This thesis presents a novel analytical solution strategy for the zero-inertia (ZI) equations of free surface flow. These equations are utilized herein for routing flood flow in open channels and for simulating excess rainfall runoff on overland planes. The novel solution approach is shown to be both accurate and robust, especially under the complicated and intricate conditions of infiltrating flow on initially dry river beds or soils, e.g., as present in arid and semiarid areas. This is underlain by comparing modeling results of the novel analytical procedure with those of validated numerical solutions. Furthermore, it is shown that the analytical ZI model can deliver a process-oriented portrayal of runoff concentration in the flood-generating parts of the catchment. Subsequently, the novel analytical ZI model is applied for a real-world water management problem in the Sultanate of Oman, Arabian Peninsula. Within an integrated flash flood routing model—which is also presented in this thesis—the novel analytical routing approach helps in accurately matching the dynamics of advancing and infiltrating ephemeral river flow, established as a consequence of release from a groundwater recharge dam. The integrated modeling system houses the aforementioned analytical downstream model and tailor-made, state-of-the-art modeling components to portray the upstream flow processes, dam operation (including evaporation), and spillway release flow. The proposed modeling system can aid in rendering a realistic image of transient transmission losses and dependent flow dynamics. This is of extremely high importance for water resources assessment, as well as for optimizing recharge dam operation strategies in order to maximize downstream transmission losses and, thus, groundwater recharge.:List of Figures List of Tables List of Algorithms List of Symbols and Acronyms 1 Introduction 1.1 The Role of Ephemeral River Flow for Groundwater Recharge 1.2 Methods for Estimating Groundwater Recharge 1.3 Groundwater Augmentation Techniques and the Involved Processes 1.4 The Role of Overland Flow for Flash Flood Formation 1.5 Objectives of the Thesis 1.6 Structure of the Work 2 Literature Review 2.1 Surface-Water Based Studies on the Estimation of Indirect Recharge 2.2 Review of Literature on Process-Oriented Overland Flow Modeling 2.3 Summary 3 Principles of Physically-Based Modeling of Infiltrating Free Surface Flows 3.1 Hydraulic Phases of an Infiltrating Flow Event 3.2 Hydrodynamic Models 3.2.1 The Saint-Venant Equations 3.2.2 Zero-Inertia Approximation 3.2.3 Kinematic Wave Approximation 3.2.4 Other Simplifications of the Full Hydrodynamic Model 3.3 Initial and Boundary Conditions 3.4 Relating Friction and Flow Properties 3.5 Accounting for Losses or Gains 3.6 Including Arbitrary Cross-Sectional Geometries 3.7 Discussion of the Reviewed Flow Models 3.7.1 Discussion of Modeling Approaches for Ephemeral River Routing 3.7.2 A Suitable Hydrodynamic Model for Overland Flow 3.7.3 On the Portrayal of Shocks with the Kinematic Wave Model 3.8 Summary 4 Solution Procedures for the Reviewed Flow Models 4.1 Method of Characteristics 4.2 Numerical Solution Procedures 4.2.1 Introduction to Finite Difference Methods 4.2.2 Mathematical Principles of Finite Difference Methods 4.3 Analytical Solution Procedures 4.4 Discussion of the Reviewed Solution Procedures 4.5 Summary and Conclusions 5 Novel Analytical Solution Approaches for the Zero-Inertia Equations 5.1 Novel Analytical Solution Approach for Zero-Inertia Open Channel Flow 5.1.1 Governing Equations 5.1.2 Including Nonprismatic Channel Geometries 5.1.3 Boundary and Initial Conditions 5.1.4 Analytical Solution of the Momentum Equation 5.1.5 Analytical Solution of the Continuity Equation 5.1.6 Algorithm for the Iterative Solution of the Nonlinear Problem 5.1.7 Coupling Surface Flow and Infiltration 5.1.8 Additional Remarks 5.2 Novel Analytical Solution Approach for Zero-Inertia Overland Flow 5.2.1 Governing Equations 5.2.2 Boundary and Initial Conditions 5.2.3 Analytical Solution 5.2.4 Algorithm for the Iterative Solution of the Nonlinear Problem 5.3 Summary 6 Comparative Studies with Generally Accepted Approaches 6.1 Open Channel Flow in Prismatic and Nonprismatic Permeable Open Channels 6.1.1 Test Setup 6.1.2 Comparison of Flow Dynamics 6.1.3 Analysis of the Geometry Parameter Sensitivity 6.1.4 Evaluating the Stability of the Analytical ZI Model 6.1.5 Summary 6.2 Overland Flow on a Plane 6.2.1 Test Setup 6.2.2 Comparison of Modeling Results 6.2.3 Summary 7 Flash Flood Routing under Transmission Losses and Dam Operation 7.1 Outline of the Structure