This dissertation focuses on a variety of vadose zone processes that impact water table fluctuations. The development of vadose zone process conceptualization has been limited due to both the lack of recognition of the importance of the vadose zone and the absence of suitable field data. Recent studies have, however, shown that vadose zone soil moisture dynamics, especially in shallow water table environments, can have a significant effect on processes such as infiltration, recharge to the water table, and evapotranspiration. This dissertation, hence, attempts to elucidate approaches for modeling vadose zone soil moisture dynamics. The ultimate objective is to predict different vertical and horizontal hydrological fluxes. The first part of the dissertation demonstrates a new methodology using soil moisture and water table data collected along a flow transect. The methodology was found to be successful in the estimation of hydrological fluxes such as evapotranspiration, infiltration, runoff, etc. The observed dataset was also used to verify an exponential model developed to quantify the ground water component of total evapotranspiration. This analysis was followed by a study which analyzed the impact of soil moisture variability in the vadose zone on water table fluctuations. It was found that antecedent soil moisture conditions in the vadose zone greatly affected the specific yield values, causing a broad range of water table fluctuations for similar boundary fluxes. Hence, use of a constant specific yield value can produce inaccurate results. Having gained insight into the process of evapotranspiration and specific yield, a threshold based model to determine evapotranspiration and subsequent water table fluctuation was conceptualized and validated. A discussion of plant root water uptake and its impact on vadose zone soil moisture dynamics is presented in the latter half of this dissertation. A methodology utilizing soil moisture and water table data to determine the root water uptake from different sections of roots is also described. It was found that, unlike traditional empirical root water uptake models, the uptake was not only proportional to the root fraction, but was also dependent on the ambient soil moisture conditions. A modeling framework based on root hydraulic characteristics is provided as well. Lastly, a preliminary analysis of observed data indicated that, under certain field conditions, air entrapment and air pressurization can significantly affect the observed water table values. A modeling technique must be developed to correct such observations.

A new methodology is proposed for estimation of evapotranspiration (ET) flux at small spatial and temporal scales. The method involves simultaneous measurement of soil moisture (SM) profiles and water table heads along transects flow paths. The method has been applied in a shallow water table field site in West-Central Florida for data collected from January 2002 through June 2004. Capacitance shift type moisture sensors were used for this research, placed at variable depth intervals starting at approximately 4 in. (10 cm) below land surface and extending well below the seasonal low water table depth of 59 in. (1.5 m). Vegetation included grassland and wetland forested flatwoods. The approach includes the ability to resolve multiple ET components including shallow and deep vadose zone, surface interception capture and depression storage ET. Other components of the water budget including infiltration, total and saturation rainfall excess runoff, net runoff, changes in storage and lateral groundwater flows are also derived from the approach. One shortcoming of the method is the reliance on open pan or other potential ET estimation techniques when the water table is at or near land surface. Results are compared with values derived for the two vegetative covers from micrometeorological and Bowen ratio methods. Advantages of the SM method include resolving component ET.

Storm surge, the pileup of seawater occurring as a result of high surface stresses and strong currents generated by extreme storm events such as hurricanes, is known to cause greater loss of life than these storms' associated winds. For example, inland flooding from the storm surge along the Gulf Coast during Hurricane Katrina killed hundreds of people. Previous storms produced even larger death tolls. Simultaneously, dune, barrier island, and channel erosion taking place during a hurricane leads to the removal of major flow controls, which significantly affects inland inundation. Also, excessive sea bed scouring around pilings can compromise the structural integrity of bridges, levees, piers, and buildings. Modeling these processes requires tightly coupling a bed morphology equation to the shallow water equations (SWE). Discontinuous Galerkin finite element methods (DGFEMs) are a natural choice for modeling this coupled system, given the need to solve these problems on large, complicated, unstructured computational meshes, as well as the desire to implement hp-adaptivity for capturing the dynamic features of the solution. Comprehensive modeling of these processes in the coastal zone presents several challenges and open questions. Most existing hydrodynamic models use a fixed-bed approach; the bottom is not allowed to evolve in response to the fluid motion. With respect to movable-bed models, there is no single, generally accepted mathematical model in use. Numerical challenges include coupling models of processes that exhibit disparate time scales during fair weather, but possibly similar time scales during intense storms. The main goals of this dissertation include implementing a robust, efficient, tightly-coupled morphological model using the local discontinuous Galerkin (LDG) method within the existing Advanced Circulation (ADCIRC) modeling framework, performing systematic code and model verification (using test cases with known solutions, proven convergence rates, or well-documented physical behavior), analyzing the stability and accuracy of the implemented numerical scheme by way of a priori error estimates, and ultimately laying some of the necessary groundwork needed to simultaneously model storm surges and bed morphodynamics during extreme storm events. / text

