Soil landscape characterization into landform elements for precision agriculture has become an important issue. As soil properties and crop yields change over the landscape, delineating landform elements as a basis for site-specific application of crop inputs has become a reality. Two different methods of delineating landform elements from agricultural fields were tested and compared. The first method delineated landform elements from digital elevation maps with the use of the LandMapR(tm) software, the second method delineated classes from IKONOS high resolution panchromatic images using an unsupervised classification algorithm. The LandMapR(tm) model delineated landform elements from true elevation data collected in the field and was considered the reference dataset to which the image classification maps were compared to. The IKONOS imagery was processed using a combination of one filtering algorithm and one unsupervised classification method prior to being compared to the classified DEM. A total of 20 filtering algorithms and two unsupervised methods were used for each of the five study sites. The study sites consisted of four agricultural fields covered with crop stubble and one field in summer fallow. Image classification accuracy assessment was reported as overall, producer’s and user’s accuracy as well as Kappa statistic. Results showed that filtering algorithms and classification methods had no effects on image classification accuracies. Highest classification accuracy of image map to landform element map comparison achieved for all study sites was 17.9 %. Classification accuracy was affected by the heterogeneity of the ground surface cover found in each field. However, the classification accuracy of the fallow field was not superior to the stubble fields.

This thesis presents a semi-automatic method to analyze morphometric features and landscape elements based on Self Organizing Map (SOM) as an unsupervised Artificial Neural Network algorithm in two completely different environments: 1) the Man and Biosphere Reserve “Eastern Carpathians” (Central Europe) as a complex mountainous humid area and 2) Lut Desert, Iran, a hyper arid region characterized by repetition of wind-eroded features. In 2003, the National Aeronautics and Space Administration (NASA) released the SRTM/ SIR-C band data with 3 arc seconds (approx. 90 m resolution) grid for approximately 80 % of Earth’s land surface. The X-band SRTM data were processed with a 1 arc second (approx. 30 m resolution) grid by the German space agency, DLR and the Italian space agency ASI, but due to the smaller X-SAR ground swath, large areas are not covered. The latest version 3.0 SRTM/C DEM and SRTM/X band DEM were re-projected to 90 and 30 m UTM grid and used to generate morphometric parameters of first order (slope) and second order (cross-sectional curvature, maximum curvatures and minimum curvature) by using a bivariate quadratic surface. The morphometric parameters are then used in a SOM to identify morphometric features (or landform elements) e.g. planar, channel, ridge in mountainous areas or yardangs (ridge) and corridors (valley) in hyper-arid areas. Geomorphic phenomena and features are scale-dependent and the characteristics of features vary when measured over different spatial extents or different spatial resolution. Morphometric parameters were derived for nine window sizes of the 90 m DEM ranging from 5 × 5 to 55 ×55. Analysis of the SOM output represents landform entities with ground areas from 450 m to 4950 m that is local to regional scale features. Effect of two SRTM resolutions, C and X bands is studied on morphometric feature identification. The difference change analysis revealed the quantity of resolution dependency of morphometric features. Increasing the DEM spatial resolution from 90 to 30 m (corresponding to X band) by interpolation resulted in a significant improvement of terrain derivatives and morphometric feature identification. Integration of morphometric parameters with climate data (e.g. Sum of active temperature above 10 ° C) in SOM resulted in delineation of morphologically homogenous discrete geo-ecological units. These units were reclassified to produce a Potential Natural Vegetation map. Finally, we combined morphometric parameters and remotely sensed spectral data from Landsat ETM+ to identify and characterize landscape elements. The single integrated data set of geo-ecosystems shows the spatial distribution of geomorphic, climatic and biotic/cultural properties in the Eastern Carpathians. The results demonstrate that a SOM is a very efficient tool to analyze geo-morphometric features under diverse environmental conditions and at different scales and resolution. Finer resolution and decreasing window size reveals information that is more detailed while increasing window size and coarser resolution emphasizes more regional patterns. It was also successfully applied to integrate climatic, morphometric parameters and Landsat ETM+ data for landscape analysis. Despite the stochastic nature of SOM, the results are not sensitive to randomization of initial weight vectors if many iterations are used. This procedure is reproducible with consistent results. / Avhandlingen presenterar en halvautomatisk metod för att analysera morfometriska kännetecken och landskapselement som bygger på Self Organizing