency and weak substrates coincide, despite low topographic relief.

3D terrestrial lidar data classification of complex natural scenes using a multi-scale dimensionality criterion: Applications in geomorphology

3D point clouds of natural environments relevant to problems in geomorphology often require classification of the data into elementary relevant classes. A typical example is the separation of riparian vegetation from ground in fluvial environments, the distinction between fresh surfaces and rockfall in cliff environments, or more generally the classification of surfaces according to their morphology. Natural surfaces are heterogeneous and their distinctive properties are seldom defined at a unique scale, prompting the use of multi-scale criteria to achieve a high degree of classification success. We have thus defined a multi-scale measure of the point cloud dimensionality around each point, which characterizes the local 3D organization. We can thus monitor how the local cloud geometry behaves across scales. We present the technique and illustrate its efficiency in separating riparian vegetation from ground and classifying a mountain stream as vegetation, rock, gravel or water surface. In these two cases, separating the vegetation from ground or other classes achieve accuracy larger than 98 %. Comparison with a single scale approach shows the superiority of the multi-scale analysis in enhancing class separability and spatial resolution. The technique is robust to missing data, shadow zones and changes in point density within the scene. The classification is fast and accurate and can account for some degree of intra-class morphological variability such as different vegetation types. A probabilistic confidence in the classification result is given at each point, allowing the user to remove the points for which the classification is uncertain. The process can be both fully automated, but also fully customized by the user including a graphical definition of the classifiers. Although developed for fully 3D data, the method can be readily applied to 2.5D airborne lidar data.

Discharge, discharge variability, and the bedrock channel profile

Long-term bedrock incision is driven by daily discharge events of variable magnitude and frequency, with ineffective events below an incision threshold. We explore theoretically how this short-term stochastic behavior controls long-term steady state incision rates and bedrock channel profiles, combining a realistic frequency-magnitude distribution of discharge with a deterministic, detachment-limited incision model in which incision rate is a power function of basal shear stress above a critical shear stress. Our model predicts a power law relationship between steady state slope and drainage area consistent with observations. The exponent of this power law is independent of discharge mean and variability, while the amplitude factor, which controls mountain belt relief, is a power law function of mean runoff (with an exponent of -0.5) and a complex function of runoff variability. In accordance with evidence that incision occurs between 6 and 20% of time in rapidly incising rivers (>1 mm/yr) our model predicts that channel steepness is virtually insensitive to runoff variability. Runoff variability can only decrease channel steepness for very slow incision rates and/or weak lithologies. The relationship between channel steepness and incision rate is always a power law whose exponent depends on the channel cross-sectional geometry and runoff variability. This contradicts models neglecting discharge stochasticity in which the steepness-incision scaling is set by the incision law exponent. Our results suggest that changes in climate variability cannot explain an increase in bedrock incision rates during the Late Cenozoic within the context of a detachment limited model.

Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bedrock channel morphology

The sediment load of a bedrock river plays an important role in the fluvial incision process by providing tools for abrasion (the tools effect) and by covering and thereby protecting the bed (the cover effect). We derive a new formulation for the cover effect, in which the fraction of exposed bed area falls exponentially with increasing sediment flux or decreasing transport capacity, and explore its consequences for the model of bedrock abrasion by saltating bed load. Erosion rates predicted by the model are higher than those predicted by earlier models. In a closed system, the maximum erosion rate is predicted to occur when sediment supply is equal to transport capacity for a flat bed. By optimizing the channel geometry to minimize the potential energy of the stream and using representative values for both discharge and grain size, we derive equations for the geometry of a bedrock river and explore how predictions for width, slope, and bed cover vary as functions of drainage area, rock uplift rate, and rock strength. The equations predict a dependence of channel width on drainage area similar to the relations using a simple shear stress incision law. The slope-area relationship is predicted to be concave up in a log-log regime, with a curvature dependent on uplift rate. However, this curvature does not deviate sufficiently from a straight line to allow discrimination between models using empirical data. Dependence of channel width and slope on rock uplift rate can be separated into two domains: for low uplift rates, channel geometry is largely insensitive to uplift rate due to a threshold effect. At high uplift rates, there is a power law dependence. Bed cover is predicted to increase progressively downstream and to increase with increasing uplift rate. In our model, the width-to-depth ratio is a function of both tectonic and climatic forcing. This indicates that the scaling between channel width and bed slope is neither a unique indicator of tectonic forcing at steady state nor a signature of transience or steady state. We conclude that sediment effects need to be taken into account when modeling bedrock channel morphology.

Reduction of long‐term bedrock incision efficiency by short‐term alluvial cover intermittency

Fluctuations of the sediment volume stored in mountain channels are driven by stochastic variations of discharge and sediment supply and can inhibit bedrock incision if sediment thickness is too large. Here, I study how this shortƒ]term stochasticity propagates into the longƒ]term reduction of bedrock incision efficiency (the cover effect) at geological time scales. I introduce a new numerical model that resolves sediment transport and bedrock incision at daily time scales, and is run for thousands of years. It incorporates (1) a transport threshold and daily stochastic variations in water discharge and sediment supply, (2) a freely evolving channel width and slope, and (3) an explicit treatment of alluvial thickness variations and corresponding bed incision reduction. For typical mountain river conditions the model predicts that alluvial cover oscillates between complete and negligible incision reduction. In this intermittent regime the longƒ]term cover effect is mainly set by the fraction of time spent in full cover, and the presentƒ]day extent of alluvial cover is not representative of longƒ]term dynamics. The longƒ]term integrated cover effect law differs strongly from proposed theoretical and experimental models, and it is controlled by sediment supply stochasticity rather than the details of cover development at the hydraulic time scale. Model results also suggest that steady state channel configuration always depends on sediment supply rate, while being never limited by transport capacity or strictly detachment limited. These results point out that discharge and sediment supply stochasticity should not be considered less important than the intricate details of incision laws to model long-term bedrock channel dynamics.

