Copula-based spatial modelling of geometallurgical variables

The most important aspect of modelling a geological variable, such as metal grade, is the spatial correlation. Spatial correlation describes the relationship between realisations of a geological variable sampled at different locations. Any method for spatially modelling such a variable should be capable of accurately estimating the true spatial correlation. Conventional kriged models are the most commonly used in mining for estimating grade or other variables at unsampled locations, and these models use the variogram or covariance function to model the spatial correlations in the process of estimation. However, this usage assumes the relationships of the observations of the variable of interest at nearby locations are only influenced by the vector distance between the locations. This means that these models assume linear spatial correlation of grade. In reality, the relationship with an observation of grade at a nearby location may be influenced by both distance between the locations and the value of the observations (ie non-linear spatial correlation, such as may exist for variables of interest in geometallurgy). Hence this may lead to inaccurate estimation of the ore reserve if a kriged model is used for estimating grade of unsampled locations when nonlinear spatial correlation is present. Copula-based methods, which are widely used in financial and actuarial modelling to quantify the non-linear dependence structures, may offer a solution. This method was introduced by Bárdossy and Li (2008) to geostatistical modelling to quantify the non-linear spatial dependence structure in a groundwater quality measurement network. Their copula-based spatial modelling is applied in this research paper to estimate the grade of 3D blocks. Furthermore, real-world mining data is used to validate this model. These copula-based grade estimates are compared with the results of conventional ordinary and lognormal kriging to present the reliability of this method.

Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

Missing in space: An evaluation of imputation methods for missing data in spatial analysis of risk factors for type II diabetes

Background Spatial analysis is increasingly important for identifying modifiable geographic risk factors for disease. However, spatial health data from surveys are often incomplete, ranging from missing data for only a few variables, to missing data for many variables. For spatial analyses of health outcomes, selection of an appropriate imputation method is critical in order to produce the most accurate inferences. Methods We present a cross-validation approach to select between three imputation methods for health survey data with correlated lifestyle covariates, using as a case study, type II diabetes mellitus (DM II) risk across 71 Queensland Local Government Areas (LGAs). We compare the accuracy of mean imputation to imputation using multivariate normal and conditional autoregressive prior distributions. Results Choice of imputation method depends upon the application and is not necessarily the most complex method. Mean imputation was selected as the most accurate method in this application. Conclusions Selecting an appropriate imputation method for health survey data, after accounting for spatial correlation and correlation between covariates, allows more complete analysis of geographic risk factors for disease with more confidence in the results to inform public policy decision-making.

Model selection with misspecified spatial covariance structure

Spatial data analysis has become more and more important in the studies of ecology and economics during the last decade. One focus of spatial data analysis is how to select predictors, variance functions and correlation functions. However, in general, the true covariance function is unknown and the working covariance structure is often misspecified. In this paper, our target is to find a good strategy to identify the best model from the candidate set using model selection criteria. This paper is to evaluate the ability of some information criteria (corrected Akaike information criterion, Bayesian information criterion (BIC) and residual information criterion (RIC)) for choosing the optimal model when the working correlation function, the working variance function and the working mean function are correct or misspecified. Simulations are carried out for small to moderate sample sizes. Four candidate covariance functions (exponential, Gaussian, Matern and rational quadratic) are used in simulation studies. With the summary in simulation results, we find that the misspecified working correlation structure can still capture some spatial correlation information in model fitting. When the sample size is large enough, BIC and RIC perform well even if the the working covariance is misspecified. Moreover, the performance of these information criteria is related to the average level of model fitting which can be indicated by the average adjusted R square ( [GRAPHICS] ), and overall RIC performs well.

