Organic carbon in atmospheric precipitation in the urbanized territory of the South of Western Siberia, Russia

This paper presents the results of studying the contents of total (TOC) and dissolved (DOC) organic carbon in atmospheric precipitation and their deposition fluxes on the territory of the city of Barnaul. Samples of atmospheric precipitation (rain and snow) were collected from May 2016 to December 2020 in the city center, additionally at the end of winter 2018–2019 samples of snow cover were taken in the territory of the city and its environs. The studies showed a significant content of organic carbon (OC) in atmospheric precipitation: the weighted average concentrations for the study period were 7.2 ± 0.6 and 4.2 ± 0.4 mg/L for TOC and DOC, respectively. The annual flux of OC deposition with atmospheric precipitation on the territory of Barnaul over the past three years has varied within 2.4–3.9 t/km2 for TOC and 1.4–2.1 t/km2 for DOC. To visualize the spatial distribution of organic matter over the territory of Barnaul, simple kriging was used, implemented in the Geostatistical Analyst module (ArcGIS® Desktop). The flow of organic carbon input into the snow cover during the winter period was used as data for the geostatistical model. According to the model, the deposition of OC from the atmosphere occurs unevenly throughout the urban area and depends on the location and intensity of pollution sources.

Review of the Kriging Technique Applications to Groundwater Quality

Kriging, a geostatistical technique, has been used for many years to evaluate groundwater quality. The best estimation data for unsampled points were determined by using this method depending on measured variables for an area. The groundwater contaminants assessment worldwide was found through many kriging methods. The present paper shows a review of the most known methods of kriging that were used in estimating and mapping the groundwater quality. Indicator kriging, simple kriging, cokriging, ordinary kriging, disjunctive kriging and lognormal kriging are the most used techniques. In addition, the concept of the disjunctive kriging method was explained in this work to be easily understood.

Mineral resource modelling using an unequal sampling pattern: An improved practice based on factorization techniques

This work addresses the problem of geostatistical simulation of cross-correlated variables by factorization approaches in the case when the sampling pattern is unequal. A solution is presented, based on a Co-Gibbs sampler algorithm, by which the missing values can be imputed. In this algorithm, a heterotopic simple cokriging approach is introduced to take into account the cross-dependency of the undersampled variable with the secondary variable that is more available over the entire region. A real gold deposit is employed to test the algorithm. The imputation results are compared with other Gibbs sampler techniques for which simple cokriging and simple kriging are used. The results show that heterotopic simple cokriging outperforms the other two techniques. The imputed values are then employed for the purpose of resource estimation by using principal component analysis (PCA) as a factorization technique, and the output compared with traditional factorization approaches where the heterotopic part of the data is removed. Comparison of the results of these two techniques shows that the latter leads to substantial losses of important information in the case of an unequal sampling pattern, while the former is capable of reproducing better recovery functions.

Geostatistical modeling of porosity and evaluating the local and global distribution

Porosity is one of the main variables needed for reservoir characterization. For this volumetric variable, there are many methods to simulate the spatial distribution. In this article, porosity was analyzed and modeled in the local and global distribution. For simulation, Sequential Gaussian simulation (SGS) and Gaussian Random Function (GRFS) were applied. Also, kriging was used to estimate the porosity at specific locations. The main purpose of this work was to investigate the porosity to compare geostatistical simulation and estimation methods in a sandstone reservoir as a real case study. First, the data sets were normalized by the Normal Scores Transformation (NST) and stratigraphic coordinate. The model of experimental variograms was fitted in the vertical and horizontal directions. For the simulation methods, 10 realizations were generated by each method. The Q-Q plots were calculated, and both sets of quintiles (Target Porosity Distribution versus Porosity realization) came from normal distributions with the following correlation coefficients: 0.93, 0.94 and 0.97 related to GRFS, SGS and Kriging, respectively. The extracted variograms from realizations showed that the kriging couldn’t reproduce the variograms with global distribution. For local validation, the cross-validation was evaluated and three wells were omitted. The re-estimation of porosity was considered at located well logs through the well sections window where the kriging had a better performance with minimum error to estimate porosity locally. Finally, the cross-sectional models were generated by each algorithm which showed that the simple kriging tries to produce smoother distribution, whereas conditional simulations (SGS and GRFS) try to represent more global-detailed sections.

Discussion on Competition for Spatial Statistics for Large Datasets

We discuss the experiences and results of the AppStatUZH team’s participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.