The pollution generated by accidental marine oil spills can cause persistent ecological disasters and lead to serious social and economical damages. Numerical simulations are a valuable tool to make proper decisions in emergency situation or to plan response actions beforehand. The main objective of this work was to improve SIMOIL, a computational model developed earlier at URV and capable of predicting the evaporation and spreading of massive oil spills in coastal areas. Specifically, a new coastal current model, based on the resolution of the shallow water equations in generalised coordinates, has been developed and validated and then coupled to SIMOIL. The model was specially designed to describe coastal oceanic flows over topography accounting for Coriolis force, eddy viscosity, seabed friction and to couple with SIMOIL in domain with complex boundaries. The equations have been discretized over generalised domains by means of finite differences of second order accuracy. The code was then implemented in FORTRAN. The code has been validated extensively against numerical and experimental flow studies of the bibliography. Finally, the new complete version of SIMOIL, coupling the shallow water model and the oil slick model, has been applied to the study of two accidental oil spills: • A massive leakage from the Repsol's floating dock in the port of Tarragona • The biggest oil spill ever occurred in the Eastern Mediterranean Sea: the 2006 Lebanon oil spill. In both cases, the new version of SIMOIL, demonstrate more accurate predictions of the behaviour of the oil spill, specially for moderate winds with complex topography. / La contaminación generada por los vertidos accidentales de petróleo puede ser reducida si se actúa y si se toman las decisiones adecuadas a tiempo. Las simulaciones numéricas de vertidos de petróleo permiten predecir la evolución de las manchas de crudo. En este trabajo, el objetivo principal era de mejorar la precisión y el rango de aplicación del código SIMOIL desarrollando e integrando al código un modelo de predicción de corrientes marinas en aguas costeras. Se han derivado las ecuaciones de aguas poco profundas en coordenadas generalizadas. Se han discretizado las ecuaciones y el código se implementó en FORTRAN 90. El modelo así como los métodos numéricos han sido validados con el estudio de flujos experimentales y numéricos de la bibliografía. Finalmente, la nueva versión de SIMOIL se aplicó con éxito a dos casos físicos de vertidos de crudo: • un vertido ficticio desde la monoboya de descarga de Repsol en el puerto de Tarragona • un vertido real, el mas grande ocurrido en el Este del mar Mediterráneo, consecuencia de la guerra en Líbano en julio de 2006. En ambos casos la nueva versión de SIMOIL proporcionó predicciones más precisas, especialmente para vientos moderados y topografías complejas.

The dynamics of the world's oceans occur at a vast range of length scales. Although there are theories that aid in understanding the dynamics at planetary scales and microscales, the motions in between are still not yet well understood. This work discusses a numerical model to study barotropic wind-driven gyre flow that is capable of resolving dynamics at the synoptic, O(1000 km), mesoscale, O(100 km) and submesoscales O(10 km). The Quasi-Geostrophic (QG) model has been used predominantly to study ocean circulations but it is limited as it can only describe motions at synoptic scales and mesoscales. The Rotating Shallow Water (SW) model that can describe dynamics at a wider range of horizontal length scales and can better describe motions at the submesoscales. Numerical methods that are capable of high-resolution simulations are discussed for both QG and SW models and the numerical results are compared. To achieve high accuracy and resolve an optimal range of length scales, spectral methods are applied to solve the governing equations and a third-order Adams-Bashforth method is used for the temporal discretization. Several simulations of both models are computed by varying the strength of dissipation. The simulations either tend to a laminar steady state, or a turbulent flow with dynamics occurring at a wide range of length and time scales. The laminar results show similar behaviours in both models, thus QG and SW tend to agree when describing slow, large-scale flows. The turbulent simulations begin to differ as QG breaks down when faster and smaller scale motions occur. Essential differences in the underlying assumptions between the QG and SW models are highlighted using the results from the numerical simulations.