Microsite occupancy and spatial structure of regeneration in three late-successional Norway spruce forests in northern Europe

A comparison of microsite occupancy and the spatial structure of regeneration in three areas of late-successional Norway spruce dominated forest. Pallas-Ylläs is understood to have been influenced only by small-scale disturbance; Dvina-Pinega has had sporadic larger-scale disturbances; Kazkim has been affected by fire. All spruce and birch trees with diameter at breast height (DBH) ?10 cm were mapped in five stands on 40 m x 400 m transects, and those with DBH < 10 cm on 2 or 4 m x 400 m subplots. Microsite type was inventoried at 1m intervals along the centre line and for each tree with DBH < 10 cm. At all study areas small seedlings (h < 0.3 m, DBH < 10 cm) preferentially occupied disturbed microsites. In contrast, spruce saplings (h ? 1.3 m, DBH <10 cm) at all study areas showed less, or no, preference. At Pallas-Ylläs spruce seedlings (h < 1.3 m, DBH < 10 cm) and saplings (h ? 1.3 m, DBH < 10 cm) exhibited spatial correlation at scales from 32-52 m. At Dvina-Pinega saplings of both spruce and birch exhibited spatial correlation at scales from 32-81 m. At Kazkim spatial correlation of seedlings and saplings of both species was exhibited over variable distances. No spatial cross-correlation was found between overstorey basal area (DBH ? 10 cm) and regeneration (h ? 1.3 m, DBH < 10 cm) at any study area. The results confirm the importance of disturbed microsites for seedling establishment, but suggest that undisturbed microsites may sometimes be more advantageous for long-term tree survival. The regeneration gap concept may not be useful in describing the regeneration dynamics of late-successional boreal forests.

Diffusion on a rugged energy landscape with spatial correlations

Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Inter-regional correlation in tree-growth variations in the western United States, 1513-1964, at ENSO, sunspot, and longer frequency bands

Cross-spectral analysis of regional tree-ring data suggests the spatial pattern of correlation between moisture variations in the Sierra Nevada of central California and in other parts of the western United States is frequency dependent. Short wavelengths (2.8 to 10.7 years), perhaps associated with El Niño/Southern Oscillation, are strongly coherent both to the north (Oregon) and to the south (Southern California). Longer wavelengths (45 to 75 years) are strongly coherent only to the north. Frequency bands corresponding to annual sunspot series were associated with relatively weak patterns of spatial correlation.

NDVI spatial pattern and its differentiation on the Mongolian Plateau

GIMMS NDVI database and geo-statistics were used to depict the spatial distribution and temporal stability of NDVI on the Mongolian Plateau. The results demonstrated that: (1) Regions of interest with high NDVI indices were distributed primarily in forested mountainous regions of the east and the north, areas with low NDVI indices were primarily distributed in the Gobi desert regions of the west and the southwest, and areas with moderate NDVI values were mainly distributed in a middle steppe strap from northwest to southeast. (2) The maximum NDVI values maintained for the past 22 years showed little variation. The average NDVI variance coefficient for the 22-year period was 15.2%. (3) NDVI distribution and vegetation cover showed spatial autocorrelations on a global scale. NDVI patterns from the vegetation cover also demonstrated anisotropy; a higher positive spatial correlation was indicated in a NW-SE direction, which suggested that vegetation cover in a NW-SE direction maintained increased integrity, and vegetation assemblage was mainly distributed in the same specific direction. (4) The NDVI spatial distribution was mainly controlled by structural factors, 88.7% of the total spatial variation was influenced by structural and 11.3% by random factors. And the global autocorrelation distance was 1178 km, and the average vegetation patch length (NW-SE) to width (NE-SW) ratio was approximately 2.4:1.0.

Spatial Variability of Durum Wheat Yield as Related to Soil Parameters in an Organic Field

The yield in organic farming is generally much lower than its potential, which is due to its specificity. The objective of the present study was to quantify the yield spatial variation of wheat and relate it to soil parameters in an organic farm located in the north of the Negev Desert. Soil samples were gathered in a triangular grid at three time intervals. Yields were measured at 73 georeferenced points before the actual harvest. Several thematic maps of soil and yield parameters were produced using geographic information system and geostatistical methods. The strongest spatial correlation was found in the weight of 1000 grains and the weakest was in carbon flow. Temporal relationships were found between soil nitrate concentration, soil water content, and leaf area index. Wheat yield varied from 1.11 to 2.84 Mg ha(-1) and this remarkable variation indicates that the spatial analysis of soil and yield parameters is significant in organic agriculture.

