Ce travail de thèse propose une approche générique pour l'estimation de l'état/ des paramètres et pour le placement de capteurs de systèmes hyperboliques non linéaires en dimension infinie. Le travail est donc divisé en deux parties principales : une partie consacrée à l'estimation optimale et une partie dédiée au placement optimal de capteurs. La méthode d'estimation optimale utilise une approche par calcul des variations et utilise la méthode des multiplicateurs de Lagrange. Ces multiplicateurs jouent un rôle important en donnant accès aux sensibilités des mesures par rapport aux variables qui doivent être estimées. Ces sensibilités, décrites par les équations adjointes, sont aussi à l'origine d'une nouvelle approche, dite méthode de l'adjoint, pour le placement optimal de capteurs. Divers exemples, construits sur la base de simulations mais également de données réelles et pour différents scénarios, sont aussi étudiées afin d'illustrer l'efficacité des approches développées. Ces exemples concernent les écoulements à surface libre (en hydrologie des bassins versants) et le trafic routier représentés par des équations aux dérivées partielles hyperboliques non linéaires. / The thesis proposes a general framework for both state/parameters estimation and sensor placement in nonlinear infinite dimensional hyperbolic systems. The work is therefore divided into two main parts: a first part devoted to the optimal estimation and a second one to optimal sensor location. The estimation method is based on the calculus of variations and the use of Lagrange multipliers. The Lagrange multipliers play an important role in giving access to the sensitivities of the measurements with respect to the variables to be estimated. These sensitivities, described by the adjoint equations, are also the key idea of a new approach, so-called the adjoint-based approach, for the optimal sensor placement. Various examples, either based on some simulations with synthetic measurements or real data sets and for different scenarios, are also studied to illustrate the effectiveness of the developed approaches. Theses examples concern the overland flow systems and the traffic flow, which are both governed by nonlinear hyperbolic partial differential equations.

Magister Scientiae - MSc / The project was conducted on a small-scale catchment at Goedertrou in the Riebeek- Kasteel district. The focus of this study was to address some of the hydrological processes active in the research catchment, namely infiltration, run-off and sediment mobilisation on different soil types. It was done to investigate the origin of Berg River pollutants. To answer the overall question about what influence the natural salt load of the Berg River, a number of subprojects have been identified, one of which is to understand the hydrological processes in the soil mantle and vadose zone. Hence, the study aimed to answer the research questions mentioned and discussed in section 1.3 of Chapter 1. Considering the results, it could be suggested that decayed root systems from the rows of plants, soil cracks, small channels and openings created by small animals, as well as slope orientation and, therefore, soil composition, all played a major role in influencing the ability of the soil to absorb the simulated rainfall. In this study, the factors that influenced run-off are micro topography, soil moisture, root system, animal activities in soil profile, soil crack dimensions and the hydraulic conductivity. The main factors that played a major role to influence sediments mobilisation are strongly believed to be the micro topography within the ring, slope gradient and length, vegetation cover and rainfall-simulation intensity. After using different techniques, the results show that farmers must be aware that with storm rainfall, particles smaller than 65 μm are subject to mobilisation. It is important to let land-users know that they need proper and appropriate methods for land-use. / South Africa

Accurate models to reliably predict sediment and chemical transport in watershed water systems enhance the ability of environmental scientists, engineers and decision makers to analyze the impact of contamination problems and to evaluate the efficacy of alternative remediation techniques and management strategies prior to incurring expense in the field. This dissertation presents the conceptual and mathematical development of a general numerical model simulating (1) sediment and reactive chemical transport in river/stream networks of watershed systems; (2) sediment and reactive chemical transport in overland shallow water of watershed systems; and (3) reactive chemical transport in three-dimensional subsurface systems. Through the decomposition of the system of species transport equations via Gauss-Jordan column reduction of the reaction network, fast reactions and slow reactions are decoupled, which enables robust numerical integrations. Species reactive transport equations are transformed into two sets: nonlinear algebraic equations representing equilibrium reactions and transport equations of kinetic-variables in terms of kinetically controlled reaction rates. As a result, the model uses kinetic-variables instead of biogeochemical species as primary dependent variables, which reduces the number of transport equations and simplifies reaction terms in these equations. For each time step, we first solve the advective-dispersive transport of kinetic-variables. We then solve the reactive chemical system node by node to yield concentrations of all species. In order to obtain accurate, efficient and robust computations, five numerical options are provided to solve the advective-dispersive transport equations; and three coupling strategies are given to deal with the reactive chemistry. Verification examples are compared with analytical solutions to demonstrate the numerical accuracy of the code and to emphasize the need of implementing various numerical options and coupling strategies to deal with different types of problems for different application circumstances. Validation examples are presented to evaluate the ability of the model to replicate behavior observed in real systems. Hypothetical examples with complex reaction networks are employed to demonstrate the design capability of the model to handle field-scale problems involving both kinetic and equilibrium reactions. The deficiency of current practices in the water quality modeling is discussed and potential improvements over current practices using this model are addressed.