of a Novel Integrated Modeling System 7.1.1 Wadi Flow Routing Models 7.1.2 Dam Simulation Model with Evaporation Component 7.2 Real-World Application of the Modeling System for an Arid Region 7.2.1 Study Area and Available Data 7.2.2 Parameter Sensitivity Analysis 7.2.3 Optimization-Based Process Parameter Estimation 7.2.4 Model Application for Wadi Ma\\\\\\\'awil 7.3 Summary 8 Summary and Conclusions 9 Outlook 9.1 The Modeling System for Improving Water Resources Assessment 9.2 The Modeling System for Optimizing Groundwater Recharge Bibliography A Mathematical Supplements A.1 Explicit First-Order Finite Difference Scheme for the Kinematic Wave Model A.2 Explicit Second-Order Finite Difference Scheme for the Kinematic Wave Model A.3 Implicit Finite Difference Scheme with Interior Point (Preissmann Scheme) A.4 Analytical Solution of the Kinematic Wave Model A.5 Details on the Derivation of the Iterative Procedure (5.47);(5.48) A.6 Details on the Evaluation of Equation (5.60) B Selected Publications of the Author B.1 Analytical Model of Surge Flow in Nonprismatic Permeable Channels B.2 Analytical Model of Surface Flow on Hillslopes B.3 Integrated Modeling System for Flash Flood Routing in Ephemeral Rivers / Diese Dissertation präsentiert einen neuartigen analytischen Lösungsansatz für das beschleunigungsfreie Wellenmodell (bzw. „Zero-Inertia-Modell“, „ZI-Modell“, oder „diffusives Wellenmodell“). Im Rahmen der Arbeit wird das hergeleitete hydrodynamische Modell sowohl zur Simulation von Freispiegelabflüssen in nichtprismatischen und durchlässigen Gerinnen, als auch für die Beschreibung von auf der Landoberfläche abfließendem Infiltrationsüberschuss eingesetzt. Es wird gezeigt, dass der neuartige analytische Ansatz — im Hinblick auf Massenerhaltung und die exakte Abbildung der Abflussdynamik — akkurate Ergebnisse liefert und gleichzeitig unter komplexen und verwickelten Prozessbedingungen anwendbar ist. So belegt eine vergleichende Analyse mit validierten numerischen Lösungsansätzen die Robustheit des analytischen ZI-Modells. Insbesondere die im Sinne der numerischen Mathematik stabile und genaue Modellierung der gekoppelten Abfluss- und Infiltrationsvorgänge in anfänglich trockenen Gerinnen ist dabei ein Novum. Weiterhin wird die Eignung und Anwendbarkeit des neuartigen Modellansatzes zur Beschreibung der Abflusskonzentrationsprozesse gezeigt. Der neuartige Lösungsansatz wird im Folgenden für ein reales Wassermanagementproblem im Sultanat Oman, Arabische Halbinsel eingesetzt. Als Bestandteil eines integrierten Modellsystems, welches ebenfalls im Rahmen der Dissertation vorgestellt wird, dient das analytische ZI-Modell zur Simulation von infiltrierendem Wadiabfluss, welcher unterstrom von Grundwasseranreicherungsdämmen starke Verluste von Masse und Impuls erfährt. Zusammen mit maßgeschneiderten und dem Stand der Technik entsprechenden Komponenten für die Betriebssimulation des Anreicherungsdammes (inklusive Verdunstung von der freien Seefläche) sowie für die Abbildung der oberstromigen hydrodynamischen Prozesse (ebenfalls inklusive Infiltration) wird der neuartige analytische Ansatz in einem Modellsystem zusammengefasst. Das Modellsystem ist in der Lage ein realistisches Bild der raumzeitlichen Dynamik des Abflusses sowie der Grundwasserneubildung aus infiltrierendem Wadiabfluss zu liefern. Damit stellt das Modellsystem ein wertvolles Werkzeug sowohl zur Wasserdargebotsermittlung, als auch für die Optimierung des Betriebes von Grundwasseranreicherungsdämmen dar.:List of Figures List of Tables List of Algorithms List of Symbols and Acronyms 1 Introduction 1.1 The Role of Ephemeral River Flow for Groundwater Recharge 1.2 Methods for Estimating Groundwater Recharge 1.3 Groundwater Augmentation Techniques and the Involved Processes 1.4 The Role of Overland Flow for Flash Flood Formation 1.5 Objectives of the Thesis 1.6 Structure of the Work 2 Literature Review 2.1 Surface-Water Based Studies on the Estimation of Indirect Recharge 2.2 Review of Literature on Process-Oriented Overland Flow Modeling 2.3 Summary 3 Principles of Physically-Based Modeling of Infiltrating Free Surface Flows 3.1 Hydraulic Phases of an Infiltrating Flow Event 3.2 Hydrodynamic Models 3.2.1 The Saint-Venant Equations 3.2.2 Zero-Inertia Approximation 3.2.3 Kinematic Wave Approximation 3.2.4 Other Simplifications of the Full Hydrodynamic Model 3.3 Initial and Boundary Conditions 3.4 Relating Friction and Flow Properties 3.5 Accounting for Losses or Gains 3.6 Including Arbitrary Cross-Sectional Geometries 3.7 Discussion of the Reviewed Flow Models 3.7.1 Discussion of Modeling Approaches for Ephemeral