Mapping Urban Air Quality from Mobile Sensors Using Spatio-Temporal Geostatistics

With the advancement of technology and the arrival of miniaturized environmental sensors that offer greater performance, the idea of building mobile network sensing for air quality has quickly emerged to increase our knowledge of air pollution in urban environments. However, with these new techniques, the difficulty of building mathematical models capable of aggregating all these data sources in order to provide precise mapping of air quality arises. In this context, we explore the spatio-temporal geostatistics methods as a solution for such a problem and evaluate three different methods: Simple Kriging (SK) in residuals, Ordinary Kriging (OK), and Kriging with External Drift (KED). On average, geostatistical models showed 26.57% improvement in the Root Mean Squared Error (RMSE) compared to the standard Inverse Distance Weighting (IDW) technique in interpolating scenarios (27.94% for KED, 26.05% for OK, and 25.71% for SK). The results showed less significant scores in extrapolating scenarios (a 12.22% decrease in the RMSE for geostatisical models compared to IDW). We conclude that univariable geostatistics is suitable for interpolating this type of data but is less appropriate for an extrapolation of non-sampled places since it does not create any information.

Distribution of Antimony and Gold in Old Tailings and Heaps at the Milešov Locality (Příbram District)

Antimony ores were extracted and processed near the village of Milešov (Příbram district) for about twenty years in the second halfof the 19th century. Large heaps and a small sludge pond were left behind after this period. In 1988, this locality was inspected andsampled in order to gather information about residual resources of gold and antimony. The original archive data from this surveywere now studied again and interpreted using modern statistical and geostatistical methods. The interpolations methods chosenfor this purpose were inverse distance weighting (IDW), simple kriging and geostatistical sequential Gaussian simulation (SGS).These procedures allowed for a much more accurate determination of the spatial distribution of the elements or substances studied.The results showed significantly higher volumes and a more accurate localization of the studied elements in both bodies (heap andtailings). This procedure can be considered as the basis of a new methodology for the assessment of similar objects.

Comparison of Metamodel Performances on an Electronic Circuit Problem

Aims: Investigation of building and validation of metamodels which of linear regression, simple kriging, ordinary kriging and radial basis function for an electronic circuit problem are the main aim of this study. Study Design: An electronic circuit problem was considered to compare the performances of the metamodels. Latin hypercube design was used for experimental design of five input variables of the considered problem. Methodology: A training data set consisting of 45 experiments and a validation data set consisting of 500 experiments were obtained using Latin hypercube design. Input variables were used by coded to calculate the spatial distances between observation points more consistently. Then using training data set linear regression, simple kriging, ordinary kriging and radial basis function metamodels were built. And, performance measures were calculated for the validation data set. Results: It has been shown that simple kriging which are applied to outputs the differences from the mean, and ordinary kriging metamodels, produce superior solutions compared to the linear regression and radial basis function metamodels for the electronic circuit problem considered in this study. Prediction superiority of SK and OK than RBF on five-dimensional problem is another important result of the study. Conclusion: Kriging metamodels are considered to be strong alternatives to the other metamodels for the problems that are considered in this study and have a similar nature. Since the superiority of metamodel methods to each other may vary from problem to problem, it is another important issue to compare their performance by considering more than one method in problem solving stage.

Spatially Continuous Land-Cover Reconstructions Through the Holocene in Southern Sweden

Climate change and human activities influence the development of ecosystems, with human demand of ecosystem services altering both land use and land cover. Fossil pollen records provide time series of vegetation characteristics, and the aim of this study was to create spatially continuous reconstructions of land cover through the Holocene in southern Sweden. The Landscape Reconstruction Algorithm (LRA) was applied to obtain quantitative reconstructions of pollen-based vegetation cover at local scales, accounting for pollen production, dispersal, and deposition mechanisms. Pollen-based local vegetation estimates were produced from 41 fossil pollen records available for the region. A comparison of 17 interpolation methods was made and evaluated by comparing with current land cover. Simple kriging with cokriging using elevation was selected to interpolate the local characteristics of past land cover, to generate more detailed reconstructions of trends and degree of variability in time and space than previous studies based on pollen data representing the regional scale. Since the Mesolithic, two main processes have acted to reshape the land cover of southern Sweden, originally mostly covered by broad-leaved forests. The natural distribution limit of coniferous forest has moved southward during periods with colder climate and retracted northward during warmer periods, and human expansion in the area and agrotechnological developments has led to a gradually more open landscape, reaching maximum openness at the beginning of the 20th century. The recent intensification of agriculture has led to abandonment of less fertile agricultural fields and afforestation with conifer forest.

A Python Based Multi-Point Geostatistics by using Direct Sampling Algorithm

Multi-Point Geostatistics (MPS) is a type of geostatistical method used to estimate the value of an unsampled location by utilizing several data points around it simultaneously. The MPS method estimates it by defining a model based on initial data in the form of a training image, which is a collection of data in the form of a geological conceptual model in the research area with the integration of geological and geophysical knowledge. The MPS method is currently starting to develop because it differs from conventional covariance-based geostatistical methods such as simple kriging and ordinary kriging, which only use a variogram based on the relationship between two points rapidly. In this study, we evaluated the use of the MPS method by using a direct sampling algorithm with Python that will directly sample the training image and then retrieve the data based on the sample data. A braided channel training image is used as the initial model to estimate the distribution of reservoir properties in lithology with sand and shale types. This study shows that MPS could reconstruct geological features better than kriging.