The variogram plays a central role in the analysis of geostatistical data. A valid variogram model is selected and the parameters of that model are estimated before kriging (spatial prediction) is performed. These inference procedures are generally based upon examination of the empirical variogram, which consists of average squared differences of data taken at sites lagged the same distance apart in the same direction. The ability of the analyst to estimate variogram parameters efficiently is affected significantly by the sampling design, i.e., the spatial configuration of sites where measurements are taken. In this paper, we propose design criteria that, in contrast to some previously proposed criteria oriented towards kriging with a known variogram, emphasize the accurate estimation of the variogram. These criteria are modifications of design criteria that are popular in the context of (nonlinear) regression models. The two main distinguishing features of the present context are that the addition of a single site to the design produces as many new lags as there are existing sites and hence also produces that many new squared differences from which the variograrn is estimated. Secondly, those squared differences are generally correlated, which inhibits the use of many standard design methods that rest upon the assumption of uncorrelated errors. Several approaches to design construction which account for these features are described and illustrated with two examples. We compare their efficiency to simple random sampling and regular and space-filling designs and find considerable improvements. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Soil is extremely important for providing food, biomass and raw materials, water and nutrient storage; supporting biodiversity and providing foundations for man-made structures. However, its health is threatened by human activities, which can greatly affect the potential of soils to fulfil their functions and, consequently, result in environmental, economic and social damage. These issues require the characterisation of the impact and spatial extent of the problems. This can be achieved through the creation of detailed and comprehensive soil maps that describe both the spatial and vertical variability of key soil properties. Detailed three-dimensional (3D) digital soil maps can be readily used and embedded into environmental models. Three-dimensional soil mapping is not a new concept. However, only with the recent development of more powerful computers has it become feasible to undertake such data processing. Common techniques to estimate soil properties in the three-dimensional space include geostatistical interpolation, or a combination of depth functions and geostatistics. However, these two methods are both partially flawed. Geostatistical interpolation and kriging in particular, estimate soil properties in unsampled locations using a weighted average of the nearby observations. In order to produce the best possible estimate, this form of interpolation minimises the variance of each weighted average, thus decreasing the standard deviation of the estimates, compared to the soil observations. This appears as a smoothing effect on the data and, as a consequence, kriging interpolation is not reliable when the dataset is not sampled with a sampling designs optimised for geostatistics. Depth function approaches, as they are generally applied in literature, implement a spline regression of the soil profile data that aims to better describe the changes of the soil properties with depth. Subsequently, the spline is resampled at determined depths and, for each of these depths, a bi-dimensional (2D) geostatistical interpolation is performed. Consequently, the 3D soil model is a combination of a series of bi-dimensional slices. This approach can effectively decrease or eliminate any smoothing issues, but the way in which the model is created, by combining several 2D horizontal slices, can potentially lead to erroneous estimations. The fact that the geostatistical interpolation is performed in 2D implies that an unsampled location is estimated only by considering values at the same depth, thus excluding the vertical variability from the mapping, and potentially undermining the accuracy of the method. For these reasons, the literature review identified a clear need for developing, a new method for accurately estimating soil properties in 3D – the target of this research, The method studied in this thesis explores the concept of soil specific depth functions, which are simple mathematical equations, chosen for their ability to describe the general profile pattern of a soil dataset. This way, fitting the depth function to a particular sample becomes a diagnostic tool. If the pattern shown in a particular soil profile is dissimilar to the average pattern described by the depth function, it means that in that region there are localised changes in the soil profiles, and these can be identified from the goodness of fit of the function. This way, areas where soil properties have a homogeneous profile pattern can be easily identified and the depth function can be changed accordingly. The application of this new mapping technique is based on the geostatistical interpolation of the depth function coefficients across the study area. Subsequently, the equation is solved for each interpolated location to create a 3D lattice of soil properties estimations. For this way of mapping, this new methodology was denoted as top-down mapping method. The methodology was assessed through three case studies, where the top-down mapping method was developed, tested, and validated. Three datasets of diverse soil properties and at different spatial extents were selected. The results were validated primarily using cross-validation and, when possible, by comparing the estimates with independently sampled datasets (independent validation). In addition, the results were compared with estimates obtained using established literature methods, such as 3D kriging interpolation and the spline approach, in order to define some basic rule of application. The results indicate that the top-down mapping method can be used in circumstances where the soil profiles present a pattern that can be described by a function with maximum three coefficients. If this condition is met, as it was with key soil properties during the research, the top-down mapping method can be used for obtaining reliable estimates at different spatial extents.