River Routing 3.7.2 A Suitable Hydrodynamic Model for Overland Flow 3.7.3 On the Portrayal of Shocks with the Kinematic Wave Model 3.8 Summary 4 Solution Procedures for the Reviewed Flow Models 4.1 Method of Characteristics 4.2 Numerical Solution Procedures 4.2.1 Introduction to Finite Difference Methods 4.2.2 Mathematical Principles of Finite Difference Methods 4.3 Analytical Solution Procedures 4.4 Discussion of the Reviewed Solution Procedures 4.5 Summary and Conclusions 5 Novel Analytical Solution Approaches for the Zero-Inertia Equations 5.1 Novel Analytical Solution Approach for Zero-Inertia Open Channel Flow 5.1.1 Governing Equations 5.1.2 Including Nonprismatic Channel Geometries 5.1.3 Boundary and Initial Conditions 5.1.4 Analytical Solution of the Momentum Equation 5.1.5 Analytical Solution of the Continuity Equation 5.1.6 Algorithm for the Iterative Solution of the Nonlinear Problem 5.1.7 Coupling Surface Flow and Infiltration 5.1.8 Additional Remarks 5.2 Novel Analytical Solution Approach for Zero-Inertia Overland Flow 5.2.1 Governing Equations 5.2.2 Boundary and Initial Conditions 5.2.3 Analytical Solution 5.2.4 Algorithm for the Iterative Solution of the Nonlinear Problem 5.3 Summary 6 Comparative Studies with Generally Accepted Approaches 6.1 Open Channel Flow in Prismatic and Nonprismatic Permeable Open Channels 6.1.1 Test Setup 6.1.2 Comparison of Flow Dynamics 6.1.3 Analysis of the Geometry Parameter Sensitivity 6.1.4 Evaluating the Stability of the Analytical ZI Model 6.1.5 Summary 6.2 Overland Flow on a Plane 6.2.1 Test Setup 6.2.2 Comparison of Modeling Results 6.2.3 Summary 7 Flash Flood Routing under Transmission Losses and Dam Operation 7.1 Outline of the Structure of a Novel Integrated Modeling System 7.1.1 Wadi Flow Routing Models 7.1.2 Dam Simulation Model with Evaporation Component 7.2 Real-World Application of the Modeling System for an Arid Region 7.2.1 Study Area and Available Data 7.2.2 Parameter Sensitivity Analysis 7.2.3 Optimization-Based Process Parameter Estimation 7.2.4 Model Application for Wadi Ma\\\\\\\'awil 7.3 Summary 8 Summary and Conclusions 9 Outlook 9.1 The Modeling System for Improving Water Resources Assessment 9.2 The Modeling System for Optimizing Groundwater Recharge Bibliography A Mathematical Supplements A.1 Explicit First-Order Finite Difference Scheme for the Kinematic Wave Model A.2 Explicit Second-Order Finite Difference Scheme for the Kinematic Wave Model A.3 Implicit Finite Difference Scheme with Interior Point (Preissmann Scheme) A.4 Analytical Solution of the Kinematic Wave Model A.5 Details on the Derivation of the Iterative Procedure (5.47);(5.48) A.6 Details on the Evaluation of Equation (5.60) B Selected Publications of the Author B.1 Analytical Model of Surge Flow in Nonprismatic Permeable Channels B.2 Analytical Model of Surface Flow on Hillslopes B.3 Integrated Modeling System for Flash Flood Routing in Ephemeral Rivers

Cette thèse vise à étudier expérimentalement, analytiquement et numériquement, les conséquences de variations et d'oscillations hydrodynamiques à forte variabilité temporelle en milieux poreux partiellement saturés. Les problèmes que nous étudions comportent des surfaces libres tant à l'extérieur qu'à l'intérieur des milieux poreux, celles-ci étant définies comme des isosurfaces de pression d'eau égale à la pression atmosphérique (Pwater = Patm). Les différentes études expérimentales réalisées en laboratoire sont, respectivement : une expérience d'imbibition dans une boite à sable avec effets capillaires importants; la transmission d'oscillations de la surface libre à travers un massif sableux intercalaire dans un petit canal à houle (IMFT, Toulouse); l'étude de la dynamique et de la propagation des oscillations des niveaux d'eau dans un grand canal à houle (HYDRALAB, Barcelone), partiellement recouvert d'un fond sableux incliné, avec mesures de niveaux d'eau en pleine eau et sous le sable, et mesures du fond sableux (érosion/dépôts). Pour les études théoriques, nous avons développés des solutions analytiques linéarisées. Un exemple de problème traité analytiquement est: l'équation linéarisée de Dupuit-Boussinesq (D-B) transitoire à surface libre, en hypothèse d'écoulements plans et vidange/remplissage instantané : oscillations forcées, transmission et dissipation d'ondes à travers une boite à sable rectangulaire. Nous avons aussi développé une solution de l'équation faiblement non linéaire de Dupuit- Boussinesq (D-B) pour étudier le problème d'imbibition avec variation abrupte du niveau d'eau amont (suivi temporel du front de saturation). Nous avons pu étudier les différents