Philippe Davy

We analyze how the process of bedrock incision by the impact of sediment grains can be described and coupled with sediment dynamics. We first point out that the key parameter is a bedrock dimensionless coefficient that describes the ratio between the volumes of impacting sediments and bedrock erosion. We then write the coupled equations by introducing a partitioning coefficient between sediment and bedrock erosions. It describes the time spent doing one or the other erosion process – or the proportion of depositing grains that impact bedrock. In a 1D along-stream system, the resulting equations lead to a similar description of the cover effect proposed by Sklar and Dietrich (2004), giving a rationale to their expression. In a second step, we extend the concept to lateral erosion or deposition fluxes. We develop analytical solutions for a river fed by uniform lateral sediment fluxes from hillslope and show why the sediment load can exceed the transport capacity. We then implement the equations in the numerical code River.lab/eros, where water depth and velocity, as well as erosion and deposition fluxes, are solved with the method of precipitons. As an example, we simulate the evolution of the Rheinfall at Schaffhausen, Switzerland, a prominent knickpoint along the Hochrhein. In contrast with sediment processes, where the knickpoint slope decreases by diffusion without upstream displacements, bedrock abrasion allows knickpoint to move upstream while retaining almost the same shape. This is consistent with detachment-limited behavior as emphasized in the theoretical part of the paper. The knickpoint shape (foot elevation and height) and retreat rates are highly dependent on the sediment load in river. Bedrock erosion first happens in a narrow canyon that propagates upstream, and then the river widens after the knickpoint passed by.

We analyze how the process of bedrock incision by the impact of sediment grains can be described and coupled with sediment dynamics. We first point out that the key parameter is a bedrock dimensionless coefficient that describes the ratio between the volumes of impacting sediments and bedrock erosion. We then write the coupled equations by introducing a partitioning coefficient between sediment and bedrock erosions. It describes the time spent doing one or the other erosion process – or the proportion of depositing grains that impact bedrock. In a 1D along-stream system, the resulting equations lead to a similar description of the cover effect proposed by Sklar and Dietrich (2004), giving a rationale to their expression. In a second step, we extend the concept to lateral erosion or deposition fluxes. We develop analytical solutions for a river fed by uniform lateral sediment fluxes from hillslope and show why the sediment load can exceed the transport capacity. We then implement the equations in the numerical code River.lab/eros, where water depth and velocity, as well as erosion and deposition fluxes, are solved with the method of precipitons. As an example, we simulate the evolution of the Rheinfall at Schaffhausen, Switzerland, a prominent knickpoint along the Hochrhein. In contrast with sediment processes, where the knickpoint slope decreases by diffusion without upstream displacements, bedrock abrasion allows knickpoint to move upstream while retaining almost the same shape. This is consistent with detachment-limited behavior as emphasized in the theoretical part of the paper. The knickpoint shape (foot elevation and height) and retreat rates are highly dependent on the sediment load in river. Bedrock erosion first happens in a narrow canyon that propagates upstream, and then the river widens after the knickpoint passed by.

We analyze how the process of bedrock incision by the impact of sediment grains can be described and coupled with sediment dynamics. We first point out that the key parameter is a bedrock dimensionless coefficient that describes the ratio between the volumes of impacting sediments and bedrock erosion. We then write the coupled equations by introducing a partitioning coefficient between sediment and bedrock erosions. It describes the time spent doing one or the other erosion process – or the proportion of depositing grains that impact bedrock. In a 1D along-stream system, the resulting equations lead to a similar description of the cover effect proposed by Sklar and Dietrich (2004), giving a rationale to their expression. In a second step, we extend the concept to lateral erosion or deposition fluxes. We develop analytical solutions for a river fed by uniform lateral sediment fluxes from hillslope and show why the sediment load can exceed the transport capacity. We then implement the equations in the numerical code River.lab/eros, where water depth and velocity, as well as erosion and deposition fluxes, are solved with the method of precipitons. As an example, we simulate the evolution of the Rheinfall at Schaffhausen, Switzerland, a prominent knickpoint along the Hochrhein. In contrast with sediment processes, where the knickpoint slope decreases by diffusion without upstream displacements, bedrock abrasion allows knickpoint to move upstream while retaining almost the same shape. This is consistent with detachment-limited behavior as emphasized in the theoretical part of the paper. The knickpoint shape (foot elevation and height) and retreat rates are highly dependent on the sediment load in river. Bedrock erosion first happens in a narrow canyon that propagates upstream, and then the river widens after the knickpoint passed by.

