Applications Of Geostatistics Research Articles

Contemporary Applications of Geostatistics to Soil Studies

This Special Issue presents carefully selected examples of Contemporary Applications of Geostatistics to Soil Studies [...]

Spatial statistical methodologies in COVID-19 Studies: A systematic review

Objective: As of August 2023, COVID-19 had claimed 7 million lives, making it the pandemic with the highest mortality rate. Therefore, The use of cutting-edge technologies and methods is essential when battling the COVID-19 epidemic. This paper aims to systematically review and synthetize applications of spatial statistical methodologies in the analysis of COVID-19. Material and Methods: 55 articles in total were screened from four main digital databases including Web of Science, SCOPUS, PubMed/MEDLINE, and Google schoolar. Three distinct concerns with the use of spatial statistical techniques in the analysis of COVID-19 are discussed, namely (i) applications of spatial regressions in the evaluation of COVID-19's effects, (ii) COVID-19 mapping using of hotspots and spatial clustering analyses, and (iii) applications of interpolation and geostatistics on COVID-19 studies, respectively. Results: Spatial regressions can support the assessment of the COVID-19 impacts on social-economy and environment. Whereas, hotspots and spatial clustering analysis can help effectively on COVID-19 mapping. Last but not least, geostatistics and interpolation are crucial for predicting COVID-19. Conclusion: This review not only emphasises the significance of spatial statistical techniques in COVID-19 studies, but it also sheds light on the practical applications of spatial statistics in COVID-19 research.

Exploring 20-year applications of geostatistics in precision agriculture in Brazil: what’s next?

Exploring 20-year applications of geostatistics in precision agriculture in Brazil: what’s next?

SciKit-GStat 1.0: a SciPy-flavored geostatistical variogram estimation toolbox written in Python

Abstract. Geostatistical methods are widely used in almost all geoscientific disciplines, i.e., for interpolation, rescaling, data assimilation or modeling. At its core, geostatistics aims to detect, quantify, describe, analyze and model spatial covariance of observations. The variogram, a tool to describe this spatial covariance in a formalized way, is at the heart of every such method. Unfortunately, many applications of geostatistics focus on the interpolation method or the result rather than the quality of the estimated variogram. Not least because estimating a variogram is commonly left as a task for computers, and some software implementations do not even show a variogram to the user. This is a miss, because the quality of the variogram largely determines whether the application of geostatistics makes sense at all. Furthermore, the Python programming language was missing a mature, well-established and tested package for variogram estimation a couple of years ago. Here I present SciKit-GStat, an open-source Python package for variogram estimation that fits well into established frameworks for scientific computing and puts the focus on the variogram before more sophisticated methods are about to be applied. SciKit-GStat is written in a mutable, object-oriented way that mimics the typical geostatistical analysis workflow. Its main strength is the ease of use and interactivity, and it is therefore usable with only a little or even no knowledge of Python. During the last few years, other libraries covering geostatistics for Python developed along with SciKit-GStat. Today, the most important ones can be interfaced by SciKit-GStat. Additionally, established data structures for scientific computing are reused internally, to keep the user from learning complex data models, just for using SciKit-GStat. Common data structures along with powerful interfaces enable the user to use SciKit-GStat along with other packages in established workflows rather than forcing the user to stick to the author's programming paradigms. SciKit-GStat ships with a large number of predefined procedures, algorithms and models, such as variogram estimators, theoretical spatial models or binning algorithms. Common approaches to estimate variograms are covered and can be used out of the box. At the same time, the base class is very flexible and can be adjusted to less common problems, as well. Last but not least, it was made sure that a user is aided in implementing new procedures or even extending the core functionality as much as possible, to extend SciKit-GStat to uncovered use cases. With broad documentation, a user guide, tutorials and good unit-test coverage, SciKit-GStat enables the user to focus on variogram estimation rather than implementation details.