Depuis maintenant près d’un siècle, des robots sous-marins ont été développés afin de réaliser des tâches spécifiques aux besoins des grands acteurs historiques du domaine (militaires, pétroliers, câbliers ou explorateurs benthiques) sans vraiment se soucier de la polyvalence et de la modularité de la plateforme. L’objectif de cette thèse est d’avoir une réflexion sur une solution technologique et scientifique avec comme domaine applicatif l’environnement faible fond ou confiné. Il s’agit en d’autres termes de concevoir un robot sous-marin que l’on peut faire évoluer aisément tant sur le plan mécanique, électronique qu’informatique. Cet objectif impose de proprement conceptualiser cette « polyvalence » en s’attachant à apporter de l’abstraction dans l’architecture de contrôle que se soit au niveau de l’automatique avec l’expression de la polyvalence liée à l’étage d’actionnement ou de l’informatique avec une architecture basée services, pouvant être composés, afin de répondre à la diversité des besoins applicatifs. L’ensemble de ces travaux a pour point de départ le robot Jack mis au point par l’entreprise Ciscrea, partenaire industriel, qui apporte un aspect économique à la nécessité de développer une solution polyvalente pouvant être décliné en une gamme de produits. Ce manuscrit traite de la conception, la réalisation et l’expérimentation de ce vecteur que ce soit en piscine où en environnement réel. / Since almost a century, underwater robots have been developed in order to respond to the specific needs of historical actors of the domain (military, hydrocarbons exploitation, underwater cabling or benthic exploration), without addressing specifically the question of versatility or modularity of the underwater platform. This thesis aims to address these questions on a technological solution dedicated to shallow water or confined environment. In other words, the objective is to realise an underwater system, able to evolve on the mechanical, electronical or software aspects. This requires to properly conceptualise this « versatility » with an abstraction of the control architecture, on the actuation aspect, with the expression of the versatility linked to the actuation systems, or on the software architecture level, with a Service-Oriented-Architecture (SOA) approach, in order to tackle the diversity of the application requirements. This study is based on the Jack system, developed by the Ciscrea Company, which is the industrial partner of this project, and brings the economical aspect as a central requirement. This underlines another view of the versatility question, the development of a range of product for the Ciscrea Company.This thesis proposes the conception, realisation and experimentation of such a versatile underwater system, with test-tank and field validation.

Este trabalho aborda a solução numérica das equações lineares de águas rasas. O método dos elementos finitos e utilizado para a discretização espacial das equações que modelam o problema, e para a discretização temporal, o esquema semi-implícito de Crank-Nicolson é empregado. Além de alguns conceitos comuns quando se trabalha com escoamentos geofísicos, são descritas também a formulação das equações de águas rasas, sua linearização e uma solução analítica para um caso onde o parâmetro de Coriolis é nulo. A escolha adequada de pares de elementos finitos é a principal dificuldade quando se trabalha com esse método para a resolução da equação de águas rasas. Assim, é discutido o uso de quatro pares de elementos finitos e técnicas de estabilização para contornar o surgimento de modos espúrios na solução discreta. Os resultados numéricos são realizados com auxílio do software FreeFem++, onde se pode notar a capacidade dos pares de elementos de reproduzirem o escoamento, através da solução discreta, além das propriedades de conservação de massa e energia de cada discretização. / This work is about the numerical solution of the linear shallow water equations. The finite element method is used for spatial discretization of the equations that model the problem and for the time discretization the semi-implicit Crank-Nicolson scheme is used. Besides the concepts related to geophysical flows, the formulation of the shallow water equations, their linearization and an analytical solution for a case where the Coriolis parameter is zero are also described. The appropriate choice of a pair of finite elements is the main difficulty when working with this method for solving the shallow water equations. The use of four pairs of finite elements and stabilization techniques to circumvent the appearance of spurious modes in the discrete solution are discussed. The numerical results are performed using the software FreeFem++, where one can notice the ability of the elements to represent the discrete solution and mass and energy conservation of each discretization.