We analyze how the process of bedrock incision by the impact of sediment grains can be described and coupled with sediment dynamics. We first point out that the key parameter is a bedrock dimensionless coefficient that describes the ratio between the volumes of impacting sediments and bedrock erosion. We then write the coupled equations by introducing a partitioning coefficient between sediment and bedrock erosions. It describes the time spent doing one or the other erosion process – or the proportion of depositing grains that impact bedrock. In a 1D along-stream system, the resulting equations lead to a similar description of the cover effect proposed by Sklar and Dietrich (2004), giving a rationale to their expression. In a second step, we extend the concept to lateral erosion or deposition fluxes. We develop analytical solutions for a river fed by uniform lateral sediment fluxes from hillslope and show why the sediment load can exceed the transport capacity. We then implement the equations in the numerical code River.lab/eros, where water depth and velocity, as well as erosion and deposition fluxes, are solved with the method of precipitons. As an example, we simulate the evolution of the Rheinfall at Schaffhausen, Switzerland, a prominent knickpoint along the Hochrhein. In contrast with sediment processes, where the knickpoint slope decreases by diffusion without upstream displacements, bedrock abrasion allows knickpoint to move upstream while retaining almost the same shape. This is consistent with detachment-limited behavior as emphasized in the theoretical part of the paper. The knickpoint shape (foot elevation and height) and retreat rates are highly dependent on the sediment load in river. Bedrock erosion first happens in a narrow canyon that propagates upstream, and then the river widens after the knickpoint passed by.

Fracture networks are preferential flow paths playing a critical role in a wide range of environmental and industrial problems. Their complex multiscale structure leads to broad distributions of fluid travel times, affecting many biogeochemical processes. Yet, the relationship between the fracture network structures, their hydrodynamic properties, and the resulting anomalous transport dynamics remains unclear. We use a large database of fracture network models to investigate the factors controlling fluid velocity and travel-time distributions across a wide range of networks, from synthetic to field-calibrated models, with aperture variability at both fracture and network scales. Analysis reveals that transport statistics have generic properties across investigated networks, including notably heavy-tailed travel time distributions. Networks of increasing complexity and heterogeneity lead to broader velocity distributions and more channeled velocity fields, where flow concentrates in a narrow channel web in the three-dimensional (3D) fracture structure. While heterogeneity in point-velocity statistics increases travel-time variability, channeling tends to reduce it. This counterintuitive phenomenon challenges current theories, which assume that long travel time power law exponents are determined solely by point-velocity statistics. By analyzing velocity and travel time statistics for different flow structures, we develop a coupled Continuous Time Random Walk framework capturing the unexpected control of the velocity field’s spatial structure on anomalous transport in fracture networks. This leads to a unique class of random walk models capturing the respective roles of velocity heterogeneity and spatial structure on transport in networks. These findings open a prospective for characterizing, modeling, and predicting transport dynamics in complex networks, with potential applications to geological, biological, and engineered networks.

Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae that coalesce due to molecular diffusion. Owing to the linearity of the advection–diffusion equation, coalescence can be envisioned as an aggregation process. Here, we demonstrate that in smooth two-dimensional chaotic flows, mixing obeys a correlated aggregation process, where the spatial distribution of the number of lamellae in aggregates is highly correlated with their elongation, and is set by the fractal properties of the advected material lines. We show that the presence of correlations makes mixing less efficient than a completely random aggregation process because lamellae with similar elongations and scalar levels tend to remain isolated from each other. We show that correlated aggregation is uniquely determined by a single exponent that quantifies the effective number of random aggregation events. These findings expand aggregation theories to a larger class of systems, which have relevance to various fundamental and applied mixing problems.