TASC3D: A program to test the admissibility in 3D of non-linear models of coregionalization

Most multivariate applications of geostatistics conveniently rely on the linear model of coregionalization (LMC). However, it is common that the secondary data represent a variable defined over a larger support than the primary variable. In these cases, the LMC cannot provide a good fit for the secondary variable variogram and the cross-variogram, leading to a loss of precision in cokriging and even more so in simulation. In the multivariate case, covariance models fitted on the direct and cross-variograms need to be checked for admissibility as a non-LMC (N-LMC). This non-trivial task is done by program TASC3D (for testing admissibility of symmetrical covariances in 3D). The admissibility verification is done based on the radial spectral densities of most common covariance functions. Two new spectral densities are derived for the penta and cubic models and expressions for anisotropic covariances are presented. The program enables checking the admissibility of 3D N-LMC coregionalization models or, alternatively, identification of the domain of admissibility for up to two free parameters. It can accommodate any number of variables, with any number of components for each structure, each component being isotropic or anisotropic. A series of examples are presented illustrating the program capacities. A simulated reference field is compared to conditional realizations from the LMC and the N-LMC. The precision of N-LMC shows improvements of 5.2% and 13.7% respectively for the primary and the secondary variables. By simplifying the modeling task, program TASC3D favors the use in applications of tailored N-LMC models.

Applications of Geostatistics in Optimal Design of Satellite Altimetry Orbits and Measurement Configurations

The Geoscience Laser Altimeter System (GLAS) aboard NASA’s Ice, Cloud and land Elevation Satellite (ICESat) is a pulse-limited laser that records measurements in a geophysical track-line ground pattern of single discrete points along a sub-satellite track. Spacing between tracks depends on latitude and repeat cycle. Derivation of digital elevation models (DEMs) of the ice surface from GLAS data requires interpolation, which due to the spatial data distribution is mathematically an extrapolation problem, best solved using a form of geostatistical estimation. In this article, we investigate the relationships between observing ice surface elevations with single-beam and multi-beam altimetry, regional coverage and spatial resolution, orbit ground track design and repeat-track spacing, analysis with ordinary and advanced universal Kriging algorithms and resultant DEM accuracy. The study is a contribution to the ICESat-2 ad-hoc Science Definition Team tasks and analyzes GLAS data and several potential multi-beam configurations proposed for the ICESat-2 instrumentation. Measurement of elevation change at the accuracy required by the U.S. National Research Council (2007) “Decadal Survey” recommendations requires understanding the effects of spatial variability of the elevation measurement, in particular for complex, rough or steep natural surfaces. This problem, which is important to correctly assess the cryosphere’s contribution to sea-level rise, is treated using scale-dependent simulation. Results indicate that multi-beam laser measurements are needed and provide a solution to the trade-off problem between repeat-mission and geodetical coverage. More generally, the article demonstrates links between space mission planning, orbit design, spatial distribution of measurements from future instrumentation and improved mathematical data processing algorithms.

Direct Multiple-Point Geostatistical Simulation of Edge Properties for Modeling Thin Irregularly Shaped Surfaces

Thin, irregularly shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous media. Clay drapes are often complex, curvilinear three-dimensional surfaces and display a very complex spatial distribution. Variogram-based stochastic approaches are also often not able to describe the spatial distribution of clay drapes since complex, curvilinear, continuous, and interconnected structures cannot be characterized using only two-point statistics. Multiple-point geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time using training images to characterize the patterns of geological heterogeneity. Multiple-point geostatistics can reproduce thin irregularly shaped surfaces such as clay drapes, but this is often computationally very intensive. This paper describes and applies a methodology to simulate thin, irregularly shaped surfaces with a smaller CPU and RAM demand than the conventional multiple-point statistical methods. The proposed method uses edge properties for indicating the presence of thin irregularly shaped surfaces. Instead of pixel values, edge properties indicating the presence of irregularly shaped surfaces are simulated using snesim. This method allows direct simulation of edge properties instead of pixel properties to make it possible to perform multiple-point geostatistical simulations with a larger cell size and thus a smaller computation time and memory demand. This method is particularly valuable for three-dimensional applications of multiple-point geostatistics.