Este trabalho aborda a solução numérica das equações lineares de águas rasas. O método dos elementos finitos e utilizado para a discretização espacial das equações que modelam o problema, e para a discretização temporal, o esquema semi-implícito de Crank-Nicolson é empregado. Além de alguns conceitos comuns quando se trabalha com escoamentos geofísicos, são descritas também a formulação das equações de águas rasas, sua linearização e uma solução analítica para um caso onde o parâmetro de Coriolis é nulo. A escolha adequada de pares de elementos finitos é a principal dificuldade quando se trabalha com esse método para a resolução da equação de águas rasas. Assim, é discutido o uso de quatro pares de elementos finitos e técnicas de estabilização para contornar o surgimento de modos espúrios na solução discreta. Os resultados numéricos são realizados com auxílio do software FreeFem++, onde se pode notar a capacidade dos pares de elementos de reproduzirem o escoamento, através da solução discreta, além das propriedades de conservação de massa e energia de cada discretização. / This work is about the numerical solution of the linear shallow water equations. The finite element method is used for spatial discretization of the equations that model the problem and for the time discretization the semi-implicit Crank-Nicolson scheme is used. Besides the concepts related to geophysical flows, the formulation of the shallow water equations, their linearization and an analytical solution for a case where the Coriolis parameter is zero are also described. The appropriate choice of a pair of finite elements is the main difficulty when working with this method for solving the shallow water equations. The use of four pairs of finite elements and stabilization techniques to circumvent the appearance of spurious modes in the discrete solution are discussed. The numerical results are performed using the software FreeFem++, where one can notice the ability of the elements to represent the discrete solution and mass and energy conservation of each discretization.

Este trabalho aborda a solução numérica das equações lineares de águas rasas. O método dos elementos finitos e utilizado para a discretização espacial das equações que modelam o problema, e para a discretização temporal, o esquema semi-implícito de Crank-Nicolson é empregado. Além de alguns conceitos comuns quando se trabalha com escoamentos geofísicos, são descritas também a formulação das equações de águas rasas, sua linearização e uma solução analítica para um caso onde o parâmetro de Coriolis é nulo. A escolha adequada de pares de elementos finitos é a principal dificuldade quando se trabalha com esse método para a resolução da equação de águas rasas. Assim, é discutido o uso de quatro pares de elementos finitos e técnicas de estabilização para contornar o surgimento de modos espúrios na solução discreta. Os resultados numéricos são realizados com auxílio do software FreeFem++, onde se pode notar a capacidade dos pares de elementos de reproduzirem o escoamento, através da solução discreta, além das propriedades de conservação de massa e energia de cada discretização. / This work is about the numerical solution of the linear shallow water equations. The finite element method is used for spatial discretization of the equations that model the problem and for the time discretization the semi-implicit Crank-Nicolson scheme is used. Besides the concepts related to geophysical flows, the formulation of the shallow water equations, their linearization and an analytical solution for a case where the Coriolis parameter is zero are also described. The appropriate choice of a pair of finite elements is the main difficulty when working with this method for solving the shallow water equations. The use of four pairs of finite elements and stabilization techniques to circumvent the appearance of spurious modes in the discrete solution are discussed. The numerical results are performed using the software FreeFem++, where one can notice the ability of the elements to represent the discrete solution and mass and energy conservation of each discretization.

Esta tese apresenta uma nova metodologia para animação de objetos líquidos em imagens. Contrariamente às técnicas existentes, este método é baseado em um modelo físico, o que proporciona efeitos realísticos. A perspectiva da imagem é obtida com a intervenção do usuário, por um esquema simples de calibração da câmera, o qual permite a projeção da camada da imagem a ser animada sobre um plano horizontal no espaço tridimensional. As equações de águas rasas conduzem a simulação e as informações de altura são projetadas de volta ao espaço da imagem utilizando traçado de raios. Além disso, efeitos de refração e iluminação são aplicados durante este estágio, resultando em animações realísticas e convincentes / This work presents a new methodology for animating liquid objects depicted in a still image. In contrast to existing techniques, the proposed method relies on a physical model to accomplish the animation, resulting in realistic effects. Image perspective is handled through a simple user assisted camera calibration scheme which allows one to project the image layers to be animated onto the horizontal plane in the three-dimensional space. Shallow-Water equations drive the simulation and the resulting height field is projected back to the image space via ray-tracing. Refraction and lighting effects are also accomplished during the ray-tracing stage, resulting in realistic and convincing animations