Made available in DSpace on 2016-12-23T14:37:40Z (GMT). No. of bitstreams: 1 Moises Zucoloto.pdf: 1357668 bytes, checksum: ddee007237f94fa0bff57f63f028d42b (MD5) Previous issue date: 2009-02-13 / O presente trabalho teve como objetivo aplicar métodos e conceitos de Agricultura de Precisão (AP), utilizando técnicas de estatística clássica e geoestatística no mapeamento da variabilidade espacial da produção da bananeira Prata Anã e correlacioná-la com os atributos químicos e físicos do solo e o estado nutricional da planta no primeiro ciclo da cultura. A lavoura comercial situa-se em um Argissolo Amarelo Distrocoeso arênico no Distrito de Jacupemba, município de Aracruz, Norte do Estado do Espírito Santo, cujas coordenadas geográficas são: 19° 49 24 de Latitude Sul e 40° 04 20 de Longitude Oeste. Dentro da área comercial foi demarcada uma malha regular, totalizando 100 pontos amostrais, espaçados 6 x 4 m. Os valores dos atributos químicos e físicos do solo, estado nutricional e produção foram determinados em cada amostra. A massa do cacho (MC) não apresenta correlação significativa com nenhuma das frações granulométricas. Os atributos areia grossa (AG), areia fina (AF), areia total (AT) e argila (AR) apresentam dependência espacial de moderada a alta, com exceção para o silte (Sil) que apresenta ausência de dependência. Apenas o H+Al do solo apresenta correlação com a massa do cacho. Todos os atributos químicos do solo apresentam dependência espacial na área de estudo. O atributo T apresenta o maior alcance de dependência espacial, portanto, maior continuidade, com melhor precisão na estimativa de valores em locais não medidos. Quanto ao estado nutricional da planta, apenas os nutrientes K e P apresentam correlação significativa positiva com a produção por planta. Todos nutrientes foliares apresentam dependência espacial, com exceção para o B e o N. O maior alcance de dependência espacial entre os nutrientes foliares é apresentado pelo K e, portanto, maior continuidade espacial, afetando positivamente na estimativa de valores em locais não medidos. As características morfológicas diâmetro do cacho, número de bananas, largura da terceira folha e número de folhas na colheita estimaram a massa do cacho por planta com um R2 de 58%

Currently in archaeological studies digital elevation models are mainly used especially in terms of shaded reliefs for the prospection of archaeological sites. Hesse (2010) provides a supporting software tool for the determination of local relief models during the prospection using LiDAR scans. Furthermore the search for relicts from WW2 is also in the focus of his research.¹ In James et al. (2006) the determined contour lines were used to reconstruct locations of archaeological artefacts such as buildings.² This study is much more and presents an innovative workflow of determining historical high resolution terrain surfaces using recent high resolution terrain models and sedimentological expert knowledge. Based on archaeological field studies (Franconian Saale near Bad Neustadt in Germany) the sedimentological analyses shows that archaeological interesting horizon and geomorphological expert knowledge in combination with particle size analyses (Köhn, DIN ISO 11277) are useful components for reconstructing surfaces of the early Middle Ages.³ Furthermore the paper traces how it is possible to use additional information (extracted from a recent digital terrain model) to support the process of determination historical surfaces. Conceptual this research is based on methodology of geomorphometry and geo-statistics. The basic idea is that the working procedure is based on the different input data. One aims at tracking the quantitative data and the other aims at processing the qualitative data. Thus, the first quantitative data were available for further processing, which were later processed with the qualitative data to convert them to historical heights. In the final stage of the work ow all gathered information are stored in a large data matrix for spatial interpolation using the geostatistical method of Kriging. Besides the historical surface, the algorithm also provides a first estimation of accuracy of the modelling. The presented workflow is characterized by a high exibility and the opportunity to include new available data in the process at any time.