Spatial statistics to estimate peat thickness using airborne radiometric data

Soil carbon stores are a major component of the annual returns required by EU governments to the Intergovernmental Panel on Climate Change. Peat has a high proportion of soil carbon due to the relatively high carbon density of peat and organic-rich soils. For this reason it has become increasingly important to measure and model soil carbon stores and changes in peat stocks to facilitate the management of carbon changes over time. The approach investigated in this research evaluates the use of airborne geophysical (radiometric) data to estimate peat thickness using the attenuation of bedrock geology radioactivity by superficial peat cover. Remotely sensed radiometric data are validated with ground peat depth measurements combined with non-invasive geophysical surveys. Two field-based case studies exemplify and validate the results. Variography and kriging are used to predict peat thickness from point measurements of peat depth and airborne radiometric data and provide an estimate of uncertainty in the predictions. Cokriging, by assessing the degree of spatial correlation between recent remote sensed geophysical monitoring and previous peat depth models, is used to examine changes in peat stocks over time. The significance of the coregionalisation is that the spatial cross correlation between the remote and ground based data can be used to update the model of peat depth. The result is that by integrating remotely sensed data with ground geophysics, the need is reduced for extensive ground-based monitoring and invasive peat depth measurements. The overall goal is to provide robust estimates of peat thickness to improve estimates of carbon stocks. The implications from the research have a broader significance that promotes a reduction in the need for damaging onsite peat thickness measurement and an increase in the use of remote sensed data for carbon stock estimations.

Spatial and Temporal Changes in Soil Organic Carbon Assessment using an Integrated Geostatistical and Compositional Data Analysis Approach

The Irish and UK governments, along with other countries, have made a commitment to limit the concentrations of greenhouse gases in the atmosphere by reducing emissions from the burning of fossil fuels. This can be achieved (in part) through increasing the sequestration of CO2 from the atmosphere including monitoring the amount stored in vegetation and soils. A large proportion of soil carbon is held within peat due to the relatively high carbon density of peat and organic-rich soils. This is particularly important for a country such as Ireland, where some 16% of the land surface is covered by peat. For Northern Ireland, it has been estimated that the total amount of carbon stored in vegetation is 4.4Mt compared to 386Mt stored within peat and soils. As a result it has become increasingly important to measure and monitor changes in stores of carbon in soils. The conservation and restoration of peat covered areas, although ongoing for many years, has become increasingly important. This is summed up in current EU policy outlined by the European Commission (2012) which seeks to assess the relative contributions of the different inputs and outputs of organic carbon and organic matter to and from soil. Results are presented from the EU-funded Tellus Border Soil Carbon Project (2011 to 2013) which aimed to improve current estimates of carbon in soil and peat across Northern Ireland and the bordering counties of the Republic of Ireland.
Historical reports and previous surveys provide baseline data. To monitor change in peat depth and soil organic carbon, these historical data are integrated with more recently acquired airborne geophysical (radiometric) data and ground-based geochemical data generated by two surveys, the Tellus Project (2004-2007: covering Northern Ireland) and the EU-funded Tellus Border project (2011-2013) covering the six bordering counties of the Republic of Ireland, Donegal, Sligo, Leitrim, Cavan, Monaghan and Louth. The concept being applied is that saturated organic-rich soil and peat attenuate gamma-radiation from underlying soils and rocks. This research uses the degree of spatial correlation (coregionalization) between peat depth, soil organic carbon (SOC) and the attenuation of the radiometric signal to update a limited sampling regime of ground-based measurements with remotely acquired data. To comply with the compositional nature of the SOC data (perturbations of loss on ignition [LOI] data), a compositional data analysis approach is investigated. Contemporaneous ground-based measurements allow corroboration for the updated mapped outputs. This provides a methodology that can be used to improve estimates of soil carbon with minimal impact to sensitive habitats (like peat bogs), but with maximum output of data and knowledge.

A Steganalysis System Utilizing Temporal Pixel Correlation Of HEVC Video

High Efficiency Video Coding (HEVC) is the most recent video codec coming after currently most popular H.264/MPEG4 codecs and has promising compression capabilities. It is conjectured that it will be a substitute for current video compression standards. However, to the best knowledge of the authors, none of the current video steganalysis methods designed or tested with HEVC video. In this paper, pixel domain steganography applied on HEVC video is targeted for the first time. Also, its the first paper that employs accordion unfolding transformation, which merges temporal and spatial correlation, in pixel domain video steganalysis. With help of the transformation, temporal correlation is incorporated into the system. Its demonstrated for three different feature sets that integrating temporal dependency substantially increased the detection accuracy.