Special Issue on Geostatistics for Environmental Applications

Until the early 90s of the last century, environmental applications of geostatistics did not share the same shining stage as the mining and petroleum applications. In some way, the small number of papers in international conferences and researchers involved in the field reflected the concern and priority level that the society and the scientific community devoted to the environmental problems. On the other hand, the dominant mainstream of methods for approaching these problems—qualitative paradigms of analyzing natural resources (e.g., forest, biodiversity, soil), deterministic modeling for characterizing environmental issues (e.g., air pollution, climate, groundwater), statistical methods that did not privilege the space–time component of those phenomena—did not contribute much for changing this scenario. During the 90s, environmental problems like ozone depletion, greenhouse effect, global warming, loss of biodiversity, desertification and drought became global and public issues, changing the environmental risk perception of people radically. The United Nations conferences and summits, from Rio (1992) to Kyoto (1997), definitively pushed those points towards most countries’ agenda, leading to significant investments in research and development. Hence, the applications of quantitative methods (particularly in geostatistics) to monitor, manage, remediate and mitigate environmental resources became an appealing challenge for

Geostatistics with the Matern semivariogram model: A library of computer programs for inference, kriging and simulation

In many modern applications of geostatistics in the earth sciences, the empirical information is abundant and with complete spatial coverage (e.g. satellite sensor images). In these cases, a critical characteristic of spatial variability is the continuity of the random field that better models the natural phenomenon of interest. Such continuity describes the smoothness of the process at very short distances and is related to the behaviour of the semivariogram near the origin. For this reason, a semivariogram model that is flexible enough to describe the spatial continuity is very convenient for applications. A model that provides such flexibility is the Matern model that controls continuity with a shape parameter. The shape parameter must be larger than zero; a value larger than 1 implies a random field that is m-times mean square differentiable if the shape parameter is larger than m. A package of computer programs is provided for performing the different steps of a geostatistical study using the Matern model and the performance and implementation are illustrated by an example.

Stochastic Hydrogeology: What Professionals Really Need?

Quantitative hydrogeology celebrated its 150th anniversary in 2006. Geostatistics is younger but has had a very large impact in hydrogeology. Today, geostatistics is used routinely to interpolate deterministically most of the parameters that are required to analyze a problem or make a quantitative analysis. In a small number of cases, geostatistics is combined with deterministic approaches to forecast uncertainty. At a more academic level, geostatistics is used extensively to study physical processes in heterogeneous aquifers. Yet, there is an important gap between the academic use and the routine applications of geostatistics. The reasons for this gap are diverse. These include aspects related to the hydrogeology consulting market, technical reasons such as the lack of widely available software, but also a number of misconceptions. A change in this situation requires acting at different levels. First, regulators must be convinced of the benefit of using geostatistics. Second, the economic potential of the approach must be emphasized to customers. Third, the relevance of the theories needs to be increased. Last, but not least, software, data sets, and computing infrastructure such as grid computing need to be widely available.

Landscape‐based geostatistics: a case study of the distribution of blue crab in Chesapeake Bay

AbstractGeostatistical techniques have gained widespread use in ecology and environmental science. Variograms are commonly used to describe and examine spatial autocorrelation, and kriging has become the method of choice for interpolating spatially‐autocorrelated variables. To date, most applications of geostatistics have defined the separation between sample points using simple Euclidean distance. In heterogeneous environments, however, certain landscape features may act as absolute or semi‐permeable barriers. This effective separation may be more accurately described by a measure of distance that accounts for the presence of barriers. Here we present an approach to geostatistics based on a lowest‐cost path (LCP) function, in which the cost of a path is a function of both the distance and the type of terrain crossed. The modified technique is applied to 13 years of survey data on blue crab abundance in Chesapeake Bay. Use of this landscape‐based distance metric significantly changed estimates of all three variogram parameters. In this case study, although local differences in kriging predictions were apparent, the use of the landscape‐based distance metric did not result in consistent improvements in kriging accuracy. Copyright © 2006 John Wiley & Sons, Ltd.

