Tracer Dispersion in Rough Open Cracks

Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface.This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained

Data assimilation method for real-time flash flood forecasting using a physically based distributed model

The MARINE model (Roux et al, 2011) is a physically based distributed model dedicated to real time flash flood forecasting on small to medium catchments. The infiltration capacity is evaluated by the Green and Ampt equation and the surface runoff calculation is divided into two parts: the land surface flow and the flow in the drainage network both based on kinematic wave hypothesis. In order to take into account rainfall spatial-temporal variability as well as the various behaviours of soil types among the catchment, the model is spatially distributed, which can also help to understand the flood driving processes. The model integrates remote sensing data such as the land coverage map with spatial resolution adapted to hydrological scales. Minimal data requirements for the model are: the Digital Elevation Model describing catchment topography and the location and description of the drainage network. Moreover some parameters are not directly measurable and need to be calibrated. Most of the sources of uncertainties can be propagated thanks to variational method (Castaings et al, 2009) and finally help to determine time dependent uncertainty intervals. This study also investigates the methodology developed for real-time flash flood forecasting using the MARINE model and data assimilation techniques. According to prior sensitivity analyses and calibrations, parameters values were determined as constants or initial guess. Then a data assimilation method called the adjoint state method is used to update some of the most sensitive parameters to improve accuracy of discharges predictions. The forecast errors are evaluated as a function of lead time and discussed from an operational point of view. Multiple strategies in term of updatable parameters set, length of time window, parameters bounds and observation threshold used to trigger the assimilation method are discussed regarding accuracy, robustness and real-time feasibility

Numerical study of geometrical dispersion in self-affine rough fractures

We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-affine curve whose exponent is equal to that of the fracture surface

Characterization of process-oriented hydrologic model behavior with temporal sensitivity analysis for flash floods in Mediterranean catchments

This paper presents a detailed analysis of 10 flash flood events in the Mediterranean region using the distributed hydrological model MARINE. Characterizing catchment response during flash flood events may provide new and valuable insight into the dynamics involved for extreme catchment response and their dependency on physiographic properties and flood severity. The main objective of this study is to analyze flash-flood-dedicated hydrologic model sensitivity with a new approach in hydrology, allowing model outputs variance decomposition for temporal patterns of parameter sensitivity analysis. Such approaches enable ranking of uncertainty sources for nonlinear and nonmonotonic mappings with a low computational cost. Hydrologic model and sensitivity analysis are used as learning tools on a large flash flood dataset. With Nash performances above 0.73 on average for this extended set of 10 validation events, the five sensitive parameters of MARINE process-oriented distributed model are analyzed. This contribution shows that soil depth explains more than 80% of model output variance when most hydrographs are peaking. Moreover, the lateral subsurface transfer is responsible for 80% of model variance for some catchment-flood events’ hydrographs during slow-declining limbs. The unexplained variance of model output representing interactions between parameters reveals to be very low during modeled flood peaks and informs that model parsimonious parameterization is appropriate to tackle the problem of flash floods. Interactions observed after model initialization or rainfall intensity peaks incite to improve water partition representation between flow components and initialization itself. This paper gives a practical framework for application of this method to other models, landscapes and climatic conditions, potentially helping to improve processes understanding and representation

A hyperbolic-elliptic-parabolic PDE model describing chemotactic E. coli colonies

We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three parabolic equations was studied numerically and analytically and gave insights into the underlying mechanisms of chemotaxis. We focus here on the parabolic-elliptic-parabolic approximation and the hyperbolic-elliptic-parabolic limiting system which describes the case of pure chemotactic movement without random diffusion. We first construct local-in-time solutions for the parabolic-elliptic-parabolic system. Then we prove uniform \textit{a priori} estimates and we use them along with a compactness argument in order to construct local-in-time solutions for the hyperbolic-elliptic-parabolic limiting system. Finally, we prove that some initial conditions give rise to solutions which blow-up in finite time in the $L^\infty$ norm in all space dimensions. This last result violet is true even in space dimension 1, which is not the case for the full parabolic or parabolic-elliptic Keller-Segel systems