Map (SOM), en oövervakad Artificiell Neural Nätverk algoritm, i två helt skilda miljöer: 1) Man and Biosphere Reserve "Eastern Carpathians" (Centraleuropa) som är ett komplext, bergigt och humid område och 2) Lut öken, Iran, en extrem torr region som kännetecknas av återkommande vinderoderade objekt. Basen för undersökningen är det C-band SRTM digital höjd modell (DEM) med 3 bågsekunder rutnät som National Aeronautics and Space Administration släppte 2003 för ungefär 80 % av jordens yta. Dessutom används i ett mindre område X-band SRTM DEM med 1 bågsekund rutnät av den tyska rymdagenturen DLR. DEM transformerades till 90 och 30 m UTM nätet och därav genererades morfometriska parametrar av första (lutning) och andra ordning (tvärsnittböjning, största och minsta böjning). De morfometriska parametrar används sedan i en SOM för att identifiera morfometriska objekt (eller landform element) t.ex. plan yta, kanal, kam i bergsområden eller yardangs (kam) och korridorer (dalgångar) i extrem torra områden. Geomorfiska fenomen och objekt är skalberoende och kännetecken varierar med geografiska områden och upplösning. Morfometriska parametrar har härletts från 90 m DEM för nio fönsterstorlekar från 5 × 5 till 55 × 55. Resultaten representerar landform enheter för områden från 450 m till 4950 m på marken dvs. lokal till regional skala. Inflytande av två SRTM upplösningar i C och X-banden har studerats för identifikation av morfometriska objekt. Förändringsanalys visade storleken av upplösningsberoende av morfometriska objekt. Ökning av DEM upplösningen från 90 till 30 m (motsvarande X-bandet) genom interpolation resulterade i en betydande förbättring av terräng parametrar och identifiering av morfometriska objekt. Integration av morfometriska parametrar med klimatdata (t.ex. summan av aktiv temperatur över 10° C) i SOM resulterade i avgränsningen av homogena geoekologiska enheter. Dessa enheter ha används för att producera en karta av potentiell naturlig vegetation. Slutligen har vi kombinerat morfometriska parametrar och multispektrala fjärranalysdata från Landsat ETM för att identifiera och karaktärisera landskapselement. Dessa integrerade ekosystem data visar den geografiska fördelningen av morfometriska, klimatologiska och biotiska/kulturella egenskaper i östra Karpaterna. Resultaten visar att SOM är ett mycket effektivt verktyg för att analysera geomorfometriska egenskaper under skilda miljöförhållanden, i olika skalor och upplösningar. Finare upplösning och minskad fönsterstorlek visar information som är mer detaljerad. Ökad fönsterstorlek och grövre upplösning betonar mer regionala mönster. Det var också mycket framgångsrikt att integrera klimatiska och morfometriska parametrar med Landsat ETM data för landskapsanalys. Trots den stokastiska natur av SOM, är resultaten inte känsliga för slumpvisa värden i de ursprungliga viktvektorerna när många iterationer används. Detta förfarande är reproducerbart med bestående resultat. / QC 20100924

In boreal catchments, stream water chemistry is influenced and controlled by several landscape factors. The influence of spatially distributed variables is in turn dependent on the hydrological scale. Headwater streams have larger variability of water chemistry, and thus together represent a large biodiversity, and therefore need to be monitored in official environmental assessments. One objective of this study was, using Geographical Information Systems (GIS), to analyse co-variation between landscape variables and water chemistry and to determine which of the landscape variables have a major influence on the concentration of dissolved organic carbon (DOC) in headwater streams. Another objective was to find a simple method for predicting sources of DOC, using official map data and publically available GIS applications. Totally 85 headwater catchments (0.1-4 km2) in the county of Värmland, western south Sweden, were used in the study. Water chemistry was analysed for water sampled at low, medium and high flows, and landscape variables were extracted from official map data sources: topographic maps, a digital elevation model (DEM, 50 m grid), and vegetation data. Statistical analyses showed that topography (mean slope and mean topographic wetness index (TWI)) and wetland cover often correlated well with DOC in headwater catchments. Official map data could satisfactorily extract landscape variables (mean slope, mean TWI) that were useful in predicting stream water chemistry (DOC). A high-resolution elevation model, which was generated by interpolation of photogrammetric data, was used to calculate and evaluate two different wetness indices and their ability to predict the occurrence of wetlands in six catchments of different sizes and topography. The SAGA (System for Automated Geoscientific Analyses) wetness index (SWI) gave substantially better results than the TWI. The effects of resolution of DEMs on calculations of the SWI were investigated using 5, 10, 25 and 50 m grids. The results showed that SWI values increased with increasing cell size. The near linear increment of mean values for resolutions 10-50 m suggests a independence of terrain type and catchment size, which supported previous findings that indicated that mean slope and mean wetness index calculated from coarse elevation models may be used for prediction of DOC in headwater streams.