Fluvial erosion/transport equation of landscape evolution models revisited

We present a mesoscale erosion/deposition model, which differs from previous landscape evolution models equations by taking explicitly into account a mass balance equation for the streamflow. The geological and hydrological complexity is lumped into two basic fluxes (erosion and deposition) and two averaged parameters (unit width discharge q and stream slope s). The model couples the dynamics of streamflow and topography through a sediment transport length function x(q), which is the average travel distance of a particle in the flow before being trapped on topography. This property reflects a time lag between erosion and deposition, which allows the streamflow not to be instantaneously at capacity. The so-called x-q model may reduce either to transport-limited or to detachment-limited erosion modes depending on x. But it also may not. We show in particular how it does or does not for steady state topographies, long-term evolution, and high-frequency base level perturbations. Apart from the unit width discharge and the settling velocity, the x(q) function depends on a dimensionless number encompassing the way sediment is transported within the streamflow. Using models of concentration profile through the water column, we show the dependency of this dimensionless coefficient on the Rouse number. We discuss how consistent the x-q model framework is with bed load scaling expressions and Einsteins conception of sediment motion.

Response of bedrock channel width to tectonic forcing: Insights from a numerical model, theoretical considerations, and comparison with field data

The morphology of bedrock river channels is controlled by climatic and tectonic conditions and substrate properties. Knowledge of tectonic controls remains scarce. This is partly due to slow tectonic rates and long response times of natural channels and partly due to the difficulty in isolating and constraining tectonic forcing conditions in the field. To study the effect of tectonic forcing on channel geometry, we have developed a numerical model of the cross-sectional evolution of a detachment-limited channel. Its predictions are matched by an analytical model based on the assumption of the minimization of potential energy expenditure. Using these models, we illustrate how local tectonics can alter the observed width-discharge scaling and discuss published field data in light of our findings. Except for one case, the models fail to correctly describe field observations of well-constrained cases. This implies that the shear stress/stream-power family of models is too simple to describe the behavior of natural channels. Additional complexities such as sediment effects and discharge variability exert a strong control on channel morphology and need to be taken into account in the modeling of channel dynamics and steady state.

Fluvial incision into bedrock: Insights from morphometric analysis and numerical modeling of gorges incising glacial hanging valleys (Western Alps, France)

Bedrock gorges incising glacial hanging valleys potentially allow measurements of fluvial bedrock incision in mountainous relief. Using digital elevation models, topographic maps, and field reconnaissance, we identified and characterized 30 tributary hanging valleys incised by gorges near their confluence with trunk streams in the Romanche watershed, French Western Alps. Longitudinal profiles of these tributaries are all convex and have abrupt knickpoints at the upper limit of oversteepened gorge reaches. We reconstructed initial glacial profiles from glacially polished bedrock knobs surrounding the gorges in order to quantify the amount of fluvial incision and knickpoint retreat. From morphometric analyses, we find that mean channel gradients and widths, as well as knickpoint retreat rates, display a drainage area dependence modulated by bedrock lithology. However, there appears to be no relation between horizontal retreat and vertical downwearing of knickpoints. Assuming a postglacial origin of these gorges, our results imply high postglacial fluvial incision (0.5-15 mm yr−1) and knickpoint retreat (1-200 mm yr−1) rates that are, however, consistent with previous estimates. Numerical modeling was used to test the capacity of different fluvial incision models to predict the inferred evolution of the gorges. Results from simple end‐member models suggest transport‐limited behavior of the bedrock gorges. A more sophisticated model including dynamic width adjustment and sediment‐dependent incision rates predicts present‐day channel geometry only if a significant supply of sediment from the gorge sidewalls (∼10 mm yr−1) is triggered by gorge deepening, combined with pronounced inhibition of bedrock incision by sediment transport and deposition.

Estimating uplift rate and erodibility from the area-slope relationship: Examples from Brittany (France) and numerical modelling

Abstract We used the local slope/drainage area relationship to derive the basic erosion and tectonic parameters from a topography. Assuming a dynamic equilibrium between uplift and erosion, this relationship is expected to depend quite simply on the rock erodibility, and on the tectonic uplift. This relationship may then be used to quantify independently the effect of lithological variation on the erodibility, and the uplift rate. We tested the method on a computer simulated topography and showed that the uplift information can be precisely calculated from the topographic analysis alone. We then analysed the topography of Brittany (France), and obtained a good agreement with uplift data from comparative levelling studies and river incision analysis.

Analogue modelling of relief dynamics

Abstract Natural landscape analysis and numerical modelling point to a lack of physical data on relief dynamics. Experimental modelling is therefore an interesting approach for obtaining physical information on eroded systems with runoff transportation and topographic incision. The main technical challenge, in reproducing regional topography at the laboratory scale, is to obtain mm-scale incisions and a limitation of the smoothing action of diffusive transport processes. An experimental design using newly developed rain making apparatus and silica as a model material, satisfies the required conditions, and allows simulation of geomorphic instabilities. An example of “plateau instability” modelling is presented to illustrate the suitability of this experimental procedure.