types de problèmes transitoires liés aux expériences citées plus haut par simulation numérique. En particulier, nous avons simulé des écoulements partiellement saturés et insaturés, en coupe verticale, à l'aide d'un code de calcul (BIGFLOW 3D) qui résoud l'équation de Richards généralisée en régime transitoire. Nous avons ainsi étudié numériquement en régime non saturé, l'expérience d'imbibition dans un sable initialement sec à frontières verticales (IMFT sandbox), puis l'expérience de propagation d'ondes dans le grand canal à houle de Barcelone (laboratoire HYDRALAB) comportant une plage de sable inclinée, avec un couplage complètement intégré entre les zones micro-poreuse (sable) et “macro-poreuse” (pleine eau). Pour analyser les résultats de cette dernière expérience et les comparer aux simulations, nous avons utilisé plusieurs méthodes de traitement et d'analyse des signaux : analyse de Fourier (spectres de fréquences) ; ondelettes discrètes multi-résolution (Daubechies) ; analyses corrélatoires simple et croisée. Ces méthodes sont combinées avec des méthodes de préfiltrage pour estimer dérives et résidus (moyennes mobiles ; ondelettes multi-résolution). Cette analyse des signaux a permis de comprendre et quantifier la propagation à travers une plage de sable. Au total, les différentes approches de modélisation mis en oeuvre, associé à des procédures de calage en situation de couplage transitoire non linéaire ont permis de reproduire globalement les phénomènes de propagation de teneur en eau et de niveau d'eau dans les différentes configurations étudiées. / This thesis aims at investigating experimentally, analytically and numerically, the consequences of hydrodynamic variations and oscillations with high temporal variability in partially saturated porous media. The problems investigated in this work involve “free surfaces” both outside and inside the porous media, the free surface being defined as the “atmospheric” water pressure isosurface (Pwater = Patm). The laboratory experiments studied in this work are, respectively: Lateral imbibition in a dry sand box with significant capillary effects; Transmission of oscillations of the free surface through a vertical sand box placed in a small wave canal (IMFT, Toulouse); Dynamics of free surface oscillations and wave propagation in a large wave canal (HYDRALAB, Barcelona), partially covered with sand, with measurements of both open water and groundwater levels, and of sand topography (erosion / deposition). For theoretical studies, we have developed linearized analytical solutions. Here is a sample problem that was treated analytically in this work: The linearized equation of Dupuit-Boussinesq (DB) for transient free surface flow, assuming horizontal flow and instantaneous wetting/drainage of the unsaturated zone: forced oscillations, wave transmission and dissipation through a rectangular sandbox. We also developed a weakly nonlinear solution of the Dupuit-Boussinesq equation to study the sudden imbibition (temporal monitoring of the wetting front). We have studied the different types of transient flow problems related to the experiments cited above by numerical simulation. In particular, we have simulated unsaturated or partially saturated transient flows in vertical cross-section, using a computer code (BIGFLOW 3D) which solves a generalized version of Richards’ equation. Thus, using the Richards / BIGFLOW 3D model, we have studied numerically the experiment of unsaturated imbibition in a dry sand (IMFT sandbox), and then, with the same model, we have also studied the partially saturated wave propagation experiment in the large Barcelona wave canal (HYDRALAB laboratory), focusing on the sloping sandy beach, with coupling between the micro-porous zone (sand) and the “macro-porous” zone (open water). To interpret the results of the latter experiment and compare them to simulations, we use several methods of signal analyzis and signal processing, such as: Fourier analysis, discrete multi-resolution wavelets (Daubechies), auto and cross-correlation functions. These methods are combined with pre-filtering methods to estimate trends and residuals (moving averages; discrete wavelet analyses). This signal analyzis has allowed us to interpret and quantify water propagation phenomena through a sandy beach. To sum up, different modeling approaches, combined with model calibration procedures, were applied to transient nonlinear coupled flow problems. These approaches have allowed us to reproduce globally the water content distributions and water level propagation in the different configurations studied in this work.