Diss. Northwestern Univ., 2007.

Diss. Northwestern Univ., 2007.

Thesis (MSc (Geography and Environmental Studies))--University of Stellenbosch, 2007. / Due to the relative scarcity of weather stations, the climate conditions of large areas are not adequately represented by a weather station. This is especially true for regions with complex topographies or low population densities. Various interpolation techniques and software packages are available with which the climate of such areas can be calculated from surrounding weather stations’ data. This study investigates the possibility of using the software package ANUSPLIN to create accurate climate maps for the Western Cape, South Africa. ANUSPLIN makes use of thin plate smoothing splines and a digital elevation model to convert point data into grid format to represent an area’s climatic conditions. This software has been used successfully throughout the world, therefore a large body of literature is available on the topic, highlighting the limitations and successes of this interpolation method. Various factors have an effect on a region’s climate, the most influential being location (distance from the poles or equator), topography (height above sea level), distance from large water bodies, and other topographical factors such as slope and aspect. Until now latitude, longitude and the elevation of a weather station have most often been used as input variables to create climate grids, but the new version of ANUSPLIN (4.3) makes provision for additional variables. This study investigates the possibility of incorporating the effect of the surrounding oceans and topography (slope and aspect) in the interpolation process in order to create climate grids with a resolution of 90m x 90m. This is done for monthly mean daily maximum and minimum temperature and the mean monthly rainfall for the study area for each month of the year. Not many projects where additional variables have been incorporated in the interpolation process using ANUSPLIN are to be found in the literature, thus further investigation into the correct transformation and the units of these variables had to be done before they could be successfully incorporated. It was found that distance to oceans influences a region’s maximum and minimum temperatures, and to a lesser extent rainfall, while aspect and slope has an influence on a region’s rainfall. In order to assess the accuracy of the interpolation process, two methods were employed, namely statistical values produced during the spline function calculations by ANUSPLIN, and the removal of a selected number of stations in order to compare the interpolated values with the actual measured values. The analysis showed that more accurate maps were obtained when additional variables were incorporated into the interpolation process. Once the best transformations and units were identified for the additional variables, climate maps were produced in order to compare them with existing climate grids available for the study area. In general the temperatures were higher than those of the existing grids. For the rainfall grids ANUSPLIN’s produced higher rainfall values throughout the study region compared to the existing grids, except for the Southwestern Cape where the rainfall values were lower on north-facing slopes and high-lying area

This thesis provides a novel investigation into rainfall-runoff processes occurring within a unique two-tiered depth-driven overland flow physical modelling environment, as well as within a numerical model context where parameterisation and DEM/building resolution influences have been investigated using an innovative de-coupled methodology. Two approaches to simulating urban rainfall-runoff responses were used. Firstly, a novel, 9 m2 physical modelling environment consisting of a: (i) a low-cost rainfall simulator component able to simulate consistent, uniformly distributed rainfall events of varying duration and intensity, and; (ii) a modular plot surface layer was used. Secondly, a numerical hydroinundation model (FloodMap2D-HydroInundation) was used to simulate a short-duration, high intensity surface water flood event (28th June 2012, Loughborough University campus). The physical model showed sensitivities to a number of meteorological and terrestrial factors. Results demonstrated intuitive model sensitivity to increasing the intensity and duration of rainfall, resulting in higher peak discharges and larger outflow volumes at the model outflow unit, as well as increases in the water depth within the physical model plot surface. Increases in percentage permeability were also shown to alter outflow flood hydrograph shape, volume, magnitude and timing due to storages within the physical model plot. Thus, a reduction in the overall volume of water received at the outflow hydrograph and a decrease in the peak of the flood event was observed with an increase in permeability