Geodesy deals with the accurate analysis of spatial and temporal variations in the geometry and physics of the Earth at local and global scales. In geodesy, least-squares collocation (LSC) is a bridge between the physical and statistical understanding of different functionals of the gravitational field of the Earth. This thesis specifically focuses on the [incorrect] implicit LSC assumptions of isotropy and homogeneity that create limitations on the application of LSC in non-stationary gravity field modeling. In particular, the work seeks to derive expressions for local and global analytical covariance functions that account for the anisotropy and heterogeneity of the Earth's gravity field. / Standard LSC assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing, e.g., of the gravity field in mountains and under-smoothing in great plains. The kernel convolution method from spatial statistics is introduced for non-stationary covariance structures, and its advantage in dealing with non-stationarity in geodetic data is demonstrated. / Tests of the new non-stationary solutions were performed over the Darling Fault, Western Australia, where the anomalous gravity field is anisotropic and non-stationary. Stationary and non-stationary covariance functions are compared in 2D LSC to the empirical example of gravity anomaly interpolation. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation. Both non-stationarity of mean and covariance are considered in planar geoid determination by LSC to test how differently non-stationarity of mean and covariance affects the LSC result compared with GPS-levelling points in this area. Non-stationarity of the mean was not very considerable in this case, but non-stationary covariances were very effective when optimising the gravimetric quasigeoid to agree with the geometric quasigeoid. / In addition, the importance of the choice of the parameters of the non-stationary covariance functions within a Bayesian framework and the improvement of the new method for different functionals on the globe are pointed out.

Thesis (M.A.)--Carleton University, 1997. / Also available in electronic format on the Internet.

Thesis (M. A.)--University of Notre Dame, 2005. / Thesis directed by Ke-Hai Yuan for the Department of Psychology. "October 2005." Includes bibliographical references (leaves 60-63).

Thesis (Ph.D. (Econometrics))-University of Pretoria, 2005. / Abstract in English. Includes bibliographical references. Available on the Internet via the World Wide Web.

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 1, 2007) Vita. Includes bibliographical references.

Orientador: Carlos Roberto Padovani / Resumo: Em muitas situações, existe a necessidade de estudar o comportamento de alguma característica em uma mesma unidade amostral ao longo do tempo, dose acumulada de algum nutriente ou medicamento. Na prática, a estrutura dos dados dessa natureza geralmente estabelece comportamentos não lineares nos parâmetros de interesse, já que estes caracterizam melhor a realidade biológica pesquisada. Essa conjuntura é propícia ao estudo de remodelação cardíaca (RC) por sobrecarga pressórica em ratos submetidos a diferentes manobras sequenciais de cálcio. Como o comportamento da RC não está claramente estabelecido, o objetivo deste trabalho consiste em fazer um estudo comparativo sobre a performance de quatro modelos de curvas de crescimento em quatro grupos experimentais, considerando erros normais $\theta$ generalizado multivariado. Além disso, a modelagem dos dados envolve duas estruturas de covariância: a homocedástica com a presença de autocorrelação lag 1 e a heterocedástica multiplicativa. No contexto metodológico, utiliza-se o procedimento de estimação por máxima verossimilhança com a aplicação da técnica de reamostragem bootstrap. Além disso, técnicas de simulações são implementadas para comprovação das propriedades metodológicas aplicadas. Para comparação entre os modelos, utilizam-se alguns avaliadores de qualidade de ajuste. Conclui-se, no presente estudo, que a estrutura homocedástica com autocorrelação lag 1 para os modelos Brody e de Von Bertalanffy, destacam-se por apresentar ... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Many situations, there is a need to study the behavior of some characteristic in the same sample unit over time, accumulated dose of some nutrient or medication. In practice, the structure of data of this nature generally establishes non-linear behaviors in the parameters of interest, since these characterize better the biological reality researched. This situation is favorable to the study of cardiac remodeling (CR) by pressure overload in rats submitted to different sequential calcium maneuvers. As the behavior of CR is not clearly established, the objective of this work is to perform a comparative study on the performance of four models of growth curves in four experimental groups, considering normalized multivariate θ standard errors. In addition, the data modeling involves two covariance structures: the homocedastic with the presence of autocorrelation lag 1 and the multiplicative heterocedastic. In the methodological context, the procedure of estimation by maximum likelihood is used with the technique of bootstrap resampling. In addition, simulation techniques are implemented to prove the methodological properties applied. For the comparison between the models, some adjustment quality evaluators are used. It is concluded in the present study that the homocedastic structure with lag 1 autocorrelation for the Brody and Von Bertalanffy models stands out for presenting excellent estimates and good quality of adjustment of the maximum developed stress (TD) as a function of t... (Complete abstract click electronic access below) / Doutor

