Atmospheric aerosols are a highly relevant component of the climate system affecting atmospheric radiative transfer and the hydrological cycle. As opposed to other key atmospheric constituents with climatic relevance, atmospheric aerosol particles are highly heterogeneous in time and space with respect to their size, concentration, chemical composition and physical properties. Many aspects of their life cycle are not understood, making them difficult to represent in climate models and hard to control as a pollutant. Aerosol-cloud interactions in particular are infamous as a major source of uncertainty in future climate predictions. Field measurements are an important source of information for the modeling community and can lead to a better understanding of chemical and microphysical processes. In this study, field data from urban, marine, and arid settings are analyzed and the impact of meteorological conditions on the evolution of aerosol particles while in the atmosphere is investigated. Particular attention is given to organic aerosols, which are a poorly understood component of atmospheric aerosols. Local wind characteristics, solar radiation, relative humidity and the presence or absence of clouds and fog are found to be crucial factors in the transport and chemical evolution of aerosol particles. Organic aerosols in particular are found to be heavily impacted by processes in the liquid phase (cloud droplets and aerosol water). The reported measurements serve to improve the process-level understanding of aerosol evolution in different environments and to inform the modeling community by providing realistic values for input parameters and validation of model calculations.

A finite volume, shock-capturing scheme is used to solve the shallow water equations on unstructured triangular meshes. The conditions are characterised by: slow flow velocities (up to 1m/s), long time scale (around 10 days), and large domains (50-100km across). Systematic verification is carried out by comparing numerical with analytical results, and by comparing parameter variation in the numerical scheme with perturbation analysis, and good agreement is found. It is the first time a shock-capturing scheme has been applied to slow flows in Moreton Bay. The scheme is used to simulate transport of a pollutant in Moreton Bay, to the east of the city of Brisbane, Australia. Tidal effects are simulated using a sinusoidal time-dependent boundary condition. An advection equation is solved to model the path of a contaminant that is released in the bay, and the effect of tide and wind on the contaminant is studied. Calibration is done by comparing numerical results with measurements made at a study site in Moreton Bay. It is found that variation in the wind speed and bed friction coefficients changes the solution in the way predicted by the asymptotics. These results vary according to the shape of the bathymetry of the domain: in shallower areas, flow is more subject to shear and hence changes in wind speed or bed friction had a greater effect in adding energy to the system. The results also show that the time-dependent boundary condition reproduces the tidal effects that are found on the Queensland coast, i.e. semi-diurnal with amplitude of about 1 metre, to a reasonable degree. It is also found that the simulated path of a pollutant agrees with field measurements. The computer model means different wind speeds and directions can be tested which allows management decisions to be made about which conditions have the least damaging effect on the area.

Presented in this study is a wide-ranging investigation into the use of properties of balance in an operational numerical weather prediction context. Initially, a joint numerical and observational study is undertaken. We used the Unified Model (UM), the suite of atmospheric and oceanic prediction software used at the UK Met Office (UKMO), to locate symmetric instabilities (SIs), an indicator of imbalanced motion. These are areas of negative Ertel potential vorticity (in the Northern hemisphere) calculated on surfaces of constant potential temperature. Once located, the SIs were compared with satellite and aircraft observational data. As a full three-dimensional calculation of Ertel PV proved outwith the scope of this study we calculated the two-dimensional, vertical component of the absolute vorticity, to assess the inertial stability criterion. We found that at the synoptic scale in the atmosphere, if there existed a symmetric instability, it was dominated by an inertial instability. With the appropriate observational data, evidence of inertial instability from the vertical component of the absolute vorticity, predicted by the UM was found at 12km horizontal grid resolution. Varying the horizontal grid resolution allowed the estimation of a grid length scale, above which, the inertial instability was not captured by the observational data, of approximately 20km. Independently, aircraft data was used to estimate that horizontal grid resolutions above 20-25km should not model any features of imbalance providing a real world estimate of the lower bound of the grid resolution that should be employed by a balanced atmospheric prediction model. A further investigation of the UM concluded that the data assimilation scheme and time of initialisation had no effect on the generation of SIs. An investigation was then made into the robustness of balanced models in the shallow water context, employing the contour-advective semi-Lagrangian (CASL) algorithm, Dritschel & Ambaum (1997), a novel numerical algorithm that exploits the underlying balance observed within a geophysical flow at leading order. Initially two algorithms were considered, which differed by the prognostic variables employed. Each algorithm had their three-time-level semi-implicit time integration scheme de-centred to mirror the time integration scheme of the UM. We found that the version with potential vorticity (PV), divergence and acceleration divergence, CA[subscript(δ,γ)], as prognostic variables preserved the Bolin-Charney balance to a much greater degree than the model with PV, divergence and depth anomaly CA[subscript(tilde{h},δ)], as prognostic variables. This demonstrated that CA[subscript(δ,γ)] was better equipped to benefit from de-centring, an essential property of any operational numerical weather prediction (NWP) model. We then investigate the robustness of CA[subscript(δ,γ)] by simulating flows with Rossby and Froude number O(1), to find the operational limits of the algorithm. We also investigated increasing the efficiency of CA[subscript(δ,γ)] by increasing the time-step Δt employed while decreasing specific convergence criteria of the algorithm while preserving accuracy. We find that significant efficiency gains are possible for predominantly mid-latitude flows, a necessary step for the use of CA[subscript(δ,γ)] in an operational NWP context. The study is concluded by employing CASL in the non-hydrostatic context under the Boussinesq approximation, which allows weak stratification to be considered, a step closer to physical reality than the shallow water case. CASL is compared to the primitive equation pseudospectral (PEPS) and vorticity-based pseudospectral (VPS) algorithms, both as the names suggest, spectral-based algorithms, which again differ by the prognostic variables employed. This comparison is drawn to highlight the computational advantages that CASL has over common numerical methods used in many operational forecast centres. We find that CASL requires significantly less artificial numerical diffusion than its pseudospectral counterparts in simulations of Rossby number ~O(1). Consequently, CASL obtains a much less diffuse, more accurate solution, at a lower resolution and therefore lower computational cost. At low Rossby number, where the flow is strongly influence by the Earth's rotation, it is found that CASL is the most cost-effective method. In addition, CASL also preserves a much greater proportion of balance, diagnosed with nonlinear quasigeostrophic balance (NQG), another significant advantage over its pseudospectral counterparts.