coverage. Increases in the density of buildings resulted in a more rapid receding limb of the hydrograph and a steeper rising limb, suggesting a more rapid hydrological response. This indicates that buildings can have a channelling influence on surface water flows as well as a blockage effect. The layout and distribution of permeable elements was also shown to affect the rainfall-runoff response recorded at the model outflow, with downstream concentrated permeability resulting in statistically different hydrograph outflow data, but the layout of buildings was not seen to result in significant changes to the outflow flood hydrographs; outflow hydrographs appeared to only be influenced by the actual quantity and density of buildings, rather than their spatial distribution and placement within the catchment. Parameterisation of hydraulic (roughness) and hydrological (drainage rate, infiltration and evapotranspiration) model variables, and the influence of mesh resolution of elevation and building elements on surface water inundation outputs, both at the global and local level, were studied. Further, the viability of crowdsourced approaches to provide external model validation data in conjunction with dGPS water depth data was assessed. Parameterisation demonstrated that drainage rate changes within the expected range of parameter values resulted in considerable losses from the numerical model domain at global and local scales. Further, the model was also shown to be moderately sensitive to hydraulic conductivity and roughness parameterisation at both scales of analysis. Conversely, the parameterisation of evapotranspiration demonstrated that the model was largely insensitive to any changes of evapotranspiration rates at the global and local scales. Detailed analyses at the hotspot level were critical to calibrate and validate the numerical model, as well as allowing small-scale variations to be understood using at-a-point hydrograph assessments. A localised analysis was shown to be especially important to identify the effects of resolution changes in the DEM and buildings which were shown to be spatially dependent on the density, presence, size and geometry of buildings within the study site. The resolution of the topographic elements of a DEM were also shown to be crucial in altering the flood characteristics at the global and localised hotspot levels. A novel de-coupled investigation of the elevation and building components of the DEM in a strategic matrix of scenarios was used to understand the independent influence of building and topographic mesh resolution effects on surface water flood outputs. Notably, the inclusion of buildings on a DEM surface was shown to have a considerable influence on the distribution of flood waters through time (regardless of resolution), with the exclusion of buildings from the DEM grid being shown to produce less accurate results than altering the overall resolution of the horizontal DEM grid cells. This suggests that future surface water flood studies should focus on the inclusion and representation of buildings and structural features present on the DEM surface as these have a crucial role in modifying rainfall-runoff responses. Focus on building representation was shown to be more vital than concentrating on advances in the horizontal resolution of the grid cells which make up a DEM, as a DEM resolution of 2 m was shown to be sufficiently detailed to conduct the urban surface water flood modelling undertaken, supporting previous inundation research.

abstract: I investigate the Black Canyon City landslide (BCC landslide), a prominent deep-seated landslide located northeast of Black Canyon City, Arizona. Although the landslide does not appear to pose a significant hazard to structures, its prominent features and high topographic relief make it an excellent site to study the geologic setting under which such features develop. This study has the potential to contribute toward understanding the landscape evolution in similar geologic and topographic settings, and for characterizing the underlying structural processes of this deep-seated feature. We use field and remotely-based surface geology and geomorphological mapping to characterize the landslide geometry and its surface displacement. We use the Structure from Motion (SfM) method to generate a 0.2 m resolution digital elevation model and rectified ortho-photo imagery from unmanned aerial vehicle (UAV) - and balloon-based images and used them as the base map for our mapping. The ~0.6 km2 landslide is easily identified through remotely-sensed imagery and in the field because of the prominent east-west trending fractures defining its upper extensional portion. The landslide displaces a series of Early and Middle Miocene volcanic and sedimentary rocks. The main head scarp is ~600 m long and oriented E-W with some NW-SE oriented minor scarps. Numerous fractures varying