GIS, geostatistics, metadata banking, and tree-based models for data analysis and mapping in environmental monitoring and epidemiology

By the example of environmental monitoring, some applications of geographic information systems (GIS), geostatistics, metadata banking, and Classification and Regression Trees (CART) are presented. These tools are recommended for mapping statistically estimated hot spots of vectors and pathogens. GIS were introduced as tools for spatially modelling the real world. The modelling can be done by mapping objects according to the spatial information content of data. Additionally, this can be supported by geostatistical and multivariate statistical modelling. This is demonstrated by the example of modelling marine habitats of benthic communities and of terrestrial ecoregions. Such ecoregionalisations may be used to predict phenomena based on the statistical relation between measurements of an interesting phenomenon such as, e.g., the incidence of medically relevant species and correlated characteristics of the ecoregions. The combination of meteorological data and data on plant phenology can enhance the spatial resolution of the information on climate change. To this end, meteorological and phenological data have to be correlated. To enable this, both data sets which are from disparate monitoring networks have to be spatially connected by means of geostatistical estimation. This is demonstrated by the example of transformation of site-specific data on plant phenology into surface data. The analysis allows for spatial comparison of the phenology during the two periods 1961–1990 and 1991–2002 covering whole Germany. The changes in both plant phenology and air temperature were proved to be statistically significant. Thus, they can be combined by GIS overlay technique to enhance the spatial resolution of the information on the climate change and use them for the prediction of vector incidences at the regional scale. The localisation of such risk hot spots can be done by geometrically merging surface data on promoting factors. This is demonstrated by the example of the transfer of heavy metals through soils. The predicted hot spots of heavy metal transfer can be validated empirically by measurement data which can be enquired by a metadata base linked with a geographic information system. A corresponding strategy for the detection of vector hot spots in medical epidemiology is recommended. Data on incidences and habitats of the Anophelinae in the marsh regions of Lower Saxony (Germany) were used to calculate a habitat model by CART, which together with climate data and data on ecoregions can be further used for the prediction of habitats of medically relevant vector species. In the future, this approach should be supported by an internet-based information system consisting of three components: metadata questionnaire, metadata base, and GIS to link metadata, surface data, and measurement data on incidences and habitats of medically relevant species and related data on climate, phenology, and ecoregional characteristic conditions.

Archaeology and geostatistics

Geostatistics is used in many different disciplines to characterise spatial variation and for spatial prediction, spatial simulation and sampling design. Archaeology is an inherently spatial discipline and the models and tools provided by geostatistics should be as valuable in archaeology as they are in other disciplines that are concerned with spatially varying properties. However, there have, so far, been few applications of geostatistics in archaeology. This paper seeks to highlight some of the key tools provided by geostatistics and to show, through two case studies, how they may be employed in archaeological applications. Some relevant literature is summarised and two case studies are presented based on the analysis of (i) Roman pottery and (ii) soil phosphate data.

A Geostatistical Approach to Modelling Positional Errors in Vector Data

As part of the theoretical development and practical applications of GISs, error issues are receiving increasing attention. This paper contributes to the debate in GIS error issues by exploring the applications of geostatistics in vector data, where positional errors are of major concern. A review is provided of the methods for handling positional errors in GIS vector data comprising points and lines. This is followed by a description of a stochastic simulation approach to modelling positional errors, which is remarkable for its ability to accommodate the spatial correlation characteristics of spatial data and their errors. Results from an experiment using photogrammetric data confirm the effectiveness of the proposed approach for modelling positional errors. The simulation approach is also examined with respect to other methods where due consideration is not given to the spatial correlation that is intrinsic to positional errors. Stochastic simulation‐based modelling of uncertain vector data via raster structures represents a valuable extension and contribution of geostatistical approaches to integrated handling of errors in heterogeneous spatial data.

Applications of Geographic Information Systems and Geostatistics in Plant Disease Epidemiology and Management.