This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons. Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations. N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare these solutions to naturally occurring shallow water waves on beaches.

This thesis examines chaotic mixing in wavy-type channels and two-layer shallow water flow. For wavy-type channels, the equations of motion for vortices and fluid particles are derived assuming two-dimensional irrotational, incompressible flow. Instantaneous positions of the vortices and particles are determined using Lagrangian tracking, and are conformally mapped to the physical domain. Unsteady vortex motion is analysed, and vortex-induced chaotic mixing in the channels studied. The dynamics of mixing associated with the evolution of the separation bubble, and the invariant manifolds are examined. Mixing efficiencies of the different channel configurations are compared statistically. Fractal enhancement of productivity is identified in the study of auto-catalytic reaction in the wavy channel. For the two-layer shallow water model, an entropy-correction free Roe type two-layer shallow water solver is developed for a hyperbolic system with non-conservative products and source terms. The scheme is well balanced and satisfies the C-property such that smooth steady solutions are second order accurate. Numerical treatment of the wet-dry front of both layers and the loss of hyperbolicity are incorporated. The solver is tested rigorously on a number of 1D and 2D benchmark test cases. For 2D implementation, a dynamically adaptive quadtree grid generation system is adopted, giving results which are in excellent agreement with those on regular grids at a much lower cost. It is also shown that algebraic balancing cannot be applied directly to a two-layer shallow water flow due to the lack of simultaneous referencing for the still water position for both layers. The adaptive two-layer shallow water solver is applied successfully to flow in an idealised tidal channel and to tidal-driven flow in Tampa Bay, Florida. Finally, chaotic advection and particle mixing is studied for wind-induced recirculation in two-layer shallow water basins, as well as Tampa Bay, Florida.