from millimeters to meters in opening were identified throughout the landslide body (mostly with longitudinal orientation). The occurrence of a distinctive layer of dark reddish basalt presents a key displaced marker to estimate the long-term deformation of the slide mass. Using this marker, the total vertical displacement is estimated to be ~70 m, with maximum movement of ~95 m to the SE. This study indicates that the landslide motion is translational with a slight rotational character. We estimate the rate of the slide motion by resurvey of monuments on and off the slide, and examination of disturbed vegetation located along the fractures. The analysis indicates a slow integrated average landslide velocity of 10-60 mm/yr. The slide motion is probably driven during annual wet periods when increased saturation of the slide mass weakens the basal slip surface and the overall mass of the slide is increased. Results from our study suggest that the slide is stable and does not pose significant hazard for the surrounding area given no extreme changes in the environmental condition. Although the landslide is categorized as very slow (according to Cruden and Varnes, 1996), monitoring the landslide is still necessary. / Dissertation/Thesis / Masters Thesis Geological Sciences 2016

Made available in DSpace on 2014-12-17T14:13:32Z (GMT). No. of bitstreams: 1 MarcioLTA_Tese.pdf: 1453040 bytes, checksum: 7c0ed7c44a56eb54d2170012eedbfa04 (MD5) Previous issue date: 2009-11-27 / The imprecision of the frontier that separates those cognitive deficits inherent to the human physiological aging process from those which represent the early signs of nervous system degenerative pathologies ,very prevalent among the elderly, has brought attention to the need of studies aiming to establish clinical and/or laboratorial criteria to allow this differentiation. Elderly people living in poor and developing countries are frequently exposed to precarious socioeconomic conditions which facilitate the development of an array of pathologies which have metabolic and nutritional dysfunctions as the established or proposed etiological agents. The levels of certain micronutrients, such as the vitamins B12 and B9 (folic acid), and of some intermediary metabolites, such as homocysteine are being thought of as etiological factors and/or as biological markers of a group of alterations which affect the normal functioning of the nervous system with important reflexes upon cognitive performance. This study aims to investigate the influence of homocysteine, B12 vitamin and folic acid levels on the cognitive performance of the low income elderly population. This transversal study took place in Natal, Rio Grande do Norte State, Brazil, and involved 205 dwelling elderly people, users of the Programa de Sa?de da Fam?lia, a public healthcare program, maintained by the city s health authorities. A multidimensional questionnaire was used to assess the socio-demographic aspects and the overall health and nutrition conditions. The cognitive performance was measured by the use of the Portuguese version of the Mini Mental State Exam (MMSE). The serum levels of homocysteine, B12 vitamin and folic acid were determined by chemiluminescence. The association between the socio-demographic and serum levels of Hcy, B12 vitamin and folic acid was determined by multiple linear regression. Serum levels higher than 13.5 &#956;mol/l, indicative of hyperhomocysteinemia (HHcy), were found on 25.4% of the sample, being more prevalent in men (p<0.05). Deficitary levels of folic acid (<5ng/mol) and of B12 vitamin (<193 pg/ml) were found on 3.9% and 10.2% of the sample respectively. A negative correlation was found between cognitive performance with both age and HHcy and a positive correlation was found between cognitive performance and schooling. The isolated HHcy R2 values were an explanation to only 4% of the variance of the MMSE scores. However, when associated with schooling and age, this model explains about 25% of this association / A imprecis?o da fronteira que separa os d?ficits pr?prios do processo de envelhecimento fisiol?gico humano daqueles que representam os sinais precoces das patologias degenerativas de grande preval?ncia entre idosos, tem chamado a aten??o para a necessidade da produ??o de estudos voltados para o estabelecimento crit?rios cl?nicos e/ou laboratoriais que permitam essa diferencia??o. Idosos de popula??es de pa?ses pobres e/ou em desenvolvimento s?o freq?entemente expostos a condi??es socioecon?micas prec?rias prop?cias ao desenvolvimento de um conjunto de patologias, disfun??es metab?licas e nutricionais. Os n?veis de determinados micronutrientes e de alguns metab?litos intermedi?rios v?m sendo vistos como fatores etiol?gicos e como marcadores biol?gicos de um conjunto de altera??es que afetam a fun??o normal do sistema nervoso com reflexos importantes sobre o desempenho cognitivo. N?veis elevados