From the Proceedings of the 1978 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 14-15, 1978, Flagstaff, Arizona / Sediment is widely recognized as a significant pollutant affecting water quality. To assess the impact of land use and management practices upon sediment yield from upland areas, it is necessary to predict erosion and sediment yield as functions of runoff, soil characteristics such as erodibility, and watershed characteristics. The combined runoff-erosion process on upland areas was modeled as overland flow on a plane, with rill and interrill erosion. Solutions to the model were previously obtained for sediment concentration in overland flow, and the combined runoff-erosion model was tested using observed runoff and sediment data. In this paper, the equations are integrated to produce a relationship between volume of runoff and total sediment yield for a given storm. The sediment yield equation is linear in runoff volume, but nonlinear in distance and, thus, watershed area. Parameters of the sediment yield equation include the hydraulic resistance parameter, rill and interrill erodibility terms, and flow depth-detachment coefficient and exponent.

L’objectif global de ce travail est d’étudier une modélisation multi échelle et de développer une méthode adaptée pour la simulation numérique du processus d’érosion à l’échelle du bassin versant. Après avoir passé en revue les différents modèles existants, nous dérivons une solution analytique non triviale pour le système couplé modélisant le transport de sédiments par charriage. Ensuite, nous étudions l’hyperbolicité de ce système avec diverses lois de sédimentation proposées dans la littérature. Concernant le schéma numérique, nous présentons le domaine de validité de la méthode de splitting, pour les équations modélisant l’écoulement et celle décrivant l’évolution du fond. Pour la modélisation du transport en suspension à l’échelle de la parcelle, nous présentons un système d’équations couplant les mécanismes d’infiltration, de ruissellement et le transport de plusieurs classes de sédiments. L’implémentation et des tests de validation d’un schéma d’ordre élevé et de volumes finis bien équilibré sont également présentés. Ensuite, nous discutons sur l’application et la calibration du modèle avec des données expérimentales sur dix parcelles au Niger. Dans le but d’aboutir la simulation à l’échelle du bassin versant, nous développons une modélisation multi échelle dans laquelle nous intégrons le taux d’inondation dans les équations d’évolution afin de prendre en compte l’effet à petite échelle de la microtopographie. Au niveau numérique, nous étudions deux schémas bien équilibrés : le schéma de Roe basé sur un chemin conservatif, et le schéma avec reconstruction hydrostatique généralisée. Enfin, nous présentons une première application du modèle avec les données expérimentales du bassin versant de Ganspoel qui nécessite la parallélisation du code. / The overall objective of this thesis is to study a multiscale modelling and to develop a suitable method for the numerical simulation of soil erosion on catchment scale. After reviewing the various existing models, we derive an analytical solution for the non-trivial coupled system modelling the bedload transport. Next, we study the hyperbolicity of the system with different sedimentation laws found in the literature. Relating to the numerical method, we present the validity domain of the time splitting method, consisting in solving separately the Shallow-Water system (modelling the flow routing) during a first time step for a fixed bed and updating afterward the topography on a second step using the Exner equation. On the modelling of transport in suspension at the plot scale, we present a system coupling the mechanisms of infiltration, runoff and transport of several classes of sediment. Numerical implementation and validation tests of a high order wellbalanced finite volume scheme are also presented. Then, we discuss on the model application and calibration using experimental data on ten 1 m2 plots of crusted soil in Niger. In order to achieve the simulation at the catchment scale, we develop a multiscale modelling in which we integrate the inundation ratio in the evolution equations to take into account the small-scale effect of the microtopography. On the numerical method, we study two well-balanced schemes : the first one is the Roe scheme based on a path conservative, and the second one is the scheme using a generalized hydrostatic reconstruction. Finally, we present a first model application with experimental data of the Ganspoel catchment where the parallel computing is also motived.