Resumo: Considerando a importância da compreensão da dinâmica espaço temporal dos componentes do balanço de energia (BE) em escala regional para o gerenciamento de recursos hídrico e o manejo agrícola, o objetivo principal desta tese foi construir e analisar uma série temporal dos componentes do BE adequada às condições de clima subtropical úmido do Estado do Rio Grande do Sul. Para tanto, inicialmente foi avaliada a adequação de modelos de estimativa de BE para o Estado. Nesta etapa foram utilizados produtos MODIS e dados de referência medidos em uma torre micrometeorológica instalada em Cruz Alta – RS, usando valores instantâneos para um período de estudo de 2009 a 2011. Na sequência foi avaliada a adequação dos modelos em representar a variabilidade espacial dos componentes do BE. Nesta etapa foram usados produtos MODIS, dados de reanálise ERA Interim, dados de referência da torre micrometeorológica e dados de estações meteorológicas do INMET, para o mesmo período de estudo. Na última etapa do trabalho foi construída a série temporal dos componentes do BE usando o modelo METRIC, a qual abrangeu um período de 14 anos, de 2002 a 2016. Os resultados demonstraram que os três modelos analisados apresentam coerência com as medidas de referência, sendo as maiores limitações apresentadas pelo modelo SEBAL, as quais se atribui principalmente às condições ecoclimáticas do Estado e a baixa resolução espacial das imagens. Na análise da variabilidade espacial, o modelo METRIC apresentou maior consistência nos resultados e proporcionou maior número de dias com resultados válidos, sendo assim apontado como o mais apto para realização do restante do estudo. A série temporal construída possibilitou a compreensão dos padrões de distribuição espaço temporal dos componentes do BE no estado do Rio Grande do Sul. Há uma marcada sazonalidade nos componentes do BE, com maiores valores no verão e menores no inverno. G (fluxo de calor no solo) é o componente de menor magnitude e sua distribuição espacial e temporal é determinada pela distribuição de Rn (saldo de radiação). Já os componentes LE (fluxo de calor latente) e H (fluxo de calor sensível), são os que mostram magnitude maior e apresentam padrões de distribuição espacial e temporal coerentes com as condições climáticas e com os tipos de uso e cobertura na área de estudo. Observase um padrão inverso, com um gradiente de LE no sentido noroeste para sudeste e para o componente H, no sentido sudeste para noroeste. Sendo estas informações de grande importância para gerenciamento de recursos hídricos em escala regional, para estudos de zoneamento agrícola. / Abstract: Given the importance of understanding the temporal and spatial dynamics of of the energy balance (EB) components in a regional scale for the management of water resources and agricultural, the main objective of this thesis was to construct and analyze a time series of the components of BE appropriate to the subtropical humid climate conditions of the State of Rio Grande do Sul. In order to reach the objective initially, the adequacy of the models for the humid climate conditions was evaluated, in this step we used MODIS data and reference data measured in a micrometeorological tower installed in Cruz Alta - RS. The analyzes performed with instantaneous values and the study period was from 2009 to 2011. The next step evaluate the spatial variability of the BE components, the data used were the MODIS products, ERA Interim reanalysis data, reference data of the micrometeorological tower and INMET meteorological stations, for the same study period. In the last stage the time series of the BE components was constructed from the METRIC model. The period series was 14 years from 2002 to 2016.The results showed that the three models analyzed were consistent with the reference measurements, with the greatest limitations presented by the SEBAL model, which are mainly attributed to the state's eco-climatic conditions and the low spatial resolution of the images In the analysis of the spatial variability, the METRIC model presented greater consistency in the results and provided greater number of days with valid results, this model thus indicated as the most suitable for the rest of the study. The time series constructed allowed us to understand the temporal distribution patterns of BE components in the state of Rio Grande do Sul. There is a marked seasonality in the BE components, with higher values in summer and lower in winter. G is the smallest magnitude component and its spatial and temporal distribution is determined by the Rn distribution. On the other hand, the LE and H components are those that show higher magnitude and present spatial and temporal distribution patterns consistent with the climatic conditions and the types of use and coverage in the study area. An inverse pattern is observed, with a LE gradient from north-west to south-east and for H-component, from southeast to northwest.

Doctor of Philosophy / Department of Agronomy / Eduardo Alvarez Santos / Measurements of methane (CH₄) emissions from livestock production could provide invaluable data to reduce uncertainties in the global CH₄ budget and to evaluate mitigation strategies to lower greenhouse gas (GHG) emissions. The eddy covariance (EC) technique has recently been applied as an alternative to measure CH₄ emissions from livestock systems, but heterogeneities in the source area and fetch limitations impose challenges to EC measurements. The main objectives of this study were to: 1) assess the performance of a closed-path EC system for measuring CH₄, CO₂, and H₂0 fluxes; 2) investigate the spatial variability of the EC fluxes in a cattle feedlot using flux footprint analysis; 3) estimate CH₄ emission rates per animal (Fanimal) from a beef cattle feedlot using the EC technique combined with two footprint models: an analytical footprint model (KM01) and a parametrization of a Lagrangian dispersion model (FFP); and 4) compare CH₄ emissions obtained using the EC technique and a footprint analysis with CH₄ emission estimates provided by a well-stablished backward-Lagrangian stochastic (bLS) model. A closed-path EC system was used to measure CH₄, CO₂, and H₂0 fluxes. To evaluate the performance of this closed-path system, a well-stablished open-path EC system was also deployed on the flux tower to measure CO₂ and H₂0 exchange. Methane concentration measurements and wind data provided by that system were used to estimate CH₄ emissions using the bLS model. The performance assessment that included comparison of gas cospectra and measured fluxes from the two EC systems showed that the closed-path system was suitable for the EC measurements. Flux values were quite variable during the field experiment. A one-dimensional flux footprint model was useful to interpret some of the flux temporal and spatial dynamics. Then, a more comprehensive data analysis was carried out using two-dimensional footprint models (FFP and KM01) to interpret fluxes and scale fluxes measured at landscape to animal level. The monthly average Fanimal, calculated using the footprint weighed stocking density ranged from 83 to 125 g animal⁻¹ d⁻¹ (KM01) and 75–114 g animal⁻¹ d⁻¹ (FFP). These emission values are consistent with the results from previous studies in feedlots however our results also suggested that in some occasions the movement of animals on the pens could have affected CH₄ emission estimates. The results from the comparisons between EC and bLS CH₄ emission estimates show good agreement (0.84; concordance coefficient) between the two methods. In addition, the precision of the EC as compared to the bLS estimates was improved by using a more rigorous fetch screening criterion. Overall, these results indicate that the eddy covariance technique can be successfully used to accurately measure CH₄ emissions from feedlot cattle. However, further work is still needed to quantify the uncertainties in Fanimal caused by errors in flux footprint model estimates and animal movement.