Although the spectral technique is frequently used for the horizontal discretization in global atmospheric models, it is not common in limited area models (LAMs) because of the non-periodic boundary conditions. We apply the Haugen-Machenhauer extension technique to a regional three-layer shallow-water model based on double Fourier series. The method extends the time-dependent boundary fields into a zone outside the integration area in a way that periodic fields are obtained. The boundary fields necessary for the regional model simulations are calculated in advance by a global simulation performed. In contrast to other studies, we use exactly the same numerical model for the global and the regional simulation, respectively. The only difference between these simulations is the model domain. Therefore, a relatively objective measure for errors associated with the extension technique can be obtained. First, we compare an analytic stationary non-linear and non-periodic solution of the governing model equations with the spectral LAM solution. Secondly, we compare the time evolution of pressure and fiow structures during a westerly fiow across an asymmetric large-scale topography in the global and regional model domains. Both simulations show a good agreement between the regional and the global solutions. The rms-errors amount to about 2 m for the layer heights and 0.2 ms-1 for the velocity components in the mountain fiow case after a 48 h integration period. Finally, we repeat this simulation with models based on 2nd and 4th order finite differences, respectively, and compare the errors of the spectral model version with the errors of the grid point versions. We demonstrate that the high accuracy of global spectral methods can also be realized in the regional model by using the Haugen-Machenhauer extension technique. / Obwohl spektrale Techniken häufig zur horizontalen Diskretisierung in globalen Atmosphärenmodellen genutzt werden, sind sie aufgrund der nicht-periodischen Randbedingungen in Regionalmodellen nicht üblich. Wir verwenden das Erweiterungsverfahren von Haugen und Machenhauer in einem Flachwassermodell mit drei Schichten, das auf doppelten Fourier-Reihen basiert. Das Verfahren setzt die zeitabhängigen Randfelder so in einen Bereich außerhalb des Integrationsgebiets fort, daß man periodische Randbedingungen erhält. Die für die Simulationen mit dem Regionalmodell benötigten Randfelder werden mittels einer zuvor durchgeführten globalen Simulation berechnet. Im Gegensatz zu anderen Untersuchungen verwenden wir genau das gleiche Modell für die globale und die regionale Simulation. Der einzige Unterschied zwischen den beiden Simulationen ist das Modellgebiet. Dadurch erhält man ein relativ objektives Maß für die Fehler, die durch die Anwendung des Erweiterungsverfahrens entstehen. Als ersten Test vergleichen wir zunächst eine analytische, stationäre, nicht-lineare und nicht-periodische Lösung der Modellgleichungen mit der spektralen Lösung des Regionalmodells. Zweitens vergleichen wir die zeitliche Entwicklung von Druck- und Strömungsmustern während einer westlichen Strömung über eine unsymmetrische, großskalige Topographie im globalen bzw. regionalen Modellgebiet. Beide Simulationen zeigen eine gute Übereinstimmung der globalen und regionalen Lösungen. Die rms-Fehler betragen ungefähr 2 m für die Schichthöhen und 0.2 ms-1 für die Geschwindigkeitskomponenten bei der Bergüberströmungssimulation nach einer Integrationszeit von 48 h. Darüberhinaus wiederholen wir diese Simulation mit auf Finiten Differenzen 2. bzw. 4. Ordnung basierenden Modellen und vergleichen die Fehler der spektralen und der Gitterpunktversionen. Wir zeigen, daß die hohe Genauigkeit der globalen spektralen Methoden durch die Anwendung des Erweiterungsverfahrens von Haugen und Machenhauer auch auf das regionale Gebiet übertragen werden kann.

Neste trabalho de pesquisa foi realizado um estudo do método de deconvolução visando melhor adequação à situação encontrada na escala de investigação rasa para a estimativa da forma de onda e da resposta impulsiva da Terra. Procedimentos determinísticos e estatísticos (métodos cegos) foram avaliados sobre dados sintéticos e dados reais adquiridos com fontes de impacto e com uma fonte pseudo-aleatória. / In this research work a study of the method of deconvolution was conducted in order to improve the adequacy to the shallow subsurface scale of investigation to the estimate of the seismic wavelet and of the earth impulse response. Deterministic and statistical (blind) procedures were evaluated over synthetic and real data acquired with impact sources and a pseudo-random source.

Este trabalho realizou um estudo sobre a aplicação de algoritmos de inversão da forma de onda completa (FWI) sobre dados de sísmica de reflexão em uma escala rasa ( 0 100 m de profundidade). A FWI foi estudada com o fim de melhorar as velocidades estimadas através do processamento de reflexão PP e PS convencional. Para um melhor entendimento da resposta obtida por este tipo de problema, a inversão foi avaliada sobre dados sintéticos por métodos de busca global e local. Na busca global foi utilizado o algoritmo de Evolução Diferencial que é uma variante de um algoritmo genético. O intuito da busca global foi avaliar a sensibilidade da função objetivo para cada parâmetro do modelo em diferentes janelas de afastamentos em relação à fonte. Na busca local foi utilizado um algoritmo de gradiente conjugado para a estimativa 2D dos parâmetros do meio. Dentre os principais resultados têm-se que a função objetivo é mais sensível aos parâmetros em janelas de afastamentos próximas da fonte. Em tais janelas, dominadas por ondas superficiais, a velocidade da onda S é facilmente estimada. Entretanto, mesmo em janelas mais afastadas a velocidade da onda S é o parâmetro do modelo que se destaca em relação aos demais. Já a busca por todos os parâmetros concomitantemente mostrou-se difícil e implicaria na necessidade de mais iterações do algoritmo de inversão. O método também foi aplicado em dados reais adquiridos no terreno do Instituto de Física da USP. A FWI foi aplicada nestes dados buscando apenas pelos valores de Vs, mantendo os valores de Vp e densidade fixos. A aplicação do algoritmo 2D nestes dados resultaram em valores de Vs coerentes com as velocidades observadas em um ensaio downhole na área. Concluindo, os resultados apresentados na tese mostram que a FWI é aplicável para a melhoria do modelo de velocidade da onda S obtido através do processamento de eventos de reflexão PP e PS. / This work carried out a study on the application of full waveform inversion algorithms (FWI) on reflection seismic data on a shallow scale (0 - 100 m depth). FWI has been studied in order to improve estimated velocities through conventional PP and PS reflection processing. For a better understanding of the response obtained by this type of problem the inversion was evaluated by global and local search methods. In the global search the algorithm employed was the Differential Evolution which is a variant of a genetic algorithm. The aim of the global search was to evaluate the sensitivity of the objective function for each parameter of the model in different windows of distance from the source. In the local search a conjugate gradient algorithm was used for a 2D estimate of the medium parameters. Among the main results is the fact that in a suitable window, for a reflection data acquisition the sensitivity is reduced in relation to a window with geophones closer to the source. However, even in more distant windows the velocity of the S wave is the parameter of the model that stands out in relation to the others. The concomitant search for all parameters at the same time is still difficult and implies the need for more iterations of the inversion algorithm. The method was also applied in a data acquired in the field of the Institute of Physics of USP. The results of the application of the 2D algorithm for this data showed modifications of the provided initial model for a velocity of the S wave coherent with the observed velocities in downhole and lithological informations from this area. In conclusion, the results found that FWI is applicable to improve the S-wave velocity model obtained by processing PP and PS reflection events.