Information management will be a key to improving farm practices in the coming decades. It makes sense to organize farm information in spatial databases because agricultural systems are inherently spatial. Biological and physical aspects of agricultural systems create spatial heterogeneity, and as a result, patchiness is the rule in the occurrence and distribution of plant pathogens and disease (3). Plant disease management practices can be improved by putting epidemiological information in the same format as other farm information using a geographic information system (GIS). A GIS is a computer system capable of assembling, storing, manipulating, and displaying data referenced by geographic coordinates (45). GIS can now be installed on any recent model desktop computer (e.g., a Pentium personal computer with at least 32 MB of RAM is adequate for most applications) and does not require an in-depth understanding of the statistical and mathematical basis of the technology. The large commercial push toward precision farming is based on combining GIS with sophisticated hardware for geographically referenced yield data and variable rate applications of fertilizers and other farm chemicals. GIS can be adapted to any size operation, and data can be incorporated at any scale from a single field to an agricultural region. Many problems should be studied at more than one scale. Part of the art of GIS database development is to decide what scale to use and which kinds of information to include at each scale. The ability of government institutions, the nation’s agricultural colleges and experiment stations, and private enterprise to provide spatially referenced information will open the way to farmers, pest control advisors, extension workers, and others to evaluate plant disease problems in a spatial context. New tools, including global positioning systems (GPS) and geostatistics, are available to use in connection with GIS. While these tools can be used at any scale, our efforts have been at the regional scale in generally arid irrigated agricultural areas. We focus on spatial relationships of landscape features that interact with the progress of an epidemic to refine cultural management strategies for plant disease control. Examples from this work will be used to illustrate the application of GPS, GIS, and geostatistics following a general

Geostatistical tools for characterizing the spatial variability of microbiological and physico-chemical soil properties

This paper reviews the main applications of geostatistics to the description and modeling of the spatial variability of microbiological and physico-chemical soil properties. First, basic geostatistical tools such as the correlogram and semivariogram are introduced to characterize the spatial variability of each attribute separately as well as their spatial interactions. Then, the key issue of fitting permissible models to experimental semivariograms is addressed for the univariate and multivariate situations. Capitalizing on this model of spatial dependence, the value of a soil property can be predicted at unsampled locations using only observations of this particular property (kriging) or incorporating additional information provided by other correlated properties (cokriging). Factorial kriging allows one to discriminate the different sources of spatial variation in soil on the basis of the scale at which they operate, and it often enhances relations between soil attributes which were blurred in a traditional correlation analysis where the different sources of variations are mixed. Geostatistics can also be used to assess the risk of exceeding critical values (regulatory thresholds, soil quality criterion) at unsampled locations, and to simulate the spatial distribution of attribute values. All the different tools are illustrated using two transects of 100 pH and electrical conductivity values measured in pasture and forest.

Exploration of geostatistical methods for mapping and estimating acoustic biomass of pelagic fish in the Gulf of St. Lawrence: size of echo-integration unit and auxiliary environmental variables

Daytime 38 kHz mean volume backscattering strength (MVBS) of small pelagic fish in the Gulf of St. Lawrence was recorded at 60-m intervals along a regular network of 11 parallel transects in August 1991. Profiles of temperature, salinity, density and transmittance were collected on a grid of 44 punctual stations along the transects. The MVBS was contagiously distributed and autocorrelated for al1 transects. No significant monotone relationship with any of the environmental variables was evidenced, except that the highest concentrations of fish were located over shallow bottoms. The anisotropic variogram of MVBS indicated three different scales of spatial structures: an unresolved small-scale variability, which accounted for only 7.7% of variance, and two structure components of along-transect scales of ~500 m (~40%) and 15 km (~50%). The theoretical variograms deduced for larger echo-integration units (EIUs) than the recorded 60-m unit, provided a good fit to the corresponding experimental variograms up to EIU of 1920-m, when the disturbing effect of outliers on the variograms was removed. Global estimates and maps produced with 240-m and 1920-m EIU data were almost identical, showing that no significant loss of information was caused by increasing the EIU. Asymmetric confidence intervals of the global estimates are obtained using two variograms, one controlled for the effect of the outliers, the other one not controlled. In an effort to take the relation of MVBS with the bottom depth into account, four different kriging methods were compared: ordinary kriging, kriging with the bottom depth or its indicator-transform as external drift, and 3-D ordinary kriging with depth as the third dimension. Because of the weak relation of MVBS with the bottom depth, ordinary kriging had the best performance. Results are discussed in the context of applications of geostatistics to estimation and mapping of acoustic survey data.