Networks have been widely used to describe interactions among objects in diverse fields. Given the interest in explaining a network by its structure, much attention has been drawn to finding clusters of nodes with dense connections within clusters but sparse connections between clusters. Such clusters are called communities, and identifying such clusters is known as community detection. Here, to perform community detection, I focus on stochastic blockmodels (SBM), a class of statistically-based generative models. I present a flexible SBM that represents different types of data as well as node attributes under a Bayesian framework. The proposed models explicitly capture community behavior by guaranteeing that connections are denser within communities than between communities. First, I present a degree-corrected SBM based on a logistic regression formulation to model binary networks. To fit the model, I obtain posterior samples via Gibbs sampling based on Polya-Gamma latent variables. I conduct inference based on a novel, canonically mapped centroid estimator that formally addresses label non-identifiability and captures representative community assignments. Next, to accommodate large-scale datasets, I further extend the degree-corrected SBM to a broader family of generalized linear models with group correction terms. To conduct exact inference efficiently, I develop an iteratively-reweighted least squares procedure that implicitly updates sufficient statistics on the network to obtain maximum a posteriori (MAP) estimators. I demonstrate the proposed model and estimation on simulated benchmark networks and various real-world datasets. Finally, I develop a Bayesian SBM for community-structured covariance selection. Here, I assume that the data at each node are Gaussian and a latent network where two nodes are not connected if their observations are conditionally independent given observations of other nodes. Under the context of biological and social applications, I expect that this latent network shows a block dependency structure that represents community behavior. Thus, to identify the latent network and detect communities, I propose a hierarchical prior in two levels: a spike-and-slab prior on off-diagonal entries of the concentration matrix for variable selection and a degree-corrected SBM to capture community behavior. I develop an efficient routine based on ridge regularization and MAP estimation to conduct inference.

abstract: The North American Monsoon System (NAMS) contributes ~55% of the annual rainfall in the Chihuahuan Desert during the summer months. Relatively frequent, intense storms during the NAMS increase soil moisture, reduce surface temperature and lead to runoff in ephemeral channels. Quantifying these processes, however, is difficult due to the sparse nature of coordinated observations. In this study, I present results from a field network of rain gauges (n = 5), soil probes (n = 48), channel flumes (n = 4), and meteorological equipment in a small desert shrubland watershed (~0.05 km2) in the Jornada Experimental. Using this high-resolution network, I characterize the temporal and spatial variability of rainfall, soil conditions and channel runoff within the watershed from June 2010 to September 2011, covering two NAMS periods. In addition, CO2, water and energy measurements at an eddy covariance tower quantify seasonal, monthly and event-scale changes in land-atmosphere states and fluxes. Results from this study indicate a strong seasonality in water and energy fluxes, with a reduction in Bowen ratio (B, the ratio of sensible to latent heat fluxes) from winter (B = 14) to summer (B = 3.3). This reduction is tied to shallow soil moisture availability during the summer (s = 0.040 m3/m3) as compared to the winter (s = 0.004 m3/m3). During the NAMS, I analyzed four consecutive rainfall-runoff events to quantify the soil moisture and channel flow responses and how water availability impacted the land-atmosphere fluxes. Spatial hydrologic variations during events occur over distances as short as ~15 m. The field network also allowed comparisons of several approaches to estimate evapotranspiration (ET). I found a more accurate ET estimate (a reduction of mean absolute error by 38%) when using distributed soil moisture data, as compared to a standard water balance approach based on the tower site. In addition, use of spatially-varied soil moisture data yielded a more reasonable relationship between ET and soil moisture, an important parameterization in many hydrologic models. The analyses illustrates the value of high-resolution sampling for quantifying seasonal fluxes in desert shrublands and their improvements in closing the water balance in small watersheds. / Dissertation/Thesis / M.S. Civil and Environmental Engineering 2011