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In geostatistical analysis, we are faced with the formidable challenge of specifying a valid spatio-temporal covariance function, either directly or through the construction of processes. This task is di cult as these functions should yield positive de nite covariance matrices. In recent years, we have seen a ourishing of methods and theories on constructing spatiotemporal covariance functions satisfying the positive de niteness requirement. The current state-of-the-art when modeling environmental processes are those that embed the associated physical laws of the system. The class of Lagrangian spatio-temporal covariance functions ful lls this requirement. Moreover, this class possesses the allure that they turn already established purely spatial covariance functions into spatio-temporal covariance functions by a direct application of the concept of Lagrangian reference frame. In the three main chapters that comprise this dissertation, several developments are proposed and new features are provided to this special class. First, the application of the Lagrangian reference frame on transported purely spatial random elds with second-order nonstationarity is explored, an appropriate estimation methodology is proposed, and the consequences of model misspeci cation is tackled. Furthermore, the new Lagrangian models and the new estimation technique are used to analyze particulate matter concentrations over Saudi Arabia. Second, a multivariate version of the Lagrangian framework is established, catering to both secondorder stationary and nonstationary spatio-temporal random elds. The capabilities of the Lagrangian spatio-temporal cross-covariance functions are demonstrated on a bivariate reanalysis climate model output dataset previously analyzed using purely spatial covariance functions. Lastly, the class of Lagrangian spatio-temporal cross-covariance functions with multiple transport behaviors is presented, its properties are explored, and its use is demonstrated on a bivariate pollutant dataset of particulate matter in Saudi Arabia. Moreover, the importance of accounting for multiple transport behaviors is discussed and validated via numerical experiments. Together, these three extensions to the Lagrangian framework makes it a more viable geostatistical approach in modeling realistic transport scenarios.

Aeolian landforms are classified based on their plan morphology, which is a function of sediment transport volume, wind direction, and vegetation. In the case of compound landforms or two-dimensional exposures (outcrops), there is insufficient information for discriminating between 3D morphotypes (e.g., barchans vs. parabolic dunes). To characterize the dip-section architecture of near end-member morphologies (interacting barchans and sparsely vegetated parabolics), a series of axial transects were selected from >25 km of high-resolution (500 MHz) ground-penetrating radar (GPR) data from the gypsum dune field of White Sands National Monument, New Mexico. For dunes of comparable size (6-7 m high), a series of attributes were analyzed for unsaturated portions along the thickest (axial) radargram sections. Given the limitations in vertical resolution (7 cm in dry sand), the average measureable slipface thickness in barchans ranged between 10-22 cm, whereas parabolic slipfaces were thinner at 10-14 cm. High-amplitude diffractions produced by buried vegetation, semi-lithified pedestals, and bioturbation structures were rare within barchans (point-source diffraction density = 0.03/m2; hyperbolics per 1-m-wide cross-sectional area of the image), in contrast to a point-source density of 0.07/m2 in parabolics. An aeolian internal complexity threshold (ϖ) is proposed, which incorporates standardized scores of slipface thickness, point-source diffraction density, and continuity of major bounding surfaces at mesoscale range determined through semivariogram analysis. For the study region, these variables were sufficient for discriminating barchans (ϖ = -2.39 to -0.25; ϖ ̅b= -1.65) from parabolic (ϖ = 0.13 to 2.87; ϖ ̅p= 1.65) dunes. This threshold has the potential for differentiating dune morphotypes in areas where surface morphology is masked and for identifying compound landforms (e.g., a re-activated parabolic dune converted into a barchan in situ). Ultimately, characterization of bedding complexity in ancient aeolian sequences will provide useful information about key paleoenvironmental variables. / Geology

A study was conducted at the Savannah River Site near Aiken, SC to: 1) characterize the spatial patterns of soil and forest floor variables (moisture, pH, soil phosphate, forest floor and soil carbon and nitrogen, and soil available nitrogen), 2) assess the spatial patterns of the plant community, and 3) investigate spatial relationships among the variables and between the variables and woody vegetation. Spatial soil and litter samples were collected on five 0.25 hectare plots, and relationships were explored using Pearson's correlation tests, canonical correlation analysis, variogram modeling and kriging. The average range of spatial autocorrelation for the forest floor variables was >45 m, while that for soil variables was 12 m. Woody stem basal area exhibited spatial autocorrelation at ranges of less than 12 m, and was only weakly correlated with forest floor and soil resource patterns. Few strong spatial correlations among the forest floor and soil variables were observed. The means and variances of the variables were low, and differences in resource levels probably had little impact on the spatial pattern of vegetation. Results indicate a weak, differential effect of species group on litter quality, a weak relationship between large pine trees and soil nitrogen patterns, and a general homogeneity of the stands. / Master of Science