Spatial and management factors associated with exposure of smallholder dairy cattle in Tanzania to tick-borne pathogens

A cross-sectional study of serum antibody responses of cattle to tick-borne pathogens (Theileria parva, Theileria mutans, Anaplasma marginale, Babesia bigemina and Babesia bovis) was conducted on smallholder dairy farms in Tanga and Iringa Regions of Tanzania. Seroprevalence was highest for T. parva (48% in Iringa and 23% in Tanga) and B. bigemina (43% in Iringa and 27% in Tanga) and lowest for B. bovis (12% in Iringa and 6% in Tanga). We use spatial and non-spatial models, fitted using classical and Bayesian methods, to explore risk factors associated with seroprevalence. These include both fixed effects (age, grazing history and breeding status) and random effects (farm and local spatial effects). In both regions, seroprevalence for all tick-borne pathogens increased significantly with age. Animals pasture grazed in the 3 months prior to the start of the sampling period were significantly more likely to be seropositive for Theileria spp. and Babesia spp. Pasture grazed animals were more likely to be seropositive than zero-grazed animals for A. marginale, but the relationship was weaker than that observed for the other four pathogens. This study did not detect any significant differences in seroprevalence associated with other management-related variables, including the method or frequency of acaricide application. After adjusting for age, there was weak evidence of localised (< 5 km) spatial correlation in exposure to some of the tick borne diseases. However, this was small compared with the 'farm-effect', suggesting that risk factors specific to the farm were more important than those common to the local neighbourhood. Many animals were seropositive for more than one pathogen and the correlation between exposure to the different pathogens remained after adjusting for the identified risk factors. Identifying the determinants of exposure to multiple tick-borne pathogens and characterizing local variation in risk will assist in the development of more effective control strategies for smallholder dairy farms. (c) 2005 Australian Society for Parasitology Inc. Published by Elsevier Ltd. All rights reserved.

Spatial Assessment of Indices for Characterizing the Erosive Force of Rainfall in El Salvador Republic

Soil erosion data in El Salvador Republic are scarce and there is no rainfall erosivity map for this region. Considering that rainfall erosivity is an important guide for planning soil erosion control practices, a spatial assessment of indices for characterizing the erosive force of rainfall in El Salvador Republic was carried out. Using pluviometric records from 25 weather stations, we applied two methods: erosivity index equation and the Fournier index. In all study area, the rainiest period is from May to November. Annual values of erosivity index ranged from 7,196 to 17,856 MJ mm ha(-1) h(-1) year(-1) and the Fournier index ranged from 52.9 to 110.0 mm. The erosivity map showed that the study area can be broadly divided into three major erosion risk zones, and the Fournier index map was divided into four zones. Both methods revealed that the erosive force is severe in all study area and presented significant spatial correlation with each other. The erosive force in the country is concentrated mainly from May to November.

GPS receivers for georeferencing of spatial variability of soil attributes

A caracterização da variabilidade espacial dos atributos do solo é indispensável para subsidiar práticas agrícolas de maneira sustentável. A utilização da geoestatística para caracterizar a variabilidade espacial desses atributos, como a resistência mecânica do solo à penetração (RP) e a umidade gravimétrica do solo (UG), é, hoje, prática usual na agricultura de precisão. O resultado da análise geoestatística é dependente da densidade amostral e de outros fatores, como o método de georreferencimento utilizado. Desta forma, o presente trabalho teve como objetivo comparar dois métodos de georreferenciamento para a caracterização da variabilidade espacial da RP e da UG, bem como a correlação espacial dessas variáveis. Foi implantada uma malha amostral de 60 pontos, espaçados em 20 m. Para as medições da RP, utilizou-se de penetrógrafo eletrônico e, para a determinação da UG, utilizou-se de trado holandês (profundidade de 0,0-0,1 m). As amostras foram georreferenciadas, utilizando-se do método de Posicionamento por Ponto Simples (PPS), com de (retirar) receptor GPS de navegação, e Posicionamento Relativo Semicinemático, com receptor GPS geodésico L1. Os resultados indicaram que o georreferenciamento realizado pelo PPS não interferiu na caracterização da variabilidade espacial da RP e da UG, assim como na estrutura espacial da relação dos atributos.