Os escorregamentos translacionais rasos são freqüentes na região da Serra do Mar, principalmente quando associados a eventos pluviométricos extremos, como em Janeiro de 1985 (380 mm, em 2 dias). Quando deflagrados de forma generalizada, podem ser catastróficos causando danos para a sociedade. Inúmeros métodos vêm sendo propostos para compreender a ocorrência destes processos na paisagem. O objetivo deste trabalho é avaliar a suscetibilidade a escorregamentos translacionais rasos na Serra do Mar por meio da aplicação de um modelo matemático em bases físicas, tendo como resultado um índice de estabilidade, que aponta, em forma de perigo relativo, áreas passíveis de instabilizações. As etapas de trabalho dividiramse na construção do Modelo Digital de Terreno e em produtos derivados (ângulo da encosta, curvatura, aspecto e área de contribuição), no mapeamento das cicatrizes de 1985 e na simulação dos cenários de suscetibilidade. Os mapas dos parâmetros topográficos, assim como, os mapas de suscetibilidade foram correlacionados com o mapa de cicatrizes e avaliados utilizando-se dos índices de Concentração de Cicatrizes (CC) e Potencial de Escorregamento (PE). Foram mapeadas 216 cicatrizes para uma área de 2,5 km² com uma produção de sedimentos estimado em 135,525m³. Os resultados apontam que encostas com ângulos entre 30° e 40° e com formato retilíneo foram as mais suscetíveis. A área foi considerada instável, segundo o modelo, em todos os cenários, tendo a melhor calibração para o cenário C2. O emprego de diferentes métodos demonstrou-se bastante satisfatório e concordante na análise do resultado final. Além disso, podem auxiliar como ferramentas de apoio de decisão no planejamento do uso do solo, principalmente em regiões onde é freqüente a ocorrência de movimentos de massa. Portanto, o resultado da avaliação a susceptibilidade a escorregamentos rasos na Serra do Mar pode direcionar ações mitigadoras político-administrativas e ambientais, tendo em vista minimizar o impacto sócio-ambiental de eventos futuros. / The shallow landslides are frequent in the Serra do Mar, especially when associated with intense rainfall events, as in January 1985 (380 mm in 2 days). When triggered generalized, causing damage to society. Several methods have been proposed to understand the occurrence of these processes in the landscape. The aim of this study is to evaluate the susceptibility to shallow landslides in the Serra do Mar by applying a physically based models, resulting in a stability index, which points in the form of relatively hazard and susceptible areas. The stages of his research were divided in building the Digital Terrain Model in their products derived (angle of slope, curvature, aspect and area of contribution), mapping the scars of 1985 and simulation of susceptibility scenarios. The maps of the parameters topographic, as well as the susceptibility maps were correlated with the scars map and evaluated using the indices of Scars Concentration (SC) and Landslide Potential (LP). 216 scars were mapped into here area of 2.5 km² with an estimated production of 135.525 m³ sediments. The results show that slopes with angles between 30° and 40° with rectilinear curvature were the most susceptible. The area was considered unstable, according to the model in all scenarios, with the best calibration for scenario C2. The use of different methods showed to be satisfactory and consistent when analyzing with these results. Moreover they can assist as tools for decision support in planning the soil use and, especially in regions where much frequent the occurrence of mass movement. Therefore, the result of susceptibility to shallow landslides in the Serra do Mar can help in the mitigation actions and politicaladministrative environment, aiming minimizes the environmental and social impact of future events.

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