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Kriging is proposed as a tool for Wi-Fi signal strength estimation for complex indoor environments. This proposal is based on two studies suggesting that kriging might be suitable for this application. Both of these studies have shortcomings in supporting this proposal, but their results encourage a more in depth investigation into this. Even though kriging is a geostatistical method developed for geographical interpolation, it has been used successfully in a wide range of other applications as well. This further suggests that kriging might be a versatile method to overcome some of the difficul- ties of existing signal strength estimation methods. Two main types of signal strength estimation are deterministic methods and empirical methods. Deterministic methods are generally very complex and requires input parameters that are difficult to obtain. Empirical methods are known to have low accuracy which makes them unreliable for practical use. Three main investigations are presented in order to evaluate the use of kriging for this application. A sampling plan is proposed as part of a generic application protocol for the practical use of kriging for Wi-Fi signal strength. It is concluded that kriging can be conffidently used as an estimation technique for Wi-Fi signal strength in complex indoor environments. Kriging is recommended for practical applications, especially where in- sufficient information is available about a building or where time consuming site surveys are not feasible. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

Kriging is proposed as a tool for Wi-Fi signal strength estimation for complex indoor environments. This proposal is based on two studies suggesting that kriging might be suitable for this application. Both of these studies have shortcomings in supporting this proposal, but their results encourage a more in depth investigation into this. Even though kriging is a geostatistical method developed for geographical interpolation, it has been used successfully in a wide range of other applications as well. This further suggests that kriging might be a versatile method to overcome some of the difficul- ties of existing signal strength estimation methods. Two main types of signal strength estimation are deterministic methods and empirical methods. Deterministic methods are generally very complex and requires input parameters that are difficult to obtain. Empirical methods are known to have low accuracy which makes them unreliable for practical use. Three main investigations are presented in order to evaluate the use of kriging for this application. A sampling plan is proposed as part of a generic application protocol for the practical use of kriging for Wi-Fi signal strength. It is concluded that kriging can be conffidently used as an estimation technique for Wi-Fi signal strength in complex indoor environments. Kriging is recommended for practical applications, especially where in- sufficient information is available about a building or where time consuming site surveys are not feasible. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2015

This is a thesis about the spatial distribution of willow warbler, nightingale, blackbird, robin and grey flycatcher in Svealand and Götaland, that is the southern third of Sweden. It explores the possibilities of using statistics to describe the distribution and variation of birds in a given region.The data was collected by observation of birds on sites called standard routes, with 25 kilometres between them. The standard routes are the points in a grid net placed upon the map of Sweden. The purpose of standard routes is to represent the birds in Sweden both geographic and biotopological.The thesis compare the results from kriging, variogram and four alternative poisson regressions. In the end I come up with the information provided by kriging and variogram and which poisson regression that bests estimates the population sizes of the birds at a given site with information about year, mean temperature from January to May and what kind of environment or habitat the site consist of.

Diversity within a habitat is determined largely by ecology and species interactions. Studies to date, however, rarely examined the role of intraspecific aggression in promoting coexistence and diversity. This is especially true in cities, where community ecology is poorly understood. This knowledge is important for basic understanding of how ecological principals come into play in our newly created habitats, as well as for reconciling human-dominated areas for wildlife.I studied the effect of human-made habitats on hummingbird abundance and diversity in Tucson, Arizona. To do that, I examined community organization and competitive interactions among four hummingbird species. I answer the questions: What is the community organization of hummingbirds in Tucson? How do characteristics of human habitats (e.g., landscaping and artificial resources) affect diversity? What mechanism underlies this pattern? And how can we apply this knowledge to conservation?To perform this study, I established a citizen science project - the Tucson Hummingbird Project (http://hummingbirds.arizona.edu). Trained participants reported abundance and behavior of hummingbirds in their backyards. Landscaping and resources (feeders and nectar plants) varied between yards.Results show that the distribution of hummingbirds in Tucson varies by species. Diversity, rather than merely abundance, increased with higher habitat heterogeneity and with more resources. Competitive interactions differ between species. Notably, intraspecific competition takes precedence over interspecific competition in the dominant and most common species, Anna's hummingbird.Based on the data, I suggest that Aggressive Resource Neglect (ARN) promotes coexistence and results in higher diversity when resources are augmented. When there are more feeders, they are distributed over a larger area. This reduces the ability of a territory-owner to defend these resources. While the territory-owner chases intruders, other individuals gain access to feeding opportunities. When dominant individuals prefer chasing conspecifics (as with Anna's hummingbird), this results in higher diversity.Besides discussing theoretical aspects, I apply this knowledge to conservation. Information on the community ecology enabled me to suggest ecologically-based ways to reconcile the city for native hummingbirds. By adding resources following an ecological protocol, we can promote biodiversity and surround ourselves with native wildlife, such as hummingbirds.