Analysis and Mapping of the Spatial Spread of African Cassava Mosaic Virus Using Geostatistics and the Kriging Technique

Lecoustre, R., Fargette, D., Fauquet, C., and de Reffye, P. 1989. Analysis and mapping of the spatial spread of African cassava mosaic virus using geostatistics and the kriging technique. Phytopathology 79: 913-920. Theories of regionalized variables and kriging were used to assess the incidence along the wind-exposed southwest field borders, disease spatial pattern of African cassava mosaic virus (ACMV). A linearlike gradients, and other less obvious features. Up to 60% of the total variance semivariogram without a range characterizes the ACMV distribution and was reconstructed from a 7% sample. Kriging was successfully applied indicates a strongly spatially dependent structure with limited random to characterize the spatial pattern of spread in cassava fields differing variation. Oriented semivariograms reveal a strong anisotropy in relation in planting date, size, arrangement, orientation, and method of sampling. to the prevailing wind direction. Further features of the semivariogram This technique was also efficient when the pattern of spread was and comparisons of semivariograms between fields and between surveys heterogenous, although more intensive surveys were then required. provide additional information and support various hypotheses on the Practical applications of geostatistics and kriging in epidemiology are pattern of spread. From a sample of limited size, kriging reproduced discussed. the main characteristics of the spatial pattern of spread, including higher Spatial patterns of disease level can provide important clues and pedology (21). to the ecology of disease (e.g., direction and distance of spread, African cassava mosaic disease is caused by a whitefly-borne importance and proximity of the sources of virus and vectors, geminivirus (2). The spatial patterns of spread of this disease vector mobility) (20). Patterns must be considered in designing have been studied intensively in the Ivory Coast (5,6) and are sampling methods and sound control measures (8,20). Hence, mainly characterized by gradients oriented in the direction of efficient methods of analysis and interpretation of spatial pattern the prevailing southwest wind. In this article, the theory of are needed to provide the greatest possible information in relation regionalized variables is used to assess the spatial patterns of to the time and effort involved. Past studies of spatial patterns the spread of African cassava mosaic virus (ACMV) in various have relied mostly on methods based on the examination of the cassava fields that differ in total area, subplot size, planting dates, mean and variance or on the frequency distribution of observed and orientation. We also describe the application of kriging to

Conditional Simulation: Geostatistical Tool Applied to Athabasca Oil-Sands Deposit: ABSTRACT

Geostatistical modeling of reservoir variability in the Athabasca oil-sands deposit prior to either surface or in-situ mining can provide valuable information to guide the extraction process. Geologic and engineering characteristics (variables), such as elevations of bitumen-saturated and waste (barren) zones, and percentage bitumen saturation, porosity, and permeability, have a controlling effect on recovery methods. Each geologic variable is considered to be a particular realization of a random function defined within a geologic domain. This function can be inferred from available data (boreholes) under the hypothesis of stationarity. Other realizations (models) of the same random function can then be generated using the technique of conditional simulation, which is End_Page 846------------------------------ a combination of kriging and simulated correlated variables. The statistical models of geologic variables so produced are in conformity with the histogram, variogram, and actual data values, and most important, they mimic spatial variability between sampled locations. The key factor in geologic applications of geostatistics is the translation of geologic reality into mathematical abstraction. Each random statistical function is a function of the physical processes that produced the deposit, which processes in turn varied in both space and time. The deposit under study has been divided into seven domains based on the best available geologic model, and different random functions established for each variable in each domain. Three-dimensional models describing the spatial fluctuation of elevations and bitumen saturations were produced and stored as grids having 25 m (82 ft) vertical and 1 m (3 ft) horizontal resolution. These models will be used to develop strategies for mine planning. End_of_Article - Last_Page 847------------