Heat transport in fractured aquifers is determined by the combined effects of flow velocity heterogeneity in the fracture system, and diffusive exchange between the fluid in the fractures and the rock matrix, which can be assumed as impervious. We analyze the impacts of this diffusive exchange on the response to heat transport, as opposite to the pure advective displacement, which governs solute transport. We focus on the post‐peak behavior where we observe pre‐asymptotic regimes with slopes that differ from the signature of matrix diffusion, which exhibits a decay rate of −3/2. This deviation is driven by the variability of both velocity field and fracture aperture field. We derive theoretical models that predict these pre‐asymptotic tails under three extreme cases that can be related with specific network structures, that is, networks dominated by large or small fractures, networks with highly or poorly channelized flow. These theoretical predictions are compared with results from numerical simulations in different sets of three‐dimensional discrete fracture networks. We determine that the combined observation of solute and heat transport responses allows classifying the network in terms of connectivity structure, and partially characterizing the fracture aperture variability in terms of upscaled parameters.

Essentially all hydrogeological processes are strongly influenced by the subsurface spatial heterogeneity and the temporal variation of environmental conditions, hydraulic properties, and solute concentrations. This spatial and temporal variability generally leads to effective behaviors and emerging phenomena that cannot be predicted from conventional approaches based on homogeneous assumptions and models. However, it is not always clear when, why, how, and at what scale the 4D (3D + time) nature of the subsurface needs to be considered in hydrogeological monitoring, modeling, and applications. In this paper, we discuss the interest and potential for the monitoring and characterization of spatial and temporal variability, including 4D imaging, in a series of hydrogeological processes: (1) groundwater fluxes, (2) solute transport and reaction, (3) vadose zone dynamics, and (4) surface–subsurface water interactions. We first identify the main challenges related to the coupling of spatial and temporal fluctuations for these processes. We then highlight recent innovations that have led to significant breakthroughs in high-resolution space–time imaging and modeling the characterization, monitoring, and modeling of these spatial and temporal fluctuations. We finally propose a classification of processes and applications at different scales according to their need and potential for high-resolution space–time imaging. We thus advocate a more systematic characterization of the dynamic and 3D nature of the subsurface for a series of critical processes and emerging applications. This calls for the validation of 4D imaging techniques at highly instrumented observatories and the harmonization of open databases to share hydrogeological data sets in their 4D components.

The objective of the paper is to better understand and quantify the flow structure in fractured rocks from flow logs, and to propose relevant indicators for validating, calibrating or even rejecting hydrogeological models. We first studied what the inflow distribution tells us about the permeability structure from a series of analyses: distribution of transmissivities as a function of depth, proportion of flowing sections as a function of section scale, and scaling of the arithmetically-averaged and geometrically-averaged permeability. We then define three indicators that describe few fundamental characteristics of the flow/permeability, whatever the scale: a percolation scale l s , the way permeability increases with scale above l s , and the variability of permeability. A 4th indicator on the representative elemental volume could in principle be defined but the data show that this volume/scale is beyond the 300 m investigated. We tested a series of numerical models built in three steps: the geo-DFN based on the observed fracture network, the open-DFN which is the part of the geo-DFN where fractures are open, and a transmissivity model applying on each fracture of the open-DFN (Discrete Fracture Network). The analysis of the models showed that the percolation scale is controlled by the open-DFN structure and that the percolation scale can be predicted from a scale analysis of the percolation parameter (basically, the third moment of the fracture size distribution that provides a measure of the network connectivity). The way permeability increases with scale above the percolation threshold is controlled by the transmissivity model and in particular by the dependence of the fracture transmissivity on either the orientation of the fractures via a stress-controlled transmissivity or their size or both. The comparison with data on the first two indicators shows that a model that matches the characteristics of the geo-DFN with an open fraction of 15% as measured adequately fits the data provided that the large fractures remain open and that the fracture transmissivity model is well selected. Most of the other models show unacceptable differences with data but other models or model combinations has still to be explored before rejecting them. The third indicator on model variability is still problematic since the natural data show a higher variability than the models but the open fraction is also much more variable in the data than in the models.