de homociste?na (Hcy) e d?ficits nutricionais e /ou metab?licos da vitamina B12 e B9 (?cido f?lico) t?m sido apontados como preditores e/ou como fatores etiol?gicos de altera??es cognitivas. O objetivo desse estudo foi avaliar a influ?ncia dos n?veis de homociste?na, Vitamina B12 e ?cido f?lico no desempenho cognitivo de idosos de baixa renda. Este estudo transversal desenvolvido em Natal, Rio Grande do Norte, Brasil, incluiu 205 idosos n?o institucionalizados atendidos pelo Programa de Sa?de da Fam?lia da Secretaria Municipal de Sa?de do munic?pio. Um question?rio multidimensional foi utilizado para avaliar os aspectos sociodemogr?ficos e as condi??es gerais de sa?de e nutri??o. O desempenho cognitivo foi aferido utilizando-se a vers?o em portugu?s do Mini-Exame do Estado Mental (MEEM). Os n?veis s?ricos de homociste?na, Vitamina B12 e ?cido f?lico foram determinados por quimioluminesc?ncia. A associa??o entre as vari?veis sociodemogr?ficas e os n?veis s?ricos de Hcy Vitamina B12 e ?cido f?lico foi determinada atrav?s de regress?o linear m?ltipla. Valores s?ricos acima de 13,5 &#956;mol/l indicativos de hiperhomocisteinemia (HHcy) foram encontrados em 25,4% da amostra sendo mais prevalente em homens (p<0,05). N?veis deficit?rios de ?cido f?lico (<5ng/ml) e de Vitamina B12 (<193 pg/ml) foram encontrados em 3,9% e 10,2% dos indiv?duos respectivamente. O desempenho cognitivo mostrou uma correla??o negativa com a idade e a HHcy e positiva com a escolaridade. Os valores R2 da HHcy isolada explicaram apenas 4% da vari?ncia da pontua??o do MEEM. Contudo, quando associada escolaridade e idade, este modelo explica aproximadamente 25% desta associa??o.

This work proposes the computational modeling of two-dimensional media mechanical behavior with a continuous approach, related to the Finite Element Method (FEM) associated with Cohesive Fracture Mechanics (CFM) models, and a discrete approach, using the Discrete Element Method (DEM). The FEM consists in a numerical tool widely used to achieve approximate solutions of Continuum Mechanics problems, involving physical and geometrical nonlinearities phenomena with quasi-static or dynamic behaviors, having already established practical applications in many areas of science and industry. On the other hand, DEM has more recent development and has been increasingly used to model discrete nature problems involving contact, impact and fragmentation phenomena and flow of particulate systems. Focused on analysis of problems with interactions between these natures, a FEMDEM coupling code is developed to solve the problem by a sub-region scheme where the FEM is used on modeling of nucleation process and crack propagation in continuous media, and DEM is employed to model granular media, whether due its nature or its conception, in a transient behavior. The possibility of opening and propagation of cracks is considered by using CFM models, intrinsically incorporated into the FEM formulation through interfaces inserted into the inner edges of the finite element mesh. Illustrative examples are presented and discussed in order to validate the proposed formulation and implementation. / FUNDEPES - Fundação Universitária de Desenvolvimento de extensão e Pesquisa / PRH-ANP - Programa de Recursos Humanos da Agência Nacional do Petróleo / Este trabalho propõe a modelagem computacional do comportamento mecânico bidimensional de meios com abordagens contínua, relacionada ao Método dos Elementos Finitos (MEF) associado a modelos da Mecânica da Fratura Coesiva (MFC) e discreta, através do Método dos Elementos Discretos (MED). O MEF consiste em uma ferramenta numérica bastante utilizada na determinação de soluções aproximadas para problemas da Mecânica do Contínuo, envolvendo fenômenos com não linearidades físicas e geométricas associadas e com comportamento quase-estático ou dinâmico, possuindo aplicações práticas já consagradas em diversas áreas do campo científico e industrial. Por outro lado, o MED tem desenvolvimento mais recente e vem sendo cada vez mais utilizado no tratamento de problemas de natureza discreta envolvendo fenômenos de contato, impacto, fragmentação e fluxo de sistemas particulados. Com foco na análise de problemas que envolvem interações entre tais naturezas, implementa-se uma estratégia de acoplamento MEF-MED para solução do problema em subregiões, onde o MEF é utilizado na modelagem de processos de nucleação e propagação de fraturas em meios contínuos e o MED é empregado na modelagem de meios granulares por natureza, ou assim concebidos, em comportamento transiente. A possibilidade de abertura e propagação de fraturas é considerada através da utilização de modelos da MFC, incorporados intrinsecamente na formulação do MEF através de interfaces inseridas nas arestas internas da malha de elementos finitos. Exemplos ilustrativos são apresentados e discutidos visando-se validar a formulação e a implementação propostas.